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Aerodynamic Shape Optimization using Simulations
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IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Aerodynamic Shape Optimization usingVortex Particle Simulations
Masterrsquos Presentation
David Gutierrez Rivera
Bauhaus Universitat Weimar
April 4 2014
David Gutierrez Rivera Aerodynamic Shape Optimization 1 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Overview
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 2 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
What is Optimization Basics of Aerodynamics
Introduction
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 3 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
What is Optimization Basics of Aerodynamics
What is Optimization
Optimization is to find the optimum value(s) to achieve certain goal(s)
David Gutierrez Rivera Aerodynamic Shape Optimization 4 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
What is Optimization Basics of Aerodynamics
What is Optimization
Optimization is to find the optimum value(s) to achieve certain goal(s)
David Gutierrez Rivera Aerodynamic Shape Optimization 4 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
What is Optimization Basics of Aerodynamics
What is Optimization
Optimization is to find the optimum value(s) to achieve certain goal(s)
David Gutierrez Rivera Aerodynamic Shape Optimization 4 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
What is Optimization Basics of Aerodynamics
What is Optimization
Optimization is to find the optimum value(s) to achieve certain goal(s)
David Gutierrez Rivera Aerodynamic Shape Optimization 4 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
What is Optimization Basics of Aerodynamics
What is Optimization
Optimization is to find the optimum value(s) to achieve certain goal(s)
David Gutierrez Rivera Aerodynamic Shape Optimization 4 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
What is Optimization Basics of Aerodynamics
What is Optimization
Optimization is to find the optimum value(s) to achieve certain goal(s)
David Gutierrez Rivera Aerodynamic Shape Optimization 4 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
What is Optimization Basics of Aerodynamics
A Mathematical View
Mathematically optimization is formulated as
minimizex
f (x)
subject to
gi (x) le 0 i = 1 mhi (x) = 0 i = 1 n
(1)
where
f (x) Rn rarr R is the objective function to be minimized
gi (x) le 0 are inequality constraints
hi (x) = 0 are equality constraints
David Gutierrez Rivera Aerodynamic Shape Optimization 5 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
What is Optimization Basics of Aerodynamics
A Mathematical View
Mathematically optimization is formulated as
minimizex
f (x)
subject to
gi (x) le 0 i = 1 mhi (x) = 0 i = 1 n
(1)
where
f (x) Rn rarr R is the objective function to be minimized
gi (x) le 0 are inequality constraints
hi (x) = 0 are equality constraints
David Gutierrez Rivera Aerodynamic Shape Optimization 5 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
What is Optimization Basics of Aerodynamics
A Programmatic View
Programmatically optimization can be viewed as a loop
David Gutierrez Rivera Aerodynamic Shape Optimization 6 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
What is Optimization Basics of Aerodynamics
Basics of Aerodynamics
The Navier-Stokes Partial Differential Equation
David Gutierrez Rivera Aerodynamic Shape Optimization 7 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
What is Optimization Basics of Aerodynamics
Computational Fluid Dynamics (CFD)
Is the branch of fluid mechanics that uses numerical methods to solvefluid flow problems
Discretization Methods
Finite Volume Method
Boundary Element Method
High-Resolution Schemes
Turbulence Models
Reynolds-AveragedNavierStokes (RANS)
Large eddy simulation (LES)
Vortex methods
David Gutierrez Rivera Aerodynamic Shape Optimization 8 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
What is Optimization Basics of Aerodynamics
Computational Fluid Dynamics (CFD)
Is the branch of fluid mechanics that uses numerical methods to solvefluid flow problems
Discretization Methods
Finite Volume Method
Boundary Element Method
High-Resolution Schemes
Turbulence Models
Reynolds-AveragedNavierStokes (RANS)
Large eddy simulation (LES)
Vortex methods
David Gutierrez Rivera Aerodynamic Shape Optimization 8 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
What is Optimization Basics of Aerodynamics
The Vortex Particle Method (VPM)
Characteristics
Is a grid-free technique for simulation of turbulent flows
It uses vortices as the computational elements
David Gutierrez Rivera Aerodynamic Shape Optimization 9 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Local Global
Optimization Algorithms
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 10 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Local Global
Optimization Algorithms
Classification
Linearity
LinearNonLinear
Constraints
UnconstrainedConstrained
Objectives
Single-ObjectiveMulti-Objective
Modality
uni-modal (Local)multi-modal (Global)
David Gutierrez Rivera Aerodynamic Shape Optimization 11 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Local Global
Optimization Algorithms
Classification
Linearity
LinearNonLinear
Constraints
UnconstrainedConstrained
Objectives
Single-ObjectiveMulti-Objective
Modality
uni-modal (Local)multi-modal (Global)
David Gutierrez Rivera Aerodynamic Shape Optimization 11 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Local Global
Global vs Local
David Gutierrez Rivera Aerodynamic Shape Optimization 12 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Local Global
Local
Gradient-free Methods
Golden Section
Simplex
Gradient-based Methods
Gradient-Descent
Newton
David Gutierrez Rivera Aerodynamic Shape Optimization 13 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Local Global
Global
non-Heuristic Methods
Deterministic
Stochastic
Heuristic Methods
Evolutionary
Genetic AlgorithmSwarm Intelligence
Swarm Intelligence
Particle SwarmAnt Colony
David Gutierrez Rivera Aerodynamic Shape Optimization 14 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Shape Optimization
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 15 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Shape Optimization
Shape optimization is formulated as
minimizeΩ
f (Ω)
subject to
gi (Ω) le 0 i = 1 mhi (Ω) = 0 i = 1 n
(2)
where
Ω is a set of variable parameters that make up the geometry that wewant to optimize
David Gutierrez Rivera Aerodynamic Shape Optimization 16 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Shape Optimization
Shape optimization is formulated as
minimizeΩ
f (Ω)
subject to
gi (Ω) le 0 i = 1 mhi (Ω) = 0 i = 1 n
(2)
where
Ω is a set of variable parameters that make up the geometry that wewant to optimize
David Gutierrez Rivera Aerodynamic Shape Optimization 16 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Parametrization
David Gutierrez Rivera Aerodynamic Shape Optimization 17 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Parametrization
David Gutierrez Rivera Aerodynamic Shape Optimization 17 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Objective Functions
Similar to mathematical functions
They involve 3 basic operations
David Gutierrez Rivera Aerodynamic Shape Optimization 18 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Objective Functions
Similar to mathematical functions
They involve 3 basic operations
Substitution
f (x) = a0 +nsum
i=1
an middot cos(n x ) +nsum
i=1
bn middot sin(n x )
David Gutierrez Rivera Aerodynamic Shape Optimization 18 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Objective Functions
Similar to mathematical functions
They involve 3 basic operations
Substitution
f (x) = a0 +nsum
i=1
an middot cos(n 31416 ) +nsum
i=1
bn middot sin(n 31416 )
Substitution
David Gutierrez Rivera Aerodynamic Shape Optimization 18 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Objective Functions
Similar to mathematical functions
They involve 3 basic operations
Evaluation
f (x) = a0 +nsum
i=1
an middot cos(n 31416 ) +nsum
i=1
bn middot sin(n 31416 )︸ ︷︷ ︸Evaluation
David Gutierrez Rivera Aerodynamic Shape Optimization 18 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Objective Functions
Similar to mathematical functions
They involve 3 basic operations
Read Output
f (x) = Value
Read Output
David Gutierrez Rivera Aerodynamic Shape Optimization 18 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Data Gathering
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 19 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Data Gathering
David Gutierrez Rivera Aerodynamic Shape Optimization 20 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Data Gathering
Data File
It is a text-based tab-delimited file containing the data points from thevariables and the corresponding values of the objective functions
Variable1 Variable2 Variablen Objective1 ObjectivemVariable1 Variable2 Variablen Objective1 Objectivem
Variable1 Variable2 Variablen Objective1 Objectivem
David Gutierrez Rivera Aerodynamic Shape Optimization 21 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Data Gathering
Data File
It is a text-based tab-delimited file containing the data points from thevariables and the corresponding values of the objective functions
Variable1 Variable2 Variablen Objective1 ObjectivemVariable1 Variable2 Variablen Objective1 Objectivem
Variable1 Variable2 Variablen Objective1 Objectivem
David Gutierrez Rivera Aerodynamic Shape Optimization 21 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Black-Box Optimization
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 22 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Black-Box Optimization
Black-Box Process
They are known from their inputs and outputs
Little is known of how it works internally
David Gutierrez Rivera Aerodynamic Shape Optimization 23 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Black-Box Optimization
David Gutierrez Rivera Aerodynamic Shape Optimization 23 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Black-Box Optimization
David Gutierrez Rivera Aerodynamic Shape Optimization 24 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Noisy Functions
David Gutierrez Rivera Aerodynamic Shape Optimization 25 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Simulation-based Optimization
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 26 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Simulation-based Optimization
David Gutierrez Rivera Aerodynamic Shape Optimization 27 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Moving Boundary Problem
David Gutierrez Rivera Aerodynamic Shape Optimization 28 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
OptiFlow
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 29 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Examples
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 30 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
M4 Neath Viaduct Wind Shield
Description
This bridge is located in South Wales and crosses the River Neath Asection of the bridge is very exposed in flat topography therefore a windshielding system is desired for reducing the overturning forces on vehicles
Description
The CFD model is the same as the one used on the VXFlow tutorial
Four small sections were used to obtain the interior drag forces
David Gutierrez Rivera Aerodynamic Shape Optimization 31 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
M4 Neath Viaduct Wind Shield
Description
The CFD model is the same as the one used on the VXFlow tutorial
Four small sections were used to obtain the interior drag forces
David Gutierrez Rivera Aerodynamic Shape Optimization 31 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
M4 Neath Viaduct Wind Shield
Description
The CFD model is the same as the one used on the VXFlow tutorial
Four small sections were used to obtain the interior drag forces
David Gutierrez Rivera Aerodynamic Shape Optimization 31 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Model
Find optimum height (h) for the Wind Shield
David Gutierrez Rivera Aerodynamic Shape Optimization 32 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Parameter File
Variables Definitions[beginvariables]define(h ) Height of Wind Screen[endvariables]define(L 300) Wind Screen Lengthdefine(t 015) Wind Screen Width Wind Screen Coordinatesdefine(x1 calc(0minus1300))define(x2 calc(x1minust))define(y1 calc(hminus025))define(y2 calc(y1+L))
4 num cornerpointsSCREEN3(SCHEME3)03 00 release distancespacing hull002 0001 00 minus01 merg1merg2merg3merg4minus4 minus3 minus1 minus3 minus1 section color codingdragliftmomentdisplrotation1 x2 y1 n11 x1 y1 n21 x1 y2 n11 x2 y2 n2
David Gutierrez Rivera Aerodynamic Shape Optimization 33 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Parameter File
Variables Definitions[beginvariables]define(h ) Height of Wind Screen[endvariables]define(L 300) Wind Screen Lengthdefine(t 015) Wind Screen Width Wind Screen Coordinatesdefine(x1 calc(0minus1300))define(x2 calc(x1minust))define(y1 calc(hminus025))define(y2 calc(y1+L))
4 num cornerpointsSCREEN3(SCHEME3)03 00 release distancespacing hull002 0001 00 minus01 merg1merg2merg3merg4minus4 minus3 minus1 minus3 minus1 section color codingdragliftmomentdisplrotation1 x2 y1 n11 x1 y1 n21 x1 y2 n11 x2 y2 n2
David Gutierrez Rivera Aerodynamic Shape Optimization 33 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Objective Function
function [Drag] = M4 Neath ViaductWS(X) M4 Neath ViaductWS Objective Functionsteps = 500
Drag(1) = VXF FORCES(XDRAGMAXstepsSECTION11)Drag(2) = VXF FORCES(XDRAGMAXstepsevalfalseSECTION12)Drag(3) = VXF FORCES(XDRAGMAXstepsevalfalseSECTION13)Drag(4) = VXF FORCES(XDRAGMAXstepsevalfalseSECTION14)
[DragLane] = max(Drag())
Call optiOUT to generate Plots and Output DataoptiOUT(X [Drag])
end
David Gutierrez Rivera Aerodynamic Shape Optimization 34 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Data Points
David Gutierrez Rivera Aerodynamic Shape Optimization 35 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Run-Time Optimization
David Gutierrez Rivera Aerodynamic Shape Optimization 36 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Vertical-Axis Wind Turbine (VAWT)
Description
The Savonius Wind Turbine is a Vertical-Axis Wind Turbine (VAWT)which main advantages are its reliability and practicality
David Gutierrez Rivera Aerodynamic Shape Optimization 37 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Model
Description
Find optimum values of ex and ey to maximize Torque or Power
Constrained to the shaded area
David Gutierrez Rivera Aerodynamic Shape Optimization 38 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Model
Description
Find optimum values of ex and ey to maximize Torque or Power
Constrained to the shaded area
David Gutierrez Rivera Aerodynamic Shape Optimization 38 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Dynamic Model
David Gutierrez Rivera Aerodynamic Shape Optimization 39 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Overview
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 2 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
What is Optimization Basics of Aerodynamics
Introduction
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 3 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
What is Optimization Basics of Aerodynamics
What is Optimization
Optimization is to find the optimum value(s) to achieve certain goal(s)
David Gutierrez Rivera Aerodynamic Shape Optimization 4 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
What is Optimization Basics of Aerodynamics
What is Optimization
Optimization is to find the optimum value(s) to achieve certain goal(s)
David Gutierrez Rivera Aerodynamic Shape Optimization 4 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
What is Optimization Basics of Aerodynamics
What is Optimization
Optimization is to find the optimum value(s) to achieve certain goal(s)
David Gutierrez Rivera Aerodynamic Shape Optimization 4 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
What is Optimization Basics of Aerodynamics
What is Optimization
Optimization is to find the optimum value(s) to achieve certain goal(s)
David Gutierrez Rivera Aerodynamic Shape Optimization 4 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
What is Optimization Basics of Aerodynamics
What is Optimization
Optimization is to find the optimum value(s) to achieve certain goal(s)
David Gutierrez Rivera Aerodynamic Shape Optimization 4 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
What is Optimization Basics of Aerodynamics
What is Optimization
Optimization is to find the optimum value(s) to achieve certain goal(s)
David Gutierrez Rivera Aerodynamic Shape Optimization 4 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
What is Optimization Basics of Aerodynamics
A Mathematical View
Mathematically optimization is formulated as
minimizex
f (x)
subject to
gi (x) le 0 i = 1 mhi (x) = 0 i = 1 n
(1)
where
f (x) Rn rarr R is the objective function to be minimized
gi (x) le 0 are inequality constraints
hi (x) = 0 are equality constraints
David Gutierrez Rivera Aerodynamic Shape Optimization 5 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
What is Optimization Basics of Aerodynamics
A Mathematical View
Mathematically optimization is formulated as
minimizex
f (x)
subject to
gi (x) le 0 i = 1 mhi (x) = 0 i = 1 n
(1)
where
f (x) Rn rarr R is the objective function to be minimized
gi (x) le 0 are inequality constraints
hi (x) = 0 are equality constraints
David Gutierrez Rivera Aerodynamic Shape Optimization 5 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
What is Optimization Basics of Aerodynamics
A Programmatic View
Programmatically optimization can be viewed as a loop
David Gutierrez Rivera Aerodynamic Shape Optimization 6 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
What is Optimization Basics of Aerodynamics
Basics of Aerodynamics
The Navier-Stokes Partial Differential Equation
David Gutierrez Rivera Aerodynamic Shape Optimization 7 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
What is Optimization Basics of Aerodynamics
Computational Fluid Dynamics (CFD)
Is the branch of fluid mechanics that uses numerical methods to solvefluid flow problems
Discretization Methods
Finite Volume Method
Boundary Element Method
High-Resolution Schemes
Turbulence Models
Reynolds-AveragedNavierStokes (RANS)
Large eddy simulation (LES)
Vortex methods
David Gutierrez Rivera Aerodynamic Shape Optimization 8 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
What is Optimization Basics of Aerodynamics
Computational Fluid Dynamics (CFD)
Is the branch of fluid mechanics that uses numerical methods to solvefluid flow problems
Discretization Methods
Finite Volume Method
Boundary Element Method
High-Resolution Schemes
Turbulence Models
Reynolds-AveragedNavierStokes (RANS)
Large eddy simulation (LES)
Vortex methods
David Gutierrez Rivera Aerodynamic Shape Optimization 8 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
What is Optimization Basics of Aerodynamics
The Vortex Particle Method (VPM)
Characteristics
Is a grid-free technique for simulation of turbulent flows
It uses vortices as the computational elements
David Gutierrez Rivera Aerodynamic Shape Optimization 9 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Local Global
Optimization Algorithms
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 10 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Local Global
Optimization Algorithms
Classification
Linearity
LinearNonLinear
Constraints
UnconstrainedConstrained
Objectives
Single-ObjectiveMulti-Objective
Modality
uni-modal (Local)multi-modal (Global)
David Gutierrez Rivera Aerodynamic Shape Optimization 11 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Local Global
Optimization Algorithms
Classification
Linearity
LinearNonLinear
Constraints
UnconstrainedConstrained
Objectives
Single-ObjectiveMulti-Objective
Modality
uni-modal (Local)multi-modal (Global)
David Gutierrez Rivera Aerodynamic Shape Optimization 11 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Local Global
Global vs Local
David Gutierrez Rivera Aerodynamic Shape Optimization 12 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Local Global
Local
Gradient-free Methods
Golden Section
Simplex
Gradient-based Methods
Gradient-Descent
Newton
David Gutierrez Rivera Aerodynamic Shape Optimization 13 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Local Global
Global
non-Heuristic Methods
Deterministic
Stochastic
Heuristic Methods
Evolutionary
Genetic AlgorithmSwarm Intelligence
Swarm Intelligence
Particle SwarmAnt Colony
David Gutierrez Rivera Aerodynamic Shape Optimization 14 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Shape Optimization
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 15 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Shape Optimization
Shape optimization is formulated as
minimizeΩ
f (Ω)
subject to
gi (Ω) le 0 i = 1 mhi (Ω) = 0 i = 1 n
(2)
where
Ω is a set of variable parameters that make up the geometry that wewant to optimize
David Gutierrez Rivera Aerodynamic Shape Optimization 16 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Shape Optimization
Shape optimization is formulated as
minimizeΩ
f (Ω)
subject to
gi (Ω) le 0 i = 1 mhi (Ω) = 0 i = 1 n
(2)
where
Ω is a set of variable parameters that make up the geometry that wewant to optimize
David Gutierrez Rivera Aerodynamic Shape Optimization 16 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Parametrization
David Gutierrez Rivera Aerodynamic Shape Optimization 17 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Parametrization
David Gutierrez Rivera Aerodynamic Shape Optimization 17 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Objective Functions
Similar to mathematical functions
They involve 3 basic operations
David Gutierrez Rivera Aerodynamic Shape Optimization 18 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Objective Functions
Similar to mathematical functions
They involve 3 basic operations
Substitution
f (x) = a0 +nsum
i=1
an middot cos(n x ) +nsum
i=1
bn middot sin(n x )
David Gutierrez Rivera Aerodynamic Shape Optimization 18 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Objective Functions
Similar to mathematical functions
They involve 3 basic operations
Substitution
f (x) = a0 +nsum
i=1
an middot cos(n 31416 ) +nsum
i=1
bn middot sin(n 31416 )
Substitution
David Gutierrez Rivera Aerodynamic Shape Optimization 18 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Objective Functions
Similar to mathematical functions
They involve 3 basic operations
Evaluation
f (x) = a0 +nsum
i=1
an middot cos(n 31416 ) +nsum
i=1
bn middot sin(n 31416 )︸ ︷︷ ︸Evaluation
David Gutierrez Rivera Aerodynamic Shape Optimization 18 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Objective Functions
Similar to mathematical functions
They involve 3 basic operations
Read Output
f (x) = Value
Read Output
David Gutierrez Rivera Aerodynamic Shape Optimization 18 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Data Gathering
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 19 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Data Gathering
David Gutierrez Rivera Aerodynamic Shape Optimization 20 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Data Gathering
Data File
It is a text-based tab-delimited file containing the data points from thevariables and the corresponding values of the objective functions
Variable1 Variable2 Variablen Objective1 ObjectivemVariable1 Variable2 Variablen Objective1 Objectivem
Variable1 Variable2 Variablen Objective1 Objectivem
David Gutierrez Rivera Aerodynamic Shape Optimization 21 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Data Gathering
Data File
It is a text-based tab-delimited file containing the data points from thevariables and the corresponding values of the objective functions
Variable1 Variable2 Variablen Objective1 ObjectivemVariable1 Variable2 Variablen Objective1 Objectivem
Variable1 Variable2 Variablen Objective1 Objectivem
David Gutierrez Rivera Aerodynamic Shape Optimization 21 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Black-Box Optimization
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 22 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Black-Box Optimization
Black-Box Process
They are known from their inputs and outputs
Little is known of how it works internally
David Gutierrez Rivera Aerodynamic Shape Optimization 23 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Black-Box Optimization
David Gutierrez Rivera Aerodynamic Shape Optimization 23 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Black-Box Optimization
David Gutierrez Rivera Aerodynamic Shape Optimization 24 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Noisy Functions
David Gutierrez Rivera Aerodynamic Shape Optimization 25 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Simulation-based Optimization
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 26 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Simulation-based Optimization
David Gutierrez Rivera Aerodynamic Shape Optimization 27 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Moving Boundary Problem
David Gutierrez Rivera Aerodynamic Shape Optimization 28 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
OptiFlow
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 29 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Examples
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 30 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
M4 Neath Viaduct Wind Shield
Description
This bridge is located in South Wales and crosses the River Neath Asection of the bridge is very exposed in flat topography therefore a windshielding system is desired for reducing the overturning forces on vehicles
Description
The CFD model is the same as the one used on the VXFlow tutorial
Four small sections were used to obtain the interior drag forces
David Gutierrez Rivera Aerodynamic Shape Optimization 31 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
M4 Neath Viaduct Wind Shield
Description
The CFD model is the same as the one used on the VXFlow tutorial
Four small sections were used to obtain the interior drag forces
David Gutierrez Rivera Aerodynamic Shape Optimization 31 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
M4 Neath Viaduct Wind Shield
Description
The CFD model is the same as the one used on the VXFlow tutorial
Four small sections were used to obtain the interior drag forces
David Gutierrez Rivera Aerodynamic Shape Optimization 31 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Model
Find optimum height (h) for the Wind Shield
David Gutierrez Rivera Aerodynamic Shape Optimization 32 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Parameter File
Variables Definitions[beginvariables]define(h ) Height of Wind Screen[endvariables]define(L 300) Wind Screen Lengthdefine(t 015) Wind Screen Width Wind Screen Coordinatesdefine(x1 calc(0minus1300))define(x2 calc(x1minust))define(y1 calc(hminus025))define(y2 calc(y1+L))
4 num cornerpointsSCREEN3(SCHEME3)03 00 release distancespacing hull002 0001 00 minus01 merg1merg2merg3merg4minus4 minus3 minus1 minus3 minus1 section color codingdragliftmomentdisplrotation1 x2 y1 n11 x1 y1 n21 x1 y2 n11 x2 y2 n2
David Gutierrez Rivera Aerodynamic Shape Optimization 33 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Parameter File
Variables Definitions[beginvariables]define(h ) Height of Wind Screen[endvariables]define(L 300) Wind Screen Lengthdefine(t 015) Wind Screen Width Wind Screen Coordinatesdefine(x1 calc(0minus1300))define(x2 calc(x1minust))define(y1 calc(hminus025))define(y2 calc(y1+L))
4 num cornerpointsSCREEN3(SCHEME3)03 00 release distancespacing hull002 0001 00 minus01 merg1merg2merg3merg4minus4 minus3 minus1 minus3 minus1 section color codingdragliftmomentdisplrotation1 x2 y1 n11 x1 y1 n21 x1 y2 n11 x2 y2 n2
David Gutierrez Rivera Aerodynamic Shape Optimization 33 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Objective Function
function [Drag] = M4 Neath ViaductWS(X) M4 Neath ViaductWS Objective Functionsteps = 500
Drag(1) = VXF FORCES(XDRAGMAXstepsSECTION11)Drag(2) = VXF FORCES(XDRAGMAXstepsevalfalseSECTION12)Drag(3) = VXF FORCES(XDRAGMAXstepsevalfalseSECTION13)Drag(4) = VXF FORCES(XDRAGMAXstepsevalfalseSECTION14)
[DragLane] = max(Drag())
Call optiOUT to generate Plots and Output DataoptiOUT(X [Drag])
end
David Gutierrez Rivera Aerodynamic Shape Optimization 34 54
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M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Data Points
David Gutierrez Rivera Aerodynamic Shape Optimization 35 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Run-Time Optimization
David Gutierrez Rivera Aerodynamic Shape Optimization 36 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Vertical-Axis Wind Turbine (VAWT)
Description
The Savonius Wind Turbine is a Vertical-Axis Wind Turbine (VAWT)which main advantages are its reliability and practicality
David Gutierrez Rivera Aerodynamic Shape Optimization 37 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Model
Description
Find optimum values of ex and ey to maximize Torque or Power
Constrained to the shaded area
David Gutierrez Rivera Aerodynamic Shape Optimization 38 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Model
Description
Find optimum values of ex and ey to maximize Torque or Power
Constrained to the shaded area
David Gutierrez Rivera Aerodynamic Shape Optimization 38 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Dynamic Model
David Gutierrez Rivera Aerodynamic Shape Optimization 39 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
What is Optimization Basics of Aerodynamics
Introduction
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 3 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
What is Optimization Basics of Aerodynamics
What is Optimization
Optimization is to find the optimum value(s) to achieve certain goal(s)
David Gutierrez Rivera Aerodynamic Shape Optimization 4 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
What is Optimization Basics of Aerodynamics
What is Optimization
Optimization is to find the optimum value(s) to achieve certain goal(s)
David Gutierrez Rivera Aerodynamic Shape Optimization 4 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
What is Optimization Basics of Aerodynamics
What is Optimization
Optimization is to find the optimum value(s) to achieve certain goal(s)
David Gutierrez Rivera Aerodynamic Shape Optimization 4 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
What is Optimization Basics of Aerodynamics
What is Optimization
Optimization is to find the optimum value(s) to achieve certain goal(s)
David Gutierrez Rivera Aerodynamic Shape Optimization 4 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
What is Optimization Basics of Aerodynamics
What is Optimization
Optimization is to find the optimum value(s) to achieve certain goal(s)
David Gutierrez Rivera Aerodynamic Shape Optimization 4 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
What is Optimization Basics of Aerodynamics
What is Optimization
Optimization is to find the optimum value(s) to achieve certain goal(s)
David Gutierrez Rivera Aerodynamic Shape Optimization 4 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
What is Optimization Basics of Aerodynamics
A Mathematical View
Mathematically optimization is formulated as
minimizex
f (x)
subject to
gi (x) le 0 i = 1 mhi (x) = 0 i = 1 n
(1)
where
f (x) Rn rarr R is the objective function to be minimized
gi (x) le 0 are inequality constraints
hi (x) = 0 are equality constraints
David Gutierrez Rivera Aerodynamic Shape Optimization 5 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
What is Optimization Basics of Aerodynamics
A Mathematical View
Mathematically optimization is formulated as
minimizex
f (x)
subject to
gi (x) le 0 i = 1 mhi (x) = 0 i = 1 n
(1)
where
f (x) Rn rarr R is the objective function to be minimized
gi (x) le 0 are inequality constraints
hi (x) = 0 are equality constraints
David Gutierrez Rivera Aerodynamic Shape Optimization 5 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
What is Optimization Basics of Aerodynamics
A Programmatic View
Programmatically optimization can be viewed as a loop
David Gutierrez Rivera Aerodynamic Shape Optimization 6 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
What is Optimization Basics of Aerodynamics
Basics of Aerodynamics
The Navier-Stokes Partial Differential Equation
David Gutierrez Rivera Aerodynamic Shape Optimization 7 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
What is Optimization Basics of Aerodynamics
Computational Fluid Dynamics (CFD)
Is the branch of fluid mechanics that uses numerical methods to solvefluid flow problems
Discretization Methods
Finite Volume Method
Boundary Element Method
High-Resolution Schemes
Turbulence Models
Reynolds-AveragedNavierStokes (RANS)
Large eddy simulation (LES)
Vortex methods
David Gutierrez Rivera Aerodynamic Shape Optimization 8 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
What is Optimization Basics of Aerodynamics
Computational Fluid Dynamics (CFD)
Is the branch of fluid mechanics that uses numerical methods to solvefluid flow problems
Discretization Methods
Finite Volume Method
Boundary Element Method
High-Resolution Schemes
Turbulence Models
Reynolds-AveragedNavierStokes (RANS)
Large eddy simulation (LES)
Vortex methods
David Gutierrez Rivera Aerodynamic Shape Optimization 8 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
What is Optimization Basics of Aerodynamics
The Vortex Particle Method (VPM)
Characteristics
Is a grid-free technique for simulation of turbulent flows
It uses vortices as the computational elements
David Gutierrez Rivera Aerodynamic Shape Optimization 9 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Local Global
Optimization Algorithms
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 10 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Local Global
Optimization Algorithms
Classification
Linearity
LinearNonLinear
Constraints
UnconstrainedConstrained
Objectives
Single-ObjectiveMulti-Objective
Modality
uni-modal (Local)multi-modal (Global)
David Gutierrez Rivera Aerodynamic Shape Optimization 11 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Local Global
Optimization Algorithms
Classification
Linearity
LinearNonLinear
Constraints
UnconstrainedConstrained
Objectives
Single-ObjectiveMulti-Objective
Modality
uni-modal (Local)multi-modal (Global)
David Gutierrez Rivera Aerodynamic Shape Optimization 11 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Local Global
Global vs Local
David Gutierrez Rivera Aerodynamic Shape Optimization 12 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Local Global
Local
Gradient-free Methods
Golden Section
Simplex
Gradient-based Methods
Gradient-Descent
Newton
David Gutierrez Rivera Aerodynamic Shape Optimization 13 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Local Global
Global
non-Heuristic Methods
Deterministic
Stochastic
Heuristic Methods
Evolutionary
Genetic AlgorithmSwarm Intelligence
Swarm Intelligence
Particle SwarmAnt Colony
David Gutierrez Rivera Aerodynamic Shape Optimization 14 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Shape Optimization
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 15 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Shape Optimization
Shape optimization is formulated as
minimizeΩ
f (Ω)
subject to
gi (Ω) le 0 i = 1 mhi (Ω) = 0 i = 1 n
(2)
where
Ω is a set of variable parameters that make up the geometry that wewant to optimize
David Gutierrez Rivera Aerodynamic Shape Optimization 16 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Shape Optimization
Shape optimization is formulated as
minimizeΩ
f (Ω)
subject to
gi (Ω) le 0 i = 1 mhi (Ω) = 0 i = 1 n
(2)
where
Ω is a set of variable parameters that make up the geometry that wewant to optimize
David Gutierrez Rivera Aerodynamic Shape Optimization 16 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Parametrization
David Gutierrez Rivera Aerodynamic Shape Optimization 17 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Parametrization
David Gutierrez Rivera Aerodynamic Shape Optimization 17 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Objective Functions
Similar to mathematical functions
They involve 3 basic operations
David Gutierrez Rivera Aerodynamic Shape Optimization 18 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Objective Functions
Similar to mathematical functions
They involve 3 basic operations
Substitution
f (x) = a0 +nsum
i=1
an middot cos(n x ) +nsum
i=1
bn middot sin(n x )
David Gutierrez Rivera Aerodynamic Shape Optimization 18 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Objective Functions
Similar to mathematical functions
They involve 3 basic operations
Substitution
f (x) = a0 +nsum
i=1
an middot cos(n 31416 ) +nsum
i=1
bn middot sin(n 31416 )
Substitution
David Gutierrez Rivera Aerodynamic Shape Optimization 18 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Objective Functions
Similar to mathematical functions
They involve 3 basic operations
Evaluation
f (x) = a0 +nsum
i=1
an middot cos(n 31416 ) +nsum
i=1
bn middot sin(n 31416 )︸ ︷︷ ︸Evaluation
David Gutierrez Rivera Aerodynamic Shape Optimization 18 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Objective Functions
Similar to mathematical functions
They involve 3 basic operations
Read Output
f (x) = Value
Read Output
David Gutierrez Rivera Aerodynamic Shape Optimization 18 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Data Gathering
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 19 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Data Gathering
David Gutierrez Rivera Aerodynamic Shape Optimization 20 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Data Gathering
Data File
It is a text-based tab-delimited file containing the data points from thevariables and the corresponding values of the objective functions
Variable1 Variable2 Variablen Objective1 ObjectivemVariable1 Variable2 Variablen Objective1 Objectivem
Variable1 Variable2 Variablen Objective1 Objectivem
David Gutierrez Rivera Aerodynamic Shape Optimization 21 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Data Gathering
Data File
It is a text-based tab-delimited file containing the data points from thevariables and the corresponding values of the objective functions
Variable1 Variable2 Variablen Objective1 ObjectivemVariable1 Variable2 Variablen Objective1 Objectivem
Variable1 Variable2 Variablen Objective1 Objectivem
David Gutierrez Rivera Aerodynamic Shape Optimization 21 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Black-Box Optimization
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 22 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Black-Box Optimization
Black-Box Process
They are known from their inputs and outputs
Little is known of how it works internally
David Gutierrez Rivera Aerodynamic Shape Optimization 23 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Black-Box Optimization
David Gutierrez Rivera Aerodynamic Shape Optimization 23 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Black-Box Optimization
David Gutierrez Rivera Aerodynamic Shape Optimization 24 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Noisy Functions
David Gutierrez Rivera Aerodynamic Shape Optimization 25 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Simulation-based Optimization
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 26 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Simulation-based Optimization
David Gutierrez Rivera Aerodynamic Shape Optimization 27 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Moving Boundary Problem
David Gutierrez Rivera Aerodynamic Shape Optimization 28 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
OptiFlow
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 29 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Examples
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 30 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
M4 Neath Viaduct Wind Shield
Description
This bridge is located in South Wales and crosses the River Neath Asection of the bridge is very exposed in flat topography therefore a windshielding system is desired for reducing the overturning forces on vehicles
Description
The CFD model is the same as the one used on the VXFlow tutorial
Four small sections were used to obtain the interior drag forces
David Gutierrez Rivera Aerodynamic Shape Optimization 31 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
M4 Neath Viaduct Wind Shield
Description
The CFD model is the same as the one used on the VXFlow tutorial
Four small sections were used to obtain the interior drag forces
David Gutierrez Rivera Aerodynamic Shape Optimization 31 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
M4 Neath Viaduct Wind Shield
Description
The CFD model is the same as the one used on the VXFlow tutorial
Four small sections were used to obtain the interior drag forces
David Gutierrez Rivera Aerodynamic Shape Optimization 31 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Model
Find optimum height (h) for the Wind Shield
David Gutierrez Rivera Aerodynamic Shape Optimization 32 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Parameter File
Variables Definitions[beginvariables]define(h ) Height of Wind Screen[endvariables]define(L 300) Wind Screen Lengthdefine(t 015) Wind Screen Width Wind Screen Coordinatesdefine(x1 calc(0minus1300))define(x2 calc(x1minust))define(y1 calc(hminus025))define(y2 calc(y1+L))
4 num cornerpointsSCREEN3(SCHEME3)03 00 release distancespacing hull002 0001 00 minus01 merg1merg2merg3merg4minus4 minus3 minus1 minus3 minus1 section color codingdragliftmomentdisplrotation1 x2 y1 n11 x1 y1 n21 x1 y2 n11 x2 y2 n2
David Gutierrez Rivera Aerodynamic Shape Optimization 33 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Parameter File
Variables Definitions[beginvariables]define(h ) Height of Wind Screen[endvariables]define(L 300) Wind Screen Lengthdefine(t 015) Wind Screen Width Wind Screen Coordinatesdefine(x1 calc(0minus1300))define(x2 calc(x1minust))define(y1 calc(hminus025))define(y2 calc(y1+L))
4 num cornerpointsSCREEN3(SCHEME3)03 00 release distancespacing hull002 0001 00 minus01 merg1merg2merg3merg4minus4 minus3 minus1 minus3 minus1 section color codingdragliftmomentdisplrotation1 x2 y1 n11 x1 y1 n21 x1 y2 n11 x2 y2 n2
David Gutierrez Rivera Aerodynamic Shape Optimization 33 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Objective Function
function [Drag] = M4 Neath ViaductWS(X) M4 Neath ViaductWS Objective Functionsteps = 500
Drag(1) = VXF FORCES(XDRAGMAXstepsSECTION11)Drag(2) = VXF FORCES(XDRAGMAXstepsevalfalseSECTION12)Drag(3) = VXF FORCES(XDRAGMAXstepsevalfalseSECTION13)Drag(4) = VXF FORCES(XDRAGMAXstepsevalfalseSECTION14)
[DragLane] = max(Drag())
Call optiOUT to generate Plots and Output DataoptiOUT(X [Drag])
end
David Gutierrez Rivera Aerodynamic Shape Optimization 34 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Data Points
David Gutierrez Rivera Aerodynamic Shape Optimization 35 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Run-Time Optimization
David Gutierrez Rivera Aerodynamic Shape Optimization 36 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Vertical-Axis Wind Turbine (VAWT)
Description
The Savonius Wind Turbine is a Vertical-Axis Wind Turbine (VAWT)which main advantages are its reliability and practicality
David Gutierrez Rivera Aerodynamic Shape Optimization 37 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Model
Description
Find optimum values of ex and ey to maximize Torque or Power
Constrained to the shaded area
David Gutierrez Rivera Aerodynamic Shape Optimization 38 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Model
Description
Find optimum values of ex and ey to maximize Torque or Power
Constrained to the shaded area
David Gutierrez Rivera Aerodynamic Shape Optimization 38 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Dynamic Model
David Gutierrez Rivera Aerodynamic Shape Optimization 39 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
What is Optimization Basics of Aerodynamics
What is Optimization
Optimization is to find the optimum value(s) to achieve certain goal(s)
David Gutierrez Rivera Aerodynamic Shape Optimization 4 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
What is Optimization Basics of Aerodynamics
What is Optimization
Optimization is to find the optimum value(s) to achieve certain goal(s)
David Gutierrez Rivera Aerodynamic Shape Optimization 4 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
What is Optimization Basics of Aerodynamics
What is Optimization
Optimization is to find the optimum value(s) to achieve certain goal(s)
David Gutierrez Rivera Aerodynamic Shape Optimization 4 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
What is Optimization Basics of Aerodynamics
What is Optimization
Optimization is to find the optimum value(s) to achieve certain goal(s)
David Gutierrez Rivera Aerodynamic Shape Optimization 4 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
What is Optimization Basics of Aerodynamics
What is Optimization
Optimization is to find the optimum value(s) to achieve certain goal(s)
David Gutierrez Rivera Aerodynamic Shape Optimization 4 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
What is Optimization Basics of Aerodynamics
What is Optimization
Optimization is to find the optimum value(s) to achieve certain goal(s)
David Gutierrez Rivera Aerodynamic Shape Optimization 4 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
What is Optimization Basics of Aerodynamics
A Mathematical View
Mathematically optimization is formulated as
minimizex
f (x)
subject to
gi (x) le 0 i = 1 mhi (x) = 0 i = 1 n
(1)
where
f (x) Rn rarr R is the objective function to be minimized
gi (x) le 0 are inequality constraints
hi (x) = 0 are equality constraints
David Gutierrez Rivera Aerodynamic Shape Optimization 5 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
What is Optimization Basics of Aerodynamics
A Mathematical View
Mathematically optimization is formulated as
minimizex
f (x)
subject to
gi (x) le 0 i = 1 mhi (x) = 0 i = 1 n
(1)
where
f (x) Rn rarr R is the objective function to be minimized
gi (x) le 0 are inequality constraints
hi (x) = 0 are equality constraints
David Gutierrez Rivera Aerodynamic Shape Optimization 5 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
What is Optimization Basics of Aerodynamics
A Programmatic View
Programmatically optimization can be viewed as a loop
David Gutierrez Rivera Aerodynamic Shape Optimization 6 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
What is Optimization Basics of Aerodynamics
Basics of Aerodynamics
The Navier-Stokes Partial Differential Equation
David Gutierrez Rivera Aerodynamic Shape Optimization 7 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
What is Optimization Basics of Aerodynamics
Computational Fluid Dynamics (CFD)
Is the branch of fluid mechanics that uses numerical methods to solvefluid flow problems
Discretization Methods
Finite Volume Method
Boundary Element Method
High-Resolution Schemes
Turbulence Models
Reynolds-AveragedNavierStokes (RANS)
Large eddy simulation (LES)
Vortex methods
David Gutierrez Rivera Aerodynamic Shape Optimization 8 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
What is Optimization Basics of Aerodynamics
Computational Fluid Dynamics (CFD)
Is the branch of fluid mechanics that uses numerical methods to solvefluid flow problems
Discretization Methods
Finite Volume Method
Boundary Element Method
High-Resolution Schemes
Turbulence Models
Reynolds-AveragedNavierStokes (RANS)
Large eddy simulation (LES)
Vortex methods
David Gutierrez Rivera Aerodynamic Shape Optimization 8 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
What is Optimization Basics of Aerodynamics
The Vortex Particle Method (VPM)
Characteristics
Is a grid-free technique for simulation of turbulent flows
It uses vortices as the computational elements
David Gutierrez Rivera Aerodynamic Shape Optimization 9 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Local Global
Optimization Algorithms
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 10 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Local Global
Optimization Algorithms
Classification
Linearity
LinearNonLinear
Constraints
UnconstrainedConstrained
Objectives
Single-ObjectiveMulti-Objective
Modality
uni-modal (Local)multi-modal (Global)
David Gutierrez Rivera Aerodynamic Shape Optimization 11 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Local Global
Optimization Algorithms
Classification
Linearity
LinearNonLinear
Constraints
UnconstrainedConstrained
Objectives
Single-ObjectiveMulti-Objective
Modality
uni-modal (Local)multi-modal (Global)
David Gutierrez Rivera Aerodynamic Shape Optimization 11 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Local Global
Global vs Local
David Gutierrez Rivera Aerodynamic Shape Optimization 12 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Local Global
Local
Gradient-free Methods
Golden Section
Simplex
Gradient-based Methods
Gradient-Descent
Newton
David Gutierrez Rivera Aerodynamic Shape Optimization 13 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Local Global
Global
non-Heuristic Methods
Deterministic
Stochastic
Heuristic Methods
Evolutionary
Genetic AlgorithmSwarm Intelligence
Swarm Intelligence
Particle SwarmAnt Colony
David Gutierrez Rivera Aerodynamic Shape Optimization 14 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Shape Optimization
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 15 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Shape Optimization
Shape optimization is formulated as
minimizeΩ
f (Ω)
subject to
gi (Ω) le 0 i = 1 mhi (Ω) = 0 i = 1 n
(2)
where
Ω is a set of variable parameters that make up the geometry that wewant to optimize
David Gutierrez Rivera Aerodynamic Shape Optimization 16 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Shape Optimization
Shape optimization is formulated as
minimizeΩ
f (Ω)
subject to
gi (Ω) le 0 i = 1 mhi (Ω) = 0 i = 1 n
(2)
where
Ω is a set of variable parameters that make up the geometry that wewant to optimize
David Gutierrez Rivera Aerodynamic Shape Optimization 16 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Parametrization
David Gutierrez Rivera Aerodynamic Shape Optimization 17 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Parametrization
David Gutierrez Rivera Aerodynamic Shape Optimization 17 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Objective Functions
Similar to mathematical functions
They involve 3 basic operations
David Gutierrez Rivera Aerodynamic Shape Optimization 18 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Objective Functions
Similar to mathematical functions
They involve 3 basic operations
Substitution
f (x) = a0 +nsum
i=1
an middot cos(n x ) +nsum
i=1
bn middot sin(n x )
David Gutierrez Rivera Aerodynamic Shape Optimization 18 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Objective Functions
Similar to mathematical functions
They involve 3 basic operations
Substitution
f (x) = a0 +nsum
i=1
an middot cos(n 31416 ) +nsum
i=1
bn middot sin(n 31416 )
Substitution
David Gutierrez Rivera Aerodynamic Shape Optimization 18 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Objective Functions
Similar to mathematical functions
They involve 3 basic operations
Evaluation
f (x) = a0 +nsum
i=1
an middot cos(n 31416 ) +nsum
i=1
bn middot sin(n 31416 )︸ ︷︷ ︸Evaluation
David Gutierrez Rivera Aerodynamic Shape Optimization 18 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Objective Functions
Similar to mathematical functions
They involve 3 basic operations
Read Output
f (x) = Value
Read Output
David Gutierrez Rivera Aerodynamic Shape Optimization 18 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Data Gathering
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 19 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Data Gathering
David Gutierrez Rivera Aerodynamic Shape Optimization 20 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Data Gathering
Data File
It is a text-based tab-delimited file containing the data points from thevariables and the corresponding values of the objective functions
Variable1 Variable2 Variablen Objective1 ObjectivemVariable1 Variable2 Variablen Objective1 Objectivem
Variable1 Variable2 Variablen Objective1 Objectivem
David Gutierrez Rivera Aerodynamic Shape Optimization 21 54
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Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Data Gathering
Data File
It is a text-based tab-delimited file containing the data points from thevariables and the corresponding values of the objective functions
Variable1 Variable2 Variablen Objective1 ObjectivemVariable1 Variable2 Variablen Objective1 Objectivem
Variable1 Variable2 Variablen Objective1 Objectivem
David Gutierrez Rivera Aerodynamic Shape Optimization 21 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Black-Box Optimization
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 22 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Black-Box Optimization
Black-Box Process
They are known from their inputs and outputs
Little is known of how it works internally
David Gutierrez Rivera Aerodynamic Shape Optimization 23 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Black-Box Optimization
David Gutierrez Rivera Aerodynamic Shape Optimization 23 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Black-Box Optimization
David Gutierrez Rivera Aerodynamic Shape Optimization 24 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Noisy Functions
David Gutierrez Rivera Aerodynamic Shape Optimization 25 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Simulation-based Optimization
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 26 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Simulation-based Optimization
David Gutierrez Rivera Aerodynamic Shape Optimization 27 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Moving Boundary Problem
David Gutierrez Rivera Aerodynamic Shape Optimization 28 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
OptiFlow
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 29 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Examples
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 30 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
M4 Neath Viaduct Wind Shield
Description
This bridge is located in South Wales and crosses the River Neath Asection of the bridge is very exposed in flat topography therefore a windshielding system is desired for reducing the overturning forces on vehicles
Description
The CFD model is the same as the one used on the VXFlow tutorial
Four small sections were used to obtain the interior drag forces
David Gutierrez Rivera Aerodynamic Shape Optimization 31 54
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Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
M4 Neath Viaduct Wind Shield
Description
The CFD model is the same as the one used on the VXFlow tutorial
Four small sections were used to obtain the interior drag forces
David Gutierrez Rivera Aerodynamic Shape Optimization 31 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
M4 Neath Viaduct Wind Shield
Description
The CFD model is the same as the one used on the VXFlow tutorial
Four small sections were used to obtain the interior drag forces
David Gutierrez Rivera Aerodynamic Shape Optimization 31 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Model
Find optimum height (h) for the Wind Shield
David Gutierrez Rivera Aerodynamic Shape Optimization 32 54
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M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Parameter File
Variables Definitions[beginvariables]define(h ) Height of Wind Screen[endvariables]define(L 300) Wind Screen Lengthdefine(t 015) Wind Screen Width Wind Screen Coordinatesdefine(x1 calc(0minus1300))define(x2 calc(x1minust))define(y1 calc(hminus025))define(y2 calc(y1+L))
4 num cornerpointsSCREEN3(SCHEME3)03 00 release distancespacing hull002 0001 00 minus01 merg1merg2merg3merg4minus4 minus3 minus1 minus3 minus1 section color codingdragliftmomentdisplrotation1 x2 y1 n11 x1 y1 n21 x1 y2 n11 x2 y2 n2
David Gutierrez Rivera Aerodynamic Shape Optimization 33 54
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M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Parameter File
Variables Definitions[beginvariables]define(h ) Height of Wind Screen[endvariables]define(L 300) Wind Screen Lengthdefine(t 015) Wind Screen Width Wind Screen Coordinatesdefine(x1 calc(0minus1300))define(x2 calc(x1minust))define(y1 calc(hminus025))define(y2 calc(y1+L))
4 num cornerpointsSCREEN3(SCHEME3)03 00 release distancespacing hull002 0001 00 minus01 merg1merg2merg3merg4minus4 minus3 minus1 minus3 minus1 section color codingdragliftmomentdisplrotation1 x2 y1 n11 x1 y1 n21 x1 y2 n11 x2 y2 n2
David Gutierrez Rivera Aerodynamic Shape Optimization 33 54
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M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Objective Function
function [Drag] = M4 Neath ViaductWS(X) M4 Neath ViaductWS Objective Functionsteps = 500
Drag(1) = VXF FORCES(XDRAGMAXstepsSECTION11)Drag(2) = VXF FORCES(XDRAGMAXstepsevalfalseSECTION12)Drag(3) = VXF FORCES(XDRAGMAXstepsevalfalseSECTION13)Drag(4) = VXF FORCES(XDRAGMAXstepsevalfalseSECTION14)
[DragLane] = max(Drag())
Call optiOUT to generate Plots and Output DataoptiOUT(X [Drag])
end
David Gutierrez Rivera Aerodynamic Shape Optimization 34 54
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M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Data Points
David Gutierrez Rivera Aerodynamic Shape Optimization 35 54
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M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Run-Time Optimization
David Gutierrez Rivera Aerodynamic Shape Optimization 36 54
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AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Vertical-Axis Wind Turbine (VAWT)
Description
The Savonius Wind Turbine is a Vertical-Axis Wind Turbine (VAWT)which main advantages are its reliability and practicality
David Gutierrez Rivera Aerodynamic Shape Optimization 37 54
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M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Model
Description
Find optimum values of ex and ey to maximize Torque or Power
Constrained to the shaded area
David Gutierrez Rivera Aerodynamic Shape Optimization 38 54
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Black-Box OptimizationSimulation-based Optimization
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AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Model
Description
Find optimum values of ex and ey to maximize Torque or Power
Constrained to the shaded area
David Gutierrez Rivera Aerodynamic Shape Optimization 38 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Dynamic Model
David Gutierrez Rivera Aerodynamic Shape Optimization 39 54
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Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
What is Optimization Basics of Aerodynamics
What is Optimization
Optimization is to find the optimum value(s) to achieve certain goal(s)
David Gutierrez Rivera Aerodynamic Shape Optimization 4 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
What is Optimization Basics of Aerodynamics
What is Optimization
Optimization is to find the optimum value(s) to achieve certain goal(s)
David Gutierrez Rivera Aerodynamic Shape Optimization 4 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
What is Optimization Basics of Aerodynamics
What is Optimization
Optimization is to find the optimum value(s) to achieve certain goal(s)
David Gutierrez Rivera Aerodynamic Shape Optimization 4 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
What is Optimization Basics of Aerodynamics
What is Optimization
Optimization is to find the optimum value(s) to achieve certain goal(s)
David Gutierrez Rivera Aerodynamic Shape Optimization 4 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
What is Optimization Basics of Aerodynamics
What is Optimization
Optimization is to find the optimum value(s) to achieve certain goal(s)
David Gutierrez Rivera Aerodynamic Shape Optimization 4 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
What is Optimization Basics of Aerodynamics
A Mathematical View
Mathematically optimization is formulated as
minimizex
f (x)
subject to
gi (x) le 0 i = 1 mhi (x) = 0 i = 1 n
(1)
where
f (x) Rn rarr R is the objective function to be minimized
gi (x) le 0 are inequality constraints
hi (x) = 0 are equality constraints
David Gutierrez Rivera Aerodynamic Shape Optimization 5 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
What is Optimization Basics of Aerodynamics
A Mathematical View
Mathematically optimization is formulated as
minimizex
f (x)
subject to
gi (x) le 0 i = 1 mhi (x) = 0 i = 1 n
(1)
where
f (x) Rn rarr R is the objective function to be minimized
gi (x) le 0 are inequality constraints
hi (x) = 0 are equality constraints
David Gutierrez Rivera Aerodynamic Shape Optimization 5 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
What is Optimization Basics of Aerodynamics
A Programmatic View
Programmatically optimization can be viewed as a loop
David Gutierrez Rivera Aerodynamic Shape Optimization 6 54
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OptiFlowOptimization Examples
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What is Optimization Basics of Aerodynamics
Basics of Aerodynamics
The Navier-Stokes Partial Differential Equation
David Gutierrez Rivera Aerodynamic Shape Optimization 7 54
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Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
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What is Optimization Basics of Aerodynamics
Computational Fluid Dynamics (CFD)
Is the branch of fluid mechanics that uses numerical methods to solvefluid flow problems
Discretization Methods
Finite Volume Method
Boundary Element Method
High-Resolution Schemes
Turbulence Models
Reynolds-AveragedNavierStokes (RANS)
Large eddy simulation (LES)
Vortex methods
David Gutierrez Rivera Aerodynamic Shape Optimization 8 54
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What is Optimization Basics of Aerodynamics
Computational Fluid Dynamics (CFD)
Is the branch of fluid mechanics that uses numerical methods to solvefluid flow problems
Discretization Methods
Finite Volume Method
Boundary Element Method
High-Resolution Schemes
Turbulence Models
Reynolds-AveragedNavierStokes (RANS)
Large eddy simulation (LES)
Vortex methods
David Gutierrez Rivera Aerodynamic Shape Optimization 8 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
What is Optimization Basics of Aerodynamics
The Vortex Particle Method (VPM)
Characteristics
Is a grid-free technique for simulation of turbulent flows
It uses vortices as the computational elements
David Gutierrez Rivera Aerodynamic Shape Optimization 9 54
IntroductionOptimization Algorithms
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AcknowledgmentsReferences
Local Global
Optimization Algorithms
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 10 54
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Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
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Local Global
Optimization Algorithms
Classification
Linearity
LinearNonLinear
Constraints
UnconstrainedConstrained
Objectives
Single-ObjectiveMulti-Objective
Modality
uni-modal (Local)multi-modal (Global)
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Local Global
Optimization Algorithms
Classification
Linearity
LinearNonLinear
Constraints
UnconstrainedConstrained
Objectives
Single-ObjectiveMulti-Objective
Modality
uni-modal (Local)multi-modal (Global)
David Gutierrez Rivera Aerodynamic Shape Optimization 11 54
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Final RemarksFuture Research
AcknowledgmentsReferences
Local Global
Global vs Local
David Gutierrez Rivera Aerodynamic Shape Optimization 12 54
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Local Global
Local
Gradient-free Methods
Golden Section
Simplex
Gradient-based Methods
Gradient-Descent
Newton
David Gutierrez Rivera Aerodynamic Shape Optimization 13 54
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Local Global
Global
non-Heuristic Methods
Deterministic
Stochastic
Heuristic Methods
Evolutionary
Genetic AlgorithmSwarm Intelligence
Swarm Intelligence
Particle SwarmAnt Colony
David Gutierrez Rivera Aerodynamic Shape Optimization 14 54
IntroductionOptimization Algorithms
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Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Shape Optimization
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 15 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Shape Optimization
Shape optimization is formulated as
minimizeΩ
f (Ω)
subject to
gi (Ω) le 0 i = 1 mhi (Ω) = 0 i = 1 n
(2)
where
Ω is a set of variable parameters that make up the geometry that wewant to optimize
David Gutierrez Rivera Aerodynamic Shape Optimization 16 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Shape Optimization
Shape optimization is formulated as
minimizeΩ
f (Ω)
subject to
gi (Ω) le 0 i = 1 mhi (Ω) = 0 i = 1 n
(2)
where
Ω is a set of variable parameters that make up the geometry that wewant to optimize
David Gutierrez Rivera Aerodynamic Shape Optimization 16 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Parametrization
David Gutierrez Rivera Aerodynamic Shape Optimization 17 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Parametrization
David Gutierrez Rivera Aerodynamic Shape Optimization 17 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Objective Functions
Similar to mathematical functions
They involve 3 basic operations
David Gutierrez Rivera Aerodynamic Shape Optimization 18 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Objective Functions
Similar to mathematical functions
They involve 3 basic operations
Substitution
f (x) = a0 +nsum
i=1
an middot cos(n x ) +nsum
i=1
bn middot sin(n x )
David Gutierrez Rivera Aerodynamic Shape Optimization 18 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Objective Functions
Similar to mathematical functions
They involve 3 basic operations
Substitution
f (x) = a0 +nsum
i=1
an middot cos(n 31416 ) +nsum
i=1
bn middot sin(n 31416 )
Substitution
David Gutierrez Rivera Aerodynamic Shape Optimization 18 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Objective Functions
Similar to mathematical functions
They involve 3 basic operations
Evaluation
f (x) = a0 +nsum
i=1
an middot cos(n 31416 ) +nsum
i=1
bn middot sin(n 31416 )︸ ︷︷ ︸Evaluation
David Gutierrez Rivera Aerodynamic Shape Optimization 18 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Objective Functions
Similar to mathematical functions
They involve 3 basic operations
Read Output
f (x) = Value
Read Output
David Gutierrez Rivera Aerodynamic Shape Optimization 18 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Data Gathering
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 19 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Data Gathering
David Gutierrez Rivera Aerodynamic Shape Optimization 20 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Data Gathering
Data File
It is a text-based tab-delimited file containing the data points from thevariables and the corresponding values of the objective functions
Variable1 Variable2 Variablen Objective1 ObjectivemVariable1 Variable2 Variablen Objective1 Objectivem
Variable1 Variable2 Variablen Objective1 Objectivem
David Gutierrez Rivera Aerodynamic Shape Optimization 21 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Data Gathering
Data File
It is a text-based tab-delimited file containing the data points from thevariables and the corresponding values of the objective functions
Variable1 Variable2 Variablen Objective1 ObjectivemVariable1 Variable2 Variablen Objective1 Objectivem
Variable1 Variable2 Variablen Objective1 Objectivem
David Gutierrez Rivera Aerodynamic Shape Optimization 21 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Black-Box Optimization
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 22 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Black-Box Optimization
Black-Box Process
They are known from their inputs and outputs
Little is known of how it works internally
David Gutierrez Rivera Aerodynamic Shape Optimization 23 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Black-Box Optimization
David Gutierrez Rivera Aerodynamic Shape Optimization 23 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Black-Box Optimization
David Gutierrez Rivera Aerodynamic Shape Optimization 24 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Noisy Functions
David Gutierrez Rivera Aerodynamic Shape Optimization 25 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Simulation-based Optimization
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 26 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Simulation-based Optimization
David Gutierrez Rivera Aerodynamic Shape Optimization 27 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Moving Boundary Problem
David Gutierrez Rivera Aerodynamic Shape Optimization 28 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
OptiFlow
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 29 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Examples
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 30 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
M4 Neath Viaduct Wind Shield
Description
This bridge is located in South Wales and crosses the River Neath Asection of the bridge is very exposed in flat topography therefore a windshielding system is desired for reducing the overturning forces on vehicles
Description
The CFD model is the same as the one used on the VXFlow tutorial
Four small sections were used to obtain the interior drag forces
David Gutierrez Rivera Aerodynamic Shape Optimization 31 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
M4 Neath Viaduct Wind Shield
Description
The CFD model is the same as the one used on the VXFlow tutorial
Four small sections were used to obtain the interior drag forces
David Gutierrez Rivera Aerodynamic Shape Optimization 31 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
M4 Neath Viaduct Wind Shield
Description
The CFD model is the same as the one used on the VXFlow tutorial
Four small sections were used to obtain the interior drag forces
David Gutierrez Rivera Aerodynamic Shape Optimization 31 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Model
Find optimum height (h) for the Wind Shield
David Gutierrez Rivera Aerodynamic Shape Optimization 32 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Parameter File
Variables Definitions[beginvariables]define(h ) Height of Wind Screen[endvariables]define(L 300) Wind Screen Lengthdefine(t 015) Wind Screen Width Wind Screen Coordinatesdefine(x1 calc(0minus1300))define(x2 calc(x1minust))define(y1 calc(hminus025))define(y2 calc(y1+L))
4 num cornerpointsSCREEN3(SCHEME3)03 00 release distancespacing hull002 0001 00 minus01 merg1merg2merg3merg4minus4 minus3 minus1 minus3 minus1 section color codingdragliftmomentdisplrotation1 x2 y1 n11 x1 y1 n21 x1 y2 n11 x2 y2 n2
David Gutierrez Rivera Aerodynamic Shape Optimization 33 54
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Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Parameter File
Variables Definitions[beginvariables]define(h ) Height of Wind Screen[endvariables]define(L 300) Wind Screen Lengthdefine(t 015) Wind Screen Width Wind Screen Coordinatesdefine(x1 calc(0minus1300))define(x2 calc(x1minust))define(y1 calc(hminus025))define(y2 calc(y1+L))
4 num cornerpointsSCREEN3(SCHEME3)03 00 release distancespacing hull002 0001 00 minus01 merg1merg2merg3merg4minus4 minus3 minus1 minus3 minus1 section color codingdragliftmomentdisplrotation1 x2 y1 n11 x1 y1 n21 x1 y2 n11 x2 y2 n2
David Gutierrez Rivera Aerodynamic Shape Optimization 33 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Objective Function
function [Drag] = M4 Neath ViaductWS(X) M4 Neath ViaductWS Objective Functionsteps = 500
Drag(1) = VXF FORCES(XDRAGMAXstepsSECTION11)Drag(2) = VXF FORCES(XDRAGMAXstepsevalfalseSECTION12)Drag(3) = VXF FORCES(XDRAGMAXstepsevalfalseSECTION13)Drag(4) = VXF FORCES(XDRAGMAXstepsevalfalseSECTION14)
[DragLane] = max(Drag())
Call optiOUT to generate Plots and Output DataoptiOUT(X [Drag])
end
David Gutierrez Rivera Aerodynamic Shape Optimization 34 54
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M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Data Points
David Gutierrez Rivera Aerodynamic Shape Optimization 35 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Run-Time Optimization
David Gutierrez Rivera Aerodynamic Shape Optimization 36 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Vertical-Axis Wind Turbine (VAWT)
Description
The Savonius Wind Turbine is a Vertical-Axis Wind Turbine (VAWT)which main advantages are its reliability and practicality
David Gutierrez Rivera Aerodynamic Shape Optimization 37 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Model
Description
Find optimum values of ex and ey to maximize Torque or Power
Constrained to the shaded area
David Gutierrez Rivera Aerodynamic Shape Optimization 38 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Model
Description
Find optimum values of ex and ey to maximize Torque or Power
Constrained to the shaded area
David Gutierrez Rivera Aerodynamic Shape Optimization 38 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Dynamic Model
David Gutierrez Rivera Aerodynamic Shape Optimization 39 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
What is Optimization Basics of Aerodynamics
What is Optimization
Optimization is to find the optimum value(s) to achieve certain goal(s)
David Gutierrez Rivera Aerodynamic Shape Optimization 4 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
What is Optimization Basics of Aerodynamics
What is Optimization
Optimization is to find the optimum value(s) to achieve certain goal(s)
David Gutierrez Rivera Aerodynamic Shape Optimization 4 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
What is Optimization Basics of Aerodynamics
What is Optimization
Optimization is to find the optimum value(s) to achieve certain goal(s)
David Gutierrez Rivera Aerodynamic Shape Optimization 4 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
What is Optimization Basics of Aerodynamics
What is Optimization
Optimization is to find the optimum value(s) to achieve certain goal(s)
David Gutierrez Rivera Aerodynamic Shape Optimization 4 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
What is Optimization Basics of Aerodynamics
A Mathematical View
Mathematically optimization is formulated as
minimizex
f (x)
subject to
gi (x) le 0 i = 1 mhi (x) = 0 i = 1 n
(1)
where
f (x) Rn rarr R is the objective function to be minimized
gi (x) le 0 are inequality constraints
hi (x) = 0 are equality constraints
David Gutierrez Rivera Aerodynamic Shape Optimization 5 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
What is Optimization Basics of Aerodynamics
A Mathematical View
Mathematically optimization is formulated as
minimizex
f (x)
subject to
gi (x) le 0 i = 1 mhi (x) = 0 i = 1 n
(1)
where
f (x) Rn rarr R is the objective function to be minimized
gi (x) le 0 are inequality constraints
hi (x) = 0 are equality constraints
David Gutierrez Rivera Aerodynamic Shape Optimization 5 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
What is Optimization Basics of Aerodynamics
A Programmatic View
Programmatically optimization can be viewed as a loop
David Gutierrez Rivera Aerodynamic Shape Optimization 6 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
What is Optimization Basics of Aerodynamics
Basics of Aerodynamics
The Navier-Stokes Partial Differential Equation
David Gutierrez Rivera Aerodynamic Shape Optimization 7 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
What is Optimization Basics of Aerodynamics
Computational Fluid Dynamics (CFD)
Is the branch of fluid mechanics that uses numerical methods to solvefluid flow problems
Discretization Methods
Finite Volume Method
Boundary Element Method
High-Resolution Schemes
Turbulence Models
Reynolds-AveragedNavierStokes (RANS)
Large eddy simulation (LES)
Vortex methods
David Gutierrez Rivera Aerodynamic Shape Optimization 8 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
What is Optimization Basics of Aerodynamics
Computational Fluid Dynamics (CFD)
Is the branch of fluid mechanics that uses numerical methods to solvefluid flow problems
Discretization Methods
Finite Volume Method
Boundary Element Method
High-Resolution Schemes
Turbulence Models
Reynolds-AveragedNavierStokes (RANS)
Large eddy simulation (LES)
Vortex methods
David Gutierrez Rivera Aerodynamic Shape Optimization 8 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
What is Optimization Basics of Aerodynamics
The Vortex Particle Method (VPM)
Characteristics
Is a grid-free technique for simulation of turbulent flows
It uses vortices as the computational elements
David Gutierrez Rivera Aerodynamic Shape Optimization 9 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Local Global
Optimization Algorithms
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 10 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Local Global
Optimization Algorithms
Classification
Linearity
LinearNonLinear
Constraints
UnconstrainedConstrained
Objectives
Single-ObjectiveMulti-Objective
Modality
uni-modal (Local)multi-modal (Global)
David Gutierrez Rivera Aerodynamic Shape Optimization 11 54
IntroductionOptimization Algorithms
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Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Local Global
Optimization Algorithms
Classification
Linearity
LinearNonLinear
Constraints
UnconstrainedConstrained
Objectives
Single-ObjectiveMulti-Objective
Modality
uni-modal (Local)multi-modal (Global)
David Gutierrez Rivera Aerodynamic Shape Optimization 11 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Local Global
Global vs Local
David Gutierrez Rivera Aerodynamic Shape Optimization 12 54
IntroductionOptimization Algorithms
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Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Local Global
Local
Gradient-free Methods
Golden Section
Simplex
Gradient-based Methods
Gradient-Descent
Newton
David Gutierrez Rivera Aerodynamic Shape Optimization 13 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Local Global
Global
non-Heuristic Methods
Deterministic
Stochastic
Heuristic Methods
Evolutionary
Genetic AlgorithmSwarm Intelligence
Swarm Intelligence
Particle SwarmAnt Colony
David Gutierrez Rivera Aerodynamic Shape Optimization 14 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Shape Optimization
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 15 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Shape Optimization
Shape optimization is formulated as
minimizeΩ
f (Ω)
subject to
gi (Ω) le 0 i = 1 mhi (Ω) = 0 i = 1 n
(2)
where
Ω is a set of variable parameters that make up the geometry that wewant to optimize
David Gutierrez Rivera Aerodynamic Shape Optimization 16 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Shape Optimization
Shape optimization is formulated as
minimizeΩ
f (Ω)
subject to
gi (Ω) le 0 i = 1 mhi (Ω) = 0 i = 1 n
(2)
where
Ω is a set of variable parameters that make up the geometry that wewant to optimize
David Gutierrez Rivera Aerodynamic Shape Optimization 16 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Parametrization
David Gutierrez Rivera Aerodynamic Shape Optimization 17 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Parametrization
David Gutierrez Rivera Aerodynamic Shape Optimization 17 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Objective Functions
Similar to mathematical functions
They involve 3 basic operations
David Gutierrez Rivera Aerodynamic Shape Optimization 18 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Objective Functions
Similar to mathematical functions
They involve 3 basic operations
Substitution
f (x) = a0 +nsum
i=1
an middot cos(n x ) +nsum
i=1
bn middot sin(n x )
David Gutierrez Rivera Aerodynamic Shape Optimization 18 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Objective Functions
Similar to mathematical functions
They involve 3 basic operations
Substitution
f (x) = a0 +nsum
i=1
an middot cos(n 31416 ) +nsum
i=1
bn middot sin(n 31416 )
Substitution
David Gutierrez Rivera Aerodynamic Shape Optimization 18 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Objective Functions
Similar to mathematical functions
They involve 3 basic operations
Evaluation
f (x) = a0 +nsum
i=1
an middot cos(n 31416 ) +nsum
i=1
bn middot sin(n 31416 )︸ ︷︷ ︸Evaluation
David Gutierrez Rivera Aerodynamic Shape Optimization 18 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Objective Functions
Similar to mathematical functions
They involve 3 basic operations
Read Output
f (x) = Value
Read Output
David Gutierrez Rivera Aerodynamic Shape Optimization 18 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Data Gathering
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 19 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Data Gathering
David Gutierrez Rivera Aerodynamic Shape Optimization 20 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Data Gathering
Data File
It is a text-based tab-delimited file containing the data points from thevariables and the corresponding values of the objective functions
Variable1 Variable2 Variablen Objective1 ObjectivemVariable1 Variable2 Variablen Objective1 Objectivem
Variable1 Variable2 Variablen Objective1 Objectivem
David Gutierrez Rivera Aerodynamic Shape Optimization 21 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Data Gathering
Data File
It is a text-based tab-delimited file containing the data points from thevariables and the corresponding values of the objective functions
Variable1 Variable2 Variablen Objective1 ObjectivemVariable1 Variable2 Variablen Objective1 Objectivem
Variable1 Variable2 Variablen Objective1 Objectivem
David Gutierrez Rivera Aerodynamic Shape Optimization 21 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Black-Box Optimization
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 22 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Black-Box Optimization
Black-Box Process
They are known from their inputs and outputs
Little is known of how it works internally
David Gutierrez Rivera Aerodynamic Shape Optimization 23 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Black-Box Optimization
David Gutierrez Rivera Aerodynamic Shape Optimization 23 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Black-Box Optimization
David Gutierrez Rivera Aerodynamic Shape Optimization 24 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Noisy Functions
David Gutierrez Rivera Aerodynamic Shape Optimization 25 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Simulation-based Optimization
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 26 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Simulation-based Optimization
David Gutierrez Rivera Aerodynamic Shape Optimization 27 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Moving Boundary Problem
David Gutierrez Rivera Aerodynamic Shape Optimization 28 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
OptiFlow
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 29 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Examples
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 30 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
M4 Neath Viaduct Wind Shield
Description
This bridge is located in South Wales and crosses the River Neath Asection of the bridge is very exposed in flat topography therefore a windshielding system is desired for reducing the overturning forces on vehicles
Description
The CFD model is the same as the one used on the VXFlow tutorial
Four small sections were used to obtain the interior drag forces
David Gutierrez Rivera Aerodynamic Shape Optimization 31 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
M4 Neath Viaduct Wind Shield
Description
The CFD model is the same as the one used on the VXFlow tutorial
Four small sections were used to obtain the interior drag forces
David Gutierrez Rivera Aerodynamic Shape Optimization 31 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
M4 Neath Viaduct Wind Shield
Description
The CFD model is the same as the one used on the VXFlow tutorial
Four small sections were used to obtain the interior drag forces
David Gutierrez Rivera Aerodynamic Shape Optimization 31 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Model
Find optimum height (h) for the Wind Shield
David Gutierrez Rivera Aerodynamic Shape Optimization 32 54
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Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Parameter File
Variables Definitions[beginvariables]define(h ) Height of Wind Screen[endvariables]define(L 300) Wind Screen Lengthdefine(t 015) Wind Screen Width Wind Screen Coordinatesdefine(x1 calc(0minus1300))define(x2 calc(x1minust))define(y1 calc(hminus025))define(y2 calc(y1+L))
4 num cornerpointsSCREEN3(SCHEME3)03 00 release distancespacing hull002 0001 00 minus01 merg1merg2merg3merg4minus4 minus3 minus1 minus3 minus1 section color codingdragliftmomentdisplrotation1 x2 y1 n11 x1 y1 n21 x1 y2 n11 x2 y2 n2
David Gutierrez Rivera Aerodynamic Shape Optimization 33 54
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Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Parameter File
Variables Definitions[beginvariables]define(h ) Height of Wind Screen[endvariables]define(L 300) Wind Screen Lengthdefine(t 015) Wind Screen Width Wind Screen Coordinatesdefine(x1 calc(0minus1300))define(x2 calc(x1minust))define(y1 calc(hminus025))define(y2 calc(y1+L))
4 num cornerpointsSCREEN3(SCHEME3)03 00 release distancespacing hull002 0001 00 minus01 merg1merg2merg3merg4minus4 minus3 minus1 minus3 minus1 section color codingdragliftmomentdisplrotation1 x2 y1 n11 x1 y1 n21 x1 y2 n11 x2 y2 n2
David Gutierrez Rivera Aerodynamic Shape Optimization 33 54
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Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Objective Function
function [Drag] = M4 Neath ViaductWS(X) M4 Neath ViaductWS Objective Functionsteps = 500
Drag(1) = VXF FORCES(XDRAGMAXstepsSECTION11)Drag(2) = VXF FORCES(XDRAGMAXstepsevalfalseSECTION12)Drag(3) = VXF FORCES(XDRAGMAXstepsevalfalseSECTION13)Drag(4) = VXF FORCES(XDRAGMAXstepsevalfalseSECTION14)
[DragLane] = max(Drag())
Call optiOUT to generate Plots and Output DataoptiOUT(X [Drag])
end
David Gutierrez Rivera Aerodynamic Shape Optimization 34 54
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M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Data Points
David Gutierrez Rivera Aerodynamic Shape Optimization 35 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Run-Time Optimization
David Gutierrez Rivera Aerodynamic Shape Optimization 36 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Vertical-Axis Wind Turbine (VAWT)
Description
The Savonius Wind Turbine is a Vertical-Axis Wind Turbine (VAWT)which main advantages are its reliability and practicality
David Gutierrez Rivera Aerodynamic Shape Optimization 37 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Model
Description
Find optimum values of ex and ey to maximize Torque or Power
Constrained to the shaded area
David Gutierrez Rivera Aerodynamic Shape Optimization 38 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Model
Description
Find optimum values of ex and ey to maximize Torque or Power
Constrained to the shaded area
David Gutierrez Rivera Aerodynamic Shape Optimization 38 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Dynamic Model
David Gutierrez Rivera Aerodynamic Shape Optimization 39 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
What is Optimization Basics of Aerodynamics
What is Optimization
Optimization is to find the optimum value(s) to achieve certain goal(s)
David Gutierrez Rivera Aerodynamic Shape Optimization 4 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
What is Optimization Basics of Aerodynamics
What is Optimization
Optimization is to find the optimum value(s) to achieve certain goal(s)
David Gutierrez Rivera Aerodynamic Shape Optimization 4 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
What is Optimization Basics of Aerodynamics
What is Optimization
Optimization is to find the optimum value(s) to achieve certain goal(s)
David Gutierrez Rivera Aerodynamic Shape Optimization 4 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
What is Optimization Basics of Aerodynamics
A Mathematical View
Mathematically optimization is formulated as
minimizex
f (x)
subject to
gi (x) le 0 i = 1 mhi (x) = 0 i = 1 n
(1)
where
f (x) Rn rarr R is the objective function to be minimized
gi (x) le 0 are inequality constraints
hi (x) = 0 are equality constraints
David Gutierrez Rivera Aerodynamic Shape Optimization 5 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
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Final RemarksFuture Research
AcknowledgmentsReferences
What is Optimization Basics of Aerodynamics
A Mathematical View
Mathematically optimization is formulated as
minimizex
f (x)
subject to
gi (x) le 0 i = 1 mhi (x) = 0 i = 1 n
(1)
where
f (x) Rn rarr R is the objective function to be minimized
gi (x) le 0 are inequality constraints
hi (x) = 0 are equality constraints
David Gutierrez Rivera Aerodynamic Shape Optimization 5 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
What is Optimization Basics of Aerodynamics
A Programmatic View
Programmatically optimization can be viewed as a loop
David Gutierrez Rivera Aerodynamic Shape Optimization 6 54
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Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
What is Optimization Basics of Aerodynamics
Basics of Aerodynamics
The Navier-Stokes Partial Differential Equation
David Gutierrez Rivera Aerodynamic Shape Optimization 7 54
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Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
What is Optimization Basics of Aerodynamics
Computational Fluid Dynamics (CFD)
Is the branch of fluid mechanics that uses numerical methods to solvefluid flow problems
Discretization Methods
Finite Volume Method
Boundary Element Method
High-Resolution Schemes
Turbulence Models
Reynolds-AveragedNavierStokes (RANS)
Large eddy simulation (LES)
Vortex methods
David Gutierrez Rivera Aerodynamic Shape Optimization 8 54
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Shape OptimizationData Gathering
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AcknowledgmentsReferences
What is Optimization Basics of Aerodynamics
Computational Fluid Dynamics (CFD)
Is the branch of fluid mechanics that uses numerical methods to solvefluid flow problems
Discretization Methods
Finite Volume Method
Boundary Element Method
High-Resolution Schemes
Turbulence Models
Reynolds-AveragedNavierStokes (RANS)
Large eddy simulation (LES)
Vortex methods
David Gutierrez Rivera Aerodynamic Shape Optimization 8 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
What is Optimization Basics of Aerodynamics
The Vortex Particle Method (VPM)
Characteristics
Is a grid-free technique for simulation of turbulent flows
It uses vortices as the computational elements
David Gutierrez Rivera Aerodynamic Shape Optimization 9 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
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Final RemarksFuture Research
AcknowledgmentsReferences
Local Global
Optimization Algorithms
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 10 54
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Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Local Global
Optimization Algorithms
Classification
Linearity
LinearNonLinear
Constraints
UnconstrainedConstrained
Objectives
Single-ObjectiveMulti-Objective
Modality
uni-modal (Local)multi-modal (Global)
David Gutierrez Rivera Aerodynamic Shape Optimization 11 54
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AcknowledgmentsReferences
Local Global
Optimization Algorithms
Classification
Linearity
LinearNonLinear
Constraints
UnconstrainedConstrained
Objectives
Single-ObjectiveMulti-Objective
Modality
uni-modal (Local)multi-modal (Global)
David Gutierrez Rivera Aerodynamic Shape Optimization 11 54
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Shape OptimizationData Gathering
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Final RemarksFuture Research
AcknowledgmentsReferences
Local Global
Global vs Local
David Gutierrez Rivera Aerodynamic Shape Optimization 12 54
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Local Global
Local
Gradient-free Methods
Golden Section
Simplex
Gradient-based Methods
Gradient-Descent
Newton
David Gutierrez Rivera Aerodynamic Shape Optimization 13 54
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Local Global
Global
non-Heuristic Methods
Deterministic
Stochastic
Heuristic Methods
Evolutionary
Genetic AlgorithmSwarm Intelligence
Swarm Intelligence
Particle SwarmAnt Colony
David Gutierrez Rivera Aerodynamic Shape Optimization 14 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Shape Optimization
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 15 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Shape Optimization
Shape optimization is formulated as
minimizeΩ
f (Ω)
subject to
gi (Ω) le 0 i = 1 mhi (Ω) = 0 i = 1 n
(2)
where
Ω is a set of variable parameters that make up the geometry that wewant to optimize
David Gutierrez Rivera Aerodynamic Shape Optimization 16 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Shape Optimization
Shape optimization is formulated as
minimizeΩ
f (Ω)
subject to
gi (Ω) le 0 i = 1 mhi (Ω) = 0 i = 1 n
(2)
where
Ω is a set of variable parameters that make up the geometry that wewant to optimize
David Gutierrez Rivera Aerodynamic Shape Optimization 16 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Parametrization
David Gutierrez Rivera Aerodynamic Shape Optimization 17 54
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Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Parametrization
David Gutierrez Rivera Aerodynamic Shape Optimization 17 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Objective Functions
Similar to mathematical functions
They involve 3 basic operations
David Gutierrez Rivera Aerodynamic Shape Optimization 18 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Objective Functions
Similar to mathematical functions
They involve 3 basic operations
Substitution
f (x) = a0 +nsum
i=1
an middot cos(n x ) +nsum
i=1
bn middot sin(n x )
David Gutierrez Rivera Aerodynamic Shape Optimization 18 54
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Shape OptimizationData Gathering
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Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Objective Functions
Similar to mathematical functions
They involve 3 basic operations
Substitution
f (x) = a0 +nsum
i=1
an middot cos(n 31416 ) +nsum
i=1
bn middot sin(n 31416 )
Substitution
David Gutierrez Rivera Aerodynamic Shape Optimization 18 54
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Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Objective Functions
Similar to mathematical functions
They involve 3 basic operations
Evaluation
f (x) = a0 +nsum
i=1
an middot cos(n 31416 ) +nsum
i=1
bn middot sin(n 31416 )︸ ︷︷ ︸Evaluation
David Gutierrez Rivera Aerodynamic Shape Optimization 18 54
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Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Objective Functions
Similar to mathematical functions
They involve 3 basic operations
Read Output
f (x) = Value
Read Output
David Gutierrez Rivera Aerodynamic Shape Optimization 18 54
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Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Data Gathering
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 19 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Data Gathering
David Gutierrez Rivera Aerodynamic Shape Optimization 20 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Data Gathering
Data File
It is a text-based tab-delimited file containing the data points from thevariables and the corresponding values of the objective functions
Variable1 Variable2 Variablen Objective1 ObjectivemVariable1 Variable2 Variablen Objective1 Objectivem
Variable1 Variable2 Variablen Objective1 Objectivem
David Gutierrez Rivera Aerodynamic Shape Optimization 21 54
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Data Gathering
Data File
It is a text-based tab-delimited file containing the data points from thevariables and the corresponding values of the objective functions
Variable1 Variable2 Variablen Objective1 ObjectivemVariable1 Variable2 Variablen Objective1 Objectivem
Variable1 Variable2 Variablen Objective1 Objectivem
David Gutierrez Rivera Aerodynamic Shape Optimization 21 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Black-Box Optimization
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 22 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Black-Box Optimization
Black-Box Process
They are known from their inputs and outputs
Little is known of how it works internally
David Gutierrez Rivera Aerodynamic Shape Optimization 23 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Black-Box Optimization
David Gutierrez Rivera Aerodynamic Shape Optimization 23 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Black-Box Optimization
David Gutierrez Rivera Aerodynamic Shape Optimization 24 54
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Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Noisy Functions
David Gutierrez Rivera Aerodynamic Shape Optimization 25 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
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Final RemarksFuture Research
AcknowledgmentsReferences
Simulation-based Optimization
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 26 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Simulation-based Optimization
David Gutierrez Rivera Aerodynamic Shape Optimization 27 54
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Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Moving Boundary Problem
David Gutierrez Rivera Aerodynamic Shape Optimization 28 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
OptiFlow
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 29 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Examples
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 30 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
M4 Neath Viaduct Wind Shield
Description
This bridge is located in South Wales and crosses the River Neath Asection of the bridge is very exposed in flat topography therefore a windshielding system is desired for reducing the overturning forces on vehicles
Description
The CFD model is the same as the one used on the VXFlow tutorial
Four small sections were used to obtain the interior drag forces
David Gutierrez Rivera Aerodynamic Shape Optimization 31 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
M4 Neath Viaduct Wind Shield
Description
The CFD model is the same as the one used on the VXFlow tutorial
Four small sections were used to obtain the interior drag forces
David Gutierrez Rivera Aerodynamic Shape Optimization 31 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
M4 Neath Viaduct Wind Shield
Description
The CFD model is the same as the one used on the VXFlow tutorial
Four small sections were used to obtain the interior drag forces
David Gutierrez Rivera Aerodynamic Shape Optimization 31 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Model
Find optimum height (h) for the Wind Shield
David Gutierrez Rivera Aerodynamic Shape Optimization 32 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Parameter File
Variables Definitions[beginvariables]define(h ) Height of Wind Screen[endvariables]define(L 300) Wind Screen Lengthdefine(t 015) Wind Screen Width Wind Screen Coordinatesdefine(x1 calc(0minus1300))define(x2 calc(x1minust))define(y1 calc(hminus025))define(y2 calc(y1+L))
4 num cornerpointsSCREEN3(SCHEME3)03 00 release distancespacing hull002 0001 00 minus01 merg1merg2merg3merg4minus4 minus3 minus1 minus3 minus1 section color codingdragliftmomentdisplrotation1 x2 y1 n11 x1 y1 n21 x1 y2 n11 x2 y2 n2
David Gutierrez Rivera Aerodynamic Shape Optimization 33 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Parameter File
Variables Definitions[beginvariables]define(h ) Height of Wind Screen[endvariables]define(L 300) Wind Screen Lengthdefine(t 015) Wind Screen Width Wind Screen Coordinatesdefine(x1 calc(0minus1300))define(x2 calc(x1minust))define(y1 calc(hminus025))define(y2 calc(y1+L))
4 num cornerpointsSCREEN3(SCHEME3)03 00 release distancespacing hull002 0001 00 minus01 merg1merg2merg3merg4minus4 minus3 minus1 minus3 minus1 section color codingdragliftmomentdisplrotation1 x2 y1 n11 x1 y1 n21 x1 y2 n11 x2 y2 n2
David Gutierrez Rivera Aerodynamic Shape Optimization 33 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Objective Function
function [Drag] = M4 Neath ViaductWS(X) M4 Neath ViaductWS Objective Functionsteps = 500
Drag(1) = VXF FORCES(XDRAGMAXstepsSECTION11)Drag(2) = VXF FORCES(XDRAGMAXstepsevalfalseSECTION12)Drag(3) = VXF FORCES(XDRAGMAXstepsevalfalseSECTION13)Drag(4) = VXF FORCES(XDRAGMAXstepsevalfalseSECTION14)
[DragLane] = max(Drag())
Call optiOUT to generate Plots and Output DataoptiOUT(X [Drag])
end
David Gutierrez Rivera Aerodynamic Shape Optimization 34 54
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M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Data Points
David Gutierrez Rivera Aerodynamic Shape Optimization 35 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Run-Time Optimization
David Gutierrez Rivera Aerodynamic Shape Optimization 36 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Vertical-Axis Wind Turbine (VAWT)
Description
The Savonius Wind Turbine is a Vertical-Axis Wind Turbine (VAWT)which main advantages are its reliability and practicality
David Gutierrez Rivera Aerodynamic Shape Optimization 37 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Model
Description
Find optimum values of ex and ey to maximize Torque or Power
Constrained to the shaded area
David Gutierrez Rivera Aerodynamic Shape Optimization 38 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Model
Description
Find optimum values of ex and ey to maximize Torque or Power
Constrained to the shaded area
David Gutierrez Rivera Aerodynamic Shape Optimization 38 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Dynamic Model
David Gutierrez Rivera Aerodynamic Shape Optimization 39 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
What is Optimization Basics of Aerodynamics
What is Optimization
Optimization is to find the optimum value(s) to achieve certain goal(s)
David Gutierrez Rivera Aerodynamic Shape Optimization 4 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
What is Optimization Basics of Aerodynamics
What is Optimization
Optimization is to find the optimum value(s) to achieve certain goal(s)
David Gutierrez Rivera Aerodynamic Shape Optimization 4 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
What is Optimization Basics of Aerodynamics
A Mathematical View
Mathematically optimization is formulated as
minimizex
f (x)
subject to
gi (x) le 0 i = 1 mhi (x) = 0 i = 1 n
(1)
where
f (x) Rn rarr R is the objective function to be minimized
gi (x) le 0 are inequality constraints
hi (x) = 0 are equality constraints
David Gutierrez Rivera Aerodynamic Shape Optimization 5 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
What is Optimization Basics of Aerodynamics
A Mathematical View
Mathematically optimization is formulated as
minimizex
f (x)
subject to
gi (x) le 0 i = 1 mhi (x) = 0 i = 1 n
(1)
where
f (x) Rn rarr R is the objective function to be minimized
gi (x) le 0 are inequality constraints
hi (x) = 0 are equality constraints
David Gutierrez Rivera Aerodynamic Shape Optimization 5 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
What is Optimization Basics of Aerodynamics
A Programmatic View
Programmatically optimization can be viewed as a loop
David Gutierrez Rivera Aerodynamic Shape Optimization 6 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
What is Optimization Basics of Aerodynamics
Basics of Aerodynamics
The Navier-Stokes Partial Differential Equation
David Gutierrez Rivera Aerodynamic Shape Optimization 7 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
What is Optimization Basics of Aerodynamics
Computational Fluid Dynamics (CFD)
Is the branch of fluid mechanics that uses numerical methods to solvefluid flow problems
Discretization Methods
Finite Volume Method
Boundary Element Method
High-Resolution Schemes
Turbulence Models
Reynolds-AveragedNavierStokes (RANS)
Large eddy simulation (LES)
Vortex methods
David Gutierrez Rivera Aerodynamic Shape Optimization 8 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
What is Optimization Basics of Aerodynamics
Computational Fluid Dynamics (CFD)
Is the branch of fluid mechanics that uses numerical methods to solvefluid flow problems
Discretization Methods
Finite Volume Method
Boundary Element Method
High-Resolution Schemes
Turbulence Models
Reynolds-AveragedNavierStokes (RANS)
Large eddy simulation (LES)
Vortex methods
David Gutierrez Rivera Aerodynamic Shape Optimization 8 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
What is Optimization Basics of Aerodynamics
The Vortex Particle Method (VPM)
Characteristics
Is a grid-free technique for simulation of turbulent flows
It uses vortices as the computational elements
David Gutierrez Rivera Aerodynamic Shape Optimization 9 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Local Global
Optimization Algorithms
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 10 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Local Global
Optimization Algorithms
Classification
Linearity
LinearNonLinear
Constraints
UnconstrainedConstrained
Objectives
Single-ObjectiveMulti-Objective
Modality
uni-modal (Local)multi-modal (Global)
David Gutierrez Rivera Aerodynamic Shape Optimization 11 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Local Global
Optimization Algorithms
Classification
Linearity
LinearNonLinear
Constraints
UnconstrainedConstrained
Objectives
Single-ObjectiveMulti-Objective
Modality
uni-modal (Local)multi-modal (Global)
David Gutierrez Rivera Aerodynamic Shape Optimization 11 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Local Global
Global vs Local
David Gutierrez Rivera Aerodynamic Shape Optimization 12 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Local Global
Local
Gradient-free Methods
Golden Section
Simplex
Gradient-based Methods
Gradient-Descent
Newton
David Gutierrez Rivera Aerodynamic Shape Optimization 13 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Local Global
Global
non-Heuristic Methods
Deterministic
Stochastic
Heuristic Methods
Evolutionary
Genetic AlgorithmSwarm Intelligence
Swarm Intelligence
Particle SwarmAnt Colony
David Gutierrez Rivera Aerodynamic Shape Optimization 14 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Shape Optimization
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 15 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Shape Optimization
Shape optimization is formulated as
minimizeΩ
f (Ω)
subject to
gi (Ω) le 0 i = 1 mhi (Ω) = 0 i = 1 n
(2)
where
Ω is a set of variable parameters that make up the geometry that wewant to optimize
David Gutierrez Rivera Aerodynamic Shape Optimization 16 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Shape Optimization
Shape optimization is formulated as
minimizeΩ
f (Ω)
subject to
gi (Ω) le 0 i = 1 mhi (Ω) = 0 i = 1 n
(2)
where
Ω is a set of variable parameters that make up the geometry that wewant to optimize
David Gutierrez Rivera Aerodynamic Shape Optimization 16 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Parametrization
David Gutierrez Rivera Aerodynamic Shape Optimization 17 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Parametrization
David Gutierrez Rivera Aerodynamic Shape Optimization 17 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Objective Functions
Similar to mathematical functions
They involve 3 basic operations
David Gutierrez Rivera Aerodynamic Shape Optimization 18 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Objective Functions
Similar to mathematical functions
They involve 3 basic operations
Substitution
f (x) = a0 +nsum
i=1
an middot cos(n x ) +nsum
i=1
bn middot sin(n x )
David Gutierrez Rivera Aerodynamic Shape Optimization 18 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Objective Functions
Similar to mathematical functions
They involve 3 basic operations
Substitution
f (x) = a0 +nsum
i=1
an middot cos(n 31416 ) +nsum
i=1
bn middot sin(n 31416 )
Substitution
David Gutierrez Rivera Aerodynamic Shape Optimization 18 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Objective Functions
Similar to mathematical functions
They involve 3 basic operations
Evaluation
f (x) = a0 +nsum
i=1
an middot cos(n 31416 ) +nsum
i=1
bn middot sin(n 31416 )︸ ︷︷ ︸Evaluation
David Gutierrez Rivera Aerodynamic Shape Optimization 18 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Objective Functions
Similar to mathematical functions
They involve 3 basic operations
Read Output
f (x) = Value
Read Output
David Gutierrez Rivera Aerodynamic Shape Optimization 18 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Data Gathering
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 19 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Data Gathering
David Gutierrez Rivera Aerodynamic Shape Optimization 20 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Data Gathering
Data File
It is a text-based tab-delimited file containing the data points from thevariables and the corresponding values of the objective functions
Variable1 Variable2 Variablen Objective1 ObjectivemVariable1 Variable2 Variablen Objective1 Objectivem
Variable1 Variable2 Variablen Objective1 Objectivem
David Gutierrez Rivera Aerodynamic Shape Optimization 21 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Data Gathering
Data File
It is a text-based tab-delimited file containing the data points from thevariables and the corresponding values of the objective functions
Variable1 Variable2 Variablen Objective1 ObjectivemVariable1 Variable2 Variablen Objective1 Objectivem
Variable1 Variable2 Variablen Objective1 Objectivem
David Gutierrez Rivera Aerodynamic Shape Optimization 21 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Black-Box Optimization
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 22 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Black-Box Optimization
Black-Box Process
They are known from their inputs and outputs
Little is known of how it works internally
David Gutierrez Rivera Aerodynamic Shape Optimization 23 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Black-Box Optimization
David Gutierrez Rivera Aerodynamic Shape Optimization 23 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Black-Box Optimization
David Gutierrez Rivera Aerodynamic Shape Optimization 24 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Noisy Functions
David Gutierrez Rivera Aerodynamic Shape Optimization 25 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Simulation-based Optimization
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 26 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Simulation-based Optimization
David Gutierrez Rivera Aerodynamic Shape Optimization 27 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Moving Boundary Problem
David Gutierrez Rivera Aerodynamic Shape Optimization 28 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
OptiFlow
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 29 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Examples
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 30 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
M4 Neath Viaduct Wind Shield
Description
This bridge is located in South Wales and crosses the River Neath Asection of the bridge is very exposed in flat topography therefore a windshielding system is desired for reducing the overturning forces on vehicles
Description
The CFD model is the same as the one used on the VXFlow tutorial
Four small sections were used to obtain the interior drag forces
David Gutierrez Rivera Aerodynamic Shape Optimization 31 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
M4 Neath Viaduct Wind Shield
Description
The CFD model is the same as the one used on the VXFlow tutorial
Four small sections were used to obtain the interior drag forces
David Gutierrez Rivera Aerodynamic Shape Optimization 31 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
M4 Neath Viaduct Wind Shield
Description
The CFD model is the same as the one used on the VXFlow tutorial
Four small sections were used to obtain the interior drag forces
David Gutierrez Rivera Aerodynamic Shape Optimization 31 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Model
Find optimum height (h) for the Wind Shield
David Gutierrez Rivera Aerodynamic Shape Optimization 32 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Parameter File
Variables Definitions[beginvariables]define(h ) Height of Wind Screen[endvariables]define(L 300) Wind Screen Lengthdefine(t 015) Wind Screen Width Wind Screen Coordinatesdefine(x1 calc(0minus1300))define(x2 calc(x1minust))define(y1 calc(hminus025))define(y2 calc(y1+L))
4 num cornerpointsSCREEN3(SCHEME3)03 00 release distancespacing hull002 0001 00 minus01 merg1merg2merg3merg4minus4 minus3 minus1 minus3 minus1 section color codingdragliftmomentdisplrotation1 x2 y1 n11 x1 y1 n21 x1 y2 n11 x2 y2 n2
David Gutierrez Rivera Aerodynamic Shape Optimization 33 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Parameter File
Variables Definitions[beginvariables]define(h ) Height of Wind Screen[endvariables]define(L 300) Wind Screen Lengthdefine(t 015) Wind Screen Width Wind Screen Coordinatesdefine(x1 calc(0minus1300))define(x2 calc(x1minust))define(y1 calc(hminus025))define(y2 calc(y1+L))
4 num cornerpointsSCREEN3(SCHEME3)03 00 release distancespacing hull002 0001 00 minus01 merg1merg2merg3merg4minus4 minus3 minus1 minus3 minus1 section color codingdragliftmomentdisplrotation1 x2 y1 n11 x1 y1 n21 x1 y2 n11 x2 y2 n2
David Gutierrez Rivera Aerodynamic Shape Optimization 33 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Objective Function
function [Drag] = M4 Neath ViaductWS(X) M4 Neath ViaductWS Objective Functionsteps = 500
Drag(1) = VXF FORCES(XDRAGMAXstepsSECTION11)Drag(2) = VXF FORCES(XDRAGMAXstepsevalfalseSECTION12)Drag(3) = VXF FORCES(XDRAGMAXstepsevalfalseSECTION13)Drag(4) = VXF FORCES(XDRAGMAXstepsevalfalseSECTION14)
[DragLane] = max(Drag())
Call optiOUT to generate Plots and Output DataoptiOUT(X [Drag])
end
David Gutierrez Rivera Aerodynamic Shape Optimization 34 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Data Points
David Gutierrez Rivera Aerodynamic Shape Optimization 35 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Run-Time Optimization
David Gutierrez Rivera Aerodynamic Shape Optimization 36 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Vertical-Axis Wind Turbine (VAWT)
Description
The Savonius Wind Turbine is a Vertical-Axis Wind Turbine (VAWT)which main advantages are its reliability and practicality
David Gutierrez Rivera Aerodynamic Shape Optimization 37 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Model
Description
Find optimum values of ex and ey to maximize Torque or Power
Constrained to the shaded area
David Gutierrez Rivera Aerodynamic Shape Optimization 38 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Model
Description
Find optimum values of ex and ey to maximize Torque or Power
Constrained to the shaded area
David Gutierrez Rivera Aerodynamic Shape Optimization 38 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Dynamic Model
David Gutierrez Rivera Aerodynamic Shape Optimization 39 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
What is Optimization Basics of Aerodynamics
What is Optimization
Optimization is to find the optimum value(s) to achieve certain goal(s)
David Gutierrez Rivera Aerodynamic Shape Optimization 4 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
What is Optimization Basics of Aerodynamics
A Mathematical View
Mathematically optimization is formulated as
minimizex
f (x)
subject to
gi (x) le 0 i = 1 mhi (x) = 0 i = 1 n
(1)
where
f (x) Rn rarr R is the objective function to be minimized
gi (x) le 0 are inequality constraints
hi (x) = 0 are equality constraints
David Gutierrez Rivera Aerodynamic Shape Optimization 5 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
What is Optimization Basics of Aerodynamics
A Mathematical View
Mathematically optimization is formulated as
minimizex
f (x)
subject to
gi (x) le 0 i = 1 mhi (x) = 0 i = 1 n
(1)
where
f (x) Rn rarr R is the objective function to be minimized
gi (x) le 0 are inequality constraints
hi (x) = 0 are equality constraints
David Gutierrez Rivera Aerodynamic Shape Optimization 5 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
What is Optimization Basics of Aerodynamics
A Programmatic View
Programmatically optimization can be viewed as a loop
David Gutierrez Rivera Aerodynamic Shape Optimization 6 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
What is Optimization Basics of Aerodynamics
Basics of Aerodynamics
The Navier-Stokes Partial Differential Equation
David Gutierrez Rivera Aerodynamic Shape Optimization 7 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
What is Optimization Basics of Aerodynamics
Computational Fluid Dynamics (CFD)
Is the branch of fluid mechanics that uses numerical methods to solvefluid flow problems
Discretization Methods
Finite Volume Method
Boundary Element Method
High-Resolution Schemes
Turbulence Models
Reynolds-AveragedNavierStokes (RANS)
Large eddy simulation (LES)
Vortex methods
David Gutierrez Rivera Aerodynamic Shape Optimization 8 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
What is Optimization Basics of Aerodynamics
Computational Fluid Dynamics (CFD)
Is the branch of fluid mechanics that uses numerical methods to solvefluid flow problems
Discretization Methods
Finite Volume Method
Boundary Element Method
High-Resolution Schemes
Turbulence Models
Reynolds-AveragedNavierStokes (RANS)
Large eddy simulation (LES)
Vortex methods
David Gutierrez Rivera Aerodynamic Shape Optimization 8 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
What is Optimization Basics of Aerodynamics
The Vortex Particle Method (VPM)
Characteristics
Is a grid-free technique for simulation of turbulent flows
It uses vortices as the computational elements
David Gutierrez Rivera Aerodynamic Shape Optimization 9 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Local Global
Optimization Algorithms
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 10 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Local Global
Optimization Algorithms
Classification
Linearity
LinearNonLinear
Constraints
UnconstrainedConstrained
Objectives
Single-ObjectiveMulti-Objective
Modality
uni-modal (Local)multi-modal (Global)
David Gutierrez Rivera Aerodynamic Shape Optimization 11 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Local Global
Optimization Algorithms
Classification
Linearity
LinearNonLinear
Constraints
UnconstrainedConstrained
Objectives
Single-ObjectiveMulti-Objective
Modality
uni-modal (Local)multi-modal (Global)
David Gutierrez Rivera Aerodynamic Shape Optimization 11 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Local Global
Global vs Local
David Gutierrez Rivera Aerodynamic Shape Optimization 12 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Local Global
Local
Gradient-free Methods
Golden Section
Simplex
Gradient-based Methods
Gradient-Descent
Newton
David Gutierrez Rivera Aerodynamic Shape Optimization 13 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Local Global
Global
non-Heuristic Methods
Deterministic
Stochastic
Heuristic Methods
Evolutionary
Genetic AlgorithmSwarm Intelligence
Swarm Intelligence
Particle SwarmAnt Colony
David Gutierrez Rivera Aerodynamic Shape Optimization 14 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Shape Optimization
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 15 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Shape Optimization
Shape optimization is formulated as
minimizeΩ
f (Ω)
subject to
gi (Ω) le 0 i = 1 mhi (Ω) = 0 i = 1 n
(2)
where
Ω is a set of variable parameters that make up the geometry that wewant to optimize
David Gutierrez Rivera Aerodynamic Shape Optimization 16 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Shape Optimization
Shape optimization is formulated as
minimizeΩ
f (Ω)
subject to
gi (Ω) le 0 i = 1 mhi (Ω) = 0 i = 1 n
(2)
where
Ω is a set of variable parameters that make up the geometry that wewant to optimize
David Gutierrez Rivera Aerodynamic Shape Optimization 16 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Parametrization
David Gutierrez Rivera Aerodynamic Shape Optimization 17 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Parametrization
David Gutierrez Rivera Aerodynamic Shape Optimization 17 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Objective Functions
Similar to mathematical functions
They involve 3 basic operations
David Gutierrez Rivera Aerodynamic Shape Optimization 18 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Objective Functions
Similar to mathematical functions
They involve 3 basic operations
Substitution
f (x) = a0 +nsum
i=1
an middot cos(n x ) +nsum
i=1
bn middot sin(n x )
David Gutierrez Rivera Aerodynamic Shape Optimization 18 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Objective Functions
Similar to mathematical functions
They involve 3 basic operations
Substitution
f (x) = a0 +nsum
i=1
an middot cos(n 31416 ) +nsum
i=1
bn middot sin(n 31416 )
Substitution
David Gutierrez Rivera Aerodynamic Shape Optimization 18 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Objective Functions
Similar to mathematical functions
They involve 3 basic operations
Evaluation
f (x) = a0 +nsum
i=1
an middot cos(n 31416 ) +nsum
i=1
bn middot sin(n 31416 )︸ ︷︷ ︸Evaluation
David Gutierrez Rivera Aerodynamic Shape Optimization 18 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Objective Functions
Similar to mathematical functions
They involve 3 basic operations
Read Output
f (x) = Value
Read Output
David Gutierrez Rivera Aerodynamic Shape Optimization 18 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Data Gathering
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 19 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Data Gathering
David Gutierrez Rivera Aerodynamic Shape Optimization 20 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Data Gathering
Data File
It is a text-based tab-delimited file containing the data points from thevariables and the corresponding values of the objective functions
Variable1 Variable2 Variablen Objective1 ObjectivemVariable1 Variable2 Variablen Objective1 Objectivem
Variable1 Variable2 Variablen Objective1 Objectivem
David Gutierrez Rivera Aerodynamic Shape Optimization 21 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Data Gathering
Data File
It is a text-based tab-delimited file containing the data points from thevariables and the corresponding values of the objective functions
Variable1 Variable2 Variablen Objective1 ObjectivemVariable1 Variable2 Variablen Objective1 Objectivem
Variable1 Variable2 Variablen Objective1 Objectivem
David Gutierrez Rivera Aerodynamic Shape Optimization 21 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Black-Box Optimization
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 22 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Black-Box Optimization
Black-Box Process
They are known from their inputs and outputs
Little is known of how it works internally
David Gutierrez Rivera Aerodynamic Shape Optimization 23 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Black-Box Optimization
David Gutierrez Rivera Aerodynamic Shape Optimization 23 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Black-Box Optimization
David Gutierrez Rivera Aerodynamic Shape Optimization 24 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Noisy Functions
David Gutierrez Rivera Aerodynamic Shape Optimization 25 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Simulation-based Optimization
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 26 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Simulation-based Optimization
David Gutierrez Rivera Aerodynamic Shape Optimization 27 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Moving Boundary Problem
David Gutierrez Rivera Aerodynamic Shape Optimization 28 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
OptiFlow
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 29 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Examples
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 30 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
M4 Neath Viaduct Wind Shield
Description
This bridge is located in South Wales and crosses the River Neath Asection of the bridge is very exposed in flat topography therefore a windshielding system is desired for reducing the overturning forces on vehicles
Description
The CFD model is the same as the one used on the VXFlow tutorial
Four small sections were used to obtain the interior drag forces
David Gutierrez Rivera Aerodynamic Shape Optimization 31 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
M4 Neath Viaduct Wind Shield
Description
The CFD model is the same as the one used on the VXFlow tutorial
Four small sections were used to obtain the interior drag forces
David Gutierrez Rivera Aerodynamic Shape Optimization 31 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
M4 Neath Viaduct Wind Shield
Description
The CFD model is the same as the one used on the VXFlow tutorial
Four small sections were used to obtain the interior drag forces
David Gutierrez Rivera Aerodynamic Shape Optimization 31 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Model
Find optimum height (h) for the Wind Shield
David Gutierrez Rivera Aerodynamic Shape Optimization 32 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Parameter File
Variables Definitions[beginvariables]define(h ) Height of Wind Screen[endvariables]define(L 300) Wind Screen Lengthdefine(t 015) Wind Screen Width Wind Screen Coordinatesdefine(x1 calc(0minus1300))define(x2 calc(x1minust))define(y1 calc(hminus025))define(y2 calc(y1+L))
4 num cornerpointsSCREEN3(SCHEME3)03 00 release distancespacing hull002 0001 00 minus01 merg1merg2merg3merg4minus4 minus3 minus1 minus3 minus1 section color codingdragliftmomentdisplrotation1 x2 y1 n11 x1 y1 n21 x1 y2 n11 x2 y2 n2
David Gutierrez Rivera Aerodynamic Shape Optimization 33 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Parameter File
Variables Definitions[beginvariables]define(h ) Height of Wind Screen[endvariables]define(L 300) Wind Screen Lengthdefine(t 015) Wind Screen Width Wind Screen Coordinatesdefine(x1 calc(0minus1300))define(x2 calc(x1minust))define(y1 calc(hminus025))define(y2 calc(y1+L))
4 num cornerpointsSCREEN3(SCHEME3)03 00 release distancespacing hull002 0001 00 minus01 merg1merg2merg3merg4minus4 minus3 minus1 minus3 minus1 section color codingdragliftmomentdisplrotation1 x2 y1 n11 x1 y1 n21 x1 y2 n11 x2 y2 n2
David Gutierrez Rivera Aerodynamic Shape Optimization 33 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Objective Function
function [Drag] = M4 Neath ViaductWS(X) M4 Neath ViaductWS Objective Functionsteps = 500
Drag(1) = VXF FORCES(XDRAGMAXstepsSECTION11)Drag(2) = VXF FORCES(XDRAGMAXstepsevalfalseSECTION12)Drag(3) = VXF FORCES(XDRAGMAXstepsevalfalseSECTION13)Drag(4) = VXF FORCES(XDRAGMAXstepsevalfalseSECTION14)
[DragLane] = max(Drag())
Call optiOUT to generate Plots and Output DataoptiOUT(X [Drag])
end
David Gutierrez Rivera Aerodynamic Shape Optimization 34 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Data Points
David Gutierrez Rivera Aerodynamic Shape Optimization 35 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Run-Time Optimization
David Gutierrez Rivera Aerodynamic Shape Optimization 36 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Vertical-Axis Wind Turbine (VAWT)
Description
The Savonius Wind Turbine is a Vertical-Axis Wind Turbine (VAWT)which main advantages are its reliability and practicality
David Gutierrez Rivera Aerodynamic Shape Optimization 37 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Model
Description
Find optimum values of ex and ey to maximize Torque or Power
Constrained to the shaded area
David Gutierrez Rivera Aerodynamic Shape Optimization 38 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Model
Description
Find optimum values of ex and ey to maximize Torque or Power
Constrained to the shaded area
David Gutierrez Rivera Aerodynamic Shape Optimization 38 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Dynamic Model
David Gutierrez Rivera Aerodynamic Shape Optimization 39 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
What is Optimization Basics of Aerodynamics
A Mathematical View
Mathematically optimization is formulated as
minimizex
f (x)
subject to
gi (x) le 0 i = 1 mhi (x) = 0 i = 1 n
(1)
where
f (x) Rn rarr R is the objective function to be minimized
gi (x) le 0 are inequality constraints
hi (x) = 0 are equality constraints
David Gutierrez Rivera Aerodynamic Shape Optimization 5 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
What is Optimization Basics of Aerodynamics
A Mathematical View
Mathematically optimization is formulated as
minimizex
f (x)
subject to
gi (x) le 0 i = 1 mhi (x) = 0 i = 1 n
(1)
where
f (x) Rn rarr R is the objective function to be minimized
gi (x) le 0 are inequality constraints
hi (x) = 0 are equality constraints
David Gutierrez Rivera Aerodynamic Shape Optimization 5 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
What is Optimization Basics of Aerodynamics
A Programmatic View
Programmatically optimization can be viewed as a loop
David Gutierrez Rivera Aerodynamic Shape Optimization 6 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
What is Optimization Basics of Aerodynamics
Basics of Aerodynamics
The Navier-Stokes Partial Differential Equation
David Gutierrez Rivera Aerodynamic Shape Optimization 7 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
What is Optimization Basics of Aerodynamics
Computational Fluid Dynamics (CFD)
Is the branch of fluid mechanics that uses numerical methods to solvefluid flow problems
Discretization Methods
Finite Volume Method
Boundary Element Method
High-Resolution Schemes
Turbulence Models
Reynolds-AveragedNavierStokes (RANS)
Large eddy simulation (LES)
Vortex methods
David Gutierrez Rivera Aerodynamic Shape Optimization 8 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
What is Optimization Basics of Aerodynamics
Computational Fluid Dynamics (CFD)
Is the branch of fluid mechanics that uses numerical methods to solvefluid flow problems
Discretization Methods
Finite Volume Method
Boundary Element Method
High-Resolution Schemes
Turbulence Models
Reynolds-AveragedNavierStokes (RANS)
Large eddy simulation (LES)
Vortex methods
David Gutierrez Rivera Aerodynamic Shape Optimization 8 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
What is Optimization Basics of Aerodynamics
The Vortex Particle Method (VPM)
Characteristics
Is a grid-free technique for simulation of turbulent flows
It uses vortices as the computational elements
David Gutierrez Rivera Aerodynamic Shape Optimization 9 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Local Global
Optimization Algorithms
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 10 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Local Global
Optimization Algorithms
Classification
Linearity
LinearNonLinear
Constraints
UnconstrainedConstrained
Objectives
Single-ObjectiveMulti-Objective
Modality
uni-modal (Local)multi-modal (Global)
David Gutierrez Rivera Aerodynamic Shape Optimization 11 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Local Global
Optimization Algorithms
Classification
Linearity
LinearNonLinear
Constraints
UnconstrainedConstrained
Objectives
Single-ObjectiveMulti-Objective
Modality
uni-modal (Local)multi-modal (Global)
David Gutierrez Rivera Aerodynamic Shape Optimization 11 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Local Global
Global vs Local
David Gutierrez Rivera Aerodynamic Shape Optimization 12 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Local Global
Local
Gradient-free Methods
Golden Section
Simplex
Gradient-based Methods
Gradient-Descent
Newton
David Gutierrez Rivera Aerodynamic Shape Optimization 13 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Local Global
Global
non-Heuristic Methods
Deterministic
Stochastic
Heuristic Methods
Evolutionary
Genetic AlgorithmSwarm Intelligence
Swarm Intelligence
Particle SwarmAnt Colony
David Gutierrez Rivera Aerodynamic Shape Optimization 14 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Shape Optimization
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 15 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Shape Optimization
Shape optimization is formulated as
minimizeΩ
f (Ω)
subject to
gi (Ω) le 0 i = 1 mhi (Ω) = 0 i = 1 n
(2)
where
Ω is a set of variable parameters that make up the geometry that wewant to optimize
David Gutierrez Rivera Aerodynamic Shape Optimization 16 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Shape Optimization
Shape optimization is formulated as
minimizeΩ
f (Ω)
subject to
gi (Ω) le 0 i = 1 mhi (Ω) = 0 i = 1 n
(2)
where
Ω is a set of variable parameters that make up the geometry that wewant to optimize
David Gutierrez Rivera Aerodynamic Shape Optimization 16 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Parametrization
David Gutierrez Rivera Aerodynamic Shape Optimization 17 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Parametrization
David Gutierrez Rivera Aerodynamic Shape Optimization 17 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Objective Functions
Similar to mathematical functions
They involve 3 basic operations
David Gutierrez Rivera Aerodynamic Shape Optimization 18 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Objective Functions
Similar to mathematical functions
They involve 3 basic operations
Substitution
f (x) = a0 +nsum
i=1
an middot cos(n x ) +nsum
i=1
bn middot sin(n x )
David Gutierrez Rivera Aerodynamic Shape Optimization 18 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Objective Functions
Similar to mathematical functions
They involve 3 basic operations
Substitution
f (x) = a0 +nsum
i=1
an middot cos(n 31416 ) +nsum
i=1
bn middot sin(n 31416 )
Substitution
David Gutierrez Rivera Aerodynamic Shape Optimization 18 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Objective Functions
Similar to mathematical functions
They involve 3 basic operations
Evaluation
f (x) = a0 +nsum
i=1
an middot cos(n 31416 ) +nsum
i=1
bn middot sin(n 31416 )︸ ︷︷ ︸Evaluation
David Gutierrez Rivera Aerodynamic Shape Optimization 18 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Objective Functions
Similar to mathematical functions
They involve 3 basic operations
Read Output
f (x) = Value
Read Output
David Gutierrez Rivera Aerodynamic Shape Optimization 18 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Data Gathering
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 19 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Data Gathering
David Gutierrez Rivera Aerodynamic Shape Optimization 20 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Data Gathering
Data File
It is a text-based tab-delimited file containing the data points from thevariables and the corresponding values of the objective functions
Variable1 Variable2 Variablen Objective1 ObjectivemVariable1 Variable2 Variablen Objective1 Objectivem
Variable1 Variable2 Variablen Objective1 Objectivem
David Gutierrez Rivera Aerodynamic Shape Optimization 21 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Data Gathering
Data File
It is a text-based tab-delimited file containing the data points from thevariables and the corresponding values of the objective functions
Variable1 Variable2 Variablen Objective1 ObjectivemVariable1 Variable2 Variablen Objective1 Objectivem
Variable1 Variable2 Variablen Objective1 Objectivem
David Gutierrez Rivera Aerodynamic Shape Optimization 21 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Black-Box Optimization
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 22 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Black-Box Optimization
Black-Box Process
They are known from their inputs and outputs
Little is known of how it works internally
David Gutierrez Rivera Aerodynamic Shape Optimization 23 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Black-Box Optimization
David Gutierrez Rivera Aerodynamic Shape Optimization 23 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Black-Box Optimization
David Gutierrez Rivera Aerodynamic Shape Optimization 24 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Noisy Functions
David Gutierrez Rivera Aerodynamic Shape Optimization 25 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Simulation-based Optimization
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 26 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Simulation-based Optimization
David Gutierrez Rivera Aerodynamic Shape Optimization 27 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Moving Boundary Problem
David Gutierrez Rivera Aerodynamic Shape Optimization 28 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
OptiFlow
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 29 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Examples
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 30 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
M4 Neath Viaduct Wind Shield
Description
This bridge is located in South Wales and crosses the River Neath Asection of the bridge is very exposed in flat topography therefore a windshielding system is desired for reducing the overturning forces on vehicles
Description
The CFD model is the same as the one used on the VXFlow tutorial
Four small sections were used to obtain the interior drag forces
David Gutierrez Rivera Aerodynamic Shape Optimization 31 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
M4 Neath Viaduct Wind Shield
Description
The CFD model is the same as the one used on the VXFlow tutorial
Four small sections were used to obtain the interior drag forces
David Gutierrez Rivera Aerodynamic Shape Optimization 31 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
M4 Neath Viaduct Wind Shield
Description
The CFD model is the same as the one used on the VXFlow tutorial
Four small sections were used to obtain the interior drag forces
David Gutierrez Rivera Aerodynamic Shape Optimization 31 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Model
Find optimum height (h) for the Wind Shield
David Gutierrez Rivera Aerodynamic Shape Optimization 32 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Parameter File
Variables Definitions[beginvariables]define(h ) Height of Wind Screen[endvariables]define(L 300) Wind Screen Lengthdefine(t 015) Wind Screen Width Wind Screen Coordinatesdefine(x1 calc(0minus1300))define(x2 calc(x1minust))define(y1 calc(hminus025))define(y2 calc(y1+L))
4 num cornerpointsSCREEN3(SCHEME3)03 00 release distancespacing hull002 0001 00 minus01 merg1merg2merg3merg4minus4 minus3 minus1 minus3 minus1 section color codingdragliftmomentdisplrotation1 x2 y1 n11 x1 y1 n21 x1 y2 n11 x2 y2 n2
David Gutierrez Rivera Aerodynamic Shape Optimization 33 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Parameter File
Variables Definitions[beginvariables]define(h ) Height of Wind Screen[endvariables]define(L 300) Wind Screen Lengthdefine(t 015) Wind Screen Width Wind Screen Coordinatesdefine(x1 calc(0minus1300))define(x2 calc(x1minust))define(y1 calc(hminus025))define(y2 calc(y1+L))
4 num cornerpointsSCREEN3(SCHEME3)03 00 release distancespacing hull002 0001 00 minus01 merg1merg2merg3merg4minus4 minus3 minus1 minus3 minus1 section color codingdragliftmomentdisplrotation1 x2 y1 n11 x1 y1 n21 x1 y2 n11 x2 y2 n2
David Gutierrez Rivera Aerodynamic Shape Optimization 33 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Objective Function
function [Drag] = M4 Neath ViaductWS(X) M4 Neath ViaductWS Objective Functionsteps = 500
Drag(1) = VXF FORCES(XDRAGMAXstepsSECTION11)Drag(2) = VXF FORCES(XDRAGMAXstepsevalfalseSECTION12)Drag(3) = VXF FORCES(XDRAGMAXstepsevalfalseSECTION13)Drag(4) = VXF FORCES(XDRAGMAXstepsevalfalseSECTION14)
[DragLane] = max(Drag())
Call optiOUT to generate Plots and Output DataoptiOUT(X [Drag])
end
David Gutierrez Rivera Aerodynamic Shape Optimization 34 54
IntroductionOptimization Algorithms
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Black-Box OptimizationSimulation-based Optimization
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Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Data Points
David Gutierrez Rivera Aerodynamic Shape Optimization 35 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Run-Time Optimization
David Gutierrez Rivera Aerodynamic Shape Optimization 36 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Vertical-Axis Wind Turbine (VAWT)
Description
The Savonius Wind Turbine is a Vertical-Axis Wind Turbine (VAWT)which main advantages are its reliability and practicality
David Gutierrez Rivera Aerodynamic Shape Optimization 37 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Model
Description
Find optimum values of ex and ey to maximize Torque or Power
Constrained to the shaded area
David Gutierrez Rivera Aerodynamic Shape Optimization 38 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Model
Description
Find optimum values of ex and ey to maximize Torque or Power
Constrained to the shaded area
David Gutierrez Rivera Aerodynamic Shape Optimization 38 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Dynamic Model
David Gutierrez Rivera Aerodynamic Shape Optimization 39 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
What is Optimization Basics of Aerodynamics
A Mathematical View
Mathematically optimization is formulated as
minimizex
f (x)
subject to
gi (x) le 0 i = 1 mhi (x) = 0 i = 1 n
(1)
where
f (x) Rn rarr R is the objective function to be minimized
gi (x) le 0 are inequality constraints
hi (x) = 0 are equality constraints
David Gutierrez Rivera Aerodynamic Shape Optimization 5 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
What is Optimization Basics of Aerodynamics
A Programmatic View
Programmatically optimization can be viewed as a loop
David Gutierrez Rivera Aerodynamic Shape Optimization 6 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
What is Optimization Basics of Aerodynamics
Basics of Aerodynamics
The Navier-Stokes Partial Differential Equation
David Gutierrez Rivera Aerodynamic Shape Optimization 7 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
What is Optimization Basics of Aerodynamics
Computational Fluid Dynamics (CFD)
Is the branch of fluid mechanics that uses numerical methods to solvefluid flow problems
Discretization Methods
Finite Volume Method
Boundary Element Method
High-Resolution Schemes
Turbulence Models
Reynolds-AveragedNavierStokes (RANS)
Large eddy simulation (LES)
Vortex methods
David Gutierrez Rivera Aerodynamic Shape Optimization 8 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
What is Optimization Basics of Aerodynamics
Computational Fluid Dynamics (CFD)
Is the branch of fluid mechanics that uses numerical methods to solvefluid flow problems
Discretization Methods
Finite Volume Method
Boundary Element Method
High-Resolution Schemes
Turbulence Models
Reynolds-AveragedNavierStokes (RANS)
Large eddy simulation (LES)
Vortex methods
David Gutierrez Rivera Aerodynamic Shape Optimization 8 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
What is Optimization Basics of Aerodynamics
The Vortex Particle Method (VPM)
Characteristics
Is a grid-free technique for simulation of turbulent flows
It uses vortices as the computational elements
David Gutierrez Rivera Aerodynamic Shape Optimization 9 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Local Global
Optimization Algorithms
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 10 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Local Global
Optimization Algorithms
Classification
Linearity
LinearNonLinear
Constraints
UnconstrainedConstrained
Objectives
Single-ObjectiveMulti-Objective
Modality
uni-modal (Local)multi-modal (Global)
David Gutierrez Rivera Aerodynamic Shape Optimization 11 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Local Global
Optimization Algorithms
Classification
Linearity
LinearNonLinear
Constraints
UnconstrainedConstrained
Objectives
Single-ObjectiveMulti-Objective
Modality
uni-modal (Local)multi-modal (Global)
David Gutierrez Rivera Aerodynamic Shape Optimization 11 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Local Global
Global vs Local
David Gutierrez Rivera Aerodynamic Shape Optimization 12 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Local Global
Local
Gradient-free Methods
Golden Section
Simplex
Gradient-based Methods
Gradient-Descent
Newton
David Gutierrez Rivera Aerodynamic Shape Optimization 13 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Local Global
Global
non-Heuristic Methods
Deterministic
Stochastic
Heuristic Methods
Evolutionary
Genetic AlgorithmSwarm Intelligence
Swarm Intelligence
Particle SwarmAnt Colony
David Gutierrez Rivera Aerodynamic Shape Optimization 14 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Shape Optimization
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 15 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Shape Optimization
Shape optimization is formulated as
minimizeΩ
f (Ω)
subject to
gi (Ω) le 0 i = 1 mhi (Ω) = 0 i = 1 n
(2)
where
Ω is a set of variable parameters that make up the geometry that wewant to optimize
David Gutierrez Rivera Aerodynamic Shape Optimization 16 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Shape Optimization
Shape optimization is formulated as
minimizeΩ
f (Ω)
subject to
gi (Ω) le 0 i = 1 mhi (Ω) = 0 i = 1 n
(2)
where
Ω is a set of variable parameters that make up the geometry that wewant to optimize
David Gutierrez Rivera Aerodynamic Shape Optimization 16 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Parametrization
David Gutierrez Rivera Aerodynamic Shape Optimization 17 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Parametrization
David Gutierrez Rivera Aerodynamic Shape Optimization 17 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Objective Functions
Similar to mathematical functions
They involve 3 basic operations
David Gutierrez Rivera Aerodynamic Shape Optimization 18 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Objective Functions
Similar to mathematical functions
They involve 3 basic operations
Substitution
f (x) = a0 +nsum
i=1
an middot cos(n x ) +nsum
i=1
bn middot sin(n x )
David Gutierrez Rivera Aerodynamic Shape Optimization 18 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Objective Functions
Similar to mathematical functions
They involve 3 basic operations
Substitution
f (x) = a0 +nsum
i=1
an middot cos(n 31416 ) +nsum
i=1
bn middot sin(n 31416 )
Substitution
David Gutierrez Rivera Aerodynamic Shape Optimization 18 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Objective Functions
Similar to mathematical functions
They involve 3 basic operations
Evaluation
f (x) = a0 +nsum
i=1
an middot cos(n 31416 ) +nsum
i=1
bn middot sin(n 31416 )︸ ︷︷ ︸Evaluation
David Gutierrez Rivera Aerodynamic Shape Optimization 18 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Objective Functions
Similar to mathematical functions
They involve 3 basic operations
Read Output
f (x) = Value
Read Output
David Gutierrez Rivera Aerodynamic Shape Optimization 18 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Data Gathering
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 19 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Data Gathering
David Gutierrez Rivera Aerodynamic Shape Optimization 20 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Data Gathering
Data File
It is a text-based tab-delimited file containing the data points from thevariables and the corresponding values of the objective functions
Variable1 Variable2 Variablen Objective1 ObjectivemVariable1 Variable2 Variablen Objective1 Objectivem
Variable1 Variable2 Variablen Objective1 Objectivem
David Gutierrez Rivera Aerodynamic Shape Optimization 21 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Data Gathering
Data File
It is a text-based tab-delimited file containing the data points from thevariables and the corresponding values of the objective functions
Variable1 Variable2 Variablen Objective1 ObjectivemVariable1 Variable2 Variablen Objective1 Objectivem
Variable1 Variable2 Variablen Objective1 Objectivem
David Gutierrez Rivera Aerodynamic Shape Optimization 21 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Black-Box Optimization
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 22 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Black-Box Optimization
Black-Box Process
They are known from their inputs and outputs
Little is known of how it works internally
David Gutierrez Rivera Aerodynamic Shape Optimization 23 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Black-Box Optimization
David Gutierrez Rivera Aerodynamic Shape Optimization 23 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Black-Box Optimization
David Gutierrez Rivera Aerodynamic Shape Optimization 24 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Noisy Functions
David Gutierrez Rivera Aerodynamic Shape Optimization 25 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Simulation-based Optimization
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 26 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Simulation-based Optimization
David Gutierrez Rivera Aerodynamic Shape Optimization 27 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Moving Boundary Problem
David Gutierrez Rivera Aerodynamic Shape Optimization 28 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
OptiFlow
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 29 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Examples
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 30 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
M4 Neath Viaduct Wind Shield
Description
This bridge is located in South Wales and crosses the River Neath Asection of the bridge is very exposed in flat topography therefore a windshielding system is desired for reducing the overturning forces on vehicles
Description
The CFD model is the same as the one used on the VXFlow tutorial
Four small sections were used to obtain the interior drag forces
David Gutierrez Rivera Aerodynamic Shape Optimization 31 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
M4 Neath Viaduct Wind Shield
Description
The CFD model is the same as the one used on the VXFlow tutorial
Four small sections were used to obtain the interior drag forces
David Gutierrez Rivera Aerodynamic Shape Optimization 31 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
M4 Neath Viaduct Wind Shield
Description
The CFD model is the same as the one used on the VXFlow tutorial
Four small sections were used to obtain the interior drag forces
David Gutierrez Rivera Aerodynamic Shape Optimization 31 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Model
Find optimum height (h) for the Wind Shield
David Gutierrez Rivera Aerodynamic Shape Optimization 32 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Parameter File
Variables Definitions[beginvariables]define(h ) Height of Wind Screen[endvariables]define(L 300) Wind Screen Lengthdefine(t 015) Wind Screen Width Wind Screen Coordinatesdefine(x1 calc(0minus1300))define(x2 calc(x1minust))define(y1 calc(hminus025))define(y2 calc(y1+L))
4 num cornerpointsSCREEN3(SCHEME3)03 00 release distancespacing hull002 0001 00 minus01 merg1merg2merg3merg4minus4 minus3 minus1 minus3 minus1 section color codingdragliftmomentdisplrotation1 x2 y1 n11 x1 y1 n21 x1 y2 n11 x2 y2 n2
David Gutierrez Rivera Aerodynamic Shape Optimization 33 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Parameter File
Variables Definitions[beginvariables]define(h ) Height of Wind Screen[endvariables]define(L 300) Wind Screen Lengthdefine(t 015) Wind Screen Width Wind Screen Coordinatesdefine(x1 calc(0minus1300))define(x2 calc(x1minust))define(y1 calc(hminus025))define(y2 calc(y1+L))
4 num cornerpointsSCREEN3(SCHEME3)03 00 release distancespacing hull002 0001 00 minus01 merg1merg2merg3merg4minus4 minus3 minus1 minus3 minus1 section color codingdragliftmomentdisplrotation1 x2 y1 n11 x1 y1 n21 x1 y2 n11 x2 y2 n2
David Gutierrez Rivera Aerodynamic Shape Optimization 33 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Objective Function
function [Drag] = M4 Neath ViaductWS(X) M4 Neath ViaductWS Objective Functionsteps = 500
Drag(1) = VXF FORCES(XDRAGMAXstepsSECTION11)Drag(2) = VXF FORCES(XDRAGMAXstepsevalfalseSECTION12)Drag(3) = VXF FORCES(XDRAGMAXstepsevalfalseSECTION13)Drag(4) = VXF FORCES(XDRAGMAXstepsevalfalseSECTION14)
[DragLane] = max(Drag())
Call optiOUT to generate Plots and Output DataoptiOUT(X [Drag])
end
David Gutierrez Rivera Aerodynamic Shape Optimization 34 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Data Points
David Gutierrez Rivera Aerodynamic Shape Optimization 35 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Run-Time Optimization
David Gutierrez Rivera Aerodynamic Shape Optimization 36 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Vertical-Axis Wind Turbine (VAWT)
Description
The Savonius Wind Turbine is a Vertical-Axis Wind Turbine (VAWT)which main advantages are its reliability and practicality
David Gutierrez Rivera Aerodynamic Shape Optimization 37 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Model
Description
Find optimum values of ex and ey to maximize Torque or Power
Constrained to the shaded area
David Gutierrez Rivera Aerodynamic Shape Optimization 38 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Model
Description
Find optimum values of ex and ey to maximize Torque or Power
Constrained to the shaded area
David Gutierrez Rivera Aerodynamic Shape Optimization 38 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Dynamic Model
David Gutierrez Rivera Aerodynamic Shape Optimization 39 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
What is Optimization Basics of Aerodynamics
A Programmatic View
Programmatically optimization can be viewed as a loop
David Gutierrez Rivera Aerodynamic Shape Optimization 6 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
What is Optimization Basics of Aerodynamics
Basics of Aerodynamics
The Navier-Stokes Partial Differential Equation
David Gutierrez Rivera Aerodynamic Shape Optimization 7 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
What is Optimization Basics of Aerodynamics
Computational Fluid Dynamics (CFD)
Is the branch of fluid mechanics that uses numerical methods to solvefluid flow problems
Discretization Methods
Finite Volume Method
Boundary Element Method
High-Resolution Schemes
Turbulence Models
Reynolds-AveragedNavierStokes (RANS)
Large eddy simulation (LES)
Vortex methods
David Gutierrez Rivera Aerodynamic Shape Optimization 8 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
What is Optimization Basics of Aerodynamics
Computational Fluid Dynamics (CFD)
Is the branch of fluid mechanics that uses numerical methods to solvefluid flow problems
Discretization Methods
Finite Volume Method
Boundary Element Method
High-Resolution Schemes
Turbulence Models
Reynolds-AveragedNavierStokes (RANS)
Large eddy simulation (LES)
Vortex methods
David Gutierrez Rivera Aerodynamic Shape Optimization 8 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
What is Optimization Basics of Aerodynamics
The Vortex Particle Method (VPM)
Characteristics
Is a grid-free technique for simulation of turbulent flows
It uses vortices as the computational elements
David Gutierrez Rivera Aerodynamic Shape Optimization 9 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Local Global
Optimization Algorithms
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 10 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Local Global
Optimization Algorithms
Classification
Linearity
LinearNonLinear
Constraints
UnconstrainedConstrained
Objectives
Single-ObjectiveMulti-Objective
Modality
uni-modal (Local)multi-modal (Global)
David Gutierrez Rivera Aerodynamic Shape Optimization 11 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Local Global
Optimization Algorithms
Classification
Linearity
LinearNonLinear
Constraints
UnconstrainedConstrained
Objectives
Single-ObjectiveMulti-Objective
Modality
uni-modal (Local)multi-modal (Global)
David Gutierrez Rivera Aerodynamic Shape Optimization 11 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Local Global
Global vs Local
David Gutierrez Rivera Aerodynamic Shape Optimization 12 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Local Global
Local
Gradient-free Methods
Golden Section
Simplex
Gradient-based Methods
Gradient-Descent
Newton
David Gutierrez Rivera Aerodynamic Shape Optimization 13 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Local Global
Global
non-Heuristic Methods
Deterministic
Stochastic
Heuristic Methods
Evolutionary
Genetic AlgorithmSwarm Intelligence
Swarm Intelligence
Particle SwarmAnt Colony
David Gutierrez Rivera Aerodynamic Shape Optimization 14 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Shape Optimization
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 15 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Shape Optimization
Shape optimization is formulated as
minimizeΩ
f (Ω)
subject to
gi (Ω) le 0 i = 1 mhi (Ω) = 0 i = 1 n
(2)
where
Ω is a set of variable parameters that make up the geometry that wewant to optimize
David Gutierrez Rivera Aerodynamic Shape Optimization 16 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Shape Optimization
Shape optimization is formulated as
minimizeΩ
f (Ω)
subject to
gi (Ω) le 0 i = 1 mhi (Ω) = 0 i = 1 n
(2)
where
Ω is a set of variable parameters that make up the geometry that wewant to optimize
David Gutierrez Rivera Aerodynamic Shape Optimization 16 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Parametrization
David Gutierrez Rivera Aerodynamic Shape Optimization 17 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Parametrization
David Gutierrez Rivera Aerodynamic Shape Optimization 17 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Objective Functions
Similar to mathematical functions
They involve 3 basic operations
David Gutierrez Rivera Aerodynamic Shape Optimization 18 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Objective Functions
Similar to mathematical functions
They involve 3 basic operations
Substitution
f (x) = a0 +nsum
i=1
an middot cos(n x ) +nsum
i=1
bn middot sin(n x )
David Gutierrez Rivera Aerodynamic Shape Optimization 18 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Objective Functions
Similar to mathematical functions
They involve 3 basic operations
Substitution
f (x) = a0 +nsum
i=1
an middot cos(n 31416 ) +nsum
i=1
bn middot sin(n 31416 )
Substitution
David Gutierrez Rivera Aerodynamic Shape Optimization 18 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Objective Functions
Similar to mathematical functions
They involve 3 basic operations
Evaluation
f (x) = a0 +nsum
i=1
an middot cos(n 31416 ) +nsum
i=1
bn middot sin(n 31416 )︸ ︷︷ ︸Evaluation
David Gutierrez Rivera Aerodynamic Shape Optimization 18 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Objective Functions
Similar to mathematical functions
They involve 3 basic operations
Read Output
f (x) = Value
Read Output
David Gutierrez Rivera Aerodynamic Shape Optimization 18 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Data Gathering
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 19 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Data Gathering
David Gutierrez Rivera Aerodynamic Shape Optimization 20 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Data Gathering
Data File
It is a text-based tab-delimited file containing the data points from thevariables and the corresponding values of the objective functions
Variable1 Variable2 Variablen Objective1 ObjectivemVariable1 Variable2 Variablen Objective1 Objectivem
Variable1 Variable2 Variablen Objective1 Objectivem
David Gutierrez Rivera Aerodynamic Shape Optimization 21 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Data Gathering
Data File
It is a text-based tab-delimited file containing the data points from thevariables and the corresponding values of the objective functions
Variable1 Variable2 Variablen Objective1 ObjectivemVariable1 Variable2 Variablen Objective1 Objectivem
Variable1 Variable2 Variablen Objective1 Objectivem
David Gutierrez Rivera Aerodynamic Shape Optimization 21 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Black-Box Optimization
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 22 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Black-Box Optimization
Black-Box Process
They are known from their inputs and outputs
Little is known of how it works internally
David Gutierrez Rivera Aerodynamic Shape Optimization 23 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Black-Box Optimization
David Gutierrez Rivera Aerodynamic Shape Optimization 23 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Black-Box Optimization
David Gutierrez Rivera Aerodynamic Shape Optimization 24 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Noisy Functions
David Gutierrez Rivera Aerodynamic Shape Optimization 25 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Simulation-based Optimization
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 26 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Simulation-based Optimization
David Gutierrez Rivera Aerodynamic Shape Optimization 27 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Moving Boundary Problem
David Gutierrez Rivera Aerodynamic Shape Optimization 28 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
OptiFlow
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 29 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Examples
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 30 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
M4 Neath Viaduct Wind Shield
Description
This bridge is located in South Wales and crosses the River Neath Asection of the bridge is very exposed in flat topography therefore a windshielding system is desired for reducing the overturning forces on vehicles
Description
The CFD model is the same as the one used on the VXFlow tutorial
Four small sections were used to obtain the interior drag forces
David Gutierrez Rivera Aerodynamic Shape Optimization 31 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
M4 Neath Viaduct Wind Shield
Description
The CFD model is the same as the one used on the VXFlow tutorial
Four small sections were used to obtain the interior drag forces
David Gutierrez Rivera Aerodynamic Shape Optimization 31 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
M4 Neath Viaduct Wind Shield
Description
The CFD model is the same as the one used on the VXFlow tutorial
Four small sections were used to obtain the interior drag forces
David Gutierrez Rivera Aerodynamic Shape Optimization 31 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Model
Find optimum height (h) for the Wind Shield
David Gutierrez Rivera Aerodynamic Shape Optimization 32 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Parameter File
Variables Definitions[beginvariables]define(h ) Height of Wind Screen[endvariables]define(L 300) Wind Screen Lengthdefine(t 015) Wind Screen Width Wind Screen Coordinatesdefine(x1 calc(0minus1300))define(x2 calc(x1minust))define(y1 calc(hminus025))define(y2 calc(y1+L))
4 num cornerpointsSCREEN3(SCHEME3)03 00 release distancespacing hull002 0001 00 minus01 merg1merg2merg3merg4minus4 minus3 minus1 minus3 minus1 section color codingdragliftmomentdisplrotation1 x2 y1 n11 x1 y1 n21 x1 y2 n11 x2 y2 n2
David Gutierrez Rivera Aerodynamic Shape Optimization 33 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Parameter File
Variables Definitions[beginvariables]define(h ) Height of Wind Screen[endvariables]define(L 300) Wind Screen Lengthdefine(t 015) Wind Screen Width Wind Screen Coordinatesdefine(x1 calc(0minus1300))define(x2 calc(x1minust))define(y1 calc(hminus025))define(y2 calc(y1+L))
4 num cornerpointsSCREEN3(SCHEME3)03 00 release distancespacing hull002 0001 00 minus01 merg1merg2merg3merg4minus4 minus3 minus1 minus3 minus1 section color codingdragliftmomentdisplrotation1 x2 y1 n11 x1 y1 n21 x1 y2 n11 x2 y2 n2
David Gutierrez Rivera Aerodynamic Shape Optimization 33 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Objective Function
function [Drag] = M4 Neath ViaductWS(X) M4 Neath ViaductWS Objective Functionsteps = 500
Drag(1) = VXF FORCES(XDRAGMAXstepsSECTION11)Drag(2) = VXF FORCES(XDRAGMAXstepsevalfalseSECTION12)Drag(3) = VXF FORCES(XDRAGMAXstepsevalfalseSECTION13)Drag(4) = VXF FORCES(XDRAGMAXstepsevalfalseSECTION14)
[DragLane] = max(Drag())
Call optiOUT to generate Plots and Output DataoptiOUT(X [Drag])
end
David Gutierrez Rivera Aerodynamic Shape Optimization 34 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Data Points
David Gutierrez Rivera Aerodynamic Shape Optimization 35 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Run-Time Optimization
David Gutierrez Rivera Aerodynamic Shape Optimization 36 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Vertical-Axis Wind Turbine (VAWT)
Description
The Savonius Wind Turbine is a Vertical-Axis Wind Turbine (VAWT)which main advantages are its reliability and practicality
David Gutierrez Rivera Aerodynamic Shape Optimization 37 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Model
Description
Find optimum values of ex and ey to maximize Torque or Power
Constrained to the shaded area
David Gutierrez Rivera Aerodynamic Shape Optimization 38 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Model
Description
Find optimum values of ex and ey to maximize Torque or Power
Constrained to the shaded area
David Gutierrez Rivera Aerodynamic Shape Optimization 38 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Dynamic Model
David Gutierrez Rivera Aerodynamic Shape Optimization 39 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
What is Optimization Basics of Aerodynamics
Basics of Aerodynamics
The Navier-Stokes Partial Differential Equation
David Gutierrez Rivera Aerodynamic Shape Optimization 7 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
What is Optimization Basics of Aerodynamics
Computational Fluid Dynamics (CFD)
Is the branch of fluid mechanics that uses numerical methods to solvefluid flow problems
Discretization Methods
Finite Volume Method
Boundary Element Method
High-Resolution Schemes
Turbulence Models
Reynolds-AveragedNavierStokes (RANS)
Large eddy simulation (LES)
Vortex methods
David Gutierrez Rivera Aerodynamic Shape Optimization 8 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
What is Optimization Basics of Aerodynamics
Computational Fluid Dynamics (CFD)
Is the branch of fluid mechanics that uses numerical methods to solvefluid flow problems
Discretization Methods
Finite Volume Method
Boundary Element Method
High-Resolution Schemes
Turbulence Models
Reynolds-AveragedNavierStokes (RANS)
Large eddy simulation (LES)
Vortex methods
David Gutierrez Rivera Aerodynamic Shape Optimization 8 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
What is Optimization Basics of Aerodynamics
The Vortex Particle Method (VPM)
Characteristics
Is a grid-free technique for simulation of turbulent flows
It uses vortices as the computational elements
David Gutierrez Rivera Aerodynamic Shape Optimization 9 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Local Global
Optimization Algorithms
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 10 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Local Global
Optimization Algorithms
Classification
Linearity
LinearNonLinear
Constraints
UnconstrainedConstrained
Objectives
Single-ObjectiveMulti-Objective
Modality
uni-modal (Local)multi-modal (Global)
David Gutierrez Rivera Aerodynamic Shape Optimization 11 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Local Global
Optimization Algorithms
Classification
Linearity
LinearNonLinear
Constraints
UnconstrainedConstrained
Objectives
Single-ObjectiveMulti-Objective
Modality
uni-modal (Local)multi-modal (Global)
David Gutierrez Rivera Aerodynamic Shape Optimization 11 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Local Global
Global vs Local
David Gutierrez Rivera Aerodynamic Shape Optimization 12 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Local Global
Local
Gradient-free Methods
Golden Section
Simplex
Gradient-based Methods
Gradient-Descent
Newton
David Gutierrez Rivera Aerodynamic Shape Optimization 13 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Local Global
Global
non-Heuristic Methods
Deterministic
Stochastic
Heuristic Methods
Evolutionary
Genetic AlgorithmSwarm Intelligence
Swarm Intelligence
Particle SwarmAnt Colony
David Gutierrez Rivera Aerodynamic Shape Optimization 14 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Shape Optimization
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 15 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Shape Optimization
Shape optimization is formulated as
minimizeΩ
f (Ω)
subject to
gi (Ω) le 0 i = 1 mhi (Ω) = 0 i = 1 n
(2)
where
Ω is a set of variable parameters that make up the geometry that wewant to optimize
David Gutierrez Rivera Aerodynamic Shape Optimization 16 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Shape Optimization
Shape optimization is formulated as
minimizeΩ
f (Ω)
subject to
gi (Ω) le 0 i = 1 mhi (Ω) = 0 i = 1 n
(2)
where
Ω is a set of variable parameters that make up the geometry that wewant to optimize
David Gutierrez Rivera Aerodynamic Shape Optimization 16 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Parametrization
David Gutierrez Rivera Aerodynamic Shape Optimization 17 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Parametrization
David Gutierrez Rivera Aerodynamic Shape Optimization 17 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Objective Functions
Similar to mathematical functions
They involve 3 basic operations
David Gutierrez Rivera Aerodynamic Shape Optimization 18 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Objective Functions
Similar to mathematical functions
They involve 3 basic operations
Substitution
f (x) = a0 +nsum
i=1
an middot cos(n x ) +nsum
i=1
bn middot sin(n x )
David Gutierrez Rivera Aerodynamic Shape Optimization 18 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Objective Functions
Similar to mathematical functions
They involve 3 basic operations
Substitution
f (x) = a0 +nsum
i=1
an middot cos(n 31416 ) +nsum
i=1
bn middot sin(n 31416 )
Substitution
David Gutierrez Rivera Aerodynamic Shape Optimization 18 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Objective Functions
Similar to mathematical functions
They involve 3 basic operations
Evaluation
f (x) = a0 +nsum
i=1
an middot cos(n 31416 ) +nsum
i=1
bn middot sin(n 31416 )︸ ︷︷ ︸Evaluation
David Gutierrez Rivera Aerodynamic Shape Optimization 18 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Objective Functions
Similar to mathematical functions
They involve 3 basic operations
Read Output
f (x) = Value
Read Output
David Gutierrez Rivera Aerodynamic Shape Optimization 18 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Data Gathering
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 19 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Data Gathering
David Gutierrez Rivera Aerodynamic Shape Optimization 20 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Data Gathering
Data File
It is a text-based tab-delimited file containing the data points from thevariables and the corresponding values of the objective functions
Variable1 Variable2 Variablen Objective1 ObjectivemVariable1 Variable2 Variablen Objective1 Objectivem
Variable1 Variable2 Variablen Objective1 Objectivem
David Gutierrez Rivera Aerodynamic Shape Optimization 21 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Data Gathering
Data File
It is a text-based tab-delimited file containing the data points from thevariables and the corresponding values of the objective functions
Variable1 Variable2 Variablen Objective1 ObjectivemVariable1 Variable2 Variablen Objective1 Objectivem
Variable1 Variable2 Variablen Objective1 Objectivem
David Gutierrez Rivera Aerodynamic Shape Optimization 21 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Black-Box Optimization
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 22 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Black-Box Optimization
Black-Box Process
They are known from their inputs and outputs
Little is known of how it works internally
David Gutierrez Rivera Aerodynamic Shape Optimization 23 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Black-Box Optimization
David Gutierrez Rivera Aerodynamic Shape Optimization 23 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Black-Box Optimization
David Gutierrez Rivera Aerodynamic Shape Optimization 24 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Noisy Functions
David Gutierrez Rivera Aerodynamic Shape Optimization 25 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Simulation-based Optimization
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 26 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Simulation-based Optimization
David Gutierrez Rivera Aerodynamic Shape Optimization 27 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Moving Boundary Problem
David Gutierrez Rivera Aerodynamic Shape Optimization 28 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
OptiFlow
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 29 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Examples
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 30 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
M4 Neath Viaduct Wind Shield
Description
This bridge is located in South Wales and crosses the River Neath Asection of the bridge is very exposed in flat topography therefore a windshielding system is desired for reducing the overturning forces on vehicles
Description
The CFD model is the same as the one used on the VXFlow tutorial
Four small sections were used to obtain the interior drag forces
David Gutierrez Rivera Aerodynamic Shape Optimization 31 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
M4 Neath Viaduct Wind Shield
Description
The CFD model is the same as the one used on the VXFlow tutorial
Four small sections were used to obtain the interior drag forces
David Gutierrez Rivera Aerodynamic Shape Optimization 31 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
M4 Neath Viaduct Wind Shield
Description
The CFD model is the same as the one used on the VXFlow tutorial
Four small sections were used to obtain the interior drag forces
David Gutierrez Rivera Aerodynamic Shape Optimization 31 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Model
Find optimum height (h) for the Wind Shield
David Gutierrez Rivera Aerodynamic Shape Optimization 32 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Parameter File
Variables Definitions[beginvariables]define(h ) Height of Wind Screen[endvariables]define(L 300) Wind Screen Lengthdefine(t 015) Wind Screen Width Wind Screen Coordinatesdefine(x1 calc(0minus1300))define(x2 calc(x1minust))define(y1 calc(hminus025))define(y2 calc(y1+L))
4 num cornerpointsSCREEN3(SCHEME3)03 00 release distancespacing hull002 0001 00 minus01 merg1merg2merg3merg4minus4 minus3 minus1 minus3 minus1 section color codingdragliftmomentdisplrotation1 x2 y1 n11 x1 y1 n21 x1 y2 n11 x2 y2 n2
David Gutierrez Rivera Aerodynamic Shape Optimization 33 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Parameter File
Variables Definitions[beginvariables]define(h ) Height of Wind Screen[endvariables]define(L 300) Wind Screen Lengthdefine(t 015) Wind Screen Width Wind Screen Coordinatesdefine(x1 calc(0minus1300))define(x2 calc(x1minust))define(y1 calc(hminus025))define(y2 calc(y1+L))
4 num cornerpointsSCREEN3(SCHEME3)03 00 release distancespacing hull002 0001 00 minus01 merg1merg2merg3merg4minus4 minus3 minus1 minus3 minus1 section color codingdragliftmomentdisplrotation1 x2 y1 n11 x1 y1 n21 x1 y2 n11 x2 y2 n2
David Gutierrez Rivera Aerodynamic Shape Optimization 33 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Objective Function
function [Drag] = M4 Neath ViaductWS(X) M4 Neath ViaductWS Objective Functionsteps = 500
Drag(1) = VXF FORCES(XDRAGMAXstepsSECTION11)Drag(2) = VXF FORCES(XDRAGMAXstepsevalfalseSECTION12)Drag(3) = VXF FORCES(XDRAGMAXstepsevalfalseSECTION13)Drag(4) = VXF FORCES(XDRAGMAXstepsevalfalseSECTION14)
[DragLane] = max(Drag())
Call optiOUT to generate Plots and Output DataoptiOUT(X [Drag])
end
David Gutierrez Rivera Aerodynamic Shape Optimization 34 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Data Points
David Gutierrez Rivera Aerodynamic Shape Optimization 35 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Run-Time Optimization
David Gutierrez Rivera Aerodynamic Shape Optimization 36 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Vertical-Axis Wind Turbine (VAWT)
Description
The Savonius Wind Turbine is a Vertical-Axis Wind Turbine (VAWT)which main advantages are its reliability and practicality
David Gutierrez Rivera Aerodynamic Shape Optimization 37 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Model
Description
Find optimum values of ex and ey to maximize Torque or Power
Constrained to the shaded area
David Gutierrez Rivera Aerodynamic Shape Optimization 38 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Model
Description
Find optimum values of ex and ey to maximize Torque or Power
Constrained to the shaded area
David Gutierrez Rivera Aerodynamic Shape Optimization 38 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Dynamic Model
David Gutierrez Rivera Aerodynamic Shape Optimization 39 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
What is Optimization Basics of Aerodynamics
Computational Fluid Dynamics (CFD)
Is the branch of fluid mechanics that uses numerical methods to solvefluid flow problems
Discretization Methods
Finite Volume Method
Boundary Element Method
High-Resolution Schemes
Turbulence Models
Reynolds-AveragedNavierStokes (RANS)
Large eddy simulation (LES)
Vortex methods
David Gutierrez Rivera Aerodynamic Shape Optimization 8 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
What is Optimization Basics of Aerodynamics
Computational Fluid Dynamics (CFD)
Is the branch of fluid mechanics that uses numerical methods to solvefluid flow problems
Discretization Methods
Finite Volume Method
Boundary Element Method
High-Resolution Schemes
Turbulence Models
Reynolds-AveragedNavierStokes (RANS)
Large eddy simulation (LES)
Vortex methods
David Gutierrez Rivera Aerodynamic Shape Optimization 8 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
What is Optimization Basics of Aerodynamics
The Vortex Particle Method (VPM)
Characteristics
Is a grid-free technique for simulation of turbulent flows
It uses vortices as the computational elements
David Gutierrez Rivera Aerodynamic Shape Optimization 9 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Local Global
Optimization Algorithms
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 10 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Local Global
Optimization Algorithms
Classification
Linearity
LinearNonLinear
Constraints
UnconstrainedConstrained
Objectives
Single-ObjectiveMulti-Objective
Modality
uni-modal (Local)multi-modal (Global)
David Gutierrez Rivera Aerodynamic Shape Optimization 11 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Local Global
Optimization Algorithms
Classification
Linearity
LinearNonLinear
Constraints
UnconstrainedConstrained
Objectives
Single-ObjectiveMulti-Objective
Modality
uni-modal (Local)multi-modal (Global)
David Gutierrez Rivera Aerodynamic Shape Optimization 11 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Local Global
Global vs Local
David Gutierrez Rivera Aerodynamic Shape Optimization 12 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Local Global
Local
Gradient-free Methods
Golden Section
Simplex
Gradient-based Methods
Gradient-Descent
Newton
David Gutierrez Rivera Aerodynamic Shape Optimization 13 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Local Global
Global
non-Heuristic Methods
Deterministic
Stochastic
Heuristic Methods
Evolutionary
Genetic AlgorithmSwarm Intelligence
Swarm Intelligence
Particle SwarmAnt Colony
David Gutierrez Rivera Aerodynamic Shape Optimization 14 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Shape Optimization
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 15 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Shape Optimization
Shape optimization is formulated as
minimizeΩ
f (Ω)
subject to
gi (Ω) le 0 i = 1 mhi (Ω) = 0 i = 1 n
(2)
where
Ω is a set of variable parameters that make up the geometry that wewant to optimize
David Gutierrez Rivera Aerodynamic Shape Optimization 16 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Shape Optimization
Shape optimization is formulated as
minimizeΩ
f (Ω)
subject to
gi (Ω) le 0 i = 1 mhi (Ω) = 0 i = 1 n
(2)
where
Ω is a set of variable parameters that make up the geometry that wewant to optimize
David Gutierrez Rivera Aerodynamic Shape Optimization 16 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Parametrization
David Gutierrez Rivera Aerodynamic Shape Optimization 17 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Parametrization
David Gutierrez Rivera Aerodynamic Shape Optimization 17 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Objective Functions
Similar to mathematical functions
They involve 3 basic operations
David Gutierrez Rivera Aerodynamic Shape Optimization 18 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Objective Functions
Similar to mathematical functions
They involve 3 basic operations
Substitution
f (x) = a0 +nsum
i=1
an middot cos(n x ) +nsum
i=1
bn middot sin(n x )
David Gutierrez Rivera Aerodynamic Shape Optimization 18 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Objective Functions
Similar to mathematical functions
They involve 3 basic operations
Substitution
f (x) = a0 +nsum
i=1
an middot cos(n 31416 ) +nsum
i=1
bn middot sin(n 31416 )
Substitution
David Gutierrez Rivera Aerodynamic Shape Optimization 18 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Objective Functions
Similar to mathematical functions
They involve 3 basic operations
Evaluation
f (x) = a0 +nsum
i=1
an middot cos(n 31416 ) +nsum
i=1
bn middot sin(n 31416 )︸ ︷︷ ︸Evaluation
David Gutierrez Rivera Aerodynamic Shape Optimization 18 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Objective Functions
Similar to mathematical functions
They involve 3 basic operations
Read Output
f (x) = Value
Read Output
David Gutierrez Rivera Aerodynamic Shape Optimization 18 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Data Gathering
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 19 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Data Gathering
David Gutierrez Rivera Aerodynamic Shape Optimization 20 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Data Gathering
Data File
It is a text-based tab-delimited file containing the data points from thevariables and the corresponding values of the objective functions
Variable1 Variable2 Variablen Objective1 ObjectivemVariable1 Variable2 Variablen Objective1 Objectivem
Variable1 Variable2 Variablen Objective1 Objectivem
David Gutierrez Rivera Aerodynamic Shape Optimization 21 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Data Gathering
Data File
It is a text-based tab-delimited file containing the data points from thevariables and the corresponding values of the objective functions
Variable1 Variable2 Variablen Objective1 ObjectivemVariable1 Variable2 Variablen Objective1 Objectivem
Variable1 Variable2 Variablen Objective1 Objectivem
David Gutierrez Rivera Aerodynamic Shape Optimization 21 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Black-Box Optimization
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 22 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Black-Box Optimization
Black-Box Process
They are known from their inputs and outputs
Little is known of how it works internally
David Gutierrez Rivera Aerodynamic Shape Optimization 23 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Black-Box Optimization
David Gutierrez Rivera Aerodynamic Shape Optimization 23 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Black-Box Optimization
David Gutierrez Rivera Aerodynamic Shape Optimization 24 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Noisy Functions
David Gutierrez Rivera Aerodynamic Shape Optimization 25 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Simulation-based Optimization
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 26 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Simulation-based Optimization
David Gutierrez Rivera Aerodynamic Shape Optimization 27 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Moving Boundary Problem
David Gutierrez Rivera Aerodynamic Shape Optimization 28 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
OptiFlow
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 29 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Examples
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 30 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
M4 Neath Viaduct Wind Shield
Description
This bridge is located in South Wales and crosses the River Neath Asection of the bridge is very exposed in flat topography therefore a windshielding system is desired for reducing the overturning forces on vehicles
Description
The CFD model is the same as the one used on the VXFlow tutorial
Four small sections were used to obtain the interior drag forces
David Gutierrez Rivera Aerodynamic Shape Optimization 31 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
M4 Neath Viaduct Wind Shield
Description
The CFD model is the same as the one used on the VXFlow tutorial
Four small sections were used to obtain the interior drag forces
David Gutierrez Rivera Aerodynamic Shape Optimization 31 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
M4 Neath Viaduct Wind Shield
Description
The CFD model is the same as the one used on the VXFlow tutorial
Four small sections were used to obtain the interior drag forces
David Gutierrez Rivera Aerodynamic Shape Optimization 31 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Model
Find optimum height (h) for the Wind Shield
David Gutierrez Rivera Aerodynamic Shape Optimization 32 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Parameter File
Variables Definitions[beginvariables]define(h ) Height of Wind Screen[endvariables]define(L 300) Wind Screen Lengthdefine(t 015) Wind Screen Width Wind Screen Coordinatesdefine(x1 calc(0minus1300))define(x2 calc(x1minust))define(y1 calc(hminus025))define(y2 calc(y1+L))
4 num cornerpointsSCREEN3(SCHEME3)03 00 release distancespacing hull002 0001 00 minus01 merg1merg2merg3merg4minus4 minus3 minus1 minus3 minus1 section color codingdragliftmomentdisplrotation1 x2 y1 n11 x1 y1 n21 x1 y2 n11 x2 y2 n2
David Gutierrez Rivera Aerodynamic Shape Optimization 33 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Parameter File
Variables Definitions[beginvariables]define(h ) Height of Wind Screen[endvariables]define(L 300) Wind Screen Lengthdefine(t 015) Wind Screen Width Wind Screen Coordinatesdefine(x1 calc(0minus1300))define(x2 calc(x1minust))define(y1 calc(hminus025))define(y2 calc(y1+L))
4 num cornerpointsSCREEN3(SCHEME3)03 00 release distancespacing hull002 0001 00 minus01 merg1merg2merg3merg4minus4 minus3 minus1 minus3 minus1 section color codingdragliftmomentdisplrotation1 x2 y1 n11 x1 y1 n21 x1 y2 n11 x2 y2 n2
David Gutierrez Rivera Aerodynamic Shape Optimization 33 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Objective Function
function [Drag] = M4 Neath ViaductWS(X) M4 Neath ViaductWS Objective Functionsteps = 500
Drag(1) = VXF FORCES(XDRAGMAXstepsSECTION11)Drag(2) = VXF FORCES(XDRAGMAXstepsevalfalseSECTION12)Drag(3) = VXF FORCES(XDRAGMAXstepsevalfalseSECTION13)Drag(4) = VXF FORCES(XDRAGMAXstepsevalfalseSECTION14)
[DragLane] = max(Drag())
Call optiOUT to generate Plots and Output DataoptiOUT(X [Drag])
end
David Gutierrez Rivera Aerodynamic Shape Optimization 34 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Data Points
David Gutierrez Rivera Aerodynamic Shape Optimization 35 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Run-Time Optimization
David Gutierrez Rivera Aerodynamic Shape Optimization 36 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Vertical-Axis Wind Turbine (VAWT)
Description
The Savonius Wind Turbine is a Vertical-Axis Wind Turbine (VAWT)which main advantages are its reliability and practicality
David Gutierrez Rivera Aerodynamic Shape Optimization 37 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Model
Description
Find optimum values of ex and ey to maximize Torque or Power
Constrained to the shaded area
David Gutierrez Rivera Aerodynamic Shape Optimization 38 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Model
Description
Find optimum values of ex and ey to maximize Torque or Power
Constrained to the shaded area
David Gutierrez Rivera Aerodynamic Shape Optimization 38 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Dynamic Model
David Gutierrez Rivera Aerodynamic Shape Optimization 39 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
What is Optimization Basics of Aerodynamics
Computational Fluid Dynamics (CFD)
Is the branch of fluid mechanics that uses numerical methods to solvefluid flow problems
Discretization Methods
Finite Volume Method
Boundary Element Method
High-Resolution Schemes
Turbulence Models
Reynolds-AveragedNavierStokes (RANS)
Large eddy simulation (LES)
Vortex methods
David Gutierrez Rivera Aerodynamic Shape Optimization 8 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
What is Optimization Basics of Aerodynamics
The Vortex Particle Method (VPM)
Characteristics
Is a grid-free technique for simulation of turbulent flows
It uses vortices as the computational elements
David Gutierrez Rivera Aerodynamic Shape Optimization 9 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Local Global
Optimization Algorithms
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 10 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Local Global
Optimization Algorithms
Classification
Linearity
LinearNonLinear
Constraints
UnconstrainedConstrained
Objectives
Single-ObjectiveMulti-Objective
Modality
uni-modal (Local)multi-modal (Global)
David Gutierrez Rivera Aerodynamic Shape Optimization 11 54
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Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Local Global
Optimization Algorithms
Classification
Linearity
LinearNonLinear
Constraints
UnconstrainedConstrained
Objectives
Single-ObjectiveMulti-Objective
Modality
uni-modal (Local)multi-modal (Global)
David Gutierrez Rivera Aerodynamic Shape Optimization 11 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Local Global
Global vs Local
David Gutierrez Rivera Aerodynamic Shape Optimization 12 54
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Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Local Global
Local
Gradient-free Methods
Golden Section
Simplex
Gradient-based Methods
Gradient-Descent
Newton
David Gutierrez Rivera Aerodynamic Shape Optimization 13 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Local Global
Global
non-Heuristic Methods
Deterministic
Stochastic
Heuristic Methods
Evolutionary
Genetic AlgorithmSwarm Intelligence
Swarm Intelligence
Particle SwarmAnt Colony
David Gutierrez Rivera Aerodynamic Shape Optimization 14 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Shape Optimization
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 15 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Shape Optimization
Shape optimization is formulated as
minimizeΩ
f (Ω)
subject to
gi (Ω) le 0 i = 1 mhi (Ω) = 0 i = 1 n
(2)
where
Ω is a set of variable parameters that make up the geometry that wewant to optimize
David Gutierrez Rivera Aerodynamic Shape Optimization 16 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Shape Optimization
Shape optimization is formulated as
minimizeΩ
f (Ω)
subject to
gi (Ω) le 0 i = 1 mhi (Ω) = 0 i = 1 n
(2)
where
Ω is a set of variable parameters that make up the geometry that wewant to optimize
David Gutierrez Rivera Aerodynamic Shape Optimization 16 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Parametrization
David Gutierrez Rivera Aerodynamic Shape Optimization 17 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Parametrization
David Gutierrez Rivera Aerodynamic Shape Optimization 17 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Objective Functions
Similar to mathematical functions
They involve 3 basic operations
David Gutierrez Rivera Aerodynamic Shape Optimization 18 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Objective Functions
Similar to mathematical functions
They involve 3 basic operations
Substitution
f (x) = a0 +nsum
i=1
an middot cos(n x ) +nsum
i=1
bn middot sin(n x )
David Gutierrez Rivera Aerodynamic Shape Optimization 18 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Objective Functions
Similar to mathematical functions
They involve 3 basic operations
Substitution
f (x) = a0 +nsum
i=1
an middot cos(n 31416 ) +nsum
i=1
bn middot sin(n 31416 )
Substitution
David Gutierrez Rivera Aerodynamic Shape Optimization 18 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Objective Functions
Similar to mathematical functions
They involve 3 basic operations
Evaluation
f (x) = a0 +nsum
i=1
an middot cos(n 31416 ) +nsum
i=1
bn middot sin(n 31416 )︸ ︷︷ ︸Evaluation
David Gutierrez Rivera Aerodynamic Shape Optimization 18 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Objective Functions
Similar to mathematical functions
They involve 3 basic operations
Read Output
f (x) = Value
Read Output
David Gutierrez Rivera Aerodynamic Shape Optimization 18 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Data Gathering
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 19 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Data Gathering
David Gutierrez Rivera Aerodynamic Shape Optimization 20 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Data Gathering
Data File
It is a text-based tab-delimited file containing the data points from thevariables and the corresponding values of the objective functions
Variable1 Variable2 Variablen Objective1 ObjectivemVariable1 Variable2 Variablen Objective1 Objectivem
Variable1 Variable2 Variablen Objective1 Objectivem
David Gutierrez Rivera Aerodynamic Shape Optimization 21 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Data Gathering
Data File
It is a text-based tab-delimited file containing the data points from thevariables and the corresponding values of the objective functions
Variable1 Variable2 Variablen Objective1 ObjectivemVariable1 Variable2 Variablen Objective1 Objectivem
Variable1 Variable2 Variablen Objective1 Objectivem
David Gutierrez Rivera Aerodynamic Shape Optimization 21 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Black-Box Optimization
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 22 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Black-Box Optimization
Black-Box Process
They are known from their inputs and outputs
Little is known of how it works internally
David Gutierrez Rivera Aerodynamic Shape Optimization 23 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Black-Box Optimization
David Gutierrez Rivera Aerodynamic Shape Optimization 23 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Black-Box Optimization
David Gutierrez Rivera Aerodynamic Shape Optimization 24 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Noisy Functions
David Gutierrez Rivera Aerodynamic Shape Optimization 25 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Simulation-based Optimization
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 26 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Simulation-based Optimization
David Gutierrez Rivera Aerodynamic Shape Optimization 27 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Moving Boundary Problem
David Gutierrez Rivera Aerodynamic Shape Optimization 28 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
OptiFlow
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 29 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Examples
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 30 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
M4 Neath Viaduct Wind Shield
Description
This bridge is located in South Wales and crosses the River Neath Asection of the bridge is very exposed in flat topography therefore a windshielding system is desired for reducing the overturning forces on vehicles
Description
The CFD model is the same as the one used on the VXFlow tutorial
Four small sections were used to obtain the interior drag forces
David Gutierrez Rivera Aerodynamic Shape Optimization 31 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
M4 Neath Viaduct Wind Shield
Description
The CFD model is the same as the one used on the VXFlow tutorial
Four small sections were used to obtain the interior drag forces
David Gutierrez Rivera Aerodynamic Shape Optimization 31 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
M4 Neath Viaduct Wind Shield
Description
The CFD model is the same as the one used on the VXFlow tutorial
Four small sections were used to obtain the interior drag forces
David Gutierrez Rivera Aerodynamic Shape Optimization 31 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Model
Find optimum height (h) for the Wind Shield
David Gutierrez Rivera Aerodynamic Shape Optimization 32 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Parameter File
Variables Definitions[beginvariables]define(h ) Height of Wind Screen[endvariables]define(L 300) Wind Screen Lengthdefine(t 015) Wind Screen Width Wind Screen Coordinatesdefine(x1 calc(0minus1300))define(x2 calc(x1minust))define(y1 calc(hminus025))define(y2 calc(y1+L))
4 num cornerpointsSCREEN3(SCHEME3)03 00 release distancespacing hull002 0001 00 minus01 merg1merg2merg3merg4minus4 minus3 minus1 minus3 minus1 section color codingdragliftmomentdisplrotation1 x2 y1 n11 x1 y1 n21 x1 y2 n11 x2 y2 n2
David Gutierrez Rivera Aerodynamic Shape Optimization 33 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Parameter File
Variables Definitions[beginvariables]define(h ) Height of Wind Screen[endvariables]define(L 300) Wind Screen Lengthdefine(t 015) Wind Screen Width Wind Screen Coordinatesdefine(x1 calc(0minus1300))define(x2 calc(x1minust))define(y1 calc(hminus025))define(y2 calc(y1+L))
4 num cornerpointsSCREEN3(SCHEME3)03 00 release distancespacing hull002 0001 00 minus01 merg1merg2merg3merg4minus4 minus3 minus1 minus3 minus1 section color codingdragliftmomentdisplrotation1 x2 y1 n11 x1 y1 n21 x1 y2 n11 x2 y2 n2
David Gutierrez Rivera Aerodynamic Shape Optimization 33 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Objective Function
function [Drag] = M4 Neath ViaductWS(X) M4 Neath ViaductWS Objective Functionsteps = 500
Drag(1) = VXF FORCES(XDRAGMAXstepsSECTION11)Drag(2) = VXF FORCES(XDRAGMAXstepsevalfalseSECTION12)Drag(3) = VXF FORCES(XDRAGMAXstepsevalfalseSECTION13)Drag(4) = VXF FORCES(XDRAGMAXstepsevalfalseSECTION14)
[DragLane] = max(Drag())
Call optiOUT to generate Plots and Output DataoptiOUT(X [Drag])
end
David Gutierrez Rivera Aerodynamic Shape Optimization 34 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
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Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Data Points
David Gutierrez Rivera Aerodynamic Shape Optimization 35 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Run-Time Optimization
David Gutierrez Rivera Aerodynamic Shape Optimization 36 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Vertical-Axis Wind Turbine (VAWT)
Description
The Savonius Wind Turbine is a Vertical-Axis Wind Turbine (VAWT)which main advantages are its reliability and practicality
David Gutierrez Rivera Aerodynamic Shape Optimization 37 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Model
Description
Find optimum values of ex and ey to maximize Torque or Power
Constrained to the shaded area
David Gutierrez Rivera Aerodynamic Shape Optimization 38 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Model
Description
Find optimum values of ex and ey to maximize Torque or Power
Constrained to the shaded area
David Gutierrez Rivera Aerodynamic Shape Optimization 38 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Dynamic Model
David Gutierrez Rivera Aerodynamic Shape Optimization 39 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
What is Optimization Basics of Aerodynamics
The Vortex Particle Method (VPM)
Characteristics
Is a grid-free technique for simulation of turbulent flows
It uses vortices as the computational elements
David Gutierrez Rivera Aerodynamic Shape Optimization 9 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Local Global
Optimization Algorithms
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 10 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Local Global
Optimization Algorithms
Classification
Linearity
LinearNonLinear
Constraints
UnconstrainedConstrained
Objectives
Single-ObjectiveMulti-Objective
Modality
uni-modal (Local)multi-modal (Global)
David Gutierrez Rivera Aerodynamic Shape Optimization 11 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Local Global
Optimization Algorithms
Classification
Linearity
LinearNonLinear
Constraints
UnconstrainedConstrained
Objectives
Single-ObjectiveMulti-Objective
Modality
uni-modal (Local)multi-modal (Global)
David Gutierrez Rivera Aerodynamic Shape Optimization 11 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Local Global
Global vs Local
David Gutierrez Rivera Aerodynamic Shape Optimization 12 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Local Global
Local
Gradient-free Methods
Golden Section
Simplex
Gradient-based Methods
Gradient-Descent
Newton
David Gutierrez Rivera Aerodynamic Shape Optimization 13 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Local Global
Global
non-Heuristic Methods
Deterministic
Stochastic
Heuristic Methods
Evolutionary
Genetic AlgorithmSwarm Intelligence
Swarm Intelligence
Particle SwarmAnt Colony
David Gutierrez Rivera Aerodynamic Shape Optimization 14 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Shape Optimization
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 15 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Shape Optimization
Shape optimization is formulated as
minimizeΩ
f (Ω)
subject to
gi (Ω) le 0 i = 1 mhi (Ω) = 0 i = 1 n
(2)
where
Ω is a set of variable parameters that make up the geometry that wewant to optimize
David Gutierrez Rivera Aerodynamic Shape Optimization 16 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Shape Optimization
Shape optimization is formulated as
minimizeΩ
f (Ω)
subject to
gi (Ω) le 0 i = 1 mhi (Ω) = 0 i = 1 n
(2)
where
Ω is a set of variable parameters that make up the geometry that wewant to optimize
David Gutierrez Rivera Aerodynamic Shape Optimization 16 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Parametrization
David Gutierrez Rivera Aerodynamic Shape Optimization 17 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Parametrization
David Gutierrez Rivera Aerodynamic Shape Optimization 17 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Objective Functions
Similar to mathematical functions
They involve 3 basic operations
David Gutierrez Rivera Aerodynamic Shape Optimization 18 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Objective Functions
Similar to mathematical functions
They involve 3 basic operations
Substitution
f (x) = a0 +nsum
i=1
an middot cos(n x ) +nsum
i=1
bn middot sin(n x )
David Gutierrez Rivera Aerodynamic Shape Optimization 18 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Objective Functions
Similar to mathematical functions
They involve 3 basic operations
Substitution
f (x) = a0 +nsum
i=1
an middot cos(n 31416 ) +nsum
i=1
bn middot sin(n 31416 )
Substitution
David Gutierrez Rivera Aerodynamic Shape Optimization 18 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Objective Functions
Similar to mathematical functions
They involve 3 basic operations
Evaluation
f (x) = a0 +nsum
i=1
an middot cos(n 31416 ) +nsum
i=1
bn middot sin(n 31416 )︸ ︷︷ ︸Evaluation
David Gutierrez Rivera Aerodynamic Shape Optimization 18 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Objective Functions
Similar to mathematical functions
They involve 3 basic operations
Read Output
f (x) = Value
Read Output
David Gutierrez Rivera Aerodynamic Shape Optimization 18 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Data Gathering
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 19 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Data Gathering
David Gutierrez Rivera Aerodynamic Shape Optimization 20 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Data Gathering
Data File
It is a text-based tab-delimited file containing the data points from thevariables and the corresponding values of the objective functions
Variable1 Variable2 Variablen Objective1 ObjectivemVariable1 Variable2 Variablen Objective1 Objectivem
Variable1 Variable2 Variablen Objective1 Objectivem
David Gutierrez Rivera Aerodynamic Shape Optimization 21 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Data Gathering
Data File
It is a text-based tab-delimited file containing the data points from thevariables and the corresponding values of the objective functions
Variable1 Variable2 Variablen Objective1 ObjectivemVariable1 Variable2 Variablen Objective1 Objectivem
Variable1 Variable2 Variablen Objective1 Objectivem
David Gutierrez Rivera Aerodynamic Shape Optimization 21 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Black-Box Optimization
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 22 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Black-Box Optimization
Black-Box Process
They are known from their inputs and outputs
Little is known of how it works internally
David Gutierrez Rivera Aerodynamic Shape Optimization 23 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Black-Box Optimization
David Gutierrez Rivera Aerodynamic Shape Optimization 23 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Black-Box Optimization
David Gutierrez Rivera Aerodynamic Shape Optimization 24 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Noisy Functions
David Gutierrez Rivera Aerodynamic Shape Optimization 25 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Simulation-based Optimization
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 26 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Simulation-based Optimization
David Gutierrez Rivera Aerodynamic Shape Optimization 27 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Moving Boundary Problem
David Gutierrez Rivera Aerodynamic Shape Optimization 28 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
OptiFlow
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 29 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Examples
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 30 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
M4 Neath Viaduct Wind Shield
Description
This bridge is located in South Wales and crosses the River Neath Asection of the bridge is very exposed in flat topography therefore a windshielding system is desired for reducing the overturning forces on vehicles
Description
The CFD model is the same as the one used on the VXFlow tutorial
Four small sections were used to obtain the interior drag forces
David Gutierrez Rivera Aerodynamic Shape Optimization 31 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
M4 Neath Viaduct Wind Shield
Description
The CFD model is the same as the one used on the VXFlow tutorial
Four small sections were used to obtain the interior drag forces
David Gutierrez Rivera Aerodynamic Shape Optimization 31 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
M4 Neath Viaduct Wind Shield
Description
The CFD model is the same as the one used on the VXFlow tutorial
Four small sections were used to obtain the interior drag forces
David Gutierrez Rivera Aerodynamic Shape Optimization 31 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Model
Find optimum height (h) for the Wind Shield
David Gutierrez Rivera Aerodynamic Shape Optimization 32 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Parameter File
Variables Definitions[beginvariables]define(h ) Height of Wind Screen[endvariables]define(L 300) Wind Screen Lengthdefine(t 015) Wind Screen Width Wind Screen Coordinatesdefine(x1 calc(0minus1300))define(x2 calc(x1minust))define(y1 calc(hminus025))define(y2 calc(y1+L))
4 num cornerpointsSCREEN3(SCHEME3)03 00 release distancespacing hull002 0001 00 minus01 merg1merg2merg3merg4minus4 minus3 minus1 minus3 minus1 section color codingdragliftmomentdisplrotation1 x2 y1 n11 x1 y1 n21 x1 y2 n11 x2 y2 n2
David Gutierrez Rivera Aerodynamic Shape Optimization 33 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Parameter File
Variables Definitions[beginvariables]define(h ) Height of Wind Screen[endvariables]define(L 300) Wind Screen Lengthdefine(t 015) Wind Screen Width Wind Screen Coordinatesdefine(x1 calc(0minus1300))define(x2 calc(x1minust))define(y1 calc(hminus025))define(y2 calc(y1+L))
4 num cornerpointsSCREEN3(SCHEME3)03 00 release distancespacing hull002 0001 00 minus01 merg1merg2merg3merg4minus4 minus3 minus1 minus3 minus1 section color codingdragliftmomentdisplrotation1 x2 y1 n11 x1 y1 n21 x1 y2 n11 x2 y2 n2
David Gutierrez Rivera Aerodynamic Shape Optimization 33 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Objective Function
function [Drag] = M4 Neath ViaductWS(X) M4 Neath ViaductWS Objective Functionsteps = 500
Drag(1) = VXF FORCES(XDRAGMAXstepsSECTION11)Drag(2) = VXF FORCES(XDRAGMAXstepsevalfalseSECTION12)Drag(3) = VXF FORCES(XDRAGMAXstepsevalfalseSECTION13)Drag(4) = VXF FORCES(XDRAGMAXstepsevalfalseSECTION14)
[DragLane] = max(Drag())
Call optiOUT to generate Plots and Output DataoptiOUT(X [Drag])
end
David Gutierrez Rivera Aerodynamic Shape Optimization 34 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Data Points
David Gutierrez Rivera Aerodynamic Shape Optimization 35 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Run-Time Optimization
David Gutierrez Rivera Aerodynamic Shape Optimization 36 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Vertical-Axis Wind Turbine (VAWT)
Description
The Savonius Wind Turbine is a Vertical-Axis Wind Turbine (VAWT)which main advantages are its reliability and practicality
David Gutierrez Rivera Aerodynamic Shape Optimization 37 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Model
Description
Find optimum values of ex and ey to maximize Torque or Power
Constrained to the shaded area
David Gutierrez Rivera Aerodynamic Shape Optimization 38 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Model
Description
Find optimum values of ex and ey to maximize Torque or Power
Constrained to the shaded area
David Gutierrez Rivera Aerodynamic Shape Optimization 38 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Dynamic Model
David Gutierrez Rivera Aerodynamic Shape Optimization 39 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Local Global
Optimization Algorithms
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 10 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Local Global
Optimization Algorithms
Classification
Linearity
LinearNonLinear
Constraints
UnconstrainedConstrained
Objectives
Single-ObjectiveMulti-Objective
Modality
uni-modal (Local)multi-modal (Global)
David Gutierrez Rivera Aerodynamic Shape Optimization 11 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Local Global
Optimization Algorithms
Classification
Linearity
LinearNonLinear
Constraints
UnconstrainedConstrained
Objectives
Single-ObjectiveMulti-Objective
Modality
uni-modal (Local)multi-modal (Global)
David Gutierrez Rivera Aerodynamic Shape Optimization 11 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Local Global
Global vs Local
David Gutierrez Rivera Aerodynamic Shape Optimization 12 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Local Global
Local
Gradient-free Methods
Golden Section
Simplex
Gradient-based Methods
Gradient-Descent
Newton
David Gutierrez Rivera Aerodynamic Shape Optimization 13 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Local Global
Global
non-Heuristic Methods
Deterministic
Stochastic
Heuristic Methods
Evolutionary
Genetic AlgorithmSwarm Intelligence
Swarm Intelligence
Particle SwarmAnt Colony
David Gutierrez Rivera Aerodynamic Shape Optimization 14 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Shape Optimization
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 15 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Shape Optimization
Shape optimization is formulated as
minimizeΩ
f (Ω)
subject to
gi (Ω) le 0 i = 1 mhi (Ω) = 0 i = 1 n
(2)
where
Ω is a set of variable parameters that make up the geometry that wewant to optimize
David Gutierrez Rivera Aerodynamic Shape Optimization 16 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Shape Optimization
Shape optimization is formulated as
minimizeΩ
f (Ω)
subject to
gi (Ω) le 0 i = 1 mhi (Ω) = 0 i = 1 n
(2)
where
Ω is a set of variable parameters that make up the geometry that wewant to optimize
David Gutierrez Rivera Aerodynamic Shape Optimization 16 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Parametrization
David Gutierrez Rivera Aerodynamic Shape Optimization 17 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Parametrization
David Gutierrez Rivera Aerodynamic Shape Optimization 17 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Objective Functions
Similar to mathematical functions
They involve 3 basic operations
David Gutierrez Rivera Aerodynamic Shape Optimization 18 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Objective Functions
Similar to mathematical functions
They involve 3 basic operations
Substitution
f (x) = a0 +nsum
i=1
an middot cos(n x ) +nsum
i=1
bn middot sin(n x )
David Gutierrez Rivera Aerodynamic Shape Optimization 18 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Objective Functions
Similar to mathematical functions
They involve 3 basic operations
Substitution
f (x) = a0 +nsum
i=1
an middot cos(n 31416 ) +nsum
i=1
bn middot sin(n 31416 )
Substitution
David Gutierrez Rivera Aerodynamic Shape Optimization 18 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Objective Functions
Similar to mathematical functions
They involve 3 basic operations
Evaluation
f (x) = a0 +nsum
i=1
an middot cos(n 31416 ) +nsum
i=1
bn middot sin(n 31416 )︸ ︷︷ ︸Evaluation
David Gutierrez Rivera Aerodynamic Shape Optimization 18 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Objective Functions
Similar to mathematical functions
They involve 3 basic operations
Read Output
f (x) = Value
Read Output
David Gutierrez Rivera Aerodynamic Shape Optimization 18 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Data Gathering
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 19 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Data Gathering
David Gutierrez Rivera Aerodynamic Shape Optimization 20 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Data Gathering
Data File
It is a text-based tab-delimited file containing the data points from thevariables and the corresponding values of the objective functions
Variable1 Variable2 Variablen Objective1 ObjectivemVariable1 Variable2 Variablen Objective1 Objectivem
Variable1 Variable2 Variablen Objective1 Objectivem
David Gutierrez Rivera Aerodynamic Shape Optimization 21 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Data Gathering
Data File
It is a text-based tab-delimited file containing the data points from thevariables and the corresponding values of the objective functions
Variable1 Variable2 Variablen Objective1 ObjectivemVariable1 Variable2 Variablen Objective1 Objectivem
Variable1 Variable2 Variablen Objective1 Objectivem
David Gutierrez Rivera Aerodynamic Shape Optimization 21 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Black-Box Optimization
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 22 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Black-Box Optimization
Black-Box Process
They are known from their inputs and outputs
Little is known of how it works internally
David Gutierrez Rivera Aerodynamic Shape Optimization 23 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Black-Box Optimization
David Gutierrez Rivera Aerodynamic Shape Optimization 23 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Black-Box Optimization
David Gutierrez Rivera Aerodynamic Shape Optimization 24 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Noisy Functions
David Gutierrez Rivera Aerodynamic Shape Optimization 25 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Simulation-based Optimization
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 26 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Simulation-based Optimization
David Gutierrez Rivera Aerodynamic Shape Optimization 27 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Moving Boundary Problem
David Gutierrez Rivera Aerodynamic Shape Optimization 28 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
OptiFlow
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 29 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Examples
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 30 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
M4 Neath Viaduct Wind Shield
Description
This bridge is located in South Wales and crosses the River Neath Asection of the bridge is very exposed in flat topography therefore a windshielding system is desired for reducing the overturning forces on vehicles
Description
The CFD model is the same as the one used on the VXFlow tutorial
Four small sections were used to obtain the interior drag forces
David Gutierrez Rivera Aerodynamic Shape Optimization 31 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
M4 Neath Viaduct Wind Shield
Description
The CFD model is the same as the one used on the VXFlow tutorial
Four small sections were used to obtain the interior drag forces
David Gutierrez Rivera Aerodynamic Shape Optimization 31 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
M4 Neath Viaduct Wind Shield
Description
The CFD model is the same as the one used on the VXFlow tutorial
Four small sections were used to obtain the interior drag forces
David Gutierrez Rivera Aerodynamic Shape Optimization 31 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Model
Find optimum height (h) for the Wind Shield
David Gutierrez Rivera Aerodynamic Shape Optimization 32 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Parameter File
Variables Definitions[beginvariables]define(h ) Height of Wind Screen[endvariables]define(L 300) Wind Screen Lengthdefine(t 015) Wind Screen Width Wind Screen Coordinatesdefine(x1 calc(0minus1300))define(x2 calc(x1minust))define(y1 calc(hminus025))define(y2 calc(y1+L))
4 num cornerpointsSCREEN3(SCHEME3)03 00 release distancespacing hull002 0001 00 minus01 merg1merg2merg3merg4minus4 minus3 minus1 minus3 minus1 section color codingdragliftmomentdisplrotation1 x2 y1 n11 x1 y1 n21 x1 y2 n11 x2 y2 n2
David Gutierrez Rivera Aerodynamic Shape Optimization 33 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Parameter File
Variables Definitions[beginvariables]define(h ) Height of Wind Screen[endvariables]define(L 300) Wind Screen Lengthdefine(t 015) Wind Screen Width Wind Screen Coordinatesdefine(x1 calc(0minus1300))define(x2 calc(x1minust))define(y1 calc(hminus025))define(y2 calc(y1+L))
4 num cornerpointsSCREEN3(SCHEME3)03 00 release distancespacing hull002 0001 00 minus01 merg1merg2merg3merg4minus4 minus3 minus1 minus3 minus1 section color codingdragliftmomentdisplrotation1 x2 y1 n11 x1 y1 n21 x1 y2 n11 x2 y2 n2
David Gutierrez Rivera Aerodynamic Shape Optimization 33 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Objective Function
function [Drag] = M4 Neath ViaductWS(X) M4 Neath ViaductWS Objective Functionsteps = 500
Drag(1) = VXF FORCES(XDRAGMAXstepsSECTION11)Drag(2) = VXF FORCES(XDRAGMAXstepsevalfalseSECTION12)Drag(3) = VXF FORCES(XDRAGMAXstepsevalfalseSECTION13)Drag(4) = VXF FORCES(XDRAGMAXstepsevalfalseSECTION14)
[DragLane] = max(Drag())
Call optiOUT to generate Plots and Output DataoptiOUT(X [Drag])
end
David Gutierrez Rivera Aerodynamic Shape Optimization 34 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Data Points
David Gutierrez Rivera Aerodynamic Shape Optimization 35 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Run-Time Optimization
David Gutierrez Rivera Aerodynamic Shape Optimization 36 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Vertical-Axis Wind Turbine (VAWT)
Description
The Savonius Wind Turbine is a Vertical-Axis Wind Turbine (VAWT)which main advantages are its reliability and practicality
David Gutierrez Rivera Aerodynamic Shape Optimization 37 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Model
Description
Find optimum values of ex and ey to maximize Torque or Power
Constrained to the shaded area
David Gutierrez Rivera Aerodynamic Shape Optimization 38 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Model
Description
Find optimum values of ex and ey to maximize Torque or Power
Constrained to the shaded area
David Gutierrez Rivera Aerodynamic Shape Optimization 38 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Dynamic Model
David Gutierrez Rivera Aerodynamic Shape Optimization 39 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Local Global
Optimization Algorithms
Classification
Linearity
LinearNonLinear
Constraints
UnconstrainedConstrained
Objectives
Single-ObjectiveMulti-Objective
Modality
uni-modal (Local)multi-modal (Global)
David Gutierrez Rivera Aerodynamic Shape Optimization 11 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Local Global
Optimization Algorithms
Classification
Linearity
LinearNonLinear
Constraints
UnconstrainedConstrained
Objectives
Single-ObjectiveMulti-Objective
Modality
uni-modal (Local)multi-modal (Global)
David Gutierrez Rivera Aerodynamic Shape Optimization 11 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Local Global
Global vs Local
David Gutierrez Rivera Aerodynamic Shape Optimization 12 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Local Global
Local
Gradient-free Methods
Golden Section
Simplex
Gradient-based Methods
Gradient-Descent
Newton
David Gutierrez Rivera Aerodynamic Shape Optimization 13 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Local Global
Global
non-Heuristic Methods
Deterministic
Stochastic
Heuristic Methods
Evolutionary
Genetic AlgorithmSwarm Intelligence
Swarm Intelligence
Particle SwarmAnt Colony
David Gutierrez Rivera Aerodynamic Shape Optimization 14 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Shape Optimization
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 15 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Shape Optimization
Shape optimization is formulated as
minimizeΩ
f (Ω)
subject to
gi (Ω) le 0 i = 1 mhi (Ω) = 0 i = 1 n
(2)
where
Ω is a set of variable parameters that make up the geometry that wewant to optimize
David Gutierrez Rivera Aerodynamic Shape Optimization 16 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Shape Optimization
Shape optimization is formulated as
minimizeΩ
f (Ω)
subject to
gi (Ω) le 0 i = 1 mhi (Ω) = 0 i = 1 n
(2)
where
Ω is a set of variable parameters that make up the geometry that wewant to optimize
David Gutierrez Rivera Aerodynamic Shape Optimization 16 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Parametrization
David Gutierrez Rivera Aerodynamic Shape Optimization 17 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Parametrization
David Gutierrez Rivera Aerodynamic Shape Optimization 17 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Objective Functions
Similar to mathematical functions
They involve 3 basic operations
David Gutierrez Rivera Aerodynamic Shape Optimization 18 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Objective Functions
Similar to mathematical functions
They involve 3 basic operations
Substitution
f (x) = a0 +nsum
i=1
an middot cos(n x ) +nsum
i=1
bn middot sin(n x )
David Gutierrez Rivera Aerodynamic Shape Optimization 18 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Objective Functions
Similar to mathematical functions
They involve 3 basic operations
Substitution
f (x) = a0 +nsum
i=1
an middot cos(n 31416 ) +nsum
i=1
bn middot sin(n 31416 )
Substitution
David Gutierrez Rivera Aerodynamic Shape Optimization 18 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Objective Functions
Similar to mathematical functions
They involve 3 basic operations
Evaluation
f (x) = a0 +nsum
i=1
an middot cos(n 31416 ) +nsum
i=1
bn middot sin(n 31416 )︸ ︷︷ ︸Evaluation
David Gutierrez Rivera Aerodynamic Shape Optimization 18 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Objective Functions
Similar to mathematical functions
They involve 3 basic operations
Read Output
f (x) = Value
Read Output
David Gutierrez Rivera Aerodynamic Shape Optimization 18 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Data Gathering
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 19 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Data Gathering
David Gutierrez Rivera Aerodynamic Shape Optimization 20 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Data Gathering
Data File
It is a text-based tab-delimited file containing the data points from thevariables and the corresponding values of the objective functions
Variable1 Variable2 Variablen Objective1 ObjectivemVariable1 Variable2 Variablen Objective1 Objectivem
Variable1 Variable2 Variablen Objective1 Objectivem
David Gutierrez Rivera Aerodynamic Shape Optimization 21 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Data Gathering
Data File
It is a text-based tab-delimited file containing the data points from thevariables and the corresponding values of the objective functions
Variable1 Variable2 Variablen Objective1 ObjectivemVariable1 Variable2 Variablen Objective1 Objectivem
Variable1 Variable2 Variablen Objective1 Objectivem
David Gutierrez Rivera Aerodynamic Shape Optimization 21 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Black-Box Optimization
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 22 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Black-Box Optimization
Black-Box Process
They are known from their inputs and outputs
Little is known of how it works internally
David Gutierrez Rivera Aerodynamic Shape Optimization 23 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Black-Box Optimization
David Gutierrez Rivera Aerodynamic Shape Optimization 23 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Black-Box Optimization
David Gutierrez Rivera Aerodynamic Shape Optimization 24 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Noisy Functions
David Gutierrez Rivera Aerodynamic Shape Optimization 25 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Simulation-based Optimization
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 26 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Simulation-based Optimization
David Gutierrez Rivera Aerodynamic Shape Optimization 27 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Moving Boundary Problem
David Gutierrez Rivera Aerodynamic Shape Optimization 28 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
OptiFlow
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 29 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Examples
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 30 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
M4 Neath Viaduct Wind Shield
Description
This bridge is located in South Wales and crosses the River Neath Asection of the bridge is very exposed in flat topography therefore a windshielding system is desired for reducing the overturning forces on vehicles
Description
The CFD model is the same as the one used on the VXFlow tutorial
Four small sections were used to obtain the interior drag forces
David Gutierrez Rivera Aerodynamic Shape Optimization 31 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
M4 Neath Viaduct Wind Shield
Description
The CFD model is the same as the one used on the VXFlow tutorial
Four small sections were used to obtain the interior drag forces
David Gutierrez Rivera Aerodynamic Shape Optimization 31 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
M4 Neath Viaduct Wind Shield
Description
The CFD model is the same as the one used on the VXFlow tutorial
Four small sections were used to obtain the interior drag forces
David Gutierrez Rivera Aerodynamic Shape Optimization 31 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Model
Find optimum height (h) for the Wind Shield
David Gutierrez Rivera Aerodynamic Shape Optimization 32 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Parameter File
Variables Definitions[beginvariables]define(h ) Height of Wind Screen[endvariables]define(L 300) Wind Screen Lengthdefine(t 015) Wind Screen Width Wind Screen Coordinatesdefine(x1 calc(0minus1300))define(x2 calc(x1minust))define(y1 calc(hminus025))define(y2 calc(y1+L))
4 num cornerpointsSCREEN3(SCHEME3)03 00 release distancespacing hull002 0001 00 minus01 merg1merg2merg3merg4minus4 minus3 minus1 minus3 minus1 section color codingdragliftmomentdisplrotation1 x2 y1 n11 x1 y1 n21 x1 y2 n11 x2 y2 n2
David Gutierrez Rivera Aerodynamic Shape Optimization 33 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Parameter File
Variables Definitions[beginvariables]define(h ) Height of Wind Screen[endvariables]define(L 300) Wind Screen Lengthdefine(t 015) Wind Screen Width Wind Screen Coordinatesdefine(x1 calc(0minus1300))define(x2 calc(x1minust))define(y1 calc(hminus025))define(y2 calc(y1+L))
4 num cornerpointsSCREEN3(SCHEME3)03 00 release distancespacing hull002 0001 00 minus01 merg1merg2merg3merg4minus4 minus3 minus1 minus3 minus1 section color codingdragliftmomentdisplrotation1 x2 y1 n11 x1 y1 n21 x1 y2 n11 x2 y2 n2
David Gutierrez Rivera Aerodynamic Shape Optimization 33 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Objective Function
function [Drag] = M4 Neath ViaductWS(X) M4 Neath ViaductWS Objective Functionsteps = 500
Drag(1) = VXF FORCES(XDRAGMAXstepsSECTION11)Drag(2) = VXF FORCES(XDRAGMAXstepsevalfalseSECTION12)Drag(3) = VXF FORCES(XDRAGMAXstepsevalfalseSECTION13)Drag(4) = VXF FORCES(XDRAGMAXstepsevalfalseSECTION14)
[DragLane] = max(Drag())
Call optiOUT to generate Plots and Output DataoptiOUT(X [Drag])
end
David Gutierrez Rivera Aerodynamic Shape Optimization 34 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Data Points
David Gutierrez Rivera Aerodynamic Shape Optimization 35 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Run-Time Optimization
David Gutierrez Rivera Aerodynamic Shape Optimization 36 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Vertical-Axis Wind Turbine (VAWT)
Description
The Savonius Wind Turbine is a Vertical-Axis Wind Turbine (VAWT)which main advantages are its reliability and practicality
David Gutierrez Rivera Aerodynamic Shape Optimization 37 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Model
Description
Find optimum values of ex and ey to maximize Torque or Power
Constrained to the shaded area
David Gutierrez Rivera Aerodynamic Shape Optimization 38 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Model
Description
Find optimum values of ex and ey to maximize Torque or Power
Constrained to the shaded area
David Gutierrez Rivera Aerodynamic Shape Optimization 38 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Dynamic Model
David Gutierrez Rivera Aerodynamic Shape Optimization 39 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Local Global
Optimization Algorithms
Classification
Linearity
LinearNonLinear
Constraints
UnconstrainedConstrained
Objectives
Single-ObjectiveMulti-Objective
Modality
uni-modal (Local)multi-modal (Global)
David Gutierrez Rivera Aerodynamic Shape Optimization 11 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Local Global
Global vs Local
David Gutierrez Rivera Aerodynamic Shape Optimization 12 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Local Global
Local
Gradient-free Methods
Golden Section
Simplex
Gradient-based Methods
Gradient-Descent
Newton
David Gutierrez Rivera Aerodynamic Shape Optimization 13 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Local Global
Global
non-Heuristic Methods
Deterministic
Stochastic
Heuristic Methods
Evolutionary
Genetic AlgorithmSwarm Intelligence
Swarm Intelligence
Particle SwarmAnt Colony
David Gutierrez Rivera Aerodynamic Shape Optimization 14 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Shape Optimization
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 15 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Shape Optimization
Shape optimization is formulated as
minimizeΩ
f (Ω)
subject to
gi (Ω) le 0 i = 1 mhi (Ω) = 0 i = 1 n
(2)
where
Ω is a set of variable parameters that make up the geometry that wewant to optimize
David Gutierrez Rivera Aerodynamic Shape Optimization 16 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Shape Optimization
Shape optimization is formulated as
minimizeΩ
f (Ω)
subject to
gi (Ω) le 0 i = 1 mhi (Ω) = 0 i = 1 n
(2)
where
Ω is a set of variable parameters that make up the geometry that wewant to optimize
David Gutierrez Rivera Aerodynamic Shape Optimization 16 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Parametrization
David Gutierrez Rivera Aerodynamic Shape Optimization 17 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Parametrization
David Gutierrez Rivera Aerodynamic Shape Optimization 17 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Objective Functions
Similar to mathematical functions
They involve 3 basic operations
David Gutierrez Rivera Aerodynamic Shape Optimization 18 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Objective Functions
Similar to mathematical functions
They involve 3 basic operations
Substitution
f (x) = a0 +nsum
i=1
an middot cos(n x ) +nsum
i=1
bn middot sin(n x )
David Gutierrez Rivera Aerodynamic Shape Optimization 18 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Objective Functions
Similar to mathematical functions
They involve 3 basic operations
Substitution
f (x) = a0 +nsum
i=1
an middot cos(n 31416 ) +nsum
i=1
bn middot sin(n 31416 )
Substitution
David Gutierrez Rivera Aerodynamic Shape Optimization 18 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Objective Functions
Similar to mathematical functions
They involve 3 basic operations
Evaluation
f (x) = a0 +nsum
i=1
an middot cos(n 31416 ) +nsum
i=1
bn middot sin(n 31416 )︸ ︷︷ ︸Evaluation
David Gutierrez Rivera Aerodynamic Shape Optimization 18 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Objective Functions
Similar to mathematical functions
They involve 3 basic operations
Read Output
f (x) = Value
Read Output
David Gutierrez Rivera Aerodynamic Shape Optimization 18 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Data Gathering
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 19 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Data Gathering
David Gutierrez Rivera Aerodynamic Shape Optimization 20 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Data Gathering
Data File
It is a text-based tab-delimited file containing the data points from thevariables and the corresponding values of the objective functions
Variable1 Variable2 Variablen Objective1 ObjectivemVariable1 Variable2 Variablen Objective1 Objectivem
Variable1 Variable2 Variablen Objective1 Objectivem
David Gutierrez Rivera Aerodynamic Shape Optimization 21 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Data Gathering
Data File
It is a text-based tab-delimited file containing the data points from thevariables and the corresponding values of the objective functions
Variable1 Variable2 Variablen Objective1 ObjectivemVariable1 Variable2 Variablen Objective1 Objectivem
Variable1 Variable2 Variablen Objective1 Objectivem
David Gutierrez Rivera Aerodynamic Shape Optimization 21 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Black-Box Optimization
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 22 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Black-Box Optimization
Black-Box Process
They are known from their inputs and outputs
Little is known of how it works internally
David Gutierrez Rivera Aerodynamic Shape Optimization 23 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Black-Box Optimization
David Gutierrez Rivera Aerodynamic Shape Optimization 23 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Black-Box Optimization
David Gutierrez Rivera Aerodynamic Shape Optimization 24 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Noisy Functions
David Gutierrez Rivera Aerodynamic Shape Optimization 25 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Simulation-based Optimization
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 26 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Simulation-based Optimization
David Gutierrez Rivera Aerodynamic Shape Optimization 27 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Moving Boundary Problem
David Gutierrez Rivera Aerodynamic Shape Optimization 28 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
OptiFlow
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 29 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Examples
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 30 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
M4 Neath Viaduct Wind Shield
Description
This bridge is located in South Wales and crosses the River Neath Asection of the bridge is very exposed in flat topography therefore a windshielding system is desired for reducing the overturning forces on vehicles
Description
The CFD model is the same as the one used on the VXFlow tutorial
Four small sections were used to obtain the interior drag forces
David Gutierrez Rivera Aerodynamic Shape Optimization 31 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
M4 Neath Viaduct Wind Shield
Description
The CFD model is the same as the one used on the VXFlow tutorial
Four small sections were used to obtain the interior drag forces
David Gutierrez Rivera Aerodynamic Shape Optimization 31 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
M4 Neath Viaduct Wind Shield
Description
The CFD model is the same as the one used on the VXFlow tutorial
Four small sections were used to obtain the interior drag forces
David Gutierrez Rivera Aerodynamic Shape Optimization 31 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Model
Find optimum height (h) for the Wind Shield
David Gutierrez Rivera Aerodynamic Shape Optimization 32 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Parameter File
Variables Definitions[beginvariables]define(h ) Height of Wind Screen[endvariables]define(L 300) Wind Screen Lengthdefine(t 015) Wind Screen Width Wind Screen Coordinatesdefine(x1 calc(0minus1300))define(x2 calc(x1minust))define(y1 calc(hminus025))define(y2 calc(y1+L))
4 num cornerpointsSCREEN3(SCHEME3)03 00 release distancespacing hull002 0001 00 minus01 merg1merg2merg3merg4minus4 minus3 minus1 minus3 minus1 section color codingdragliftmomentdisplrotation1 x2 y1 n11 x1 y1 n21 x1 y2 n11 x2 y2 n2
David Gutierrez Rivera Aerodynamic Shape Optimization 33 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Parameter File
Variables Definitions[beginvariables]define(h ) Height of Wind Screen[endvariables]define(L 300) Wind Screen Lengthdefine(t 015) Wind Screen Width Wind Screen Coordinatesdefine(x1 calc(0minus1300))define(x2 calc(x1minust))define(y1 calc(hminus025))define(y2 calc(y1+L))
4 num cornerpointsSCREEN3(SCHEME3)03 00 release distancespacing hull002 0001 00 minus01 merg1merg2merg3merg4minus4 minus3 minus1 minus3 minus1 section color codingdragliftmomentdisplrotation1 x2 y1 n11 x1 y1 n21 x1 y2 n11 x2 y2 n2
David Gutierrez Rivera Aerodynamic Shape Optimization 33 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Objective Function
function [Drag] = M4 Neath ViaductWS(X) M4 Neath ViaductWS Objective Functionsteps = 500
Drag(1) = VXF FORCES(XDRAGMAXstepsSECTION11)Drag(2) = VXF FORCES(XDRAGMAXstepsevalfalseSECTION12)Drag(3) = VXF FORCES(XDRAGMAXstepsevalfalseSECTION13)Drag(4) = VXF FORCES(XDRAGMAXstepsevalfalseSECTION14)
[DragLane] = max(Drag())
Call optiOUT to generate Plots and Output DataoptiOUT(X [Drag])
end
David Gutierrez Rivera Aerodynamic Shape Optimization 34 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Data Points
David Gutierrez Rivera Aerodynamic Shape Optimization 35 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Run-Time Optimization
David Gutierrez Rivera Aerodynamic Shape Optimization 36 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Vertical-Axis Wind Turbine (VAWT)
Description
The Savonius Wind Turbine is a Vertical-Axis Wind Turbine (VAWT)which main advantages are its reliability and practicality
David Gutierrez Rivera Aerodynamic Shape Optimization 37 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Model
Description
Find optimum values of ex and ey to maximize Torque or Power
Constrained to the shaded area
David Gutierrez Rivera Aerodynamic Shape Optimization 38 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Model
Description
Find optimum values of ex and ey to maximize Torque or Power
Constrained to the shaded area
David Gutierrez Rivera Aerodynamic Shape Optimization 38 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Dynamic Model
David Gutierrez Rivera Aerodynamic Shape Optimization 39 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Local Global
Global vs Local
David Gutierrez Rivera Aerodynamic Shape Optimization 12 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Local Global
Local
Gradient-free Methods
Golden Section
Simplex
Gradient-based Methods
Gradient-Descent
Newton
David Gutierrez Rivera Aerodynamic Shape Optimization 13 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Local Global
Global
non-Heuristic Methods
Deterministic
Stochastic
Heuristic Methods
Evolutionary
Genetic AlgorithmSwarm Intelligence
Swarm Intelligence
Particle SwarmAnt Colony
David Gutierrez Rivera Aerodynamic Shape Optimization 14 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Shape Optimization
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 15 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Shape Optimization
Shape optimization is formulated as
minimizeΩ
f (Ω)
subject to
gi (Ω) le 0 i = 1 mhi (Ω) = 0 i = 1 n
(2)
where
Ω is a set of variable parameters that make up the geometry that wewant to optimize
David Gutierrez Rivera Aerodynamic Shape Optimization 16 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Shape Optimization
Shape optimization is formulated as
minimizeΩ
f (Ω)
subject to
gi (Ω) le 0 i = 1 mhi (Ω) = 0 i = 1 n
(2)
where
Ω is a set of variable parameters that make up the geometry that wewant to optimize
David Gutierrez Rivera Aerodynamic Shape Optimization 16 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Parametrization
David Gutierrez Rivera Aerodynamic Shape Optimization 17 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Parametrization
David Gutierrez Rivera Aerodynamic Shape Optimization 17 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Objective Functions
Similar to mathematical functions
They involve 3 basic operations
David Gutierrez Rivera Aerodynamic Shape Optimization 18 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Objective Functions
Similar to mathematical functions
They involve 3 basic operations
Substitution
f (x) = a0 +nsum
i=1
an middot cos(n x ) +nsum
i=1
bn middot sin(n x )
David Gutierrez Rivera Aerodynamic Shape Optimization 18 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Objective Functions
Similar to mathematical functions
They involve 3 basic operations
Substitution
f (x) = a0 +nsum
i=1
an middot cos(n 31416 ) +nsum
i=1
bn middot sin(n 31416 )
Substitution
David Gutierrez Rivera Aerodynamic Shape Optimization 18 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Objective Functions
Similar to mathematical functions
They involve 3 basic operations
Evaluation
f (x) = a0 +nsum
i=1
an middot cos(n 31416 ) +nsum
i=1
bn middot sin(n 31416 )︸ ︷︷ ︸Evaluation
David Gutierrez Rivera Aerodynamic Shape Optimization 18 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Objective Functions
Similar to mathematical functions
They involve 3 basic operations
Read Output
f (x) = Value
Read Output
David Gutierrez Rivera Aerodynamic Shape Optimization 18 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Data Gathering
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 19 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Data Gathering
David Gutierrez Rivera Aerodynamic Shape Optimization 20 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Data Gathering
Data File
It is a text-based tab-delimited file containing the data points from thevariables and the corresponding values of the objective functions
Variable1 Variable2 Variablen Objective1 ObjectivemVariable1 Variable2 Variablen Objective1 Objectivem
Variable1 Variable2 Variablen Objective1 Objectivem
David Gutierrez Rivera Aerodynamic Shape Optimization 21 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Data Gathering
Data File
It is a text-based tab-delimited file containing the data points from thevariables and the corresponding values of the objective functions
Variable1 Variable2 Variablen Objective1 ObjectivemVariable1 Variable2 Variablen Objective1 Objectivem
Variable1 Variable2 Variablen Objective1 Objectivem
David Gutierrez Rivera Aerodynamic Shape Optimization 21 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Black-Box Optimization
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 22 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Black-Box Optimization
Black-Box Process
They are known from their inputs and outputs
Little is known of how it works internally
David Gutierrez Rivera Aerodynamic Shape Optimization 23 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Black-Box Optimization
David Gutierrez Rivera Aerodynamic Shape Optimization 23 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Black-Box Optimization
David Gutierrez Rivera Aerodynamic Shape Optimization 24 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Noisy Functions
David Gutierrez Rivera Aerodynamic Shape Optimization 25 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Simulation-based Optimization
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 26 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Simulation-based Optimization
David Gutierrez Rivera Aerodynamic Shape Optimization 27 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Moving Boundary Problem
David Gutierrez Rivera Aerodynamic Shape Optimization 28 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
OptiFlow
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 29 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Examples
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 30 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
M4 Neath Viaduct Wind Shield
Description
This bridge is located in South Wales and crosses the River Neath Asection of the bridge is very exposed in flat topography therefore a windshielding system is desired for reducing the overturning forces on vehicles
Description
The CFD model is the same as the one used on the VXFlow tutorial
Four small sections were used to obtain the interior drag forces
David Gutierrez Rivera Aerodynamic Shape Optimization 31 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
M4 Neath Viaduct Wind Shield
Description
The CFD model is the same as the one used on the VXFlow tutorial
Four small sections were used to obtain the interior drag forces
David Gutierrez Rivera Aerodynamic Shape Optimization 31 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
M4 Neath Viaduct Wind Shield
Description
The CFD model is the same as the one used on the VXFlow tutorial
Four small sections were used to obtain the interior drag forces
David Gutierrez Rivera Aerodynamic Shape Optimization 31 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Model
Find optimum height (h) for the Wind Shield
David Gutierrez Rivera Aerodynamic Shape Optimization 32 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Parameter File
Variables Definitions[beginvariables]define(h ) Height of Wind Screen[endvariables]define(L 300) Wind Screen Lengthdefine(t 015) Wind Screen Width Wind Screen Coordinatesdefine(x1 calc(0minus1300))define(x2 calc(x1minust))define(y1 calc(hminus025))define(y2 calc(y1+L))
4 num cornerpointsSCREEN3(SCHEME3)03 00 release distancespacing hull002 0001 00 minus01 merg1merg2merg3merg4minus4 minus3 minus1 minus3 minus1 section color codingdragliftmomentdisplrotation1 x2 y1 n11 x1 y1 n21 x1 y2 n11 x2 y2 n2
David Gutierrez Rivera Aerodynamic Shape Optimization 33 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Parameter File
Variables Definitions[beginvariables]define(h ) Height of Wind Screen[endvariables]define(L 300) Wind Screen Lengthdefine(t 015) Wind Screen Width Wind Screen Coordinatesdefine(x1 calc(0minus1300))define(x2 calc(x1minust))define(y1 calc(hminus025))define(y2 calc(y1+L))
4 num cornerpointsSCREEN3(SCHEME3)03 00 release distancespacing hull002 0001 00 minus01 merg1merg2merg3merg4minus4 minus3 minus1 minus3 minus1 section color codingdragliftmomentdisplrotation1 x2 y1 n11 x1 y1 n21 x1 y2 n11 x2 y2 n2
David Gutierrez Rivera Aerodynamic Shape Optimization 33 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Objective Function
function [Drag] = M4 Neath ViaductWS(X) M4 Neath ViaductWS Objective Functionsteps = 500
Drag(1) = VXF FORCES(XDRAGMAXstepsSECTION11)Drag(2) = VXF FORCES(XDRAGMAXstepsevalfalseSECTION12)Drag(3) = VXF FORCES(XDRAGMAXstepsevalfalseSECTION13)Drag(4) = VXF FORCES(XDRAGMAXstepsevalfalseSECTION14)
[DragLane] = max(Drag())
Call optiOUT to generate Plots and Output DataoptiOUT(X [Drag])
end
David Gutierrez Rivera Aerodynamic Shape Optimization 34 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Data Points
David Gutierrez Rivera Aerodynamic Shape Optimization 35 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Run-Time Optimization
David Gutierrez Rivera Aerodynamic Shape Optimization 36 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Vertical-Axis Wind Turbine (VAWT)
Description
The Savonius Wind Turbine is a Vertical-Axis Wind Turbine (VAWT)which main advantages are its reliability and practicality
David Gutierrez Rivera Aerodynamic Shape Optimization 37 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Model
Description
Find optimum values of ex and ey to maximize Torque or Power
Constrained to the shaded area
David Gutierrez Rivera Aerodynamic Shape Optimization 38 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Model
Description
Find optimum values of ex and ey to maximize Torque or Power
Constrained to the shaded area
David Gutierrez Rivera Aerodynamic Shape Optimization 38 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Dynamic Model
David Gutierrez Rivera Aerodynamic Shape Optimization 39 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Local Global
Local
Gradient-free Methods
Golden Section
Simplex
Gradient-based Methods
Gradient-Descent
Newton
David Gutierrez Rivera Aerodynamic Shape Optimization 13 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Local Global
Global
non-Heuristic Methods
Deterministic
Stochastic
Heuristic Methods
Evolutionary
Genetic AlgorithmSwarm Intelligence
Swarm Intelligence
Particle SwarmAnt Colony
David Gutierrez Rivera Aerodynamic Shape Optimization 14 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Shape Optimization
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 15 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Shape Optimization
Shape optimization is formulated as
minimizeΩ
f (Ω)
subject to
gi (Ω) le 0 i = 1 mhi (Ω) = 0 i = 1 n
(2)
where
Ω is a set of variable parameters that make up the geometry that wewant to optimize
David Gutierrez Rivera Aerodynamic Shape Optimization 16 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Shape Optimization
Shape optimization is formulated as
minimizeΩ
f (Ω)
subject to
gi (Ω) le 0 i = 1 mhi (Ω) = 0 i = 1 n
(2)
where
Ω is a set of variable parameters that make up the geometry that wewant to optimize
David Gutierrez Rivera Aerodynamic Shape Optimization 16 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Parametrization
David Gutierrez Rivera Aerodynamic Shape Optimization 17 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Parametrization
David Gutierrez Rivera Aerodynamic Shape Optimization 17 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Objective Functions
Similar to mathematical functions
They involve 3 basic operations
David Gutierrez Rivera Aerodynamic Shape Optimization 18 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Objective Functions
Similar to mathematical functions
They involve 3 basic operations
Substitution
f (x) = a0 +nsum
i=1
an middot cos(n x ) +nsum
i=1
bn middot sin(n x )
David Gutierrez Rivera Aerodynamic Shape Optimization 18 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Objective Functions
Similar to mathematical functions
They involve 3 basic operations
Substitution
f (x) = a0 +nsum
i=1
an middot cos(n 31416 ) +nsum
i=1
bn middot sin(n 31416 )
Substitution
David Gutierrez Rivera Aerodynamic Shape Optimization 18 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Objective Functions
Similar to mathematical functions
They involve 3 basic operations
Evaluation
f (x) = a0 +nsum
i=1
an middot cos(n 31416 ) +nsum
i=1
bn middot sin(n 31416 )︸ ︷︷ ︸Evaluation
David Gutierrez Rivera Aerodynamic Shape Optimization 18 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Objective Functions
Similar to mathematical functions
They involve 3 basic operations
Read Output
f (x) = Value
Read Output
David Gutierrez Rivera Aerodynamic Shape Optimization 18 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Data Gathering
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 19 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Data Gathering
David Gutierrez Rivera Aerodynamic Shape Optimization 20 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Data Gathering
Data File
It is a text-based tab-delimited file containing the data points from thevariables and the corresponding values of the objective functions
Variable1 Variable2 Variablen Objective1 ObjectivemVariable1 Variable2 Variablen Objective1 Objectivem
Variable1 Variable2 Variablen Objective1 Objectivem
David Gutierrez Rivera Aerodynamic Shape Optimization 21 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Data Gathering
Data File
It is a text-based tab-delimited file containing the data points from thevariables and the corresponding values of the objective functions
Variable1 Variable2 Variablen Objective1 ObjectivemVariable1 Variable2 Variablen Objective1 Objectivem
Variable1 Variable2 Variablen Objective1 Objectivem
David Gutierrez Rivera Aerodynamic Shape Optimization 21 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Black-Box Optimization
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 22 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Black-Box Optimization
Black-Box Process
They are known from their inputs and outputs
Little is known of how it works internally
David Gutierrez Rivera Aerodynamic Shape Optimization 23 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Black-Box Optimization
David Gutierrez Rivera Aerodynamic Shape Optimization 23 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Black-Box Optimization
David Gutierrez Rivera Aerodynamic Shape Optimization 24 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Noisy Functions
David Gutierrez Rivera Aerodynamic Shape Optimization 25 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Simulation-based Optimization
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 26 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Simulation-based Optimization
David Gutierrez Rivera Aerodynamic Shape Optimization 27 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Moving Boundary Problem
David Gutierrez Rivera Aerodynamic Shape Optimization 28 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
OptiFlow
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 29 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Examples
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 30 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
M4 Neath Viaduct Wind Shield
Description
This bridge is located in South Wales and crosses the River Neath Asection of the bridge is very exposed in flat topography therefore a windshielding system is desired for reducing the overturning forces on vehicles
Description
The CFD model is the same as the one used on the VXFlow tutorial
Four small sections were used to obtain the interior drag forces
David Gutierrez Rivera Aerodynamic Shape Optimization 31 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
M4 Neath Viaduct Wind Shield
Description
The CFD model is the same as the one used on the VXFlow tutorial
Four small sections were used to obtain the interior drag forces
David Gutierrez Rivera Aerodynamic Shape Optimization 31 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
M4 Neath Viaduct Wind Shield
Description
The CFD model is the same as the one used on the VXFlow tutorial
Four small sections were used to obtain the interior drag forces
David Gutierrez Rivera Aerodynamic Shape Optimization 31 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Model
Find optimum height (h) for the Wind Shield
David Gutierrez Rivera Aerodynamic Shape Optimization 32 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Parameter File
Variables Definitions[beginvariables]define(h ) Height of Wind Screen[endvariables]define(L 300) Wind Screen Lengthdefine(t 015) Wind Screen Width Wind Screen Coordinatesdefine(x1 calc(0minus1300))define(x2 calc(x1minust))define(y1 calc(hminus025))define(y2 calc(y1+L))
4 num cornerpointsSCREEN3(SCHEME3)03 00 release distancespacing hull002 0001 00 minus01 merg1merg2merg3merg4minus4 minus3 minus1 minus3 minus1 section color codingdragliftmomentdisplrotation1 x2 y1 n11 x1 y1 n21 x1 y2 n11 x2 y2 n2
David Gutierrez Rivera Aerodynamic Shape Optimization 33 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Parameter File
Variables Definitions[beginvariables]define(h ) Height of Wind Screen[endvariables]define(L 300) Wind Screen Lengthdefine(t 015) Wind Screen Width Wind Screen Coordinatesdefine(x1 calc(0minus1300))define(x2 calc(x1minust))define(y1 calc(hminus025))define(y2 calc(y1+L))
4 num cornerpointsSCREEN3(SCHEME3)03 00 release distancespacing hull002 0001 00 minus01 merg1merg2merg3merg4minus4 minus3 minus1 minus3 minus1 section color codingdragliftmomentdisplrotation1 x2 y1 n11 x1 y1 n21 x1 y2 n11 x2 y2 n2
David Gutierrez Rivera Aerodynamic Shape Optimization 33 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Objective Function
function [Drag] = M4 Neath ViaductWS(X) M4 Neath ViaductWS Objective Functionsteps = 500
Drag(1) = VXF FORCES(XDRAGMAXstepsSECTION11)Drag(2) = VXF FORCES(XDRAGMAXstepsevalfalseSECTION12)Drag(3) = VXF FORCES(XDRAGMAXstepsevalfalseSECTION13)Drag(4) = VXF FORCES(XDRAGMAXstepsevalfalseSECTION14)
[DragLane] = max(Drag())
Call optiOUT to generate Plots and Output DataoptiOUT(X [Drag])
end
David Gutierrez Rivera Aerodynamic Shape Optimization 34 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Data Points
David Gutierrez Rivera Aerodynamic Shape Optimization 35 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Run-Time Optimization
David Gutierrez Rivera Aerodynamic Shape Optimization 36 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Vertical-Axis Wind Turbine (VAWT)
Description
The Savonius Wind Turbine is a Vertical-Axis Wind Turbine (VAWT)which main advantages are its reliability and practicality
David Gutierrez Rivera Aerodynamic Shape Optimization 37 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Model
Description
Find optimum values of ex and ey to maximize Torque or Power
Constrained to the shaded area
David Gutierrez Rivera Aerodynamic Shape Optimization 38 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Model
Description
Find optimum values of ex and ey to maximize Torque or Power
Constrained to the shaded area
David Gutierrez Rivera Aerodynamic Shape Optimization 38 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Dynamic Model
David Gutierrez Rivera Aerodynamic Shape Optimization 39 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Local Global
Global
non-Heuristic Methods
Deterministic
Stochastic
Heuristic Methods
Evolutionary
Genetic AlgorithmSwarm Intelligence
Swarm Intelligence
Particle SwarmAnt Colony
David Gutierrez Rivera Aerodynamic Shape Optimization 14 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Shape Optimization
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 15 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Shape Optimization
Shape optimization is formulated as
minimizeΩ
f (Ω)
subject to
gi (Ω) le 0 i = 1 mhi (Ω) = 0 i = 1 n
(2)
where
Ω is a set of variable parameters that make up the geometry that wewant to optimize
David Gutierrez Rivera Aerodynamic Shape Optimization 16 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Shape Optimization
Shape optimization is formulated as
minimizeΩ
f (Ω)
subject to
gi (Ω) le 0 i = 1 mhi (Ω) = 0 i = 1 n
(2)
where
Ω is a set of variable parameters that make up the geometry that wewant to optimize
David Gutierrez Rivera Aerodynamic Shape Optimization 16 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Parametrization
David Gutierrez Rivera Aerodynamic Shape Optimization 17 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Parametrization
David Gutierrez Rivera Aerodynamic Shape Optimization 17 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Objective Functions
Similar to mathematical functions
They involve 3 basic operations
David Gutierrez Rivera Aerodynamic Shape Optimization 18 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Objective Functions
Similar to mathematical functions
They involve 3 basic operations
Substitution
f (x) = a0 +nsum
i=1
an middot cos(n x ) +nsum
i=1
bn middot sin(n x )
David Gutierrez Rivera Aerodynamic Shape Optimization 18 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Objective Functions
Similar to mathematical functions
They involve 3 basic operations
Substitution
f (x) = a0 +nsum
i=1
an middot cos(n 31416 ) +nsum
i=1
bn middot sin(n 31416 )
Substitution
David Gutierrez Rivera Aerodynamic Shape Optimization 18 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Objective Functions
Similar to mathematical functions
They involve 3 basic operations
Evaluation
f (x) = a0 +nsum
i=1
an middot cos(n 31416 ) +nsum
i=1
bn middot sin(n 31416 )︸ ︷︷ ︸Evaluation
David Gutierrez Rivera Aerodynamic Shape Optimization 18 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Objective Functions
Similar to mathematical functions
They involve 3 basic operations
Read Output
f (x) = Value
Read Output
David Gutierrez Rivera Aerodynamic Shape Optimization 18 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Data Gathering
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 19 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Data Gathering
David Gutierrez Rivera Aerodynamic Shape Optimization 20 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Data Gathering
Data File
It is a text-based tab-delimited file containing the data points from thevariables and the corresponding values of the objective functions
Variable1 Variable2 Variablen Objective1 ObjectivemVariable1 Variable2 Variablen Objective1 Objectivem
Variable1 Variable2 Variablen Objective1 Objectivem
David Gutierrez Rivera Aerodynamic Shape Optimization 21 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Data Gathering
Data File
It is a text-based tab-delimited file containing the data points from thevariables and the corresponding values of the objective functions
Variable1 Variable2 Variablen Objective1 ObjectivemVariable1 Variable2 Variablen Objective1 Objectivem
Variable1 Variable2 Variablen Objective1 Objectivem
David Gutierrez Rivera Aerodynamic Shape Optimization 21 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Black-Box Optimization
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 22 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Black-Box Optimization
Black-Box Process
They are known from their inputs and outputs
Little is known of how it works internally
David Gutierrez Rivera Aerodynamic Shape Optimization 23 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Black-Box Optimization
David Gutierrez Rivera Aerodynamic Shape Optimization 23 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Black-Box Optimization
David Gutierrez Rivera Aerodynamic Shape Optimization 24 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Noisy Functions
David Gutierrez Rivera Aerodynamic Shape Optimization 25 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Simulation-based Optimization
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 26 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Simulation-based Optimization
David Gutierrez Rivera Aerodynamic Shape Optimization 27 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Moving Boundary Problem
David Gutierrez Rivera Aerodynamic Shape Optimization 28 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
OptiFlow
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 29 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Examples
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 30 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
M4 Neath Viaduct Wind Shield
Description
This bridge is located in South Wales and crosses the River Neath Asection of the bridge is very exposed in flat topography therefore a windshielding system is desired for reducing the overturning forces on vehicles
Description
The CFD model is the same as the one used on the VXFlow tutorial
Four small sections were used to obtain the interior drag forces
David Gutierrez Rivera Aerodynamic Shape Optimization 31 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
M4 Neath Viaduct Wind Shield
Description
The CFD model is the same as the one used on the VXFlow tutorial
Four small sections were used to obtain the interior drag forces
David Gutierrez Rivera Aerodynamic Shape Optimization 31 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
M4 Neath Viaduct Wind Shield
Description
The CFD model is the same as the one used on the VXFlow tutorial
Four small sections were used to obtain the interior drag forces
David Gutierrez Rivera Aerodynamic Shape Optimization 31 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Model
Find optimum height (h) for the Wind Shield
David Gutierrez Rivera Aerodynamic Shape Optimization 32 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Parameter File
Variables Definitions[beginvariables]define(h ) Height of Wind Screen[endvariables]define(L 300) Wind Screen Lengthdefine(t 015) Wind Screen Width Wind Screen Coordinatesdefine(x1 calc(0minus1300))define(x2 calc(x1minust))define(y1 calc(hminus025))define(y2 calc(y1+L))
4 num cornerpointsSCREEN3(SCHEME3)03 00 release distancespacing hull002 0001 00 minus01 merg1merg2merg3merg4minus4 minus3 minus1 minus3 minus1 section color codingdragliftmomentdisplrotation1 x2 y1 n11 x1 y1 n21 x1 y2 n11 x2 y2 n2
David Gutierrez Rivera Aerodynamic Shape Optimization 33 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Parameter File
Variables Definitions[beginvariables]define(h ) Height of Wind Screen[endvariables]define(L 300) Wind Screen Lengthdefine(t 015) Wind Screen Width Wind Screen Coordinatesdefine(x1 calc(0minus1300))define(x2 calc(x1minust))define(y1 calc(hminus025))define(y2 calc(y1+L))
4 num cornerpointsSCREEN3(SCHEME3)03 00 release distancespacing hull002 0001 00 minus01 merg1merg2merg3merg4minus4 minus3 minus1 minus3 minus1 section color codingdragliftmomentdisplrotation1 x2 y1 n11 x1 y1 n21 x1 y2 n11 x2 y2 n2
David Gutierrez Rivera Aerodynamic Shape Optimization 33 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Objective Function
function [Drag] = M4 Neath ViaductWS(X) M4 Neath ViaductWS Objective Functionsteps = 500
Drag(1) = VXF FORCES(XDRAGMAXstepsSECTION11)Drag(2) = VXF FORCES(XDRAGMAXstepsevalfalseSECTION12)Drag(3) = VXF FORCES(XDRAGMAXstepsevalfalseSECTION13)Drag(4) = VXF FORCES(XDRAGMAXstepsevalfalseSECTION14)
[DragLane] = max(Drag())
Call optiOUT to generate Plots and Output DataoptiOUT(X [Drag])
end
David Gutierrez Rivera Aerodynamic Shape Optimization 34 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Data Points
David Gutierrez Rivera Aerodynamic Shape Optimization 35 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Run-Time Optimization
David Gutierrez Rivera Aerodynamic Shape Optimization 36 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Vertical-Axis Wind Turbine (VAWT)
Description
The Savonius Wind Turbine is a Vertical-Axis Wind Turbine (VAWT)which main advantages are its reliability and practicality
David Gutierrez Rivera Aerodynamic Shape Optimization 37 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Model
Description
Find optimum values of ex and ey to maximize Torque or Power
Constrained to the shaded area
David Gutierrez Rivera Aerodynamic Shape Optimization 38 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Model
Description
Find optimum values of ex and ey to maximize Torque or Power
Constrained to the shaded area
David Gutierrez Rivera Aerodynamic Shape Optimization 38 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Dynamic Model
David Gutierrez Rivera Aerodynamic Shape Optimization 39 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Shape Optimization
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 15 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Shape Optimization
Shape optimization is formulated as
minimizeΩ
f (Ω)
subject to
gi (Ω) le 0 i = 1 mhi (Ω) = 0 i = 1 n
(2)
where
Ω is a set of variable parameters that make up the geometry that wewant to optimize
David Gutierrez Rivera Aerodynamic Shape Optimization 16 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Shape Optimization
Shape optimization is formulated as
minimizeΩ
f (Ω)
subject to
gi (Ω) le 0 i = 1 mhi (Ω) = 0 i = 1 n
(2)
where
Ω is a set of variable parameters that make up the geometry that wewant to optimize
David Gutierrez Rivera Aerodynamic Shape Optimization 16 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Parametrization
David Gutierrez Rivera Aerodynamic Shape Optimization 17 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Parametrization
David Gutierrez Rivera Aerodynamic Shape Optimization 17 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Objective Functions
Similar to mathematical functions
They involve 3 basic operations
David Gutierrez Rivera Aerodynamic Shape Optimization 18 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Objective Functions
Similar to mathematical functions
They involve 3 basic operations
Substitution
f (x) = a0 +nsum
i=1
an middot cos(n x ) +nsum
i=1
bn middot sin(n x )
David Gutierrez Rivera Aerodynamic Shape Optimization 18 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Objective Functions
Similar to mathematical functions
They involve 3 basic operations
Substitution
f (x) = a0 +nsum
i=1
an middot cos(n 31416 ) +nsum
i=1
bn middot sin(n 31416 )
Substitution
David Gutierrez Rivera Aerodynamic Shape Optimization 18 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Objective Functions
Similar to mathematical functions
They involve 3 basic operations
Evaluation
f (x) = a0 +nsum
i=1
an middot cos(n 31416 ) +nsum
i=1
bn middot sin(n 31416 )︸ ︷︷ ︸Evaluation
David Gutierrez Rivera Aerodynamic Shape Optimization 18 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Objective Functions
Similar to mathematical functions
They involve 3 basic operations
Read Output
f (x) = Value
Read Output
David Gutierrez Rivera Aerodynamic Shape Optimization 18 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Data Gathering
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 19 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Data Gathering
David Gutierrez Rivera Aerodynamic Shape Optimization 20 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Data Gathering
Data File
It is a text-based tab-delimited file containing the data points from thevariables and the corresponding values of the objective functions
Variable1 Variable2 Variablen Objective1 ObjectivemVariable1 Variable2 Variablen Objective1 Objectivem
Variable1 Variable2 Variablen Objective1 Objectivem
David Gutierrez Rivera Aerodynamic Shape Optimization 21 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Data Gathering
Data File
It is a text-based tab-delimited file containing the data points from thevariables and the corresponding values of the objective functions
Variable1 Variable2 Variablen Objective1 ObjectivemVariable1 Variable2 Variablen Objective1 Objectivem
Variable1 Variable2 Variablen Objective1 Objectivem
David Gutierrez Rivera Aerodynamic Shape Optimization 21 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Black-Box Optimization
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 22 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Black-Box Optimization
Black-Box Process
They are known from their inputs and outputs
Little is known of how it works internally
David Gutierrez Rivera Aerodynamic Shape Optimization 23 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Black-Box Optimization
David Gutierrez Rivera Aerodynamic Shape Optimization 23 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Black-Box Optimization
David Gutierrez Rivera Aerodynamic Shape Optimization 24 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Noisy Functions
David Gutierrez Rivera Aerodynamic Shape Optimization 25 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Simulation-based Optimization
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 26 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Simulation-based Optimization
David Gutierrez Rivera Aerodynamic Shape Optimization 27 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Moving Boundary Problem
David Gutierrez Rivera Aerodynamic Shape Optimization 28 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
OptiFlow
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 29 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Examples
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 30 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
M4 Neath Viaduct Wind Shield
Description
This bridge is located in South Wales and crosses the River Neath Asection of the bridge is very exposed in flat topography therefore a windshielding system is desired for reducing the overturning forces on vehicles
Description
The CFD model is the same as the one used on the VXFlow tutorial
Four small sections were used to obtain the interior drag forces
David Gutierrez Rivera Aerodynamic Shape Optimization 31 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
M4 Neath Viaduct Wind Shield
Description
The CFD model is the same as the one used on the VXFlow tutorial
Four small sections were used to obtain the interior drag forces
David Gutierrez Rivera Aerodynamic Shape Optimization 31 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
M4 Neath Viaduct Wind Shield
Description
The CFD model is the same as the one used on the VXFlow tutorial
Four small sections were used to obtain the interior drag forces
David Gutierrez Rivera Aerodynamic Shape Optimization 31 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Model
Find optimum height (h) for the Wind Shield
David Gutierrez Rivera Aerodynamic Shape Optimization 32 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Parameter File
Variables Definitions[beginvariables]define(h ) Height of Wind Screen[endvariables]define(L 300) Wind Screen Lengthdefine(t 015) Wind Screen Width Wind Screen Coordinatesdefine(x1 calc(0minus1300))define(x2 calc(x1minust))define(y1 calc(hminus025))define(y2 calc(y1+L))
4 num cornerpointsSCREEN3(SCHEME3)03 00 release distancespacing hull002 0001 00 minus01 merg1merg2merg3merg4minus4 minus3 minus1 minus3 minus1 section color codingdragliftmomentdisplrotation1 x2 y1 n11 x1 y1 n21 x1 y2 n11 x2 y2 n2
David Gutierrez Rivera Aerodynamic Shape Optimization 33 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Parameter File
Variables Definitions[beginvariables]define(h ) Height of Wind Screen[endvariables]define(L 300) Wind Screen Lengthdefine(t 015) Wind Screen Width Wind Screen Coordinatesdefine(x1 calc(0minus1300))define(x2 calc(x1minust))define(y1 calc(hminus025))define(y2 calc(y1+L))
4 num cornerpointsSCREEN3(SCHEME3)03 00 release distancespacing hull002 0001 00 minus01 merg1merg2merg3merg4minus4 minus3 minus1 minus3 minus1 section color codingdragliftmomentdisplrotation1 x2 y1 n11 x1 y1 n21 x1 y2 n11 x2 y2 n2
David Gutierrez Rivera Aerodynamic Shape Optimization 33 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Objective Function
function [Drag] = M4 Neath ViaductWS(X) M4 Neath ViaductWS Objective Functionsteps = 500
Drag(1) = VXF FORCES(XDRAGMAXstepsSECTION11)Drag(2) = VXF FORCES(XDRAGMAXstepsevalfalseSECTION12)Drag(3) = VXF FORCES(XDRAGMAXstepsevalfalseSECTION13)Drag(4) = VXF FORCES(XDRAGMAXstepsevalfalseSECTION14)
[DragLane] = max(Drag())
Call optiOUT to generate Plots and Output DataoptiOUT(X [Drag])
end
David Gutierrez Rivera Aerodynamic Shape Optimization 34 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Data Points
David Gutierrez Rivera Aerodynamic Shape Optimization 35 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Run-Time Optimization
David Gutierrez Rivera Aerodynamic Shape Optimization 36 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Vertical-Axis Wind Turbine (VAWT)
Description
The Savonius Wind Turbine is a Vertical-Axis Wind Turbine (VAWT)which main advantages are its reliability and practicality
David Gutierrez Rivera Aerodynamic Shape Optimization 37 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Model
Description
Find optimum values of ex and ey to maximize Torque or Power
Constrained to the shaded area
David Gutierrez Rivera Aerodynamic Shape Optimization 38 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Model
Description
Find optimum values of ex and ey to maximize Torque or Power
Constrained to the shaded area
David Gutierrez Rivera Aerodynamic Shape Optimization 38 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Dynamic Model
David Gutierrez Rivera Aerodynamic Shape Optimization 39 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Shape Optimization
Shape optimization is formulated as
minimizeΩ
f (Ω)
subject to
gi (Ω) le 0 i = 1 mhi (Ω) = 0 i = 1 n
(2)
where
Ω is a set of variable parameters that make up the geometry that wewant to optimize
David Gutierrez Rivera Aerodynamic Shape Optimization 16 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Shape Optimization
Shape optimization is formulated as
minimizeΩ
f (Ω)
subject to
gi (Ω) le 0 i = 1 mhi (Ω) = 0 i = 1 n
(2)
where
Ω is a set of variable parameters that make up the geometry that wewant to optimize
David Gutierrez Rivera Aerodynamic Shape Optimization 16 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Parametrization
David Gutierrez Rivera Aerodynamic Shape Optimization 17 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Parametrization
David Gutierrez Rivera Aerodynamic Shape Optimization 17 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Objective Functions
Similar to mathematical functions
They involve 3 basic operations
David Gutierrez Rivera Aerodynamic Shape Optimization 18 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Objective Functions
Similar to mathematical functions
They involve 3 basic operations
Substitution
f (x) = a0 +nsum
i=1
an middot cos(n x ) +nsum
i=1
bn middot sin(n x )
David Gutierrez Rivera Aerodynamic Shape Optimization 18 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Objective Functions
Similar to mathematical functions
They involve 3 basic operations
Substitution
f (x) = a0 +nsum
i=1
an middot cos(n 31416 ) +nsum
i=1
bn middot sin(n 31416 )
Substitution
David Gutierrez Rivera Aerodynamic Shape Optimization 18 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Objective Functions
Similar to mathematical functions
They involve 3 basic operations
Evaluation
f (x) = a0 +nsum
i=1
an middot cos(n 31416 ) +nsum
i=1
bn middot sin(n 31416 )︸ ︷︷ ︸Evaluation
David Gutierrez Rivera Aerodynamic Shape Optimization 18 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Objective Functions
Similar to mathematical functions
They involve 3 basic operations
Read Output
f (x) = Value
Read Output
David Gutierrez Rivera Aerodynamic Shape Optimization 18 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Data Gathering
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 19 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Data Gathering
David Gutierrez Rivera Aerodynamic Shape Optimization 20 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Data Gathering
Data File
It is a text-based tab-delimited file containing the data points from thevariables and the corresponding values of the objective functions
Variable1 Variable2 Variablen Objective1 ObjectivemVariable1 Variable2 Variablen Objective1 Objectivem
Variable1 Variable2 Variablen Objective1 Objectivem
David Gutierrez Rivera Aerodynamic Shape Optimization 21 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Data Gathering
Data File
It is a text-based tab-delimited file containing the data points from thevariables and the corresponding values of the objective functions
Variable1 Variable2 Variablen Objective1 ObjectivemVariable1 Variable2 Variablen Objective1 Objectivem
Variable1 Variable2 Variablen Objective1 Objectivem
David Gutierrez Rivera Aerodynamic Shape Optimization 21 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Black-Box Optimization
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 22 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Black-Box Optimization
Black-Box Process
They are known from their inputs and outputs
Little is known of how it works internally
David Gutierrez Rivera Aerodynamic Shape Optimization 23 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Black-Box Optimization
David Gutierrez Rivera Aerodynamic Shape Optimization 23 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Black-Box Optimization
David Gutierrez Rivera Aerodynamic Shape Optimization 24 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Noisy Functions
David Gutierrez Rivera Aerodynamic Shape Optimization 25 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Simulation-based Optimization
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 26 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Simulation-based Optimization
David Gutierrez Rivera Aerodynamic Shape Optimization 27 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Moving Boundary Problem
David Gutierrez Rivera Aerodynamic Shape Optimization 28 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
OptiFlow
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 29 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Examples
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 30 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
M4 Neath Viaduct Wind Shield
Description
This bridge is located in South Wales and crosses the River Neath Asection of the bridge is very exposed in flat topography therefore a windshielding system is desired for reducing the overturning forces on vehicles
Description
The CFD model is the same as the one used on the VXFlow tutorial
Four small sections were used to obtain the interior drag forces
David Gutierrez Rivera Aerodynamic Shape Optimization 31 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
M4 Neath Viaduct Wind Shield
Description
The CFD model is the same as the one used on the VXFlow tutorial
Four small sections were used to obtain the interior drag forces
David Gutierrez Rivera Aerodynamic Shape Optimization 31 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
M4 Neath Viaduct Wind Shield
Description
The CFD model is the same as the one used on the VXFlow tutorial
Four small sections were used to obtain the interior drag forces
David Gutierrez Rivera Aerodynamic Shape Optimization 31 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Model
Find optimum height (h) for the Wind Shield
David Gutierrez Rivera Aerodynamic Shape Optimization 32 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Parameter File
Variables Definitions[beginvariables]define(h ) Height of Wind Screen[endvariables]define(L 300) Wind Screen Lengthdefine(t 015) Wind Screen Width Wind Screen Coordinatesdefine(x1 calc(0minus1300))define(x2 calc(x1minust))define(y1 calc(hminus025))define(y2 calc(y1+L))
4 num cornerpointsSCREEN3(SCHEME3)03 00 release distancespacing hull002 0001 00 minus01 merg1merg2merg3merg4minus4 minus3 minus1 minus3 minus1 section color codingdragliftmomentdisplrotation1 x2 y1 n11 x1 y1 n21 x1 y2 n11 x2 y2 n2
David Gutierrez Rivera Aerodynamic Shape Optimization 33 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Parameter File
Variables Definitions[beginvariables]define(h ) Height of Wind Screen[endvariables]define(L 300) Wind Screen Lengthdefine(t 015) Wind Screen Width Wind Screen Coordinatesdefine(x1 calc(0minus1300))define(x2 calc(x1minust))define(y1 calc(hminus025))define(y2 calc(y1+L))
4 num cornerpointsSCREEN3(SCHEME3)03 00 release distancespacing hull002 0001 00 minus01 merg1merg2merg3merg4minus4 minus3 minus1 minus3 minus1 section color codingdragliftmomentdisplrotation1 x2 y1 n11 x1 y1 n21 x1 y2 n11 x2 y2 n2
David Gutierrez Rivera Aerodynamic Shape Optimization 33 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Objective Function
function [Drag] = M4 Neath ViaductWS(X) M4 Neath ViaductWS Objective Functionsteps = 500
Drag(1) = VXF FORCES(XDRAGMAXstepsSECTION11)Drag(2) = VXF FORCES(XDRAGMAXstepsevalfalseSECTION12)Drag(3) = VXF FORCES(XDRAGMAXstepsevalfalseSECTION13)Drag(4) = VXF FORCES(XDRAGMAXstepsevalfalseSECTION14)
[DragLane] = max(Drag())
Call optiOUT to generate Plots and Output DataoptiOUT(X [Drag])
end
David Gutierrez Rivera Aerodynamic Shape Optimization 34 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Data Points
David Gutierrez Rivera Aerodynamic Shape Optimization 35 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Run-Time Optimization
David Gutierrez Rivera Aerodynamic Shape Optimization 36 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Vertical-Axis Wind Turbine (VAWT)
Description
The Savonius Wind Turbine is a Vertical-Axis Wind Turbine (VAWT)which main advantages are its reliability and practicality
David Gutierrez Rivera Aerodynamic Shape Optimization 37 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Model
Description
Find optimum values of ex and ey to maximize Torque or Power
Constrained to the shaded area
David Gutierrez Rivera Aerodynamic Shape Optimization 38 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Model
Description
Find optimum values of ex and ey to maximize Torque or Power
Constrained to the shaded area
David Gutierrez Rivera Aerodynamic Shape Optimization 38 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Dynamic Model
David Gutierrez Rivera Aerodynamic Shape Optimization 39 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Shape Optimization
Shape optimization is formulated as
minimizeΩ
f (Ω)
subject to
gi (Ω) le 0 i = 1 mhi (Ω) = 0 i = 1 n
(2)
where
Ω is a set of variable parameters that make up the geometry that wewant to optimize
David Gutierrez Rivera Aerodynamic Shape Optimization 16 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Parametrization
David Gutierrez Rivera Aerodynamic Shape Optimization 17 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Parametrization
David Gutierrez Rivera Aerodynamic Shape Optimization 17 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Objective Functions
Similar to mathematical functions
They involve 3 basic operations
David Gutierrez Rivera Aerodynamic Shape Optimization 18 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Objective Functions
Similar to mathematical functions
They involve 3 basic operations
Substitution
f (x) = a0 +nsum
i=1
an middot cos(n x ) +nsum
i=1
bn middot sin(n x )
David Gutierrez Rivera Aerodynamic Shape Optimization 18 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Objective Functions
Similar to mathematical functions
They involve 3 basic operations
Substitution
f (x) = a0 +nsum
i=1
an middot cos(n 31416 ) +nsum
i=1
bn middot sin(n 31416 )
Substitution
David Gutierrez Rivera Aerodynamic Shape Optimization 18 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Objective Functions
Similar to mathematical functions
They involve 3 basic operations
Evaluation
f (x) = a0 +nsum
i=1
an middot cos(n 31416 ) +nsum
i=1
bn middot sin(n 31416 )︸ ︷︷ ︸Evaluation
David Gutierrez Rivera Aerodynamic Shape Optimization 18 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Objective Functions
Similar to mathematical functions
They involve 3 basic operations
Read Output
f (x) = Value
Read Output
David Gutierrez Rivera Aerodynamic Shape Optimization 18 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Data Gathering
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 19 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Data Gathering
David Gutierrez Rivera Aerodynamic Shape Optimization 20 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Data Gathering
Data File
It is a text-based tab-delimited file containing the data points from thevariables and the corresponding values of the objective functions
Variable1 Variable2 Variablen Objective1 ObjectivemVariable1 Variable2 Variablen Objective1 Objectivem
Variable1 Variable2 Variablen Objective1 Objectivem
David Gutierrez Rivera Aerodynamic Shape Optimization 21 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Data Gathering
Data File
It is a text-based tab-delimited file containing the data points from thevariables and the corresponding values of the objective functions
Variable1 Variable2 Variablen Objective1 ObjectivemVariable1 Variable2 Variablen Objective1 Objectivem
Variable1 Variable2 Variablen Objective1 Objectivem
David Gutierrez Rivera Aerodynamic Shape Optimization 21 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Black-Box Optimization
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 22 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Black-Box Optimization
Black-Box Process
They are known from their inputs and outputs
Little is known of how it works internally
David Gutierrez Rivera Aerodynamic Shape Optimization 23 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Black-Box Optimization
David Gutierrez Rivera Aerodynamic Shape Optimization 23 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Black-Box Optimization
David Gutierrez Rivera Aerodynamic Shape Optimization 24 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Noisy Functions
David Gutierrez Rivera Aerodynamic Shape Optimization 25 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Simulation-based Optimization
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 26 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Simulation-based Optimization
David Gutierrez Rivera Aerodynamic Shape Optimization 27 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Moving Boundary Problem
David Gutierrez Rivera Aerodynamic Shape Optimization 28 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
OptiFlow
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 29 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Examples
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 30 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
M4 Neath Viaduct Wind Shield
Description
This bridge is located in South Wales and crosses the River Neath Asection of the bridge is very exposed in flat topography therefore a windshielding system is desired for reducing the overturning forces on vehicles
Description
The CFD model is the same as the one used on the VXFlow tutorial
Four small sections were used to obtain the interior drag forces
David Gutierrez Rivera Aerodynamic Shape Optimization 31 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
M4 Neath Viaduct Wind Shield
Description
The CFD model is the same as the one used on the VXFlow tutorial
Four small sections were used to obtain the interior drag forces
David Gutierrez Rivera Aerodynamic Shape Optimization 31 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
M4 Neath Viaduct Wind Shield
Description
The CFD model is the same as the one used on the VXFlow tutorial
Four small sections were used to obtain the interior drag forces
David Gutierrez Rivera Aerodynamic Shape Optimization 31 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Model
Find optimum height (h) for the Wind Shield
David Gutierrez Rivera Aerodynamic Shape Optimization 32 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Parameter File
Variables Definitions[beginvariables]define(h ) Height of Wind Screen[endvariables]define(L 300) Wind Screen Lengthdefine(t 015) Wind Screen Width Wind Screen Coordinatesdefine(x1 calc(0minus1300))define(x2 calc(x1minust))define(y1 calc(hminus025))define(y2 calc(y1+L))
4 num cornerpointsSCREEN3(SCHEME3)03 00 release distancespacing hull002 0001 00 minus01 merg1merg2merg3merg4minus4 minus3 minus1 minus3 minus1 section color codingdragliftmomentdisplrotation1 x2 y1 n11 x1 y1 n21 x1 y2 n11 x2 y2 n2
David Gutierrez Rivera Aerodynamic Shape Optimization 33 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Parameter File
Variables Definitions[beginvariables]define(h ) Height of Wind Screen[endvariables]define(L 300) Wind Screen Lengthdefine(t 015) Wind Screen Width Wind Screen Coordinatesdefine(x1 calc(0minus1300))define(x2 calc(x1minust))define(y1 calc(hminus025))define(y2 calc(y1+L))
4 num cornerpointsSCREEN3(SCHEME3)03 00 release distancespacing hull002 0001 00 minus01 merg1merg2merg3merg4minus4 minus3 minus1 minus3 minus1 section color codingdragliftmomentdisplrotation1 x2 y1 n11 x1 y1 n21 x1 y2 n11 x2 y2 n2
David Gutierrez Rivera Aerodynamic Shape Optimization 33 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Objective Function
function [Drag] = M4 Neath ViaductWS(X) M4 Neath ViaductWS Objective Functionsteps = 500
Drag(1) = VXF FORCES(XDRAGMAXstepsSECTION11)Drag(2) = VXF FORCES(XDRAGMAXstepsevalfalseSECTION12)Drag(3) = VXF FORCES(XDRAGMAXstepsevalfalseSECTION13)Drag(4) = VXF FORCES(XDRAGMAXstepsevalfalseSECTION14)
[DragLane] = max(Drag())
Call optiOUT to generate Plots and Output DataoptiOUT(X [Drag])
end
David Gutierrez Rivera Aerodynamic Shape Optimization 34 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Data Points
David Gutierrez Rivera Aerodynamic Shape Optimization 35 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Run-Time Optimization
David Gutierrez Rivera Aerodynamic Shape Optimization 36 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Vertical-Axis Wind Turbine (VAWT)
Description
The Savonius Wind Turbine is a Vertical-Axis Wind Turbine (VAWT)which main advantages are its reliability and practicality
David Gutierrez Rivera Aerodynamic Shape Optimization 37 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Model
Description
Find optimum values of ex and ey to maximize Torque or Power
Constrained to the shaded area
David Gutierrez Rivera Aerodynamic Shape Optimization 38 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Model
Description
Find optimum values of ex and ey to maximize Torque or Power
Constrained to the shaded area
David Gutierrez Rivera Aerodynamic Shape Optimization 38 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Dynamic Model
David Gutierrez Rivera Aerodynamic Shape Optimization 39 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Parametrization
David Gutierrez Rivera Aerodynamic Shape Optimization 17 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Parametrization
David Gutierrez Rivera Aerodynamic Shape Optimization 17 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Objective Functions
Similar to mathematical functions
They involve 3 basic operations
David Gutierrez Rivera Aerodynamic Shape Optimization 18 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Objective Functions
Similar to mathematical functions
They involve 3 basic operations
Substitution
f (x) = a0 +nsum
i=1
an middot cos(n x ) +nsum
i=1
bn middot sin(n x )
David Gutierrez Rivera Aerodynamic Shape Optimization 18 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Objective Functions
Similar to mathematical functions
They involve 3 basic operations
Substitution
f (x) = a0 +nsum
i=1
an middot cos(n 31416 ) +nsum
i=1
bn middot sin(n 31416 )
Substitution
David Gutierrez Rivera Aerodynamic Shape Optimization 18 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Objective Functions
Similar to mathematical functions
They involve 3 basic operations
Evaluation
f (x) = a0 +nsum
i=1
an middot cos(n 31416 ) +nsum
i=1
bn middot sin(n 31416 )︸ ︷︷ ︸Evaluation
David Gutierrez Rivera Aerodynamic Shape Optimization 18 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Objective Functions
Similar to mathematical functions
They involve 3 basic operations
Read Output
f (x) = Value
Read Output
David Gutierrez Rivera Aerodynamic Shape Optimization 18 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Data Gathering
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 19 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Data Gathering
David Gutierrez Rivera Aerodynamic Shape Optimization 20 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Data Gathering
Data File
It is a text-based tab-delimited file containing the data points from thevariables and the corresponding values of the objective functions
Variable1 Variable2 Variablen Objective1 ObjectivemVariable1 Variable2 Variablen Objective1 Objectivem
Variable1 Variable2 Variablen Objective1 Objectivem
David Gutierrez Rivera Aerodynamic Shape Optimization 21 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Data Gathering
Data File
It is a text-based tab-delimited file containing the data points from thevariables and the corresponding values of the objective functions
Variable1 Variable2 Variablen Objective1 ObjectivemVariable1 Variable2 Variablen Objective1 Objectivem
Variable1 Variable2 Variablen Objective1 Objectivem
David Gutierrez Rivera Aerodynamic Shape Optimization 21 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Black-Box Optimization
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 22 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Black-Box Optimization
Black-Box Process
They are known from their inputs and outputs
Little is known of how it works internally
David Gutierrez Rivera Aerodynamic Shape Optimization 23 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Black-Box Optimization
David Gutierrez Rivera Aerodynamic Shape Optimization 23 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Black-Box Optimization
David Gutierrez Rivera Aerodynamic Shape Optimization 24 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Noisy Functions
David Gutierrez Rivera Aerodynamic Shape Optimization 25 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Simulation-based Optimization
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 26 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Simulation-based Optimization
David Gutierrez Rivera Aerodynamic Shape Optimization 27 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Moving Boundary Problem
David Gutierrez Rivera Aerodynamic Shape Optimization 28 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
OptiFlow
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 29 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Examples
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 30 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
M4 Neath Viaduct Wind Shield
Description
This bridge is located in South Wales and crosses the River Neath Asection of the bridge is very exposed in flat topography therefore a windshielding system is desired for reducing the overturning forces on vehicles
Description
The CFD model is the same as the one used on the VXFlow tutorial
Four small sections were used to obtain the interior drag forces
David Gutierrez Rivera Aerodynamic Shape Optimization 31 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
M4 Neath Viaduct Wind Shield
Description
The CFD model is the same as the one used on the VXFlow tutorial
Four small sections were used to obtain the interior drag forces
David Gutierrez Rivera Aerodynamic Shape Optimization 31 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
M4 Neath Viaduct Wind Shield
Description
The CFD model is the same as the one used on the VXFlow tutorial
Four small sections were used to obtain the interior drag forces
David Gutierrez Rivera Aerodynamic Shape Optimization 31 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Model
Find optimum height (h) for the Wind Shield
David Gutierrez Rivera Aerodynamic Shape Optimization 32 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Parameter File
Variables Definitions[beginvariables]define(h ) Height of Wind Screen[endvariables]define(L 300) Wind Screen Lengthdefine(t 015) Wind Screen Width Wind Screen Coordinatesdefine(x1 calc(0minus1300))define(x2 calc(x1minust))define(y1 calc(hminus025))define(y2 calc(y1+L))
4 num cornerpointsSCREEN3(SCHEME3)03 00 release distancespacing hull002 0001 00 minus01 merg1merg2merg3merg4minus4 minus3 minus1 minus3 minus1 section color codingdragliftmomentdisplrotation1 x2 y1 n11 x1 y1 n21 x1 y2 n11 x2 y2 n2
David Gutierrez Rivera Aerodynamic Shape Optimization 33 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Parameter File
Variables Definitions[beginvariables]define(h ) Height of Wind Screen[endvariables]define(L 300) Wind Screen Lengthdefine(t 015) Wind Screen Width Wind Screen Coordinatesdefine(x1 calc(0minus1300))define(x2 calc(x1minust))define(y1 calc(hminus025))define(y2 calc(y1+L))
4 num cornerpointsSCREEN3(SCHEME3)03 00 release distancespacing hull002 0001 00 minus01 merg1merg2merg3merg4minus4 minus3 minus1 minus3 minus1 section color codingdragliftmomentdisplrotation1 x2 y1 n11 x1 y1 n21 x1 y2 n11 x2 y2 n2
David Gutierrez Rivera Aerodynamic Shape Optimization 33 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Objective Function
function [Drag] = M4 Neath ViaductWS(X) M4 Neath ViaductWS Objective Functionsteps = 500
Drag(1) = VXF FORCES(XDRAGMAXstepsSECTION11)Drag(2) = VXF FORCES(XDRAGMAXstepsevalfalseSECTION12)Drag(3) = VXF FORCES(XDRAGMAXstepsevalfalseSECTION13)Drag(4) = VXF FORCES(XDRAGMAXstepsevalfalseSECTION14)
[DragLane] = max(Drag())
Call optiOUT to generate Plots and Output DataoptiOUT(X [Drag])
end
David Gutierrez Rivera Aerodynamic Shape Optimization 34 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Data Points
David Gutierrez Rivera Aerodynamic Shape Optimization 35 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Run-Time Optimization
David Gutierrez Rivera Aerodynamic Shape Optimization 36 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Vertical-Axis Wind Turbine (VAWT)
Description
The Savonius Wind Turbine is a Vertical-Axis Wind Turbine (VAWT)which main advantages are its reliability and practicality
David Gutierrez Rivera Aerodynamic Shape Optimization 37 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Model
Description
Find optimum values of ex and ey to maximize Torque or Power
Constrained to the shaded area
David Gutierrez Rivera Aerodynamic Shape Optimization 38 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Model
Description
Find optimum values of ex and ey to maximize Torque or Power
Constrained to the shaded area
David Gutierrez Rivera Aerodynamic Shape Optimization 38 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Dynamic Model
David Gutierrez Rivera Aerodynamic Shape Optimization 39 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Parametrization
David Gutierrez Rivera Aerodynamic Shape Optimization 17 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Objective Functions
Similar to mathematical functions
They involve 3 basic operations
David Gutierrez Rivera Aerodynamic Shape Optimization 18 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Objective Functions
Similar to mathematical functions
They involve 3 basic operations
Substitution
f (x) = a0 +nsum
i=1
an middot cos(n x ) +nsum
i=1
bn middot sin(n x )
David Gutierrez Rivera Aerodynamic Shape Optimization 18 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Objective Functions
Similar to mathematical functions
They involve 3 basic operations
Substitution
f (x) = a0 +nsum
i=1
an middot cos(n 31416 ) +nsum
i=1
bn middot sin(n 31416 )
Substitution
David Gutierrez Rivera Aerodynamic Shape Optimization 18 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Objective Functions
Similar to mathematical functions
They involve 3 basic operations
Evaluation
f (x) = a0 +nsum
i=1
an middot cos(n 31416 ) +nsum
i=1
bn middot sin(n 31416 )︸ ︷︷ ︸Evaluation
David Gutierrez Rivera Aerodynamic Shape Optimization 18 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Objective Functions
Similar to mathematical functions
They involve 3 basic operations
Read Output
f (x) = Value
Read Output
David Gutierrez Rivera Aerodynamic Shape Optimization 18 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Data Gathering
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 19 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Data Gathering
David Gutierrez Rivera Aerodynamic Shape Optimization 20 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Data Gathering
Data File
It is a text-based tab-delimited file containing the data points from thevariables and the corresponding values of the objective functions
Variable1 Variable2 Variablen Objective1 ObjectivemVariable1 Variable2 Variablen Objective1 Objectivem
Variable1 Variable2 Variablen Objective1 Objectivem
David Gutierrez Rivera Aerodynamic Shape Optimization 21 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Data Gathering
Data File
It is a text-based tab-delimited file containing the data points from thevariables and the corresponding values of the objective functions
Variable1 Variable2 Variablen Objective1 ObjectivemVariable1 Variable2 Variablen Objective1 Objectivem
Variable1 Variable2 Variablen Objective1 Objectivem
David Gutierrez Rivera Aerodynamic Shape Optimization 21 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Black-Box Optimization
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 22 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Black-Box Optimization
Black-Box Process
They are known from their inputs and outputs
Little is known of how it works internally
David Gutierrez Rivera Aerodynamic Shape Optimization 23 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Black-Box Optimization
David Gutierrez Rivera Aerodynamic Shape Optimization 23 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Black-Box Optimization
David Gutierrez Rivera Aerodynamic Shape Optimization 24 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Noisy Functions
David Gutierrez Rivera Aerodynamic Shape Optimization 25 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Simulation-based Optimization
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 26 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Simulation-based Optimization
David Gutierrez Rivera Aerodynamic Shape Optimization 27 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Moving Boundary Problem
David Gutierrez Rivera Aerodynamic Shape Optimization 28 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
OptiFlow
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 29 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Examples
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 30 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
M4 Neath Viaduct Wind Shield
Description
This bridge is located in South Wales and crosses the River Neath Asection of the bridge is very exposed in flat topography therefore a windshielding system is desired for reducing the overturning forces on vehicles
Description
The CFD model is the same as the one used on the VXFlow tutorial
Four small sections were used to obtain the interior drag forces
David Gutierrez Rivera Aerodynamic Shape Optimization 31 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
M4 Neath Viaduct Wind Shield
Description
The CFD model is the same as the one used on the VXFlow tutorial
Four small sections were used to obtain the interior drag forces
David Gutierrez Rivera Aerodynamic Shape Optimization 31 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
M4 Neath Viaduct Wind Shield
Description
The CFD model is the same as the one used on the VXFlow tutorial
Four small sections were used to obtain the interior drag forces
David Gutierrez Rivera Aerodynamic Shape Optimization 31 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Model
Find optimum height (h) for the Wind Shield
David Gutierrez Rivera Aerodynamic Shape Optimization 32 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Parameter File
Variables Definitions[beginvariables]define(h ) Height of Wind Screen[endvariables]define(L 300) Wind Screen Lengthdefine(t 015) Wind Screen Width Wind Screen Coordinatesdefine(x1 calc(0minus1300))define(x2 calc(x1minust))define(y1 calc(hminus025))define(y2 calc(y1+L))
4 num cornerpointsSCREEN3(SCHEME3)03 00 release distancespacing hull002 0001 00 minus01 merg1merg2merg3merg4minus4 minus3 minus1 minus3 minus1 section color codingdragliftmomentdisplrotation1 x2 y1 n11 x1 y1 n21 x1 y2 n11 x2 y2 n2
David Gutierrez Rivera Aerodynamic Shape Optimization 33 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Parameter File
Variables Definitions[beginvariables]define(h ) Height of Wind Screen[endvariables]define(L 300) Wind Screen Lengthdefine(t 015) Wind Screen Width Wind Screen Coordinatesdefine(x1 calc(0minus1300))define(x2 calc(x1minust))define(y1 calc(hminus025))define(y2 calc(y1+L))
4 num cornerpointsSCREEN3(SCHEME3)03 00 release distancespacing hull002 0001 00 minus01 merg1merg2merg3merg4minus4 minus3 minus1 minus3 minus1 section color codingdragliftmomentdisplrotation1 x2 y1 n11 x1 y1 n21 x1 y2 n11 x2 y2 n2
David Gutierrez Rivera Aerodynamic Shape Optimization 33 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Objective Function
function [Drag] = M4 Neath ViaductWS(X) M4 Neath ViaductWS Objective Functionsteps = 500
Drag(1) = VXF FORCES(XDRAGMAXstepsSECTION11)Drag(2) = VXF FORCES(XDRAGMAXstepsevalfalseSECTION12)Drag(3) = VXF FORCES(XDRAGMAXstepsevalfalseSECTION13)Drag(4) = VXF FORCES(XDRAGMAXstepsevalfalseSECTION14)
[DragLane] = max(Drag())
Call optiOUT to generate Plots and Output DataoptiOUT(X [Drag])
end
David Gutierrez Rivera Aerodynamic Shape Optimization 34 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Data Points
David Gutierrez Rivera Aerodynamic Shape Optimization 35 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Run-Time Optimization
David Gutierrez Rivera Aerodynamic Shape Optimization 36 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Vertical-Axis Wind Turbine (VAWT)
Description
The Savonius Wind Turbine is a Vertical-Axis Wind Turbine (VAWT)which main advantages are its reliability and practicality
David Gutierrez Rivera Aerodynamic Shape Optimization 37 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Model
Description
Find optimum values of ex and ey to maximize Torque or Power
Constrained to the shaded area
David Gutierrez Rivera Aerodynamic Shape Optimization 38 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Model
Description
Find optimum values of ex and ey to maximize Torque or Power
Constrained to the shaded area
David Gutierrez Rivera Aerodynamic Shape Optimization 38 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Dynamic Model
David Gutierrez Rivera Aerodynamic Shape Optimization 39 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Objective Functions
Similar to mathematical functions
They involve 3 basic operations
David Gutierrez Rivera Aerodynamic Shape Optimization 18 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Objective Functions
Similar to mathematical functions
They involve 3 basic operations
Substitution
f (x) = a0 +nsum
i=1
an middot cos(n x ) +nsum
i=1
bn middot sin(n x )
David Gutierrez Rivera Aerodynamic Shape Optimization 18 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Objective Functions
Similar to mathematical functions
They involve 3 basic operations
Substitution
f (x) = a0 +nsum
i=1
an middot cos(n 31416 ) +nsum
i=1
bn middot sin(n 31416 )
Substitution
David Gutierrez Rivera Aerodynamic Shape Optimization 18 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Objective Functions
Similar to mathematical functions
They involve 3 basic operations
Evaluation
f (x) = a0 +nsum
i=1
an middot cos(n 31416 ) +nsum
i=1
bn middot sin(n 31416 )︸ ︷︷ ︸Evaluation
David Gutierrez Rivera Aerodynamic Shape Optimization 18 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Objective Functions
Similar to mathematical functions
They involve 3 basic operations
Read Output
f (x) = Value
Read Output
David Gutierrez Rivera Aerodynamic Shape Optimization 18 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Data Gathering
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 19 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Data Gathering
David Gutierrez Rivera Aerodynamic Shape Optimization 20 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Data Gathering
Data File
It is a text-based tab-delimited file containing the data points from thevariables and the corresponding values of the objective functions
Variable1 Variable2 Variablen Objective1 ObjectivemVariable1 Variable2 Variablen Objective1 Objectivem
Variable1 Variable2 Variablen Objective1 Objectivem
David Gutierrez Rivera Aerodynamic Shape Optimization 21 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Data Gathering
Data File
It is a text-based tab-delimited file containing the data points from thevariables and the corresponding values of the objective functions
Variable1 Variable2 Variablen Objective1 ObjectivemVariable1 Variable2 Variablen Objective1 Objectivem
Variable1 Variable2 Variablen Objective1 Objectivem
David Gutierrez Rivera Aerodynamic Shape Optimization 21 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Black-Box Optimization
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 22 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Black-Box Optimization
Black-Box Process
They are known from their inputs and outputs
Little is known of how it works internally
David Gutierrez Rivera Aerodynamic Shape Optimization 23 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Black-Box Optimization
David Gutierrez Rivera Aerodynamic Shape Optimization 23 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Black-Box Optimization
David Gutierrez Rivera Aerodynamic Shape Optimization 24 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Noisy Functions
David Gutierrez Rivera Aerodynamic Shape Optimization 25 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Simulation-based Optimization
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 26 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Simulation-based Optimization
David Gutierrez Rivera Aerodynamic Shape Optimization 27 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Moving Boundary Problem
David Gutierrez Rivera Aerodynamic Shape Optimization 28 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
OptiFlow
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 29 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Examples
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 30 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
M4 Neath Viaduct Wind Shield
Description
This bridge is located in South Wales and crosses the River Neath Asection of the bridge is very exposed in flat topography therefore a windshielding system is desired for reducing the overturning forces on vehicles
Description
The CFD model is the same as the one used on the VXFlow tutorial
Four small sections were used to obtain the interior drag forces
David Gutierrez Rivera Aerodynamic Shape Optimization 31 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
M4 Neath Viaduct Wind Shield
Description
The CFD model is the same as the one used on the VXFlow tutorial
Four small sections were used to obtain the interior drag forces
David Gutierrez Rivera Aerodynamic Shape Optimization 31 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
M4 Neath Viaduct Wind Shield
Description
The CFD model is the same as the one used on the VXFlow tutorial
Four small sections were used to obtain the interior drag forces
David Gutierrez Rivera Aerodynamic Shape Optimization 31 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Model
Find optimum height (h) for the Wind Shield
David Gutierrez Rivera Aerodynamic Shape Optimization 32 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Parameter File
Variables Definitions[beginvariables]define(h ) Height of Wind Screen[endvariables]define(L 300) Wind Screen Lengthdefine(t 015) Wind Screen Width Wind Screen Coordinatesdefine(x1 calc(0minus1300))define(x2 calc(x1minust))define(y1 calc(hminus025))define(y2 calc(y1+L))
4 num cornerpointsSCREEN3(SCHEME3)03 00 release distancespacing hull002 0001 00 minus01 merg1merg2merg3merg4minus4 minus3 minus1 minus3 minus1 section color codingdragliftmomentdisplrotation1 x2 y1 n11 x1 y1 n21 x1 y2 n11 x2 y2 n2
David Gutierrez Rivera Aerodynamic Shape Optimization 33 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Parameter File
Variables Definitions[beginvariables]define(h ) Height of Wind Screen[endvariables]define(L 300) Wind Screen Lengthdefine(t 015) Wind Screen Width Wind Screen Coordinatesdefine(x1 calc(0minus1300))define(x2 calc(x1minust))define(y1 calc(hminus025))define(y2 calc(y1+L))
4 num cornerpointsSCREEN3(SCHEME3)03 00 release distancespacing hull002 0001 00 minus01 merg1merg2merg3merg4minus4 minus3 minus1 minus3 minus1 section color codingdragliftmomentdisplrotation1 x2 y1 n11 x1 y1 n21 x1 y2 n11 x2 y2 n2
David Gutierrez Rivera Aerodynamic Shape Optimization 33 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Objective Function
function [Drag] = M4 Neath ViaductWS(X) M4 Neath ViaductWS Objective Functionsteps = 500
Drag(1) = VXF FORCES(XDRAGMAXstepsSECTION11)Drag(2) = VXF FORCES(XDRAGMAXstepsevalfalseSECTION12)Drag(3) = VXF FORCES(XDRAGMAXstepsevalfalseSECTION13)Drag(4) = VXF FORCES(XDRAGMAXstepsevalfalseSECTION14)
[DragLane] = max(Drag())
Call optiOUT to generate Plots and Output DataoptiOUT(X [Drag])
end
David Gutierrez Rivera Aerodynamic Shape Optimization 34 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Data Points
David Gutierrez Rivera Aerodynamic Shape Optimization 35 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Run-Time Optimization
David Gutierrez Rivera Aerodynamic Shape Optimization 36 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Vertical-Axis Wind Turbine (VAWT)
Description
The Savonius Wind Turbine is a Vertical-Axis Wind Turbine (VAWT)which main advantages are its reliability and practicality
David Gutierrez Rivera Aerodynamic Shape Optimization 37 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Model
Description
Find optimum values of ex and ey to maximize Torque or Power
Constrained to the shaded area
David Gutierrez Rivera Aerodynamic Shape Optimization 38 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Model
Description
Find optimum values of ex and ey to maximize Torque or Power
Constrained to the shaded area
David Gutierrez Rivera Aerodynamic Shape Optimization 38 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Dynamic Model
David Gutierrez Rivera Aerodynamic Shape Optimization 39 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Objective Functions
Similar to mathematical functions
They involve 3 basic operations
Substitution
f (x) = a0 +nsum
i=1
an middot cos(n x ) +nsum
i=1
bn middot sin(n x )
David Gutierrez Rivera Aerodynamic Shape Optimization 18 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Objective Functions
Similar to mathematical functions
They involve 3 basic operations
Substitution
f (x) = a0 +nsum
i=1
an middot cos(n 31416 ) +nsum
i=1
bn middot sin(n 31416 )
Substitution
David Gutierrez Rivera Aerodynamic Shape Optimization 18 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Objective Functions
Similar to mathematical functions
They involve 3 basic operations
Evaluation
f (x) = a0 +nsum
i=1
an middot cos(n 31416 ) +nsum
i=1
bn middot sin(n 31416 )︸ ︷︷ ︸Evaluation
David Gutierrez Rivera Aerodynamic Shape Optimization 18 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Objective Functions
Similar to mathematical functions
They involve 3 basic operations
Read Output
f (x) = Value
Read Output
David Gutierrez Rivera Aerodynamic Shape Optimization 18 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Data Gathering
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 19 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Data Gathering
David Gutierrez Rivera Aerodynamic Shape Optimization 20 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Data Gathering
Data File
It is a text-based tab-delimited file containing the data points from thevariables and the corresponding values of the objective functions
Variable1 Variable2 Variablen Objective1 ObjectivemVariable1 Variable2 Variablen Objective1 Objectivem
Variable1 Variable2 Variablen Objective1 Objectivem
David Gutierrez Rivera Aerodynamic Shape Optimization 21 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Data Gathering
Data File
It is a text-based tab-delimited file containing the data points from thevariables and the corresponding values of the objective functions
Variable1 Variable2 Variablen Objective1 ObjectivemVariable1 Variable2 Variablen Objective1 Objectivem
Variable1 Variable2 Variablen Objective1 Objectivem
David Gutierrez Rivera Aerodynamic Shape Optimization 21 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Black-Box Optimization
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 22 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Black-Box Optimization
Black-Box Process
They are known from their inputs and outputs
Little is known of how it works internally
David Gutierrez Rivera Aerodynamic Shape Optimization 23 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Black-Box Optimization
David Gutierrez Rivera Aerodynamic Shape Optimization 23 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Black-Box Optimization
David Gutierrez Rivera Aerodynamic Shape Optimization 24 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Noisy Functions
David Gutierrez Rivera Aerodynamic Shape Optimization 25 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Simulation-based Optimization
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 26 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Simulation-based Optimization
David Gutierrez Rivera Aerodynamic Shape Optimization 27 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Moving Boundary Problem
David Gutierrez Rivera Aerodynamic Shape Optimization 28 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
OptiFlow
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 29 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Examples
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 30 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
M4 Neath Viaduct Wind Shield
Description
This bridge is located in South Wales and crosses the River Neath Asection of the bridge is very exposed in flat topography therefore a windshielding system is desired for reducing the overturning forces on vehicles
Description
The CFD model is the same as the one used on the VXFlow tutorial
Four small sections were used to obtain the interior drag forces
David Gutierrez Rivera Aerodynamic Shape Optimization 31 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
M4 Neath Viaduct Wind Shield
Description
The CFD model is the same as the one used on the VXFlow tutorial
Four small sections were used to obtain the interior drag forces
David Gutierrez Rivera Aerodynamic Shape Optimization 31 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
M4 Neath Viaduct Wind Shield
Description
The CFD model is the same as the one used on the VXFlow tutorial
Four small sections were used to obtain the interior drag forces
David Gutierrez Rivera Aerodynamic Shape Optimization 31 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Model
Find optimum height (h) for the Wind Shield
David Gutierrez Rivera Aerodynamic Shape Optimization 32 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Parameter File
Variables Definitions[beginvariables]define(h ) Height of Wind Screen[endvariables]define(L 300) Wind Screen Lengthdefine(t 015) Wind Screen Width Wind Screen Coordinatesdefine(x1 calc(0minus1300))define(x2 calc(x1minust))define(y1 calc(hminus025))define(y2 calc(y1+L))
4 num cornerpointsSCREEN3(SCHEME3)03 00 release distancespacing hull002 0001 00 minus01 merg1merg2merg3merg4minus4 minus3 minus1 minus3 minus1 section color codingdragliftmomentdisplrotation1 x2 y1 n11 x1 y1 n21 x1 y2 n11 x2 y2 n2
David Gutierrez Rivera Aerodynamic Shape Optimization 33 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Parameter File
Variables Definitions[beginvariables]define(h ) Height of Wind Screen[endvariables]define(L 300) Wind Screen Lengthdefine(t 015) Wind Screen Width Wind Screen Coordinatesdefine(x1 calc(0minus1300))define(x2 calc(x1minust))define(y1 calc(hminus025))define(y2 calc(y1+L))
4 num cornerpointsSCREEN3(SCHEME3)03 00 release distancespacing hull002 0001 00 minus01 merg1merg2merg3merg4minus4 minus3 minus1 minus3 minus1 section color codingdragliftmomentdisplrotation1 x2 y1 n11 x1 y1 n21 x1 y2 n11 x2 y2 n2
David Gutierrez Rivera Aerodynamic Shape Optimization 33 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Objective Function
function [Drag] = M4 Neath ViaductWS(X) M4 Neath ViaductWS Objective Functionsteps = 500
Drag(1) = VXF FORCES(XDRAGMAXstepsSECTION11)Drag(2) = VXF FORCES(XDRAGMAXstepsevalfalseSECTION12)Drag(3) = VXF FORCES(XDRAGMAXstepsevalfalseSECTION13)Drag(4) = VXF FORCES(XDRAGMAXstepsevalfalseSECTION14)
[DragLane] = max(Drag())
Call optiOUT to generate Plots and Output DataoptiOUT(X [Drag])
end
David Gutierrez Rivera Aerodynamic Shape Optimization 34 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Data Points
David Gutierrez Rivera Aerodynamic Shape Optimization 35 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Run-Time Optimization
David Gutierrez Rivera Aerodynamic Shape Optimization 36 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Vertical-Axis Wind Turbine (VAWT)
Description
The Savonius Wind Turbine is a Vertical-Axis Wind Turbine (VAWT)which main advantages are its reliability and practicality
David Gutierrez Rivera Aerodynamic Shape Optimization 37 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Model
Description
Find optimum values of ex and ey to maximize Torque or Power
Constrained to the shaded area
David Gutierrez Rivera Aerodynamic Shape Optimization 38 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Model
Description
Find optimum values of ex and ey to maximize Torque or Power
Constrained to the shaded area
David Gutierrez Rivera Aerodynamic Shape Optimization 38 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Dynamic Model
David Gutierrez Rivera Aerodynamic Shape Optimization 39 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Objective Functions
Similar to mathematical functions
They involve 3 basic operations
Substitution
f (x) = a0 +nsum
i=1
an middot cos(n 31416 ) +nsum
i=1
bn middot sin(n 31416 )
Substitution
David Gutierrez Rivera Aerodynamic Shape Optimization 18 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Objective Functions
Similar to mathematical functions
They involve 3 basic operations
Evaluation
f (x) = a0 +nsum
i=1
an middot cos(n 31416 ) +nsum
i=1
bn middot sin(n 31416 )︸ ︷︷ ︸Evaluation
David Gutierrez Rivera Aerodynamic Shape Optimization 18 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Objective Functions
Similar to mathematical functions
They involve 3 basic operations
Read Output
f (x) = Value
Read Output
David Gutierrez Rivera Aerodynamic Shape Optimization 18 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Data Gathering
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 19 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Data Gathering
David Gutierrez Rivera Aerodynamic Shape Optimization 20 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Data Gathering
Data File
It is a text-based tab-delimited file containing the data points from thevariables and the corresponding values of the objective functions
Variable1 Variable2 Variablen Objective1 ObjectivemVariable1 Variable2 Variablen Objective1 Objectivem
Variable1 Variable2 Variablen Objective1 Objectivem
David Gutierrez Rivera Aerodynamic Shape Optimization 21 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Data Gathering
Data File
It is a text-based tab-delimited file containing the data points from thevariables and the corresponding values of the objective functions
Variable1 Variable2 Variablen Objective1 ObjectivemVariable1 Variable2 Variablen Objective1 Objectivem
Variable1 Variable2 Variablen Objective1 Objectivem
David Gutierrez Rivera Aerodynamic Shape Optimization 21 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Black-Box Optimization
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 22 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Black-Box Optimization
Black-Box Process
They are known from their inputs and outputs
Little is known of how it works internally
David Gutierrez Rivera Aerodynamic Shape Optimization 23 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Black-Box Optimization
David Gutierrez Rivera Aerodynamic Shape Optimization 23 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Black-Box Optimization
David Gutierrez Rivera Aerodynamic Shape Optimization 24 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Noisy Functions
David Gutierrez Rivera Aerodynamic Shape Optimization 25 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Simulation-based Optimization
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 26 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Simulation-based Optimization
David Gutierrez Rivera Aerodynamic Shape Optimization 27 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Moving Boundary Problem
David Gutierrez Rivera Aerodynamic Shape Optimization 28 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
OptiFlow
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 29 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Examples
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 30 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
M4 Neath Viaduct Wind Shield
Description
This bridge is located in South Wales and crosses the River Neath Asection of the bridge is very exposed in flat topography therefore a windshielding system is desired for reducing the overturning forces on vehicles
Description
The CFD model is the same as the one used on the VXFlow tutorial
Four small sections were used to obtain the interior drag forces
David Gutierrez Rivera Aerodynamic Shape Optimization 31 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
M4 Neath Viaduct Wind Shield
Description
The CFD model is the same as the one used on the VXFlow tutorial
Four small sections were used to obtain the interior drag forces
David Gutierrez Rivera Aerodynamic Shape Optimization 31 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
M4 Neath Viaduct Wind Shield
Description
The CFD model is the same as the one used on the VXFlow tutorial
Four small sections were used to obtain the interior drag forces
David Gutierrez Rivera Aerodynamic Shape Optimization 31 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Model
Find optimum height (h) for the Wind Shield
David Gutierrez Rivera Aerodynamic Shape Optimization 32 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Parameter File
Variables Definitions[beginvariables]define(h ) Height of Wind Screen[endvariables]define(L 300) Wind Screen Lengthdefine(t 015) Wind Screen Width Wind Screen Coordinatesdefine(x1 calc(0minus1300))define(x2 calc(x1minust))define(y1 calc(hminus025))define(y2 calc(y1+L))
4 num cornerpointsSCREEN3(SCHEME3)03 00 release distancespacing hull002 0001 00 minus01 merg1merg2merg3merg4minus4 minus3 minus1 minus3 minus1 section color codingdragliftmomentdisplrotation1 x2 y1 n11 x1 y1 n21 x1 y2 n11 x2 y2 n2
David Gutierrez Rivera Aerodynamic Shape Optimization 33 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Parameter File
Variables Definitions[beginvariables]define(h ) Height of Wind Screen[endvariables]define(L 300) Wind Screen Lengthdefine(t 015) Wind Screen Width Wind Screen Coordinatesdefine(x1 calc(0minus1300))define(x2 calc(x1minust))define(y1 calc(hminus025))define(y2 calc(y1+L))
4 num cornerpointsSCREEN3(SCHEME3)03 00 release distancespacing hull002 0001 00 minus01 merg1merg2merg3merg4minus4 minus3 minus1 minus3 minus1 section color codingdragliftmomentdisplrotation1 x2 y1 n11 x1 y1 n21 x1 y2 n11 x2 y2 n2
David Gutierrez Rivera Aerodynamic Shape Optimization 33 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Objective Function
function [Drag] = M4 Neath ViaductWS(X) M4 Neath ViaductWS Objective Functionsteps = 500
Drag(1) = VXF FORCES(XDRAGMAXstepsSECTION11)Drag(2) = VXF FORCES(XDRAGMAXstepsevalfalseSECTION12)Drag(3) = VXF FORCES(XDRAGMAXstepsevalfalseSECTION13)Drag(4) = VXF FORCES(XDRAGMAXstepsevalfalseSECTION14)
[DragLane] = max(Drag())
Call optiOUT to generate Plots and Output DataoptiOUT(X [Drag])
end
David Gutierrez Rivera Aerodynamic Shape Optimization 34 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Data Points
David Gutierrez Rivera Aerodynamic Shape Optimization 35 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Run-Time Optimization
David Gutierrez Rivera Aerodynamic Shape Optimization 36 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Vertical-Axis Wind Turbine (VAWT)
Description
The Savonius Wind Turbine is a Vertical-Axis Wind Turbine (VAWT)which main advantages are its reliability and practicality
David Gutierrez Rivera Aerodynamic Shape Optimization 37 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Model
Description
Find optimum values of ex and ey to maximize Torque or Power
Constrained to the shaded area
David Gutierrez Rivera Aerodynamic Shape Optimization 38 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Model
Description
Find optimum values of ex and ey to maximize Torque or Power
Constrained to the shaded area
David Gutierrez Rivera Aerodynamic Shape Optimization 38 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Dynamic Model
David Gutierrez Rivera Aerodynamic Shape Optimization 39 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Objective Functions
Similar to mathematical functions
They involve 3 basic operations
Evaluation
f (x) = a0 +nsum
i=1
an middot cos(n 31416 ) +nsum
i=1
bn middot sin(n 31416 )︸ ︷︷ ︸Evaluation
David Gutierrez Rivera Aerodynamic Shape Optimization 18 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Objective Functions
Similar to mathematical functions
They involve 3 basic operations
Read Output
f (x) = Value
Read Output
David Gutierrez Rivera Aerodynamic Shape Optimization 18 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Data Gathering
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 19 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Data Gathering
David Gutierrez Rivera Aerodynamic Shape Optimization 20 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Data Gathering
Data File
It is a text-based tab-delimited file containing the data points from thevariables and the corresponding values of the objective functions
Variable1 Variable2 Variablen Objective1 ObjectivemVariable1 Variable2 Variablen Objective1 Objectivem
Variable1 Variable2 Variablen Objective1 Objectivem
David Gutierrez Rivera Aerodynamic Shape Optimization 21 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Data Gathering
Data File
It is a text-based tab-delimited file containing the data points from thevariables and the corresponding values of the objective functions
Variable1 Variable2 Variablen Objective1 ObjectivemVariable1 Variable2 Variablen Objective1 Objectivem
Variable1 Variable2 Variablen Objective1 Objectivem
David Gutierrez Rivera Aerodynamic Shape Optimization 21 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Black-Box Optimization
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 22 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Black-Box Optimization
Black-Box Process
They are known from their inputs and outputs
Little is known of how it works internally
David Gutierrez Rivera Aerodynamic Shape Optimization 23 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Black-Box Optimization
David Gutierrez Rivera Aerodynamic Shape Optimization 23 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Black-Box Optimization
David Gutierrez Rivera Aerodynamic Shape Optimization 24 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Noisy Functions
David Gutierrez Rivera Aerodynamic Shape Optimization 25 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Simulation-based Optimization
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 26 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Simulation-based Optimization
David Gutierrez Rivera Aerodynamic Shape Optimization 27 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Moving Boundary Problem
David Gutierrez Rivera Aerodynamic Shape Optimization 28 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
OptiFlow
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 29 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Examples
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 30 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
M4 Neath Viaduct Wind Shield
Description
This bridge is located in South Wales and crosses the River Neath Asection of the bridge is very exposed in flat topography therefore a windshielding system is desired for reducing the overturning forces on vehicles
Description
The CFD model is the same as the one used on the VXFlow tutorial
Four small sections were used to obtain the interior drag forces
David Gutierrez Rivera Aerodynamic Shape Optimization 31 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
M4 Neath Viaduct Wind Shield
Description
The CFD model is the same as the one used on the VXFlow tutorial
Four small sections were used to obtain the interior drag forces
David Gutierrez Rivera Aerodynamic Shape Optimization 31 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
M4 Neath Viaduct Wind Shield
Description
The CFD model is the same as the one used on the VXFlow tutorial
Four small sections were used to obtain the interior drag forces
David Gutierrez Rivera Aerodynamic Shape Optimization 31 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Model
Find optimum height (h) for the Wind Shield
David Gutierrez Rivera Aerodynamic Shape Optimization 32 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Parameter File
Variables Definitions[beginvariables]define(h ) Height of Wind Screen[endvariables]define(L 300) Wind Screen Lengthdefine(t 015) Wind Screen Width Wind Screen Coordinatesdefine(x1 calc(0minus1300))define(x2 calc(x1minust))define(y1 calc(hminus025))define(y2 calc(y1+L))
4 num cornerpointsSCREEN3(SCHEME3)03 00 release distancespacing hull002 0001 00 minus01 merg1merg2merg3merg4minus4 minus3 minus1 minus3 minus1 section color codingdragliftmomentdisplrotation1 x2 y1 n11 x1 y1 n21 x1 y2 n11 x2 y2 n2
David Gutierrez Rivera Aerodynamic Shape Optimization 33 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Parameter File
Variables Definitions[beginvariables]define(h ) Height of Wind Screen[endvariables]define(L 300) Wind Screen Lengthdefine(t 015) Wind Screen Width Wind Screen Coordinatesdefine(x1 calc(0minus1300))define(x2 calc(x1minust))define(y1 calc(hminus025))define(y2 calc(y1+L))
4 num cornerpointsSCREEN3(SCHEME3)03 00 release distancespacing hull002 0001 00 minus01 merg1merg2merg3merg4minus4 minus3 minus1 minus3 minus1 section color codingdragliftmomentdisplrotation1 x2 y1 n11 x1 y1 n21 x1 y2 n11 x2 y2 n2
David Gutierrez Rivera Aerodynamic Shape Optimization 33 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Objective Function
function [Drag] = M4 Neath ViaductWS(X) M4 Neath ViaductWS Objective Functionsteps = 500
Drag(1) = VXF FORCES(XDRAGMAXstepsSECTION11)Drag(2) = VXF FORCES(XDRAGMAXstepsevalfalseSECTION12)Drag(3) = VXF FORCES(XDRAGMAXstepsevalfalseSECTION13)Drag(4) = VXF FORCES(XDRAGMAXstepsevalfalseSECTION14)
[DragLane] = max(Drag())
Call optiOUT to generate Plots and Output DataoptiOUT(X [Drag])
end
David Gutierrez Rivera Aerodynamic Shape Optimization 34 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Data Points
David Gutierrez Rivera Aerodynamic Shape Optimization 35 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Run-Time Optimization
David Gutierrez Rivera Aerodynamic Shape Optimization 36 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Vertical-Axis Wind Turbine (VAWT)
Description
The Savonius Wind Turbine is a Vertical-Axis Wind Turbine (VAWT)which main advantages are its reliability and practicality
David Gutierrez Rivera Aerodynamic Shape Optimization 37 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Model
Description
Find optimum values of ex and ey to maximize Torque or Power
Constrained to the shaded area
David Gutierrez Rivera Aerodynamic Shape Optimization 38 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Model
Description
Find optimum values of ex and ey to maximize Torque or Power
Constrained to the shaded area
David Gutierrez Rivera Aerodynamic Shape Optimization 38 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Dynamic Model
David Gutierrez Rivera Aerodynamic Shape Optimization 39 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Parametrization Objective Functions
Objective Functions
Similar to mathematical functions
They involve 3 basic operations
Read Output
f (x) = Value
Read Output
David Gutierrez Rivera Aerodynamic Shape Optimization 18 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Data Gathering
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 19 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Data Gathering
David Gutierrez Rivera Aerodynamic Shape Optimization 20 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Data Gathering
Data File
It is a text-based tab-delimited file containing the data points from thevariables and the corresponding values of the objective functions
Variable1 Variable2 Variablen Objective1 ObjectivemVariable1 Variable2 Variablen Objective1 Objectivem
Variable1 Variable2 Variablen Objective1 Objectivem
David Gutierrez Rivera Aerodynamic Shape Optimization 21 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Data Gathering
Data File
It is a text-based tab-delimited file containing the data points from thevariables and the corresponding values of the objective functions
Variable1 Variable2 Variablen Objective1 ObjectivemVariable1 Variable2 Variablen Objective1 Objectivem
Variable1 Variable2 Variablen Objective1 Objectivem
David Gutierrez Rivera Aerodynamic Shape Optimization 21 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Black-Box Optimization
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 22 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Black-Box Optimization
Black-Box Process
They are known from their inputs and outputs
Little is known of how it works internally
David Gutierrez Rivera Aerodynamic Shape Optimization 23 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Black-Box Optimization
David Gutierrez Rivera Aerodynamic Shape Optimization 23 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Black-Box Optimization
David Gutierrez Rivera Aerodynamic Shape Optimization 24 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Noisy Functions
David Gutierrez Rivera Aerodynamic Shape Optimization 25 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Simulation-based Optimization
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 26 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Simulation-based Optimization
David Gutierrez Rivera Aerodynamic Shape Optimization 27 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Moving Boundary Problem
David Gutierrez Rivera Aerodynamic Shape Optimization 28 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
OptiFlow
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 29 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Examples
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 30 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
M4 Neath Viaduct Wind Shield
Description
This bridge is located in South Wales and crosses the River Neath Asection of the bridge is very exposed in flat topography therefore a windshielding system is desired for reducing the overturning forces on vehicles
Description
The CFD model is the same as the one used on the VXFlow tutorial
Four small sections were used to obtain the interior drag forces
David Gutierrez Rivera Aerodynamic Shape Optimization 31 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
M4 Neath Viaduct Wind Shield
Description
The CFD model is the same as the one used on the VXFlow tutorial
Four small sections were used to obtain the interior drag forces
David Gutierrez Rivera Aerodynamic Shape Optimization 31 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
M4 Neath Viaduct Wind Shield
Description
The CFD model is the same as the one used on the VXFlow tutorial
Four small sections were used to obtain the interior drag forces
David Gutierrez Rivera Aerodynamic Shape Optimization 31 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Model
Find optimum height (h) for the Wind Shield
David Gutierrez Rivera Aerodynamic Shape Optimization 32 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Parameter File
Variables Definitions[beginvariables]define(h ) Height of Wind Screen[endvariables]define(L 300) Wind Screen Lengthdefine(t 015) Wind Screen Width Wind Screen Coordinatesdefine(x1 calc(0minus1300))define(x2 calc(x1minust))define(y1 calc(hminus025))define(y2 calc(y1+L))
4 num cornerpointsSCREEN3(SCHEME3)03 00 release distancespacing hull002 0001 00 minus01 merg1merg2merg3merg4minus4 minus3 minus1 minus3 minus1 section color codingdragliftmomentdisplrotation1 x2 y1 n11 x1 y1 n21 x1 y2 n11 x2 y2 n2
David Gutierrez Rivera Aerodynamic Shape Optimization 33 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Parameter File
Variables Definitions[beginvariables]define(h ) Height of Wind Screen[endvariables]define(L 300) Wind Screen Lengthdefine(t 015) Wind Screen Width Wind Screen Coordinatesdefine(x1 calc(0minus1300))define(x2 calc(x1minust))define(y1 calc(hminus025))define(y2 calc(y1+L))
4 num cornerpointsSCREEN3(SCHEME3)03 00 release distancespacing hull002 0001 00 minus01 merg1merg2merg3merg4minus4 minus3 minus1 minus3 minus1 section color codingdragliftmomentdisplrotation1 x2 y1 n11 x1 y1 n21 x1 y2 n11 x2 y2 n2
David Gutierrez Rivera Aerodynamic Shape Optimization 33 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Objective Function
function [Drag] = M4 Neath ViaductWS(X) M4 Neath ViaductWS Objective Functionsteps = 500
Drag(1) = VXF FORCES(XDRAGMAXstepsSECTION11)Drag(2) = VXF FORCES(XDRAGMAXstepsevalfalseSECTION12)Drag(3) = VXF FORCES(XDRAGMAXstepsevalfalseSECTION13)Drag(4) = VXF FORCES(XDRAGMAXstepsevalfalseSECTION14)
[DragLane] = max(Drag())
Call optiOUT to generate Plots and Output DataoptiOUT(X [Drag])
end
David Gutierrez Rivera Aerodynamic Shape Optimization 34 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Data Points
David Gutierrez Rivera Aerodynamic Shape Optimization 35 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Run-Time Optimization
David Gutierrez Rivera Aerodynamic Shape Optimization 36 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Vertical-Axis Wind Turbine (VAWT)
Description
The Savonius Wind Turbine is a Vertical-Axis Wind Turbine (VAWT)which main advantages are its reliability and practicality
David Gutierrez Rivera Aerodynamic Shape Optimization 37 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Model
Description
Find optimum values of ex and ey to maximize Torque or Power
Constrained to the shaded area
David Gutierrez Rivera Aerodynamic Shape Optimization 38 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Model
Description
Find optimum values of ex and ey to maximize Torque or Power
Constrained to the shaded area
David Gutierrez Rivera Aerodynamic Shape Optimization 38 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Dynamic Model
David Gutierrez Rivera Aerodynamic Shape Optimization 39 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Data Gathering
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 19 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Data Gathering
David Gutierrez Rivera Aerodynamic Shape Optimization 20 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Data Gathering
Data File
It is a text-based tab-delimited file containing the data points from thevariables and the corresponding values of the objective functions
Variable1 Variable2 Variablen Objective1 ObjectivemVariable1 Variable2 Variablen Objective1 Objectivem
Variable1 Variable2 Variablen Objective1 Objectivem
David Gutierrez Rivera Aerodynamic Shape Optimization 21 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Data Gathering
Data File
It is a text-based tab-delimited file containing the data points from thevariables and the corresponding values of the objective functions
Variable1 Variable2 Variablen Objective1 ObjectivemVariable1 Variable2 Variablen Objective1 Objectivem
Variable1 Variable2 Variablen Objective1 Objectivem
David Gutierrez Rivera Aerodynamic Shape Optimization 21 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Black-Box Optimization
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 22 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Black-Box Optimization
Black-Box Process
They are known from their inputs and outputs
Little is known of how it works internally
David Gutierrez Rivera Aerodynamic Shape Optimization 23 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Black-Box Optimization
David Gutierrez Rivera Aerodynamic Shape Optimization 23 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Black-Box Optimization
David Gutierrez Rivera Aerodynamic Shape Optimization 24 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Noisy Functions
David Gutierrez Rivera Aerodynamic Shape Optimization 25 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Simulation-based Optimization
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 26 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Simulation-based Optimization
David Gutierrez Rivera Aerodynamic Shape Optimization 27 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Moving Boundary Problem
David Gutierrez Rivera Aerodynamic Shape Optimization 28 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
OptiFlow
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 29 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Examples
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 30 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
M4 Neath Viaduct Wind Shield
Description
This bridge is located in South Wales and crosses the River Neath Asection of the bridge is very exposed in flat topography therefore a windshielding system is desired for reducing the overturning forces on vehicles
Description
The CFD model is the same as the one used on the VXFlow tutorial
Four small sections were used to obtain the interior drag forces
David Gutierrez Rivera Aerodynamic Shape Optimization 31 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
M4 Neath Viaduct Wind Shield
Description
The CFD model is the same as the one used on the VXFlow tutorial
Four small sections were used to obtain the interior drag forces
David Gutierrez Rivera Aerodynamic Shape Optimization 31 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
M4 Neath Viaduct Wind Shield
Description
The CFD model is the same as the one used on the VXFlow tutorial
Four small sections were used to obtain the interior drag forces
David Gutierrez Rivera Aerodynamic Shape Optimization 31 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Model
Find optimum height (h) for the Wind Shield
David Gutierrez Rivera Aerodynamic Shape Optimization 32 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Parameter File
Variables Definitions[beginvariables]define(h ) Height of Wind Screen[endvariables]define(L 300) Wind Screen Lengthdefine(t 015) Wind Screen Width Wind Screen Coordinatesdefine(x1 calc(0minus1300))define(x2 calc(x1minust))define(y1 calc(hminus025))define(y2 calc(y1+L))
4 num cornerpointsSCREEN3(SCHEME3)03 00 release distancespacing hull002 0001 00 minus01 merg1merg2merg3merg4minus4 minus3 minus1 minus3 minus1 section color codingdragliftmomentdisplrotation1 x2 y1 n11 x1 y1 n21 x1 y2 n11 x2 y2 n2
David Gutierrez Rivera Aerodynamic Shape Optimization 33 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Parameter File
Variables Definitions[beginvariables]define(h ) Height of Wind Screen[endvariables]define(L 300) Wind Screen Lengthdefine(t 015) Wind Screen Width Wind Screen Coordinatesdefine(x1 calc(0minus1300))define(x2 calc(x1minust))define(y1 calc(hminus025))define(y2 calc(y1+L))
4 num cornerpointsSCREEN3(SCHEME3)03 00 release distancespacing hull002 0001 00 minus01 merg1merg2merg3merg4minus4 minus3 minus1 minus3 minus1 section color codingdragliftmomentdisplrotation1 x2 y1 n11 x1 y1 n21 x1 y2 n11 x2 y2 n2
David Gutierrez Rivera Aerodynamic Shape Optimization 33 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Objective Function
function [Drag] = M4 Neath ViaductWS(X) M4 Neath ViaductWS Objective Functionsteps = 500
Drag(1) = VXF FORCES(XDRAGMAXstepsSECTION11)Drag(2) = VXF FORCES(XDRAGMAXstepsevalfalseSECTION12)Drag(3) = VXF FORCES(XDRAGMAXstepsevalfalseSECTION13)Drag(4) = VXF FORCES(XDRAGMAXstepsevalfalseSECTION14)
[DragLane] = max(Drag())
Call optiOUT to generate Plots and Output DataoptiOUT(X [Drag])
end
David Gutierrez Rivera Aerodynamic Shape Optimization 34 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Data Points
David Gutierrez Rivera Aerodynamic Shape Optimization 35 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Run-Time Optimization
David Gutierrez Rivera Aerodynamic Shape Optimization 36 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Vertical-Axis Wind Turbine (VAWT)
Description
The Savonius Wind Turbine is a Vertical-Axis Wind Turbine (VAWT)which main advantages are its reliability and practicality
David Gutierrez Rivera Aerodynamic Shape Optimization 37 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Model
Description
Find optimum values of ex and ey to maximize Torque or Power
Constrained to the shaded area
David Gutierrez Rivera Aerodynamic Shape Optimization 38 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Model
Description
Find optimum values of ex and ey to maximize Torque or Power
Constrained to the shaded area
David Gutierrez Rivera Aerodynamic Shape Optimization 38 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Dynamic Model
David Gutierrez Rivera Aerodynamic Shape Optimization 39 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Data Gathering
David Gutierrez Rivera Aerodynamic Shape Optimization 20 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Data Gathering
Data File
It is a text-based tab-delimited file containing the data points from thevariables and the corresponding values of the objective functions
Variable1 Variable2 Variablen Objective1 ObjectivemVariable1 Variable2 Variablen Objective1 Objectivem
Variable1 Variable2 Variablen Objective1 Objectivem
David Gutierrez Rivera Aerodynamic Shape Optimization 21 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Data Gathering
Data File
It is a text-based tab-delimited file containing the data points from thevariables and the corresponding values of the objective functions
Variable1 Variable2 Variablen Objective1 ObjectivemVariable1 Variable2 Variablen Objective1 Objectivem
Variable1 Variable2 Variablen Objective1 Objectivem
David Gutierrez Rivera Aerodynamic Shape Optimization 21 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Black-Box Optimization
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 22 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Black-Box Optimization
Black-Box Process
They are known from their inputs and outputs
Little is known of how it works internally
David Gutierrez Rivera Aerodynamic Shape Optimization 23 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Black-Box Optimization
David Gutierrez Rivera Aerodynamic Shape Optimization 23 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Black-Box Optimization
David Gutierrez Rivera Aerodynamic Shape Optimization 24 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Noisy Functions
David Gutierrez Rivera Aerodynamic Shape Optimization 25 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Simulation-based Optimization
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 26 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Simulation-based Optimization
David Gutierrez Rivera Aerodynamic Shape Optimization 27 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Moving Boundary Problem
David Gutierrez Rivera Aerodynamic Shape Optimization 28 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
OptiFlow
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 29 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Examples
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 30 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
M4 Neath Viaduct Wind Shield
Description
This bridge is located in South Wales and crosses the River Neath Asection of the bridge is very exposed in flat topography therefore a windshielding system is desired for reducing the overturning forces on vehicles
Description
The CFD model is the same as the one used on the VXFlow tutorial
Four small sections were used to obtain the interior drag forces
David Gutierrez Rivera Aerodynamic Shape Optimization 31 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
M4 Neath Viaduct Wind Shield
Description
The CFD model is the same as the one used on the VXFlow tutorial
Four small sections were used to obtain the interior drag forces
David Gutierrez Rivera Aerodynamic Shape Optimization 31 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
M4 Neath Viaduct Wind Shield
Description
The CFD model is the same as the one used on the VXFlow tutorial
Four small sections were used to obtain the interior drag forces
David Gutierrez Rivera Aerodynamic Shape Optimization 31 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Model
Find optimum height (h) for the Wind Shield
David Gutierrez Rivera Aerodynamic Shape Optimization 32 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Parameter File
Variables Definitions[beginvariables]define(h ) Height of Wind Screen[endvariables]define(L 300) Wind Screen Lengthdefine(t 015) Wind Screen Width Wind Screen Coordinatesdefine(x1 calc(0minus1300))define(x2 calc(x1minust))define(y1 calc(hminus025))define(y2 calc(y1+L))
4 num cornerpointsSCREEN3(SCHEME3)03 00 release distancespacing hull002 0001 00 minus01 merg1merg2merg3merg4minus4 minus3 minus1 minus3 minus1 section color codingdragliftmomentdisplrotation1 x2 y1 n11 x1 y1 n21 x1 y2 n11 x2 y2 n2
David Gutierrez Rivera Aerodynamic Shape Optimization 33 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Parameter File
Variables Definitions[beginvariables]define(h ) Height of Wind Screen[endvariables]define(L 300) Wind Screen Lengthdefine(t 015) Wind Screen Width Wind Screen Coordinatesdefine(x1 calc(0minus1300))define(x2 calc(x1minust))define(y1 calc(hminus025))define(y2 calc(y1+L))
4 num cornerpointsSCREEN3(SCHEME3)03 00 release distancespacing hull002 0001 00 minus01 merg1merg2merg3merg4minus4 minus3 minus1 minus3 minus1 section color codingdragliftmomentdisplrotation1 x2 y1 n11 x1 y1 n21 x1 y2 n11 x2 y2 n2
David Gutierrez Rivera Aerodynamic Shape Optimization 33 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Objective Function
function [Drag] = M4 Neath ViaductWS(X) M4 Neath ViaductWS Objective Functionsteps = 500
Drag(1) = VXF FORCES(XDRAGMAXstepsSECTION11)Drag(2) = VXF FORCES(XDRAGMAXstepsevalfalseSECTION12)Drag(3) = VXF FORCES(XDRAGMAXstepsevalfalseSECTION13)Drag(4) = VXF FORCES(XDRAGMAXstepsevalfalseSECTION14)
[DragLane] = max(Drag())
Call optiOUT to generate Plots and Output DataoptiOUT(X [Drag])
end
David Gutierrez Rivera Aerodynamic Shape Optimization 34 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Data Points
David Gutierrez Rivera Aerodynamic Shape Optimization 35 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Run-Time Optimization
David Gutierrez Rivera Aerodynamic Shape Optimization 36 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Vertical-Axis Wind Turbine (VAWT)
Description
The Savonius Wind Turbine is a Vertical-Axis Wind Turbine (VAWT)which main advantages are its reliability and practicality
David Gutierrez Rivera Aerodynamic Shape Optimization 37 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Model
Description
Find optimum values of ex and ey to maximize Torque or Power
Constrained to the shaded area
David Gutierrez Rivera Aerodynamic Shape Optimization 38 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Model
Description
Find optimum values of ex and ey to maximize Torque or Power
Constrained to the shaded area
David Gutierrez Rivera Aerodynamic Shape Optimization 38 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Dynamic Model
David Gutierrez Rivera Aerodynamic Shape Optimization 39 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Data Gathering
Data File
It is a text-based tab-delimited file containing the data points from thevariables and the corresponding values of the objective functions
Variable1 Variable2 Variablen Objective1 ObjectivemVariable1 Variable2 Variablen Objective1 Objectivem
Variable1 Variable2 Variablen Objective1 Objectivem
David Gutierrez Rivera Aerodynamic Shape Optimization 21 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Data Gathering
Data File
It is a text-based tab-delimited file containing the data points from thevariables and the corresponding values of the objective functions
Variable1 Variable2 Variablen Objective1 ObjectivemVariable1 Variable2 Variablen Objective1 Objectivem
Variable1 Variable2 Variablen Objective1 Objectivem
David Gutierrez Rivera Aerodynamic Shape Optimization 21 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Black-Box Optimization
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 22 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Black-Box Optimization
Black-Box Process
They are known from their inputs and outputs
Little is known of how it works internally
David Gutierrez Rivera Aerodynamic Shape Optimization 23 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Black-Box Optimization
David Gutierrez Rivera Aerodynamic Shape Optimization 23 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Black-Box Optimization
David Gutierrez Rivera Aerodynamic Shape Optimization 24 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Noisy Functions
David Gutierrez Rivera Aerodynamic Shape Optimization 25 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Simulation-based Optimization
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 26 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Simulation-based Optimization
David Gutierrez Rivera Aerodynamic Shape Optimization 27 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Moving Boundary Problem
David Gutierrez Rivera Aerodynamic Shape Optimization 28 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
OptiFlow
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 29 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Examples
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 30 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
M4 Neath Viaduct Wind Shield
Description
This bridge is located in South Wales and crosses the River Neath Asection of the bridge is very exposed in flat topography therefore a windshielding system is desired for reducing the overturning forces on vehicles
Description
The CFD model is the same as the one used on the VXFlow tutorial
Four small sections were used to obtain the interior drag forces
David Gutierrez Rivera Aerodynamic Shape Optimization 31 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
M4 Neath Viaduct Wind Shield
Description
The CFD model is the same as the one used on the VXFlow tutorial
Four small sections were used to obtain the interior drag forces
David Gutierrez Rivera Aerodynamic Shape Optimization 31 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
M4 Neath Viaduct Wind Shield
Description
The CFD model is the same as the one used on the VXFlow tutorial
Four small sections were used to obtain the interior drag forces
David Gutierrez Rivera Aerodynamic Shape Optimization 31 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Model
Find optimum height (h) for the Wind Shield
David Gutierrez Rivera Aerodynamic Shape Optimization 32 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Parameter File
Variables Definitions[beginvariables]define(h ) Height of Wind Screen[endvariables]define(L 300) Wind Screen Lengthdefine(t 015) Wind Screen Width Wind Screen Coordinatesdefine(x1 calc(0minus1300))define(x2 calc(x1minust))define(y1 calc(hminus025))define(y2 calc(y1+L))
4 num cornerpointsSCREEN3(SCHEME3)03 00 release distancespacing hull002 0001 00 minus01 merg1merg2merg3merg4minus4 minus3 minus1 minus3 minus1 section color codingdragliftmomentdisplrotation1 x2 y1 n11 x1 y1 n21 x1 y2 n11 x2 y2 n2
David Gutierrez Rivera Aerodynamic Shape Optimization 33 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Parameter File
Variables Definitions[beginvariables]define(h ) Height of Wind Screen[endvariables]define(L 300) Wind Screen Lengthdefine(t 015) Wind Screen Width Wind Screen Coordinatesdefine(x1 calc(0minus1300))define(x2 calc(x1minust))define(y1 calc(hminus025))define(y2 calc(y1+L))
4 num cornerpointsSCREEN3(SCHEME3)03 00 release distancespacing hull002 0001 00 minus01 merg1merg2merg3merg4minus4 minus3 minus1 minus3 minus1 section color codingdragliftmomentdisplrotation1 x2 y1 n11 x1 y1 n21 x1 y2 n11 x2 y2 n2
David Gutierrez Rivera Aerodynamic Shape Optimization 33 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Objective Function
function [Drag] = M4 Neath ViaductWS(X) M4 Neath ViaductWS Objective Functionsteps = 500
Drag(1) = VXF FORCES(XDRAGMAXstepsSECTION11)Drag(2) = VXF FORCES(XDRAGMAXstepsevalfalseSECTION12)Drag(3) = VXF FORCES(XDRAGMAXstepsevalfalseSECTION13)Drag(4) = VXF FORCES(XDRAGMAXstepsevalfalseSECTION14)
[DragLane] = max(Drag())
Call optiOUT to generate Plots and Output DataoptiOUT(X [Drag])
end
David Gutierrez Rivera Aerodynamic Shape Optimization 34 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Data Points
David Gutierrez Rivera Aerodynamic Shape Optimization 35 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Run-Time Optimization
David Gutierrez Rivera Aerodynamic Shape Optimization 36 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Vertical-Axis Wind Turbine (VAWT)
Description
The Savonius Wind Turbine is a Vertical-Axis Wind Turbine (VAWT)which main advantages are its reliability and practicality
David Gutierrez Rivera Aerodynamic Shape Optimization 37 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Model
Description
Find optimum values of ex and ey to maximize Torque or Power
Constrained to the shaded area
David Gutierrez Rivera Aerodynamic Shape Optimization 38 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Model
Description
Find optimum values of ex and ey to maximize Torque or Power
Constrained to the shaded area
David Gutierrez Rivera Aerodynamic Shape Optimization 38 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Dynamic Model
David Gutierrez Rivera Aerodynamic Shape Optimization 39 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Data Gathering
Data File
It is a text-based tab-delimited file containing the data points from thevariables and the corresponding values of the objective functions
Variable1 Variable2 Variablen Objective1 ObjectivemVariable1 Variable2 Variablen Objective1 Objectivem
Variable1 Variable2 Variablen Objective1 Objectivem
David Gutierrez Rivera Aerodynamic Shape Optimization 21 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Black-Box Optimization
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 22 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Black-Box Optimization
Black-Box Process
They are known from their inputs and outputs
Little is known of how it works internally
David Gutierrez Rivera Aerodynamic Shape Optimization 23 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Black-Box Optimization
David Gutierrez Rivera Aerodynamic Shape Optimization 23 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Black-Box Optimization
David Gutierrez Rivera Aerodynamic Shape Optimization 24 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Noisy Functions
David Gutierrez Rivera Aerodynamic Shape Optimization 25 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Simulation-based Optimization
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 26 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Simulation-based Optimization
David Gutierrez Rivera Aerodynamic Shape Optimization 27 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Moving Boundary Problem
David Gutierrez Rivera Aerodynamic Shape Optimization 28 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
OptiFlow
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 29 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Examples
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 30 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
M4 Neath Viaduct Wind Shield
Description
This bridge is located in South Wales and crosses the River Neath Asection of the bridge is very exposed in flat topography therefore a windshielding system is desired for reducing the overturning forces on vehicles
Description
The CFD model is the same as the one used on the VXFlow tutorial
Four small sections were used to obtain the interior drag forces
David Gutierrez Rivera Aerodynamic Shape Optimization 31 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
M4 Neath Viaduct Wind Shield
Description
The CFD model is the same as the one used on the VXFlow tutorial
Four small sections were used to obtain the interior drag forces
David Gutierrez Rivera Aerodynamic Shape Optimization 31 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
M4 Neath Viaduct Wind Shield
Description
The CFD model is the same as the one used on the VXFlow tutorial
Four small sections were used to obtain the interior drag forces
David Gutierrez Rivera Aerodynamic Shape Optimization 31 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Model
Find optimum height (h) for the Wind Shield
David Gutierrez Rivera Aerodynamic Shape Optimization 32 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Parameter File
Variables Definitions[beginvariables]define(h ) Height of Wind Screen[endvariables]define(L 300) Wind Screen Lengthdefine(t 015) Wind Screen Width Wind Screen Coordinatesdefine(x1 calc(0minus1300))define(x2 calc(x1minust))define(y1 calc(hminus025))define(y2 calc(y1+L))
4 num cornerpointsSCREEN3(SCHEME3)03 00 release distancespacing hull002 0001 00 minus01 merg1merg2merg3merg4minus4 minus3 minus1 minus3 minus1 section color codingdragliftmomentdisplrotation1 x2 y1 n11 x1 y1 n21 x1 y2 n11 x2 y2 n2
David Gutierrez Rivera Aerodynamic Shape Optimization 33 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Parameter File
Variables Definitions[beginvariables]define(h ) Height of Wind Screen[endvariables]define(L 300) Wind Screen Lengthdefine(t 015) Wind Screen Width Wind Screen Coordinatesdefine(x1 calc(0minus1300))define(x2 calc(x1minust))define(y1 calc(hminus025))define(y2 calc(y1+L))
4 num cornerpointsSCREEN3(SCHEME3)03 00 release distancespacing hull002 0001 00 minus01 merg1merg2merg3merg4minus4 minus3 minus1 minus3 minus1 section color codingdragliftmomentdisplrotation1 x2 y1 n11 x1 y1 n21 x1 y2 n11 x2 y2 n2
David Gutierrez Rivera Aerodynamic Shape Optimization 33 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Objective Function
function [Drag] = M4 Neath ViaductWS(X) M4 Neath ViaductWS Objective Functionsteps = 500
Drag(1) = VXF FORCES(XDRAGMAXstepsSECTION11)Drag(2) = VXF FORCES(XDRAGMAXstepsevalfalseSECTION12)Drag(3) = VXF FORCES(XDRAGMAXstepsevalfalseSECTION13)Drag(4) = VXF FORCES(XDRAGMAXstepsevalfalseSECTION14)
[DragLane] = max(Drag())
Call optiOUT to generate Plots and Output DataoptiOUT(X [Drag])
end
David Gutierrez Rivera Aerodynamic Shape Optimization 34 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Data Points
David Gutierrez Rivera Aerodynamic Shape Optimization 35 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Run-Time Optimization
David Gutierrez Rivera Aerodynamic Shape Optimization 36 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Vertical-Axis Wind Turbine (VAWT)
Description
The Savonius Wind Turbine is a Vertical-Axis Wind Turbine (VAWT)which main advantages are its reliability and practicality
David Gutierrez Rivera Aerodynamic Shape Optimization 37 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Model
Description
Find optimum values of ex and ey to maximize Torque or Power
Constrained to the shaded area
David Gutierrez Rivera Aerodynamic Shape Optimization 38 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Model
Description
Find optimum values of ex and ey to maximize Torque or Power
Constrained to the shaded area
David Gutierrez Rivera Aerodynamic Shape Optimization 38 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Dynamic Model
David Gutierrez Rivera Aerodynamic Shape Optimization 39 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Black-Box Optimization
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 22 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Black-Box Optimization
Black-Box Process
They are known from their inputs and outputs
Little is known of how it works internally
David Gutierrez Rivera Aerodynamic Shape Optimization 23 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Black-Box Optimization
David Gutierrez Rivera Aerodynamic Shape Optimization 23 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Black-Box Optimization
David Gutierrez Rivera Aerodynamic Shape Optimization 24 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Noisy Functions
David Gutierrez Rivera Aerodynamic Shape Optimization 25 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Simulation-based Optimization
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 26 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Simulation-based Optimization
David Gutierrez Rivera Aerodynamic Shape Optimization 27 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Moving Boundary Problem
David Gutierrez Rivera Aerodynamic Shape Optimization 28 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
OptiFlow
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 29 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Examples
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 30 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
M4 Neath Viaduct Wind Shield
Description
This bridge is located in South Wales and crosses the River Neath Asection of the bridge is very exposed in flat topography therefore a windshielding system is desired for reducing the overturning forces on vehicles
Description
The CFD model is the same as the one used on the VXFlow tutorial
Four small sections were used to obtain the interior drag forces
David Gutierrez Rivera Aerodynamic Shape Optimization 31 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
M4 Neath Viaduct Wind Shield
Description
The CFD model is the same as the one used on the VXFlow tutorial
Four small sections were used to obtain the interior drag forces
David Gutierrez Rivera Aerodynamic Shape Optimization 31 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
M4 Neath Viaduct Wind Shield
Description
The CFD model is the same as the one used on the VXFlow tutorial
Four small sections were used to obtain the interior drag forces
David Gutierrez Rivera Aerodynamic Shape Optimization 31 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Model
Find optimum height (h) for the Wind Shield
David Gutierrez Rivera Aerodynamic Shape Optimization 32 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Parameter File
Variables Definitions[beginvariables]define(h ) Height of Wind Screen[endvariables]define(L 300) Wind Screen Lengthdefine(t 015) Wind Screen Width Wind Screen Coordinatesdefine(x1 calc(0minus1300))define(x2 calc(x1minust))define(y1 calc(hminus025))define(y2 calc(y1+L))
4 num cornerpointsSCREEN3(SCHEME3)03 00 release distancespacing hull002 0001 00 minus01 merg1merg2merg3merg4minus4 minus3 minus1 minus3 minus1 section color codingdragliftmomentdisplrotation1 x2 y1 n11 x1 y1 n21 x1 y2 n11 x2 y2 n2
David Gutierrez Rivera Aerodynamic Shape Optimization 33 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Parameter File
Variables Definitions[beginvariables]define(h ) Height of Wind Screen[endvariables]define(L 300) Wind Screen Lengthdefine(t 015) Wind Screen Width Wind Screen Coordinatesdefine(x1 calc(0minus1300))define(x2 calc(x1minust))define(y1 calc(hminus025))define(y2 calc(y1+L))
4 num cornerpointsSCREEN3(SCHEME3)03 00 release distancespacing hull002 0001 00 minus01 merg1merg2merg3merg4minus4 minus3 minus1 minus3 minus1 section color codingdragliftmomentdisplrotation1 x2 y1 n11 x1 y1 n21 x1 y2 n11 x2 y2 n2
David Gutierrez Rivera Aerodynamic Shape Optimization 33 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Objective Function
function [Drag] = M4 Neath ViaductWS(X) M4 Neath ViaductWS Objective Functionsteps = 500
Drag(1) = VXF FORCES(XDRAGMAXstepsSECTION11)Drag(2) = VXF FORCES(XDRAGMAXstepsevalfalseSECTION12)Drag(3) = VXF FORCES(XDRAGMAXstepsevalfalseSECTION13)Drag(4) = VXF FORCES(XDRAGMAXstepsevalfalseSECTION14)
[DragLane] = max(Drag())
Call optiOUT to generate Plots and Output DataoptiOUT(X [Drag])
end
David Gutierrez Rivera Aerodynamic Shape Optimization 34 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Data Points
David Gutierrez Rivera Aerodynamic Shape Optimization 35 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Run-Time Optimization
David Gutierrez Rivera Aerodynamic Shape Optimization 36 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Vertical-Axis Wind Turbine (VAWT)
Description
The Savonius Wind Turbine is a Vertical-Axis Wind Turbine (VAWT)which main advantages are its reliability and practicality
David Gutierrez Rivera Aerodynamic Shape Optimization 37 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Model
Description
Find optimum values of ex and ey to maximize Torque or Power
Constrained to the shaded area
David Gutierrez Rivera Aerodynamic Shape Optimization 38 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Model
Description
Find optimum values of ex and ey to maximize Torque or Power
Constrained to the shaded area
David Gutierrez Rivera Aerodynamic Shape Optimization 38 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Dynamic Model
David Gutierrez Rivera Aerodynamic Shape Optimization 39 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Black-Box Optimization
Black-Box Process
They are known from their inputs and outputs
Little is known of how it works internally
David Gutierrez Rivera Aerodynamic Shape Optimization 23 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Black-Box Optimization
David Gutierrez Rivera Aerodynamic Shape Optimization 23 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Black-Box Optimization
David Gutierrez Rivera Aerodynamic Shape Optimization 24 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Noisy Functions
David Gutierrez Rivera Aerodynamic Shape Optimization 25 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Simulation-based Optimization
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 26 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Simulation-based Optimization
David Gutierrez Rivera Aerodynamic Shape Optimization 27 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Moving Boundary Problem
David Gutierrez Rivera Aerodynamic Shape Optimization 28 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
OptiFlow
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 29 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Examples
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 30 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
M4 Neath Viaduct Wind Shield
Description
This bridge is located in South Wales and crosses the River Neath Asection of the bridge is very exposed in flat topography therefore a windshielding system is desired for reducing the overturning forces on vehicles
Description
The CFD model is the same as the one used on the VXFlow tutorial
Four small sections were used to obtain the interior drag forces
David Gutierrez Rivera Aerodynamic Shape Optimization 31 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
M4 Neath Viaduct Wind Shield
Description
The CFD model is the same as the one used on the VXFlow tutorial
Four small sections were used to obtain the interior drag forces
David Gutierrez Rivera Aerodynamic Shape Optimization 31 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
M4 Neath Viaduct Wind Shield
Description
The CFD model is the same as the one used on the VXFlow tutorial
Four small sections were used to obtain the interior drag forces
David Gutierrez Rivera Aerodynamic Shape Optimization 31 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Model
Find optimum height (h) for the Wind Shield
David Gutierrez Rivera Aerodynamic Shape Optimization 32 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Parameter File
Variables Definitions[beginvariables]define(h ) Height of Wind Screen[endvariables]define(L 300) Wind Screen Lengthdefine(t 015) Wind Screen Width Wind Screen Coordinatesdefine(x1 calc(0minus1300))define(x2 calc(x1minust))define(y1 calc(hminus025))define(y2 calc(y1+L))
4 num cornerpointsSCREEN3(SCHEME3)03 00 release distancespacing hull002 0001 00 minus01 merg1merg2merg3merg4minus4 minus3 minus1 minus3 minus1 section color codingdragliftmomentdisplrotation1 x2 y1 n11 x1 y1 n21 x1 y2 n11 x2 y2 n2
David Gutierrez Rivera Aerodynamic Shape Optimization 33 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Parameter File
Variables Definitions[beginvariables]define(h ) Height of Wind Screen[endvariables]define(L 300) Wind Screen Lengthdefine(t 015) Wind Screen Width Wind Screen Coordinatesdefine(x1 calc(0minus1300))define(x2 calc(x1minust))define(y1 calc(hminus025))define(y2 calc(y1+L))
4 num cornerpointsSCREEN3(SCHEME3)03 00 release distancespacing hull002 0001 00 minus01 merg1merg2merg3merg4minus4 minus3 minus1 minus3 minus1 section color codingdragliftmomentdisplrotation1 x2 y1 n11 x1 y1 n21 x1 y2 n11 x2 y2 n2
David Gutierrez Rivera Aerodynamic Shape Optimization 33 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Objective Function
function [Drag] = M4 Neath ViaductWS(X) M4 Neath ViaductWS Objective Functionsteps = 500
Drag(1) = VXF FORCES(XDRAGMAXstepsSECTION11)Drag(2) = VXF FORCES(XDRAGMAXstepsevalfalseSECTION12)Drag(3) = VXF FORCES(XDRAGMAXstepsevalfalseSECTION13)Drag(4) = VXF FORCES(XDRAGMAXstepsevalfalseSECTION14)
[DragLane] = max(Drag())
Call optiOUT to generate Plots and Output DataoptiOUT(X [Drag])
end
David Gutierrez Rivera Aerodynamic Shape Optimization 34 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Data Points
David Gutierrez Rivera Aerodynamic Shape Optimization 35 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Run-Time Optimization
David Gutierrez Rivera Aerodynamic Shape Optimization 36 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Vertical-Axis Wind Turbine (VAWT)
Description
The Savonius Wind Turbine is a Vertical-Axis Wind Turbine (VAWT)which main advantages are its reliability and practicality
David Gutierrez Rivera Aerodynamic Shape Optimization 37 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Model
Description
Find optimum values of ex and ey to maximize Torque or Power
Constrained to the shaded area
David Gutierrez Rivera Aerodynamic Shape Optimization 38 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Model
Description
Find optimum values of ex and ey to maximize Torque or Power
Constrained to the shaded area
David Gutierrez Rivera Aerodynamic Shape Optimization 38 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Dynamic Model
David Gutierrez Rivera Aerodynamic Shape Optimization 39 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Black-Box Optimization
David Gutierrez Rivera Aerodynamic Shape Optimization 23 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Black-Box Optimization
David Gutierrez Rivera Aerodynamic Shape Optimization 24 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Noisy Functions
David Gutierrez Rivera Aerodynamic Shape Optimization 25 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Simulation-based Optimization
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 26 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Simulation-based Optimization
David Gutierrez Rivera Aerodynamic Shape Optimization 27 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Moving Boundary Problem
David Gutierrez Rivera Aerodynamic Shape Optimization 28 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
OptiFlow
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 29 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Examples
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 30 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
M4 Neath Viaduct Wind Shield
Description
This bridge is located in South Wales and crosses the River Neath Asection of the bridge is very exposed in flat topography therefore a windshielding system is desired for reducing the overturning forces on vehicles
Description
The CFD model is the same as the one used on the VXFlow tutorial
Four small sections were used to obtain the interior drag forces
David Gutierrez Rivera Aerodynamic Shape Optimization 31 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
M4 Neath Viaduct Wind Shield
Description
The CFD model is the same as the one used on the VXFlow tutorial
Four small sections were used to obtain the interior drag forces
David Gutierrez Rivera Aerodynamic Shape Optimization 31 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
M4 Neath Viaduct Wind Shield
Description
The CFD model is the same as the one used on the VXFlow tutorial
Four small sections were used to obtain the interior drag forces
David Gutierrez Rivera Aerodynamic Shape Optimization 31 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Model
Find optimum height (h) for the Wind Shield
David Gutierrez Rivera Aerodynamic Shape Optimization 32 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Parameter File
Variables Definitions[beginvariables]define(h ) Height of Wind Screen[endvariables]define(L 300) Wind Screen Lengthdefine(t 015) Wind Screen Width Wind Screen Coordinatesdefine(x1 calc(0minus1300))define(x2 calc(x1minust))define(y1 calc(hminus025))define(y2 calc(y1+L))
4 num cornerpointsSCREEN3(SCHEME3)03 00 release distancespacing hull002 0001 00 minus01 merg1merg2merg3merg4minus4 minus3 minus1 minus3 minus1 section color codingdragliftmomentdisplrotation1 x2 y1 n11 x1 y1 n21 x1 y2 n11 x2 y2 n2
David Gutierrez Rivera Aerodynamic Shape Optimization 33 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Parameter File
Variables Definitions[beginvariables]define(h ) Height of Wind Screen[endvariables]define(L 300) Wind Screen Lengthdefine(t 015) Wind Screen Width Wind Screen Coordinatesdefine(x1 calc(0minus1300))define(x2 calc(x1minust))define(y1 calc(hminus025))define(y2 calc(y1+L))
4 num cornerpointsSCREEN3(SCHEME3)03 00 release distancespacing hull002 0001 00 minus01 merg1merg2merg3merg4minus4 minus3 minus1 minus3 minus1 section color codingdragliftmomentdisplrotation1 x2 y1 n11 x1 y1 n21 x1 y2 n11 x2 y2 n2
David Gutierrez Rivera Aerodynamic Shape Optimization 33 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Objective Function
function [Drag] = M4 Neath ViaductWS(X) M4 Neath ViaductWS Objective Functionsteps = 500
Drag(1) = VXF FORCES(XDRAGMAXstepsSECTION11)Drag(2) = VXF FORCES(XDRAGMAXstepsevalfalseSECTION12)Drag(3) = VXF FORCES(XDRAGMAXstepsevalfalseSECTION13)Drag(4) = VXF FORCES(XDRAGMAXstepsevalfalseSECTION14)
[DragLane] = max(Drag())
Call optiOUT to generate Plots and Output DataoptiOUT(X [Drag])
end
David Gutierrez Rivera Aerodynamic Shape Optimization 34 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Data Points
David Gutierrez Rivera Aerodynamic Shape Optimization 35 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Run-Time Optimization
David Gutierrez Rivera Aerodynamic Shape Optimization 36 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Vertical-Axis Wind Turbine (VAWT)
Description
The Savonius Wind Turbine is a Vertical-Axis Wind Turbine (VAWT)which main advantages are its reliability and practicality
David Gutierrez Rivera Aerodynamic Shape Optimization 37 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Model
Description
Find optimum values of ex and ey to maximize Torque or Power
Constrained to the shaded area
David Gutierrez Rivera Aerodynamic Shape Optimization 38 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Model
Description
Find optimum values of ex and ey to maximize Torque or Power
Constrained to the shaded area
David Gutierrez Rivera Aerodynamic Shape Optimization 38 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Dynamic Model
David Gutierrez Rivera Aerodynamic Shape Optimization 39 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Black-Box Optimization
David Gutierrez Rivera Aerodynamic Shape Optimization 24 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Noisy Functions
David Gutierrez Rivera Aerodynamic Shape Optimization 25 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Simulation-based Optimization
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 26 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Simulation-based Optimization
David Gutierrez Rivera Aerodynamic Shape Optimization 27 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Moving Boundary Problem
David Gutierrez Rivera Aerodynamic Shape Optimization 28 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
OptiFlow
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 29 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Examples
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 30 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
M4 Neath Viaduct Wind Shield
Description
This bridge is located in South Wales and crosses the River Neath Asection of the bridge is very exposed in flat topography therefore a windshielding system is desired for reducing the overturning forces on vehicles
Description
The CFD model is the same as the one used on the VXFlow tutorial
Four small sections were used to obtain the interior drag forces
David Gutierrez Rivera Aerodynamic Shape Optimization 31 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
M4 Neath Viaduct Wind Shield
Description
The CFD model is the same as the one used on the VXFlow tutorial
Four small sections were used to obtain the interior drag forces
David Gutierrez Rivera Aerodynamic Shape Optimization 31 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
M4 Neath Viaduct Wind Shield
Description
The CFD model is the same as the one used on the VXFlow tutorial
Four small sections were used to obtain the interior drag forces
David Gutierrez Rivera Aerodynamic Shape Optimization 31 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Model
Find optimum height (h) for the Wind Shield
David Gutierrez Rivera Aerodynamic Shape Optimization 32 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Parameter File
Variables Definitions[beginvariables]define(h ) Height of Wind Screen[endvariables]define(L 300) Wind Screen Lengthdefine(t 015) Wind Screen Width Wind Screen Coordinatesdefine(x1 calc(0minus1300))define(x2 calc(x1minust))define(y1 calc(hminus025))define(y2 calc(y1+L))
4 num cornerpointsSCREEN3(SCHEME3)03 00 release distancespacing hull002 0001 00 minus01 merg1merg2merg3merg4minus4 minus3 minus1 minus3 minus1 section color codingdragliftmomentdisplrotation1 x2 y1 n11 x1 y1 n21 x1 y2 n11 x2 y2 n2
David Gutierrez Rivera Aerodynamic Shape Optimization 33 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Parameter File
Variables Definitions[beginvariables]define(h ) Height of Wind Screen[endvariables]define(L 300) Wind Screen Lengthdefine(t 015) Wind Screen Width Wind Screen Coordinatesdefine(x1 calc(0minus1300))define(x2 calc(x1minust))define(y1 calc(hminus025))define(y2 calc(y1+L))
4 num cornerpointsSCREEN3(SCHEME3)03 00 release distancespacing hull002 0001 00 minus01 merg1merg2merg3merg4minus4 minus3 minus1 minus3 minus1 section color codingdragliftmomentdisplrotation1 x2 y1 n11 x1 y1 n21 x1 y2 n11 x2 y2 n2
David Gutierrez Rivera Aerodynamic Shape Optimization 33 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Objective Function
function [Drag] = M4 Neath ViaductWS(X) M4 Neath ViaductWS Objective Functionsteps = 500
Drag(1) = VXF FORCES(XDRAGMAXstepsSECTION11)Drag(2) = VXF FORCES(XDRAGMAXstepsevalfalseSECTION12)Drag(3) = VXF FORCES(XDRAGMAXstepsevalfalseSECTION13)Drag(4) = VXF FORCES(XDRAGMAXstepsevalfalseSECTION14)
[DragLane] = max(Drag())
Call optiOUT to generate Plots and Output DataoptiOUT(X [Drag])
end
David Gutierrez Rivera Aerodynamic Shape Optimization 34 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Data Points
David Gutierrez Rivera Aerodynamic Shape Optimization 35 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Run-Time Optimization
David Gutierrez Rivera Aerodynamic Shape Optimization 36 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Vertical-Axis Wind Turbine (VAWT)
Description
The Savonius Wind Turbine is a Vertical-Axis Wind Turbine (VAWT)which main advantages are its reliability and practicality
David Gutierrez Rivera Aerodynamic Shape Optimization 37 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Model
Description
Find optimum values of ex and ey to maximize Torque or Power
Constrained to the shaded area
David Gutierrez Rivera Aerodynamic Shape Optimization 38 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Model
Description
Find optimum values of ex and ey to maximize Torque or Power
Constrained to the shaded area
David Gutierrez Rivera Aerodynamic Shape Optimization 38 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Dynamic Model
David Gutierrez Rivera Aerodynamic Shape Optimization 39 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Noisy Functions
David Gutierrez Rivera Aerodynamic Shape Optimization 25 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Simulation-based Optimization
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 26 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Simulation-based Optimization
David Gutierrez Rivera Aerodynamic Shape Optimization 27 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Moving Boundary Problem
David Gutierrez Rivera Aerodynamic Shape Optimization 28 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
OptiFlow
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 29 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Examples
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 30 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
M4 Neath Viaduct Wind Shield
Description
This bridge is located in South Wales and crosses the River Neath Asection of the bridge is very exposed in flat topography therefore a windshielding system is desired for reducing the overturning forces on vehicles
Description
The CFD model is the same as the one used on the VXFlow tutorial
Four small sections were used to obtain the interior drag forces
David Gutierrez Rivera Aerodynamic Shape Optimization 31 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
M4 Neath Viaduct Wind Shield
Description
The CFD model is the same as the one used on the VXFlow tutorial
Four small sections were used to obtain the interior drag forces
David Gutierrez Rivera Aerodynamic Shape Optimization 31 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
M4 Neath Viaduct Wind Shield
Description
The CFD model is the same as the one used on the VXFlow tutorial
Four small sections were used to obtain the interior drag forces
David Gutierrez Rivera Aerodynamic Shape Optimization 31 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Model
Find optimum height (h) for the Wind Shield
David Gutierrez Rivera Aerodynamic Shape Optimization 32 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Parameter File
Variables Definitions[beginvariables]define(h ) Height of Wind Screen[endvariables]define(L 300) Wind Screen Lengthdefine(t 015) Wind Screen Width Wind Screen Coordinatesdefine(x1 calc(0minus1300))define(x2 calc(x1minust))define(y1 calc(hminus025))define(y2 calc(y1+L))
4 num cornerpointsSCREEN3(SCHEME3)03 00 release distancespacing hull002 0001 00 minus01 merg1merg2merg3merg4minus4 minus3 minus1 minus3 minus1 section color codingdragliftmomentdisplrotation1 x2 y1 n11 x1 y1 n21 x1 y2 n11 x2 y2 n2
David Gutierrez Rivera Aerodynamic Shape Optimization 33 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Parameter File
Variables Definitions[beginvariables]define(h ) Height of Wind Screen[endvariables]define(L 300) Wind Screen Lengthdefine(t 015) Wind Screen Width Wind Screen Coordinatesdefine(x1 calc(0minus1300))define(x2 calc(x1minust))define(y1 calc(hminus025))define(y2 calc(y1+L))
4 num cornerpointsSCREEN3(SCHEME3)03 00 release distancespacing hull002 0001 00 minus01 merg1merg2merg3merg4minus4 minus3 minus1 minus3 minus1 section color codingdragliftmomentdisplrotation1 x2 y1 n11 x1 y1 n21 x1 y2 n11 x2 y2 n2
David Gutierrez Rivera Aerodynamic Shape Optimization 33 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Objective Function
function [Drag] = M4 Neath ViaductWS(X) M4 Neath ViaductWS Objective Functionsteps = 500
Drag(1) = VXF FORCES(XDRAGMAXstepsSECTION11)Drag(2) = VXF FORCES(XDRAGMAXstepsevalfalseSECTION12)Drag(3) = VXF FORCES(XDRAGMAXstepsevalfalseSECTION13)Drag(4) = VXF FORCES(XDRAGMAXstepsevalfalseSECTION14)
[DragLane] = max(Drag())
Call optiOUT to generate Plots and Output DataoptiOUT(X [Drag])
end
David Gutierrez Rivera Aerodynamic Shape Optimization 34 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Data Points
David Gutierrez Rivera Aerodynamic Shape Optimization 35 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Run-Time Optimization
David Gutierrez Rivera Aerodynamic Shape Optimization 36 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Vertical-Axis Wind Turbine (VAWT)
Description
The Savonius Wind Turbine is a Vertical-Axis Wind Turbine (VAWT)which main advantages are its reliability and practicality
David Gutierrez Rivera Aerodynamic Shape Optimization 37 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Model
Description
Find optimum values of ex and ey to maximize Torque or Power
Constrained to the shaded area
David Gutierrez Rivera Aerodynamic Shape Optimization 38 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Model
Description
Find optimum values of ex and ey to maximize Torque or Power
Constrained to the shaded area
David Gutierrez Rivera Aerodynamic Shape Optimization 38 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Dynamic Model
David Gutierrez Rivera Aerodynamic Shape Optimization 39 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Simulation-based Optimization
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 26 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Simulation-based Optimization
David Gutierrez Rivera Aerodynamic Shape Optimization 27 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Moving Boundary Problem
David Gutierrez Rivera Aerodynamic Shape Optimization 28 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
OptiFlow
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 29 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Examples
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 30 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
M4 Neath Viaduct Wind Shield
Description
This bridge is located in South Wales and crosses the River Neath Asection of the bridge is very exposed in flat topography therefore a windshielding system is desired for reducing the overturning forces on vehicles
Description
The CFD model is the same as the one used on the VXFlow tutorial
Four small sections were used to obtain the interior drag forces
David Gutierrez Rivera Aerodynamic Shape Optimization 31 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
M4 Neath Viaduct Wind Shield
Description
The CFD model is the same as the one used on the VXFlow tutorial
Four small sections were used to obtain the interior drag forces
David Gutierrez Rivera Aerodynamic Shape Optimization 31 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
M4 Neath Viaduct Wind Shield
Description
The CFD model is the same as the one used on the VXFlow tutorial
Four small sections were used to obtain the interior drag forces
David Gutierrez Rivera Aerodynamic Shape Optimization 31 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Model
Find optimum height (h) for the Wind Shield
David Gutierrez Rivera Aerodynamic Shape Optimization 32 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Parameter File
Variables Definitions[beginvariables]define(h ) Height of Wind Screen[endvariables]define(L 300) Wind Screen Lengthdefine(t 015) Wind Screen Width Wind Screen Coordinatesdefine(x1 calc(0minus1300))define(x2 calc(x1minust))define(y1 calc(hminus025))define(y2 calc(y1+L))
4 num cornerpointsSCREEN3(SCHEME3)03 00 release distancespacing hull002 0001 00 minus01 merg1merg2merg3merg4minus4 minus3 minus1 minus3 minus1 section color codingdragliftmomentdisplrotation1 x2 y1 n11 x1 y1 n21 x1 y2 n11 x2 y2 n2
David Gutierrez Rivera Aerodynamic Shape Optimization 33 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Parameter File
Variables Definitions[beginvariables]define(h ) Height of Wind Screen[endvariables]define(L 300) Wind Screen Lengthdefine(t 015) Wind Screen Width Wind Screen Coordinatesdefine(x1 calc(0minus1300))define(x2 calc(x1minust))define(y1 calc(hminus025))define(y2 calc(y1+L))
4 num cornerpointsSCREEN3(SCHEME3)03 00 release distancespacing hull002 0001 00 minus01 merg1merg2merg3merg4minus4 minus3 minus1 minus3 minus1 section color codingdragliftmomentdisplrotation1 x2 y1 n11 x1 y1 n21 x1 y2 n11 x2 y2 n2
David Gutierrez Rivera Aerodynamic Shape Optimization 33 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Objective Function
function [Drag] = M4 Neath ViaductWS(X) M4 Neath ViaductWS Objective Functionsteps = 500
Drag(1) = VXF FORCES(XDRAGMAXstepsSECTION11)Drag(2) = VXF FORCES(XDRAGMAXstepsevalfalseSECTION12)Drag(3) = VXF FORCES(XDRAGMAXstepsevalfalseSECTION13)Drag(4) = VXF FORCES(XDRAGMAXstepsevalfalseSECTION14)
[DragLane] = max(Drag())
Call optiOUT to generate Plots and Output DataoptiOUT(X [Drag])
end
David Gutierrez Rivera Aerodynamic Shape Optimization 34 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Data Points
David Gutierrez Rivera Aerodynamic Shape Optimization 35 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Run-Time Optimization
David Gutierrez Rivera Aerodynamic Shape Optimization 36 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Vertical-Axis Wind Turbine (VAWT)
Description
The Savonius Wind Turbine is a Vertical-Axis Wind Turbine (VAWT)which main advantages are its reliability and practicality
David Gutierrez Rivera Aerodynamic Shape Optimization 37 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Model
Description
Find optimum values of ex and ey to maximize Torque or Power
Constrained to the shaded area
David Gutierrez Rivera Aerodynamic Shape Optimization 38 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Model
Description
Find optimum values of ex and ey to maximize Torque or Power
Constrained to the shaded area
David Gutierrez Rivera Aerodynamic Shape Optimization 38 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Dynamic Model
David Gutierrez Rivera Aerodynamic Shape Optimization 39 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Simulation-based Optimization
David Gutierrez Rivera Aerodynamic Shape Optimization 27 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Moving Boundary Problem
David Gutierrez Rivera Aerodynamic Shape Optimization 28 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
OptiFlow
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 29 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Examples
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 30 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
M4 Neath Viaduct Wind Shield
Description
This bridge is located in South Wales and crosses the River Neath Asection of the bridge is very exposed in flat topography therefore a windshielding system is desired for reducing the overturning forces on vehicles
Description
The CFD model is the same as the one used on the VXFlow tutorial
Four small sections were used to obtain the interior drag forces
David Gutierrez Rivera Aerodynamic Shape Optimization 31 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
M4 Neath Viaduct Wind Shield
Description
The CFD model is the same as the one used on the VXFlow tutorial
Four small sections were used to obtain the interior drag forces
David Gutierrez Rivera Aerodynamic Shape Optimization 31 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
M4 Neath Viaduct Wind Shield
Description
The CFD model is the same as the one used on the VXFlow tutorial
Four small sections were used to obtain the interior drag forces
David Gutierrez Rivera Aerodynamic Shape Optimization 31 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Model
Find optimum height (h) for the Wind Shield
David Gutierrez Rivera Aerodynamic Shape Optimization 32 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Parameter File
Variables Definitions[beginvariables]define(h ) Height of Wind Screen[endvariables]define(L 300) Wind Screen Lengthdefine(t 015) Wind Screen Width Wind Screen Coordinatesdefine(x1 calc(0minus1300))define(x2 calc(x1minust))define(y1 calc(hminus025))define(y2 calc(y1+L))
4 num cornerpointsSCREEN3(SCHEME3)03 00 release distancespacing hull002 0001 00 minus01 merg1merg2merg3merg4minus4 minus3 minus1 minus3 minus1 section color codingdragliftmomentdisplrotation1 x2 y1 n11 x1 y1 n21 x1 y2 n11 x2 y2 n2
David Gutierrez Rivera Aerodynamic Shape Optimization 33 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Parameter File
Variables Definitions[beginvariables]define(h ) Height of Wind Screen[endvariables]define(L 300) Wind Screen Lengthdefine(t 015) Wind Screen Width Wind Screen Coordinatesdefine(x1 calc(0minus1300))define(x2 calc(x1minust))define(y1 calc(hminus025))define(y2 calc(y1+L))
4 num cornerpointsSCREEN3(SCHEME3)03 00 release distancespacing hull002 0001 00 minus01 merg1merg2merg3merg4minus4 minus3 minus1 minus3 minus1 section color codingdragliftmomentdisplrotation1 x2 y1 n11 x1 y1 n21 x1 y2 n11 x2 y2 n2
David Gutierrez Rivera Aerodynamic Shape Optimization 33 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Objective Function
function [Drag] = M4 Neath ViaductWS(X) M4 Neath ViaductWS Objective Functionsteps = 500
Drag(1) = VXF FORCES(XDRAGMAXstepsSECTION11)Drag(2) = VXF FORCES(XDRAGMAXstepsevalfalseSECTION12)Drag(3) = VXF FORCES(XDRAGMAXstepsevalfalseSECTION13)Drag(4) = VXF FORCES(XDRAGMAXstepsevalfalseSECTION14)
[DragLane] = max(Drag())
Call optiOUT to generate Plots and Output DataoptiOUT(X [Drag])
end
David Gutierrez Rivera Aerodynamic Shape Optimization 34 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Data Points
David Gutierrez Rivera Aerodynamic Shape Optimization 35 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Run-Time Optimization
David Gutierrez Rivera Aerodynamic Shape Optimization 36 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Vertical-Axis Wind Turbine (VAWT)
Description
The Savonius Wind Turbine is a Vertical-Axis Wind Turbine (VAWT)which main advantages are its reliability and practicality
David Gutierrez Rivera Aerodynamic Shape Optimization 37 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Model
Description
Find optimum values of ex and ey to maximize Torque or Power
Constrained to the shaded area
David Gutierrez Rivera Aerodynamic Shape Optimization 38 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Model
Description
Find optimum values of ex and ey to maximize Torque or Power
Constrained to the shaded area
David Gutierrez Rivera Aerodynamic Shape Optimization 38 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Dynamic Model
David Gutierrez Rivera Aerodynamic Shape Optimization 39 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Moving Boundary Problem
David Gutierrez Rivera Aerodynamic Shape Optimization 28 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
OptiFlow
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 29 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Examples
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 30 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
M4 Neath Viaduct Wind Shield
Description
This bridge is located in South Wales and crosses the River Neath Asection of the bridge is very exposed in flat topography therefore a windshielding system is desired for reducing the overturning forces on vehicles
Description
The CFD model is the same as the one used on the VXFlow tutorial
Four small sections were used to obtain the interior drag forces
David Gutierrez Rivera Aerodynamic Shape Optimization 31 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
M4 Neath Viaduct Wind Shield
Description
The CFD model is the same as the one used on the VXFlow tutorial
Four small sections were used to obtain the interior drag forces
David Gutierrez Rivera Aerodynamic Shape Optimization 31 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
M4 Neath Viaduct Wind Shield
Description
The CFD model is the same as the one used on the VXFlow tutorial
Four small sections were used to obtain the interior drag forces
David Gutierrez Rivera Aerodynamic Shape Optimization 31 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Model
Find optimum height (h) for the Wind Shield
David Gutierrez Rivera Aerodynamic Shape Optimization 32 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Parameter File
Variables Definitions[beginvariables]define(h ) Height of Wind Screen[endvariables]define(L 300) Wind Screen Lengthdefine(t 015) Wind Screen Width Wind Screen Coordinatesdefine(x1 calc(0minus1300))define(x2 calc(x1minust))define(y1 calc(hminus025))define(y2 calc(y1+L))
4 num cornerpointsSCREEN3(SCHEME3)03 00 release distancespacing hull002 0001 00 minus01 merg1merg2merg3merg4minus4 minus3 minus1 minus3 minus1 section color codingdragliftmomentdisplrotation1 x2 y1 n11 x1 y1 n21 x1 y2 n11 x2 y2 n2
David Gutierrez Rivera Aerodynamic Shape Optimization 33 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Parameter File
Variables Definitions[beginvariables]define(h ) Height of Wind Screen[endvariables]define(L 300) Wind Screen Lengthdefine(t 015) Wind Screen Width Wind Screen Coordinatesdefine(x1 calc(0minus1300))define(x2 calc(x1minust))define(y1 calc(hminus025))define(y2 calc(y1+L))
4 num cornerpointsSCREEN3(SCHEME3)03 00 release distancespacing hull002 0001 00 minus01 merg1merg2merg3merg4minus4 minus3 minus1 minus3 minus1 section color codingdragliftmomentdisplrotation1 x2 y1 n11 x1 y1 n21 x1 y2 n11 x2 y2 n2
David Gutierrez Rivera Aerodynamic Shape Optimization 33 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Objective Function
function [Drag] = M4 Neath ViaductWS(X) M4 Neath ViaductWS Objective Functionsteps = 500
Drag(1) = VXF FORCES(XDRAGMAXstepsSECTION11)Drag(2) = VXF FORCES(XDRAGMAXstepsevalfalseSECTION12)Drag(3) = VXF FORCES(XDRAGMAXstepsevalfalseSECTION13)Drag(4) = VXF FORCES(XDRAGMAXstepsevalfalseSECTION14)
[DragLane] = max(Drag())
Call optiOUT to generate Plots and Output DataoptiOUT(X [Drag])
end
David Gutierrez Rivera Aerodynamic Shape Optimization 34 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Data Points
David Gutierrez Rivera Aerodynamic Shape Optimization 35 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Run-Time Optimization
David Gutierrez Rivera Aerodynamic Shape Optimization 36 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Vertical-Axis Wind Turbine (VAWT)
Description
The Savonius Wind Turbine is a Vertical-Axis Wind Turbine (VAWT)which main advantages are its reliability and practicality
David Gutierrez Rivera Aerodynamic Shape Optimization 37 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Model
Description
Find optimum values of ex and ey to maximize Torque or Power
Constrained to the shaded area
David Gutierrez Rivera Aerodynamic Shape Optimization 38 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Model
Description
Find optimum values of ex and ey to maximize Torque or Power
Constrained to the shaded area
David Gutierrez Rivera Aerodynamic Shape Optimization 38 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Dynamic Model
David Gutierrez Rivera Aerodynamic Shape Optimization 39 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
OptiFlow
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 29 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Examples
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 30 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
M4 Neath Viaduct Wind Shield
Description
This bridge is located in South Wales and crosses the River Neath Asection of the bridge is very exposed in flat topography therefore a windshielding system is desired for reducing the overturning forces on vehicles
Description
The CFD model is the same as the one used on the VXFlow tutorial
Four small sections were used to obtain the interior drag forces
David Gutierrez Rivera Aerodynamic Shape Optimization 31 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
M4 Neath Viaduct Wind Shield
Description
The CFD model is the same as the one used on the VXFlow tutorial
Four small sections were used to obtain the interior drag forces
David Gutierrez Rivera Aerodynamic Shape Optimization 31 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
M4 Neath Viaduct Wind Shield
Description
The CFD model is the same as the one used on the VXFlow tutorial
Four small sections were used to obtain the interior drag forces
David Gutierrez Rivera Aerodynamic Shape Optimization 31 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Model
Find optimum height (h) for the Wind Shield
David Gutierrez Rivera Aerodynamic Shape Optimization 32 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Parameter File
Variables Definitions[beginvariables]define(h ) Height of Wind Screen[endvariables]define(L 300) Wind Screen Lengthdefine(t 015) Wind Screen Width Wind Screen Coordinatesdefine(x1 calc(0minus1300))define(x2 calc(x1minust))define(y1 calc(hminus025))define(y2 calc(y1+L))
4 num cornerpointsSCREEN3(SCHEME3)03 00 release distancespacing hull002 0001 00 minus01 merg1merg2merg3merg4minus4 minus3 minus1 minus3 minus1 section color codingdragliftmomentdisplrotation1 x2 y1 n11 x1 y1 n21 x1 y2 n11 x2 y2 n2
David Gutierrez Rivera Aerodynamic Shape Optimization 33 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Parameter File
Variables Definitions[beginvariables]define(h ) Height of Wind Screen[endvariables]define(L 300) Wind Screen Lengthdefine(t 015) Wind Screen Width Wind Screen Coordinatesdefine(x1 calc(0minus1300))define(x2 calc(x1minust))define(y1 calc(hminus025))define(y2 calc(y1+L))
4 num cornerpointsSCREEN3(SCHEME3)03 00 release distancespacing hull002 0001 00 minus01 merg1merg2merg3merg4minus4 minus3 minus1 minus3 minus1 section color codingdragliftmomentdisplrotation1 x2 y1 n11 x1 y1 n21 x1 y2 n11 x2 y2 n2
David Gutierrez Rivera Aerodynamic Shape Optimization 33 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Objective Function
function [Drag] = M4 Neath ViaductWS(X) M4 Neath ViaductWS Objective Functionsteps = 500
Drag(1) = VXF FORCES(XDRAGMAXstepsSECTION11)Drag(2) = VXF FORCES(XDRAGMAXstepsevalfalseSECTION12)Drag(3) = VXF FORCES(XDRAGMAXstepsevalfalseSECTION13)Drag(4) = VXF FORCES(XDRAGMAXstepsevalfalseSECTION14)
[DragLane] = max(Drag())
Call optiOUT to generate Plots and Output DataoptiOUT(X [Drag])
end
David Gutierrez Rivera Aerodynamic Shape Optimization 34 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Data Points
David Gutierrez Rivera Aerodynamic Shape Optimization 35 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Run-Time Optimization
David Gutierrez Rivera Aerodynamic Shape Optimization 36 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Vertical-Axis Wind Turbine (VAWT)
Description
The Savonius Wind Turbine is a Vertical-Axis Wind Turbine (VAWT)which main advantages are its reliability and practicality
David Gutierrez Rivera Aerodynamic Shape Optimization 37 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Model
Description
Find optimum values of ex and ey to maximize Torque or Power
Constrained to the shaded area
David Gutierrez Rivera Aerodynamic Shape Optimization 38 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Model
Description
Find optimum values of ex and ey to maximize Torque or Power
Constrained to the shaded area
David Gutierrez Rivera Aerodynamic Shape Optimization 38 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Dynamic Model
David Gutierrez Rivera Aerodynamic Shape Optimization 39 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Examples
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 30 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
M4 Neath Viaduct Wind Shield
Description
This bridge is located in South Wales and crosses the River Neath Asection of the bridge is very exposed in flat topography therefore a windshielding system is desired for reducing the overturning forces on vehicles
Description
The CFD model is the same as the one used on the VXFlow tutorial
Four small sections were used to obtain the interior drag forces
David Gutierrez Rivera Aerodynamic Shape Optimization 31 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
M4 Neath Viaduct Wind Shield
Description
The CFD model is the same as the one used on the VXFlow tutorial
Four small sections were used to obtain the interior drag forces
David Gutierrez Rivera Aerodynamic Shape Optimization 31 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
M4 Neath Viaduct Wind Shield
Description
The CFD model is the same as the one used on the VXFlow tutorial
Four small sections were used to obtain the interior drag forces
David Gutierrez Rivera Aerodynamic Shape Optimization 31 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Model
Find optimum height (h) for the Wind Shield
David Gutierrez Rivera Aerodynamic Shape Optimization 32 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Parameter File
Variables Definitions[beginvariables]define(h ) Height of Wind Screen[endvariables]define(L 300) Wind Screen Lengthdefine(t 015) Wind Screen Width Wind Screen Coordinatesdefine(x1 calc(0minus1300))define(x2 calc(x1minust))define(y1 calc(hminus025))define(y2 calc(y1+L))
4 num cornerpointsSCREEN3(SCHEME3)03 00 release distancespacing hull002 0001 00 minus01 merg1merg2merg3merg4minus4 minus3 minus1 minus3 minus1 section color codingdragliftmomentdisplrotation1 x2 y1 n11 x1 y1 n21 x1 y2 n11 x2 y2 n2
David Gutierrez Rivera Aerodynamic Shape Optimization 33 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Parameter File
Variables Definitions[beginvariables]define(h ) Height of Wind Screen[endvariables]define(L 300) Wind Screen Lengthdefine(t 015) Wind Screen Width Wind Screen Coordinatesdefine(x1 calc(0minus1300))define(x2 calc(x1minust))define(y1 calc(hminus025))define(y2 calc(y1+L))
4 num cornerpointsSCREEN3(SCHEME3)03 00 release distancespacing hull002 0001 00 minus01 merg1merg2merg3merg4minus4 minus3 minus1 minus3 minus1 section color codingdragliftmomentdisplrotation1 x2 y1 n11 x1 y1 n21 x1 y2 n11 x2 y2 n2
David Gutierrez Rivera Aerodynamic Shape Optimization 33 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Objective Function
function [Drag] = M4 Neath ViaductWS(X) M4 Neath ViaductWS Objective Functionsteps = 500
Drag(1) = VXF FORCES(XDRAGMAXstepsSECTION11)Drag(2) = VXF FORCES(XDRAGMAXstepsevalfalseSECTION12)Drag(3) = VXF FORCES(XDRAGMAXstepsevalfalseSECTION13)Drag(4) = VXF FORCES(XDRAGMAXstepsevalfalseSECTION14)
[DragLane] = max(Drag())
Call optiOUT to generate Plots and Output DataoptiOUT(X [Drag])
end
David Gutierrez Rivera Aerodynamic Shape Optimization 34 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Data Points
David Gutierrez Rivera Aerodynamic Shape Optimization 35 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Run-Time Optimization
David Gutierrez Rivera Aerodynamic Shape Optimization 36 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Vertical-Axis Wind Turbine (VAWT)
Description
The Savonius Wind Turbine is a Vertical-Axis Wind Turbine (VAWT)which main advantages are its reliability and practicality
David Gutierrez Rivera Aerodynamic Shape Optimization 37 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Model
Description
Find optimum values of ex and ey to maximize Torque or Power
Constrained to the shaded area
David Gutierrez Rivera Aerodynamic Shape Optimization 38 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Model
Description
Find optimum values of ex and ey to maximize Torque or Power
Constrained to the shaded area
David Gutierrez Rivera Aerodynamic Shape Optimization 38 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Dynamic Model
David Gutierrez Rivera Aerodynamic Shape Optimization 39 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
M4 Neath Viaduct Wind Shield
Description
This bridge is located in South Wales and crosses the River Neath Asection of the bridge is very exposed in flat topography therefore a windshielding system is desired for reducing the overturning forces on vehicles
Description
The CFD model is the same as the one used on the VXFlow tutorial
Four small sections were used to obtain the interior drag forces
David Gutierrez Rivera Aerodynamic Shape Optimization 31 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
M4 Neath Viaduct Wind Shield
Description
The CFD model is the same as the one used on the VXFlow tutorial
Four small sections were used to obtain the interior drag forces
David Gutierrez Rivera Aerodynamic Shape Optimization 31 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
M4 Neath Viaduct Wind Shield
Description
The CFD model is the same as the one used on the VXFlow tutorial
Four small sections were used to obtain the interior drag forces
David Gutierrez Rivera Aerodynamic Shape Optimization 31 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Model
Find optimum height (h) for the Wind Shield
David Gutierrez Rivera Aerodynamic Shape Optimization 32 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Parameter File
Variables Definitions[beginvariables]define(h ) Height of Wind Screen[endvariables]define(L 300) Wind Screen Lengthdefine(t 015) Wind Screen Width Wind Screen Coordinatesdefine(x1 calc(0minus1300))define(x2 calc(x1minust))define(y1 calc(hminus025))define(y2 calc(y1+L))
4 num cornerpointsSCREEN3(SCHEME3)03 00 release distancespacing hull002 0001 00 minus01 merg1merg2merg3merg4minus4 minus3 minus1 minus3 minus1 section color codingdragliftmomentdisplrotation1 x2 y1 n11 x1 y1 n21 x1 y2 n11 x2 y2 n2
David Gutierrez Rivera Aerodynamic Shape Optimization 33 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Parameter File
Variables Definitions[beginvariables]define(h ) Height of Wind Screen[endvariables]define(L 300) Wind Screen Lengthdefine(t 015) Wind Screen Width Wind Screen Coordinatesdefine(x1 calc(0minus1300))define(x2 calc(x1minust))define(y1 calc(hminus025))define(y2 calc(y1+L))
4 num cornerpointsSCREEN3(SCHEME3)03 00 release distancespacing hull002 0001 00 minus01 merg1merg2merg3merg4minus4 minus3 minus1 minus3 minus1 section color codingdragliftmomentdisplrotation1 x2 y1 n11 x1 y1 n21 x1 y2 n11 x2 y2 n2
David Gutierrez Rivera Aerodynamic Shape Optimization 33 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Objective Function
function [Drag] = M4 Neath ViaductWS(X) M4 Neath ViaductWS Objective Functionsteps = 500
Drag(1) = VXF FORCES(XDRAGMAXstepsSECTION11)Drag(2) = VXF FORCES(XDRAGMAXstepsevalfalseSECTION12)Drag(3) = VXF FORCES(XDRAGMAXstepsevalfalseSECTION13)Drag(4) = VXF FORCES(XDRAGMAXstepsevalfalseSECTION14)
[DragLane] = max(Drag())
Call optiOUT to generate Plots and Output DataoptiOUT(X [Drag])
end
David Gutierrez Rivera Aerodynamic Shape Optimization 34 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Data Points
David Gutierrez Rivera Aerodynamic Shape Optimization 35 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Run-Time Optimization
David Gutierrez Rivera Aerodynamic Shape Optimization 36 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Vertical-Axis Wind Turbine (VAWT)
Description
The Savonius Wind Turbine is a Vertical-Axis Wind Turbine (VAWT)which main advantages are its reliability and practicality
David Gutierrez Rivera Aerodynamic Shape Optimization 37 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Model
Description
Find optimum values of ex and ey to maximize Torque or Power
Constrained to the shaded area
David Gutierrez Rivera Aerodynamic Shape Optimization 38 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Model
Description
Find optimum values of ex and ey to maximize Torque or Power
Constrained to the shaded area
David Gutierrez Rivera Aerodynamic Shape Optimization 38 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Dynamic Model
David Gutierrez Rivera Aerodynamic Shape Optimization 39 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
M4 Neath Viaduct Wind Shield
Description
The CFD model is the same as the one used on the VXFlow tutorial
Four small sections were used to obtain the interior drag forces
David Gutierrez Rivera Aerodynamic Shape Optimization 31 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
M4 Neath Viaduct Wind Shield
Description
The CFD model is the same as the one used on the VXFlow tutorial
Four small sections were used to obtain the interior drag forces
David Gutierrez Rivera Aerodynamic Shape Optimization 31 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Model
Find optimum height (h) for the Wind Shield
David Gutierrez Rivera Aerodynamic Shape Optimization 32 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Parameter File
Variables Definitions[beginvariables]define(h ) Height of Wind Screen[endvariables]define(L 300) Wind Screen Lengthdefine(t 015) Wind Screen Width Wind Screen Coordinatesdefine(x1 calc(0minus1300))define(x2 calc(x1minust))define(y1 calc(hminus025))define(y2 calc(y1+L))
4 num cornerpointsSCREEN3(SCHEME3)03 00 release distancespacing hull002 0001 00 minus01 merg1merg2merg3merg4minus4 minus3 minus1 minus3 minus1 section color codingdragliftmomentdisplrotation1 x2 y1 n11 x1 y1 n21 x1 y2 n11 x2 y2 n2
David Gutierrez Rivera Aerodynamic Shape Optimization 33 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Parameter File
Variables Definitions[beginvariables]define(h ) Height of Wind Screen[endvariables]define(L 300) Wind Screen Lengthdefine(t 015) Wind Screen Width Wind Screen Coordinatesdefine(x1 calc(0minus1300))define(x2 calc(x1minust))define(y1 calc(hminus025))define(y2 calc(y1+L))
4 num cornerpointsSCREEN3(SCHEME3)03 00 release distancespacing hull002 0001 00 minus01 merg1merg2merg3merg4minus4 minus3 minus1 minus3 minus1 section color codingdragliftmomentdisplrotation1 x2 y1 n11 x1 y1 n21 x1 y2 n11 x2 y2 n2
David Gutierrez Rivera Aerodynamic Shape Optimization 33 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Objective Function
function [Drag] = M4 Neath ViaductWS(X) M4 Neath ViaductWS Objective Functionsteps = 500
Drag(1) = VXF FORCES(XDRAGMAXstepsSECTION11)Drag(2) = VXF FORCES(XDRAGMAXstepsevalfalseSECTION12)Drag(3) = VXF FORCES(XDRAGMAXstepsevalfalseSECTION13)Drag(4) = VXF FORCES(XDRAGMAXstepsevalfalseSECTION14)
[DragLane] = max(Drag())
Call optiOUT to generate Plots and Output DataoptiOUT(X [Drag])
end
David Gutierrez Rivera Aerodynamic Shape Optimization 34 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Data Points
David Gutierrez Rivera Aerodynamic Shape Optimization 35 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Run-Time Optimization
David Gutierrez Rivera Aerodynamic Shape Optimization 36 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Vertical-Axis Wind Turbine (VAWT)
Description
The Savonius Wind Turbine is a Vertical-Axis Wind Turbine (VAWT)which main advantages are its reliability and practicality
David Gutierrez Rivera Aerodynamic Shape Optimization 37 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Model
Description
Find optimum values of ex and ey to maximize Torque or Power
Constrained to the shaded area
David Gutierrez Rivera Aerodynamic Shape Optimization 38 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Model
Description
Find optimum values of ex and ey to maximize Torque or Power
Constrained to the shaded area
David Gutierrez Rivera Aerodynamic Shape Optimization 38 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Dynamic Model
David Gutierrez Rivera Aerodynamic Shape Optimization 39 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
M4 Neath Viaduct Wind Shield
Description
The CFD model is the same as the one used on the VXFlow tutorial
Four small sections were used to obtain the interior drag forces
David Gutierrez Rivera Aerodynamic Shape Optimization 31 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Model
Find optimum height (h) for the Wind Shield
David Gutierrez Rivera Aerodynamic Shape Optimization 32 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Parameter File
Variables Definitions[beginvariables]define(h ) Height of Wind Screen[endvariables]define(L 300) Wind Screen Lengthdefine(t 015) Wind Screen Width Wind Screen Coordinatesdefine(x1 calc(0minus1300))define(x2 calc(x1minust))define(y1 calc(hminus025))define(y2 calc(y1+L))
4 num cornerpointsSCREEN3(SCHEME3)03 00 release distancespacing hull002 0001 00 minus01 merg1merg2merg3merg4minus4 minus3 minus1 minus3 minus1 section color codingdragliftmomentdisplrotation1 x2 y1 n11 x1 y1 n21 x1 y2 n11 x2 y2 n2
David Gutierrez Rivera Aerodynamic Shape Optimization 33 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Parameter File
Variables Definitions[beginvariables]define(h ) Height of Wind Screen[endvariables]define(L 300) Wind Screen Lengthdefine(t 015) Wind Screen Width Wind Screen Coordinatesdefine(x1 calc(0minus1300))define(x2 calc(x1minust))define(y1 calc(hminus025))define(y2 calc(y1+L))
4 num cornerpointsSCREEN3(SCHEME3)03 00 release distancespacing hull002 0001 00 minus01 merg1merg2merg3merg4minus4 minus3 minus1 minus3 minus1 section color codingdragliftmomentdisplrotation1 x2 y1 n11 x1 y1 n21 x1 y2 n11 x2 y2 n2
David Gutierrez Rivera Aerodynamic Shape Optimization 33 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Objective Function
function [Drag] = M4 Neath ViaductWS(X) M4 Neath ViaductWS Objective Functionsteps = 500
Drag(1) = VXF FORCES(XDRAGMAXstepsSECTION11)Drag(2) = VXF FORCES(XDRAGMAXstepsevalfalseSECTION12)Drag(3) = VXF FORCES(XDRAGMAXstepsevalfalseSECTION13)Drag(4) = VXF FORCES(XDRAGMAXstepsevalfalseSECTION14)
[DragLane] = max(Drag())
Call optiOUT to generate Plots and Output DataoptiOUT(X [Drag])
end
David Gutierrez Rivera Aerodynamic Shape Optimization 34 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Data Points
David Gutierrez Rivera Aerodynamic Shape Optimization 35 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Run-Time Optimization
David Gutierrez Rivera Aerodynamic Shape Optimization 36 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Vertical-Axis Wind Turbine (VAWT)
Description
The Savonius Wind Turbine is a Vertical-Axis Wind Turbine (VAWT)which main advantages are its reliability and practicality
David Gutierrez Rivera Aerodynamic Shape Optimization 37 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Model
Description
Find optimum values of ex and ey to maximize Torque or Power
Constrained to the shaded area
David Gutierrez Rivera Aerodynamic Shape Optimization 38 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Model
Description
Find optimum values of ex and ey to maximize Torque or Power
Constrained to the shaded area
David Gutierrez Rivera Aerodynamic Shape Optimization 38 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Dynamic Model
David Gutierrez Rivera Aerodynamic Shape Optimization 39 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Model
Find optimum height (h) for the Wind Shield
David Gutierrez Rivera Aerodynamic Shape Optimization 32 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Parameter File
Variables Definitions[beginvariables]define(h ) Height of Wind Screen[endvariables]define(L 300) Wind Screen Lengthdefine(t 015) Wind Screen Width Wind Screen Coordinatesdefine(x1 calc(0minus1300))define(x2 calc(x1minust))define(y1 calc(hminus025))define(y2 calc(y1+L))
4 num cornerpointsSCREEN3(SCHEME3)03 00 release distancespacing hull002 0001 00 minus01 merg1merg2merg3merg4minus4 minus3 minus1 minus3 minus1 section color codingdragliftmomentdisplrotation1 x2 y1 n11 x1 y1 n21 x1 y2 n11 x2 y2 n2
David Gutierrez Rivera Aerodynamic Shape Optimization 33 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Parameter File
Variables Definitions[beginvariables]define(h ) Height of Wind Screen[endvariables]define(L 300) Wind Screen Lengthdefine(t 015) Wind Screen Width Wind Screen Coordinatesdefine(x1 calc(0minus1300))define(x2 calc(x1minust))define(y1 calc(hminus025))define(y2 calc(y1+L))
4 num cornerpointsSCREEN3(SCHEME3)03 00 release distancespacing hull002 0001 00 minus01 merg1merg2merg3merg4minus4 minus3 minus1 minus3 minus1 section color codingdragliftmomentdisplrotation1 x2 y1 n11 x1 y1 n21 x1 y2 n11 x2 y2 n2
David Gutierrez Rivera Aerodynamic Shape Optimization 33 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Objective Function
function [Drag] = M4 Neath ViaductWS(X) M4 Neath ViaductWS Objective Functionsteps = 500
Drag(1) = VXF FORCES(XDRAGMAXstepsSECTION11)Drag(2) = VXF FORCES(XDRAGMAXstepsevalfalseSECTION12)Drag(3) = VXF FORCES(XDRAGMAXstepsevalfalseSECTION13)Drag(4) = VXF FORCES(XDRAGMAXstepsevalfalseSECTION14)
[DragLane] = max(Drag())
Call optiOUT to generate Plots and Output DataoptiOUT(X [Drag])
end
David Gutierrez Rivera Aerodynamic Shape Optimization 34 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Data Points
David Gutierrez Rivera Aerodynamic Shape Optimization 35 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Run-Time Optimization
David Gutierrez Rivera Aerodynamic Shape Optimization 36 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Vertical-Axis Wind Turbine (VAWT)
Description
The Savonius Wind Turbine is a Vertical-Axis Wind Turbine (VAWT)which main advantages are its reliability and practicality
David Gutierrez Rivera Aerodynamic Shape Optimization 37 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Model
Description
Find optimum values of ex and ey to maximize Torque or Power
Constrained to the shaded area
David Gutierrez Rivera Aerodynamic Shape Optimization 38 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Model
Description
Find optimum values of ex and ey to maximize Torque or Power
Constrained to the shaded area
David Gutierrez Rivera Aerodynamic Shape Optimization 38 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Dynamic Model
David Gutierrez Rivera Aerodynamic Shape Optimization 39 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Parameter File
Variables Definitions[beginvariables]define(h ) Height of Wind Screen[endvariables]define(L 300) Wind Screen Lengthdefine(t 015) Wind Screen Width Wind Screen Coordinatesdefine(x1 calc(0minus1300))define(x2 calc(x1minust))define(y1 calc(hminus025))define(y2 calc(y1+L))
4 num cornerpointsSCREEN3(SCHEME3)03 00 release distancespacing hull002 0001 00 minus01 merg1merg2merg3merg4minus4 minus3 minus1 minus3 minus1 section color codingdragliftmomentdisplrotation1 x2 y1 n11 x1 y1 n21 x1 y2 n11 x2 y2 n2
David Gutierrez Rivera Aerodynamic Shape Optimization 33 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Parameter File
Variables Definitions[beginvariables]define(h ) Height of Wind Screen[endvariables]define(L 300) Wind Screen Lengthdefine(t 015) Wind Screen Width Wind Screen Coordinatesdefine(x1 calc(0minus1300))define(x2 calc(x1minust))define(y1 calc(hminus025))define(y2 calc(y1+L))
4 num cornerpointsSCREEN3(SCHEME3)03 00 release distancespacing hull002 0001 00 minus01 merg1merg2merg3merg4minus4 minus3 minus1 minus3 minus1 section color codingdragliftmomentdisplrotation1 x2 y1 n11 x1 y1 n21 x1 y2 n11 x2 y2 n2
David Gutierrez Rivera Aerodynamic Shape Optimization 33 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Objective Function
function [Drag] = M4 Neath ViaductWS(X) M4 Neath ViaductWS Objective Functionsteps = 500
Drag(1) = VXF FORCES(XDRAGMAXstepsSECTION11)Drag(2) = VXF FORCES(XDRAGMAXstepsevalfalseSECTION12)Drag(3) = VXF FORCES(XDRAGMAXstepsevalfalseSECTION13)Drag(4) = VXF FORCES(XDRAGMAXstepsevalfalseSECTION14)
[DragLane] = max(Drag())
Call optiOUT to generate Plots and Output DataoptiOUT(X [Drag])
end
David Gutierrez Rivera Aerodynamic Shape Optimization 34 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Data Points
David Gutierrez Rivera Aerodynamic Shape Optimization 35 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Run-Time Optimization
David Gutierrez Rivera Aerodynamic Shape Optimization 36 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Vertical-Axis Wind Turbine (VAWT)
Description
The Savonius Wind Turbine is a Vertical-Axis Wind Turbine (VAWT)which main advantages are its reliability and practicality
David Gutierrez Rivera Aerodynamic Shape Optimization 37 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Model
Description
Find optimum values of ex and ey to maximize Torque or Power
Constrained to the shaded area
David Gutierrez Rivera Aerodynamic Shape Optimization 38 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Model
Description
Find optimum values of ex and ey to maximize Torque or Power
Constrained to the shaded area
David Gutierrez Rivera Aerodynamic Shape Optimization 38 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Dynamic Model
David Gutierrez Rivera Aerodynamic Shape Optimization 39 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Parameter File
Variables Definitions[beginvariables]define(h ) Height of Wind Screen[endvariables]define(L 300) Wind Screen Lengthdefine(t 015) Wind Screen Width Wind Screen Coordinatesdefine(x1 calc(0minus1300))define(x2 calc(x1minust))define(y1 calc(hminus025))define(y2 calc(y1+L))
4 num cornerpointsSCREEN3(SCHEME3)03 00 release distancespacing hull002 0001 00 minus01 merg1merg2merg3merg4minus4 minus3 minus1 minus3 minus1 section color codingdragliftmomentdisplrotation1 x2 y1 n11 x1 y1 n21 x1 y2 n11 x2 y2 n2
David Gutierrez Rivera Aerodynamic Shape Optimization 33 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Objective Function
function [Drag] = M4 Neath ViaductWS(X) M4 Neath ViaductWS Objective Functionsteps = 500
Drag(1) = VXF FORCES(XDRAGMAXstepsSECTION11)Drag(2) = VXF FORCES(XDRAGMAXstepsevalfalseSECTION12)Drag(3) = VXF FORCES(XDRAGMAXstepsevalfalseSECTION13)Drag(4) = VXF FORCES(XDRAGMAXstepsevalfalseSECTION14)
[DragLane] = max(Drag())
Call optiOUT to generate Plots and Output DataoptiOUT(X [Drag])
end
David Gutierrez Rivera Aerodynamic Shape Optimization 34 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Data Points
David Gutierrez Rivera Aerodynamic Shape Optimization 35 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Run-Time Optimization
David Gutierrez Rivera Aerodynamic Shape Optimization 36 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Vertical-Axis Wind Turbine (VAWT)
Description
The Savonius Wind Turbine is a Vertical-Axis Wind Turbine (VAWT)which main advantages are its reliability and practicality
David Gutierrez Rivera Aerodynamic Shape Optimization 37 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Model
Description
Find optimum values of ex and ey to maximize Torque or Power
Constrained to the shaded area
David Gutierrez Rivera Aerodynamic Shape Optimization 38 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Model
Description
Find optimum values of ex and ey to maximize Torque or Power
Constrained to the shaded area
David Gutierrez Rivera Aerodynamic Shape Optimization 38 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Dynamic Model
David Gutierrez Rivera Aerodynamic Shape Optimization 39 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Objective Function
function [Drag] = M4 Neath ViaductWS(X) M4 Neath ViaductWS Objective Functionsteps = 500
Drag(1) = VXF FORCES(XDRAGMAXstepsSECTION11)Drag(2) = VXF FORCES(XDRAGMAXstepsevalfalseSECTION12)Drag(3) = VXF FORCES(XDRAGMAXstepsevalfalseSECTION13)Drag(4) = VXF FORCES(XDRAGMAXstepsevalfalseSECTION14)
[DragLane] = max(Drag())
Call optiOUT to generate Plots and Output DataoptiOUT(X [Drag])
end
David Gutierrez Rivera Aerodynamic Shape Optimization 34 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Data Points
David Gutierrez Rivera Aerodynamic Shape Optimization 35 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Run-Time Optimization
David Gutierrez Rivera Aerodynamic Shape Optimization 36 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Vertical-Axis Wind Turbine (VAWT)
Description
The Savonius Wind Turbine is a Vertical-Axis Wind Turbine (VAWT)which main advantages are its reliability and practicality
David Gutierrez Rivera Aerodynamic Shape Optimization 37 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Model
Description
Find optimum values of ex and ey to maximize Torque or Power
Constrained to the shaded area
David Gutierrez Rivera Aerodynamic Shape Optimization 38 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Model
Description
Find optimum values of ex and ey to maximize Torque or Power
Constrained to the shaded area
David Gutierrez Rivera Aerodynamic Shape Optimization 38 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Dynamic Model
David Gutierrez Rivera Aerodynamic Shape Optimization 39 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Data Points
David Gutierrez Rivera Aerodynamic Shape Optimization 35 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Run-Time Optimization
David Gutierrez Rivera Aerodynamic Shape Optimization 36 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Vertical-Axis Wind Turbine (VAWT)
Description
The Savonius Wind Turbine is a Vertical-Axis Wind Turbine (VAWT)which main advantages are its reliability and practicality
David Gutierrez Rivera Aerodynamic Shape Optimization 37 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Model
Description
Find optimum values of ex and ey to maximize Torque or Power
Constrained to the shaded area
David Gutierrez Rivera Aerodynamic Shape Optimization 38 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Model
Description
Find optimum values of ex and ey to maximize Torque or Power
Constrained to the shaded area
David Gutierrez Rivera Aerodynamic Shape Optimization 38 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Dynamic Model
David Gutierrez Rivera Aerodynamic Shape Optimization 39 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Run-Time Optimization
David Gutierrez Rivera Aerodynamic Shape Optimization 36 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Vertical-Axis Wind Turbine (VAWT)
Description
The Savonius Wind Turbine is a Vertical-Axis Wind Turbine (VAWT)which main advantages are its reliability and practicality
David Gutierrez Rivera Aerodynamic Shape Optimization 37 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Model
Description
Find optimum values of ex and ey to maximize Torque or Power
Constrained to the shaded area
David Gutierrez Rivera Aerodynamic Shape Optimization 38 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Model
Description
Find optimum values of ex and ey to maximize Torque or Power
Constrained to the shaded area
David Gutierrez Rivera Aerodynamic Shape Optimization 38 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Dynamic Model
David Gutierrez Rivera Aerodynamic Shape Optimization 39 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Vertical-Axis Wind Turbine (VAWT)
Description
The Savonius Wind Turbine is a Vertical-Axis Wind Turbine (VAWT)which main advantages are its reliability and practicality
David Gutierrez Rivera Aerodynamic Shape Optimization 37 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Model
Description
Find optimum values of ex and ey to maximize Torque or Power
Constrained to the shaded area
David Gutierrez Rivera Aerodynamic Shape Optimization 38 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Model
Description
Find optimum values of ex and ey to maximize Torque or Power
Constrained to the shaded area
David Gutierrez Rivera Aerodynamic Shape Optimization 38 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Dynamic Model
David Gutierrez Rivera Aerodynamic Shape Optimization 39 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Model
Description
Find optimum values of ex and ey to maximize Torque or Power
Constrained to the shaded area
David Gutierrez Rivera Aerodynamic Shape Optimization 38 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Model
Description
Find optimum values of ex and ey to maximize Torque or Power
Constrained to the shaded area
David Gutierrez Rivera Aerodynamic Shape Optimization 38 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Dynamic Model
David Gutierrez Rivera Aerodynamic Shape Optimization 39 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Optimization Model
Description
Find optimum values of ex and ey to maximize Torque or Power
Constrained to the shaded area
David Gutierrez Rivera Aerodynamic Shape Optimization 38 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Dynamic Model
David Gutierrez Rivera Aerodynamic Shape Optimization 39 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Dynamic Model
David Gutierrez Rivera Aerodynamic Shape Optimization 39 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Parameter File
Variables Definitions[beginvariables]define(ex calc(01+Imper)) Eccentricity in XminusDirdefine(ey calc(01+Imper)) Eccentricity in YminusDir[endvariables] Rotor Dimensionsdefine(D1 0572) Rotor Inside Diameterdefine(D2 0584) Rotor Outside Diameterdefine(t calc(D2minusD1)) Rotor Thickness
David Gutierrez Rivera Aerodynamic Shape Optimization 40 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Parameter File
Coord Calculations
Section 1define(x1 calc(minus(ex2)))define(y11 calc(D1minus(ey2)))define(y12 calc(y11minusD1))define(y13 calc(y12minust))define(y14 calc(y11+t))define(xc1 calc(minus(ex2)))define(yc1 calc(y11minusD12))
Section 2define(x2 calc(ex2))define(y21 calc(minusD1+(ey2)))define(y22 calc(y21+D1))define(y23 calc(y22+t))define(y24 calc(y21minust))define(xc2 calc(ex2))define(yc2 calc(y21+D12))
David Gutierrez Rivera Aerodynamic Shape Optimization 41 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Parameter File
4 num cornerpoints02 00 release distancespacing hull00 0002 00 minus002 merg1merg2merg3merg4minus4 4 minus1 minus3 minus1 section color codingdragliftmomentdisplrotation3 x1 y11 nd1 xc1 yc11 x1 y12 nt2 x1 y13 nd2 xc1 yc11 x1 y14 nt4 num cornerpoints02 00 release distancespacing hull00 0002 00 minus002 merg1merg2merg3merg4minus4 4 minus1 minus3 minus1 section color codingdragliftmomentdisplrotation3 x2 y21 nd1 xc2 yc21 x2 y22 nt2 x2 y23 nd2 xc2 yc21 x2 y24 nt
David Gutierrez Rivera Aerodynamic Shape Optimization 42 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Objective Function
f u n c t i o n [ Power ] = r o t o r d y n a (X) r o t o r d y n a O b j e c t i v e F u n c t i o nV a r i a b l e s = g e t a p p d a t a ( 0 V a r i a b l e s ) V a r i a b l e s DatamodelPATH = g e t a p p d a t a ( 0 modelPATH ) Model Path
S a v o n i o u s Rotor DataD = 0 5 7 8 Rotor Avg Diameter [m]m = 1 0 Mass [ kg ]
C a l c u l a t e Arm v e c t o rArm = [minusX( 1 ) 2 minusX( 2 ) 2 ] + [ ( 4 6 )lowastD pi D 2 ] Arm = norm (Arm )
C a l c u l a t e I n e r t i a l MassMass = 2lowastmlowastArm ˆ 2
m4Mod( MASS22 Mass f u l l f i l e ( modelPATH V a r i a b l e s FILE ) )
Angu la r V e l o c i t yOmega = VXF DERIV (X RDISPL TIME 5 0 SECTION 1 ) Omega = mean (Omega )
T o r s i o n a l ForceTorque = VXF FORCES(X MOMENT MEAN 5 0 e v a l f a l s e ) Power = Torque lowast Omega
C a l l optiOUT to g e n e r a t e P l o t s and Output DataoptiOUT (X [ Power ] )
end
David Gutierrez Rivera Aerodynamic Shape Optimization 43 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Data Points
David Gutierrez Rivera Aerodynamic Shape Optimization 44 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Final Shape
David Gutierrez Rivera Aerodynamic Shape Optimization 45 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Final Remarks
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 46 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Final Remarks
The Vortex Particle Method is a
Relatively low computational cost and highly accurate simulation
A mesh-free numerical method
David Gutierrez Rivera Aerodynamic Shape Optimization 47 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Final Remarks
The Vortex Particle Method is a
Relatively low computational cost and highly accurate simulation
A mesh-free numerical method
David Gutierrez Rivera Aerodynamic Shape Optimization 47 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Final Remarks
The Vortex Particle Method is a
Relatively low computational cost and highly accurate simulation
A mesh-free numerical method
David Gutierrez Rivera Aerodynamic Shape Optimization 47 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Final Remarks
Some Recommendations
Tweak Local Optimization Algorithms
Run-Time Smoothing
Global Optimization Algorithms
Parallelization
David Gutierrez Rivera Aerodynamic Shape Optimization 48 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Final Remarks
Some Recommendations
Tweak Local Optimization Algorithms
Run-Time Smoothing
Global Optimization Algorithms
Parallelization
David Gutierrez Rivera Aerodynamic Shape Optimization 48 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Final Remarks
Some Recommendations
Tweak Local Optimization Algorithms
Run-Time Smoothing
Global Optimization Algorithms
Parallelization
David Gutierrez Rivera Aerodynamic Shape Optimization 48 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Final Remarks
Some Recommendations
Tweak Local Optimization Algorithms
Run-Time Smoothing
Global Optimization Algorithms
Parallelization
David Gutierrez Rivera Aerodynamic Shape Optimization 48 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Final Remarks
Some Recommendations
Tweak Local Optimization Algorithms
Run-Time Smoothing
Global Optimization Algorithms
Parallelization
David Gutierrez Rivera Aerodynamic Shape Optimization 48 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Future Research
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 49 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Future Research
Some ideas
Multi-Disciplinary Optimization (MDO)
Life-Cycle Design
Development of Optimization Algorithms
David Gutierrez Rivera Aerodynamic Shape Optimization 50 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Future Research
Some ideas
Multi-Disciplinary Optimization (MDO)
Life-Cycle Design
Development of Optimization Algorithms
David Gutierrez Rivera Aerodynamic Shape Optimization 50 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Future Research
Some ideas
Multi-Disciplinary Optimization (MDO)
Life-Cycle Design
Development of Optimization Algorithms
David Gutierrez Rivera Aerodynamic Shape Optimization 50 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Future Research
Some ideas
Multi-Disciplinary Optimization (MDO)
Life-Cycle Design
Development of Optimization Algorithms
David Gutierrez Rivera Aerodynamic Shape Optimization 50 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Acknowledgments
Many Thanks to
Prof Guido Morgenthal
MSc Khaled Ibrahim
MSc Benjamin Bendig
MSc Samir Chawdhury
Shanmugam Narayanan
David Gutierrez Rivera Aerodynamic Shape Optimization 51 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
References
Stephen Boyd and Lieven Vandenberghe Convex OptimizationCambridge University Press The Edinburgh Building Cambridge CB28RU UK 2004 Pages 1-11 455-496httpwwwstanfordedu~boydcvxbookbv_cvxbookpdf
Jorge Nocedal and Stephen J Wright Numerical Optimization Springer175 Fifth Avenue New York NY 10010 USA 1999 Pages 2-3 4-710-30
Igor Griva Stephen G Nash and Ariela Sofer Linear and NonlinearOptimization Siam 3600 Market Street 6th Floor Philadelphia PA19104-2688 USA 2nd edition 2009 Pages 35-40 54-58 355-450
David G Luenberger and Yinyu Ye Linear and Nonlinear ProgrammingSpringer 233 Spring Street New YorkNY 10013 USA 3rd edition2008 Pages 2-7 183-257
David Gutierrez Rivera Aerodynamic Shape Optimization 52 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
References
Florent Brunet Contributions to Parametric Image Registration and 3DSurface Reconstruction Universite drsquoAuvergne PhD ThesisNovember 2010 Chapter 2 Pages 27-44httpwwwbrnteupublicationsbrunet2010phdpdf
Prof DK Chaturvedi Advances in Evolutionary OptimizationTechniques YouTube November 2013httpswwwyoutubecomwatchv=ftxiiaHNweQ
David Gutierrez Rivera OptiFlow v061a Weimar Germany March2014 OptiFlow Userguide
Guido Morgenthal Aerodynamic Analysis of Structures UsingHigh-resolution Vortex Particle Methods University of CambridgePhD Thesis October 2002 Pages 21-31 121-142
Wikipedia Savonius wind turbine The Wikimedia Foundation March2014 httpenwikipediaorgwikiSavonius_wind_turbine
David Gutierrez Rivera Aerodynamic Shape Optimization 53 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
References
John James Tomick On Convergence of the Nelder-Mead SimplexAlgorithm for Unconstrained Stochastic Optimization ThePennsylvania State University PhD Thesis May 1995httpwwwdticmildtictrfulltextu2a289453pdf
David Gutierrez Rivera Aerodynamic Shape Optimization 54 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Parameter File
Coord Calculations
Section 1define(x1 calc(minus(ex2)))define(y11 calc(D1minus(ey2)))define(y12 calc(y11minusD1))define(y13 calc(y12minust))define(y14 calc(y11+t))define(xc1 calc(minus(ex2)))define(yc1 calc(y11minusD12))
Section 2define(x2 calc(ex2))define(y21 calc(minusD1+(ey2)))define(y22 calc(y21+D1))define(y23 calc(y22+t))define(y24 calc(y21minust))define(xc2 calc(ex2))define(yc2 calc(y21+D12))
David Gutierrez Rivera Aerodynamic Shape Optimization 41 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Parameter File
4 num cornerpoints02 00 release distancespacing hull00 0002 00 minus002 merg1merg2merg3merg4minus4 4 minus1 minus3 minus1 section color codingdragliftmomentdisplrotation3 x1 y11 nd1 xc1 yc11 x1 y12 nt2 x1 y13 nd2 xc1 yc11 x1 y14 nt4 num cornerpoints02 00 release distancespacing hull00 0002 00 minus002 merg1merg2merg3merg4minus4 4 minus1 minus3 minus1 section color codingdragliftmomentdisplrotation3 x2 y21 nd1 xc2 yc21 x2 y22 nt2 x2 y23 nd2 xc2 yc21 x2 y24 nt
David Gutierrez Rivera Aerodynamic Shape Optimization 42 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Objective Function
f u n c t i o n [ Power ] = r o t o r d y n a (X) r o t o r d y n a O b j e c t i v e F u n c t i o nV a r i a b l e s = g e t a p p d a t a ( 0 V a r i a b l e s ) V a r i a b l e s DatamodelPATH = g e t a p p d a t a ( 0 modelPATH ) Model Path
S a v o n i o u s Rotor DataD = 0 5 7 8 Rotor Avg Diameter [m]m = 1 0 Mass [ kg ]
C a l c u l a t e Arm v e c t o rArm = [minusX( 1 ) 2 minusX( 2 ) 2 ] + [ ( 4 6 )lowastD pi D 2 ] Arm = norm (Arm )
C a l c u l a t e I n e r t i a l MassMass = 2lowastmlowastArm ˆ 2
m4Mod( MASS22 Mass f u l l f i l e ( modelPATH V a r i a b l e s FILE ) )
Angu la r V e l o c i t yOmega = VXF DERIV (X RDISPL TIME 5 0 SECTION 1 ) Omega = mean (Omega )
T o r s i o n a l ForceTorque = VXF FORCES(X MOMENT MEAN 5 0 e v a l f a l s e ) Power = Torque lowast Omega
C a l l optiOUT to g e n e r a t e P l o t s and Output DataoptiOUT (X [ Power ] )
end
David Gutierrez Rivera Aerodynamic Shape Optimization 43 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Data Points
David Gutierrez Rivera Aerodynamic Shape Optimization 44 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Final Shape
David Gutierrez Rivera Aerodynamic Shape Optimization 45 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Final Remarks
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 46 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Final Remarks
The Vortex Particle Method is a
Relatively low computational cost and highly accurate simulation
A mesh-free numerical method
David Gutierrez Rivera Aerodynamic Shape Optimization 47 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Final Remarks
The Vortex Particle Method is a
Relatively low computational cost and highly accurate simulation
A mesh-free numerical method
David Gutierrez Rivera Aerodynamic Shape Optimization 47 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Final Remarks
The Vortex Particle Method is a
Relatively low computational cost and highly accurate simulation
A mesh-free numerical method
David Gutierrez Rivera Aerodynamic Shape Optimization 47 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Final Remarks
Some Recommendations
Tweak Local Optimization Algorithms
Run-Time Smoothing
Global Optimization Algorithms
Parallelization
David Gutierrez Rivera Aerodynamic Shape Optimization 48 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Final Remarks
Some Recommendations
Tweak Local Optimization Algorithms
Run-Time Smoothing
Global Optimization Algorithms
Parallelization
David Gutierrez Rivera Aerodynamic Shape Optimization 48 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Final Remarks
Some Recommendations
Tweak Local Optimization Algorithms
Run-Time Smoothing
Global Optimization Algorithms
Parallelization
David Gutierrez Rivera Aerodynamic Shape Optimization 48 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Final Remarks
Some Recommendations
Tweak Local Optimization Algorithms
Run-Time Smoothing
Global Optimization Algorithms
Parallelization
David Gutierrez Rivera Aerodynamic Shape Optimization 48 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Final Remarks
Some Recommendations
Tweak Local Optimization Algorithms
Run-Time Smoothing
Global Optimization Algorithms
Parallelization
David Gutierrez Rivera Aerodynamic Shape Optimization 48 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Future Research
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 49 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Future Research
Some ideas
Multi-Disciplinary Optimization (MDO)
Life-Cycle Design
Development of Optimization Algorithms
David Gutierrez Rivera Aerodynamic Shape Optimization 50 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Future Research
Some ideas
Multi-Disciplinary Optimization (MDO)
Life-Cycle Design
Development of Optimization Algorithms
David Gutierrez Rivera Aerodynamic Shape Optimization 50 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Future Research
Some ideas
Multi-Disciplinary Optimization (MDO)
Life-Cycle Design
Development of Optimization Algorithms
David Gutierrez Rivera Aerodynamic Shape Optimization 50 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Future Research
Some ideas
Multi-Disciplinary Optimization (MDO)
Life-Cycle Design
Development of Optimization Algorithms
David Gutierrez Rivera Aerodynamic Shape Optimization 50 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Acknowledgments
Many Thanks to
Prof Guido Morgenthal
MSc Khaled Ibrahim
MSc Benjamin Bendig
MSc Samir Chawdhury
Shanmugam Narayanan
David Gutierrez Rivera Aerodynamic Shape Optimization 51 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
References
Stephen Boyd and Lieven Vandenberghe Convex OptimizationCambridge University Press The Edinburgh Building Cambridge CB28RU UK 2004 Pages 1-11 455-496httpwwwstanfordedu~boydcvxbookbv_cvxbookpdf
Jorge Nocedal and Stephen J Wright Numerical Optimization Springer175 Fifth Avenue New York NY 10010 USA 1999 Pages 2-3 4-710-30
Igor Griva Stephen G Nash and Ariela Sofer Linear and NonlinearOptimization Siam 3600 Market Street 6th Floor Philadelphia PA19104-2688 USA 2nd edition 2009 Pages 35-40 54-58 355-450
David G Luenberger and Yinyu Ye Linear and Nonlinear ProgrammingSpringer 233 Spring Street New YorkNY 10013 USA 3rd edition2008 Pages 2-7 183-257
David Gutierrez Rivera Aerodynamic Shape Optimization 52 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
References
Florent Brunet Contributions to Parametric Image Registration and 3DSurface Reconstruction Universite drsquoAuvergne PhD ThesisNovember 2010 Chapter 2 Pages 27-44httpwwwbrnteupublicationsbrunet2010phdpdf
Prof DK Chaturvedi Advances in Evolutionary OptimizationTechniques YouTube November 2013httpswwwyoutubecomwatchv=ftxiiaHNweQ
David Gutierrez Rivera OptiFlow v061a Weimar Germany March2014 OptiFlow Userguide
Guido Morgenthal Aerodynamic Analysis of Structures UsingHigh-resolution Vortex Particle Methods University of CambridgePhD Thesis October 2002 Pages 21-31 121-142
Wikipedia Savonius wind turbine The Wikimedia Foundation March2014 httpenwikipediaorgwikiSavonius_wind_turbine
David Gutierrez Rivera Aerodynamic Shape Optimization 53 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
References
John James Tomick On Convergence of the Nelder-Mead SimplexAlgorithm for Unconstrained Stochastic Optimization ThePennsylvania State University PhD Thesis May 1995httpwwwdticmildtictrfulltextu2a289453pdf
David Gutierrez Rivera Aerodynamic Shape Optimization 54 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Parameter File
4 num cornerpoints02 00 release distancespacing hull00 0002 00 minus002 merg1merg2merg3merg4minus4 4 minus1 minus3 minus1 section color codingdragliftmomentdisplrotation3 x1 y11 nd1 xc1 yc11 x1 y12 nt2 x1 y13 nd2 xc1 yc11 x1 y14 nt4 num cornerpoints02 00 release distancespacing hull00 0002 00 minus002 merg1merg2merg3merg4minus4 4 minus1 minus3 minus1 section color codingdragliftmomentdisplrotation3 x2 y21 nd1 xc2 yc21 x2 y22 nt2 x2 y23 nd2 xc2 yc21 x2 y24 nt
David Gutierrez Rivera Aerodynamic Shape Optimization 42 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Objective Function
f u n c t i o n [ Power ] = r o t o r d y n a (X) r o t o r d y n a O b j e c t i v e F u n c t i o nV a r i a b l e s = g e t a p p d a t a ( 0 V a r i a b l e s ) V a r i a b l e s DatamodelPATH = g e t a p p d a t a ( 0 modelPATH ) Model Path
S a v o n i o u s Rotor DataD = 0 5 7 8 Rotor Avg Diameter [m]m = 1 0 Mass [ kg ]
C a l c u l a t e Arm v e c t o rArm = [minusX( 1 ) 2 minusX( 2 ) 2 ] + [ ( 4 6 )lowastD pi D 2 ] Arm = norm (Arm )
C a l c u l a t e I n e r t i a l MassMass = 2lowastmlowastArm ˆ 2
m4Mod( MASS22 Mass f u l l f i l e ( modelPATH V a r i a b l e s FILE ) )
Angu la r V e l o c i t yOmega = VXF DERIV (X RDISPL TIME 5 0 SECTION 1 ) Omega = mean (Omega )
T o r s i o n a l ForceTorque = VXF FORCES(X MOMENT MEAN 5 0 e v a l f a l s e ) Power = Torque lowast Omega
C a l l optiOUT to g e n e r a t e P l o t s and Output DataoptiOUT (X [ Power ] )
end
David Gutierrez Rivera Aerodynamic Shape Optimization 43 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Data Points
David Gutierrez Rivera Aerodynamic Shape Optimization 44 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Final Shape
David Gutierrez Rivera Aerodynamic Shape Optimization 45 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Final Remarks
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 46 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Final Remarks
The Vortex Particle Method is a
Relatively low computational cost and highly accurate simulation
A mesh-free numerical method
David Gutierrez Rivera Aerodynamic Shape Optimization 47 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Final Remarks
The Vortex Particle Method is a
Relatively low computational cost and highly accurate simulation
A mesh-free numerical method
David Gutierrez Rivera Aerodynamic Shape Optimization 47 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Final Remarks
The Vortex Particle Method is a
Relatively low computational cost and highly accurate simulation
A mesh-free numerical method
David Gutierrez Rivera Aerodynamic Shape Optimization 47 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Final Remarks
Some Recommendations
Tweak Local Optimization Algorithms
Run-Time Smoothing
Global Optimization Algorithms
Parallelization
David Gutierrez Rivera Aerodynamic Shape Optimization 48 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Final Remarks
Some Recommendations
Tweak Local Optimization Algorithms
Run-Time Smoothing
Global Optimization Algorithms
Parallelization
David Gutierrez Rivera Aerodynamic Shape Optimization 48 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Final Remarks
Some Recommendations
Tweak Local Optimization Algorithms
Run-Time Smoothing
Global Optimization Algorithms
Parallelization
David Gutierrez Rivera Aerodynamic Shape Optimization 48 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Final Remarks
Some Recommendations
Tweak Local Optimization Algorithms
Run-Time Smoothing
Global Optimization Algorithms
Parallelization
David Gutierrez Rivera Aerodynamic Shape Optimization 48 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Final Remarks
Some Recommendations
Tweak Local Optimization Algorithms
Run-Time Smoothing
Global Optimization Algorithms
Parallelization
David Gutierrez Rivera Aerodynamic Shape Optimization 48 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Future Research
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 49 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Future Research
Some ideas
Multi-Disciplinary Optimization (MDO)
Life-Cycle Design
Development of Optimization Algorithms
David Gutierrez Rivera Aerodynamic Shape Optimization 50 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Future Research
Some ideas
Multi-Disciplinary Optimization (MDO)
Life-Cycle Design
Development of Optimization Algorithms
David Gutierrez Rivera Aerodynamic Shape Optimization 50 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Future Research
Some ideas
Multi-Disciplinary Optimization (MDO)
Life-Cycle Design
Development of Optimization Algorithms
David Gutierrez Rivera Aerodynamic Shape Optimization 50 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Future Research
Some ideas
Multi-Disciplinary Optimization (MDO)
Life-Cycle Design
Development of Optimization Algorithms
David Gutierrez Rivera Aerodynamic Shape Optimization 50 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Acknowledgments
Many Thanks to
Prof Guido Morgenthal
MSc Khaled Ibrahim
MSc Benjamin Bendig
MSc Samir Chawdhury
Shanmugam Narayanan
David Gutierrez Rivera Aerodynamic Shape Optimization 51 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
References
Stephen Boyd and Lieven Vandenberghe Convex OptimizationCambridge University Press The Edinburgh Building Cambridge CB28RU UK 2004 Pages 1-11 455-496httpwwwstanfordedu~boydcvxbookbv_cvxbookpdf
Jorge Nocedal and Stephen J Wright Numerical Optimization Springer175 Fifth Avenue New York NY 10010 USA 1999 Pages 2-3 4-710-30
Igor Griva Stephen G Nash and Ariela Sofer Linear and NonlinearOptimization Siam 3600 Market Street 6th Floor Philadelphia PA19104-2688 USA 2nd edition 2009 Pages 35-40 54-58 355-450
David G Luenberger and Yinyu Ye Linear and Nonlinear ProgrammingSpringer 233 Spring Street New YorkNY 10013 USA 3rd edition2008 Pages 2-7 183-257
David Gutierrez Rivera Aerodynamic Shape Optimization 52 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
References
Florent Brunet Contributions to Parametric Image Registration and 3DSurface Reconstruction Universite drsquoAuvergne PhD ThesisNovember 2010 Chapter 2 Pages 27-44httpwwwbrnteupublicationsbrunet2010phdpdf
Prof DK Chaturvedi Advances in Evolutionary OptimizationTechniques YouTube November 2013httpswwwyoutubecomwatchv=ftxiiaHNweQ
David Gutierrez Rivera OptiFlow v061a Weimar Germany March2014 OptiFlow Userguide
Guido Morgenthal Aerodynamic Analysis of Structures UsingHigh-resolution Vortex Particle Methods University of CambridgePhD Thesis October 2002 Pages 21-31 121-142
Wikipedia Savonius wind turbine The Wikimedia Foundation March2014 httpenwikipediaorgwikiSavonius_wind_turbine
David Gutierrez Rivera Aerodynamic Shape Optimization 53 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
References
John James Tomick On Convergence of the Nelder-Mead SimplexAlgorithm for Unconstrained Stochastic Optimization ThePennsylvania State University PhD Thesis May 1995httpwwwdticmildtictrfulltextu2a289453pdf
David Gutierrez Rivera Aerodynamic Shape Optimization 54 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Objective Function
f u n c t i o n [ Power ] = r o t o r d y n a (X) r o t o r d y n a O b j e c t i v e F u n c t i o nV a r i a b l e s = g e t a p p d a t a ( 0 V a r i a b l e s ) V a r i a b l e s DatamodelPATH = g e t a p p d a t a ( 0 modelPATH ) Model Path
S a v o n i o u s Rotor DataD = 0 5 7 8 Rotor Avg Diameter [m]m = 1 0 Mass [ kg ]
C a l c u l a t e Arm v e c t o rArm = [minusX( 1 ) 2 minusX( 2 ) 2 ] + [ ( 4 6 )lowastD pi D 2 ] Arm = norm (Arm )
C a l c u l a t e I n e r t i a l MassMass = 2lowastmlowastArm ˆ 2
m4Mod( MASS22 Mass f u l l f i l e ( modelPATH V a r i a b l e s FILE ) )
Angu la r V e l o c i t yOmega = VXF DERIV (X RDISPL TIME 5 0 SECTION 1 ) Omega = mean (Omega )
T o r s i o n a l ForceTorque = VXF FORCES(X MOMENT MEAN 5 0 e v a l f a l s e ) Power = Torque lowast Omega
C a l l optiOUT to g e n e r a t e P l o t s and Output DataoptiOUT (X [ Power ] )
end
David Gutierrez Rivera Aerodynamic Shape Optimization 43 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Data Points
David Gutierrez Rivera Aerodynamic Shape Optimization 44 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Final Shape
David Gutierrez Rivera Aerodynamic Shape Optimization 45 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Final Remarks
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 46 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Final Remarks
The Vortex Particle Method is a
Relatively low computational cost and highly accurate simulation
A mesh-free numerical method
David Gutierrez Rivera Aerodynamic Shape Optimization 47 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Final Remarks
The Vortex Particle Method is a
Relatively low computational cost and highly accurate simulation
A mesh-free numerical method
David Gutierrez Rivera Aerodynamic Shape Optimization 47 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Final Remarks
The Vortex Particle Method is a
Relatively low computational cost and highly accurate simulation
A mesh-free numerical method
David Gutierrez Rivera Aerodynamic Shape Optimization 47 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Final Remarks
Some Recommendations
Tweak Local Optimization Algorithms
Run-Time Smoothing
Global Optimization Algorithms
Parallelization
David Gutierrez Rivera Aerodynamic Shape Optimization 48 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Final Remarks
Some Recommendations
Tweak Local Optimization Algorithms
Run-Time Smoothing
Global Optimization Algorithms
Parallelization
David Gutierrez Rivera Aerodynamic Shape Optimization 48 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Final Remarks
Some Recommendations
Tweak Local Optimization Algorithms
Run-Time Smoothing
Global Optimization Algorithms
Parallelization
David Gutierrez Rivera Aerodynamic Shape Optimization 48 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Final Remarks
Some Recommendations
Tweak Local Optimization Algorithms
Run-Time Smoothing
Global Optimization Algorithms
Parallelization
David Gutierrez Rivera Aerodynamic Shape Optimization 48 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Final Remarks
Some Recommendations
Tweak Local Optimization Algorithms
Run-Time Smoothing
Global Optimization Algorithms
Parallelization
David Gutierrez Rivera Aerodynamic Shape Optimization 48 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Future Research
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 49 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Future Research
Some ideas
Multi-Disciplinary Optimization (MDO)
Life-Cycle Design
Development of Optimization Algorithms
David Gutierrez Rivera Aerodynamic Shape Optimization 50 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Future Research
Some ideas
Multi-Disciplinary Optimization (MDO)
Life-Cycle Design
Development of Optimization Algorithms
David Gutierrez Rivera Aerodynamic Shape Optimization 50 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Future Research
Some ideas
Multi-Disciplinary Optimization (MDO)
Life-Cycle Design
Development of Optimization Algorithms
David Gutierrez Rivera Aerodynamic Shape Optimization 50 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Future Research
Some ideas
Multi-Disciplinary Optimization (MDO)
Life-Cycle Design
Development of Optimization Algorithms
David Gutierrez Rivera Aerodynamic Shape Optimization 50 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Acknowledgments
Many Thanks to
Prof Guido Morgenthal
MSc Khaled Ibrahim
MSc Benjamin Bendig
MSc Samir Chawdhury
Shanmugam Narayanan
David Gutierrez Rivera Aerodynamic Shape Optimization 51 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
References
Stephen Boyd and Lieven Vandenberghe Convex OptimizationCambridge University Press The Edinburgh Building Cambridge CB28RU UK 2004 Pages 1-11 455-496httpwwwstanfordedu~boydcvxbookbv_cvxbookpdf
Jorge Nocedal and Stephen J Wright Numerical Optimization Springer175 Fifth Avenue New York NY 10010 USA 1999 Pages 2-3 4-710-30
Igor Griva Stephen G Nash and Ariela Sofer Linear and NonlinearOptimization Siam 3600 Market Street 6th Floor Philadelphia PA19104-2688 USA 2nd edition 2009 Pages 35-40 54-58 355-450
David G Luenberger and Yinyu Ye Linear and Nonlinear ProgrammingSpringer 233 Spring Street New YorkNY 10013 USA 3rd edition2008 Pages 2-7 183-257
David Gutierrez Rivera Aerodynamic Shape Optimization 52 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
References
Florent Brunet Contributions to Parametric Image Registration and 3DSurface Reconstruction Universite drsquoAuvergne PhD ThesisNovember 2010 Chapter 2 Pages 27-44httpwwwbrnteupublicationsbrunet2010phdpdf
Prof DK Chaturvedi Advances in Evolutionary OptimizationTechniques YouTube November 2013httpswwwyoutubecomwatchv=ftxiiaHNweQ
David Gutierrez Rivera OptiFlow v061a Weimar Germany March2014 OptiFlow Userguide
Guido Morgenthal Aerodynamic Analysis of Structures UsingHigh-resolution Vortex Particle Methods University of CambridgePhD Thesis October 2002 Pages 21-31 121-142
Wikipedia Savonius wind turbine The Wikimedia Foundation March2014 httpenwikipediaorgwikiSavonius_wind_turbine
David Gutierrez Rivera Aerodynamic Shape Optimization 53 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
References
John James Tomick On Convergence of the Nelder-Mead SimplexAlgorithm for Unconstrained Stochastic Optimization ThePennsylvania State University PhD Thesis May 1995httpwwwdticmildtictrfulltextu2a289453pdf
David Gutierrez Rivera Aerodynamic Shape Optimization 54 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Data Points
David Gutierrez Rivera Aerodynamic Shape Optimization 44 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Final Shape
David Gutierrez Rivera Aerodynamic Shape Optimization 45 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Final Remarks
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 46 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Final Remarks
The Vortex Particle Method is a
Relatively low computational cost and highly accurate simulation
A mesh-free numerical method
David Gutierrez Rivera Aerodynamic Shape Optimization 47 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Final Remarks
The Vortex Particle Method is a
Relatively low computational cost and highly accurate simulation
A mesh-free numerical method
David Gutierrez Rivera Aerodynamic Shape Optimization 47 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Final Remarks
The Vortex Particle Method is a
Relatively low computational cost and highly accurate simulation
A mesh-free numerical method
David Gutierrez Rivera Aerodynamic Shape Optimization 47 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Final Remarks
Some Recommendations
Tweak Local Optimization Algorithms
Run-Time Smoothing
Global Optimization Algorithms
Parallelization
David Gutierrez Rivera Aerodynamic Shape Optimization 48 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Final Remarks
Some Recommendations
Tweak Local Optimization Algorithms
Run-Time Smoothing
Global Optimization Algorithms
Parallelization
David Gutierrez Rivera Aerodynamic Shape Optimization 48 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Final Remarks
Some Recommendations
Tweak Local Optimization Algorithms
Run-Time Smoothing
Global Optimization Algorithms
Parallelization
David Gutierrez Rivera Aerodynamic Shape Optimization 48 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Final Remarks
Some Recommendations
Tweak Local Optimization Algorithms
Run-Time Smoothing
Global Optimization Algorithms
Parallelization
David Gutierrez Rivera Aerodynamic Shape Optimization 48 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Final Remarks
Some Recommendations
Tweak Local Optimization Algorithms
Run-Time Smoothing
Global Optimization Algorithms
Parallelization
David Gutierrez Rivera Aerodynamic Shape Optimization 48 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Future Research
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 49 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Future Research
Some ideas
Multi-Disciplinary Optimization (MDO)
Life-Cycle Design
Development of Optimization Algorithms
David Gutierrez Rivera Aerodynamic Shape Optimization 50 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Future Research
Some ideas
Multi-Disciplinary Optimization (MDO)
Life-Cycle Design
Development of Optimization Algorithms
David Gutierrez Rivera Aerodynamic Shape Optimization 50 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Future Research
Some ideas
Multi-Disciplinary Optimization (MDO)
Life-Cycle Design
Development of Optimization Algorithms
David Gutierrez Rivera Aerodynamic Shape Optimization 50 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Future Research
Some ideas
Multi-Disciplinary Optimization (MDO)
Life-Cycle Design
Development of Optimization Algorithms
David Gutierrez Rivera Aerodynamic Shape Optimization 50 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Acknowledgments
Many Thanks to
Prof Guido Morgenthal
MSc Khaled Ibrahim
MSc Benjamin Bendig
MSc Samir Chawdhury
Shanmugam Narayanan
David Gutierrez Rivera Aerodynamic Shape Optimization 51 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
References
Stephen Boyd and Lieven Vandenberghe Convex OptimizationCambridge University Press The Edinburgh Building Cambridge CB28RU UK 2004 Pages 1-11 455-496httpwwwstanfordedu~boydcvxbookbv_cvxbookpdf
Jorge Nocedal and Stephen J Wright Numerical Optimization Springer175 Fifth Avenue New York NY 10010 USA 1999 Pages 2-3 4-710-30
Igor Griva Stephen G Nash and Ariela Sofer Linear and NonlinearOptimization Siam 3600 Market Street 6th Floor Philadelphia PA19104-2688 USA 2nd edition 2009 Pages 35-40 54-58 355-450
David G Luenberger and Yinyu Ye Linear and Nonlinear ProgrammingSpringer 233 Spring Street New YorkNY 10013 USA 3rd edition2008 Pages 2-7 183-257
David Gutierrez Rivera Aerodynamic Shape Optimization 52 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
References
Florent Brunet Contributions to Parametric Image Registration and 3DSurface Reconstruction Universite drsquoAuvergne PhD ThesisNovember 2010 Chapter 2 Pages 27-44httpwwwbrnteupublicationsbrunet2010phdpdf
Prof DK Chaturvedi Advances in Evolutionary OptimizationTechniques YouTube November 2013httpswwwyoutubecomwatchv=ftxiiaHNweQ
David Gutierrez Rivera OptiFlow v061a Weimar Germany March2014 OptiFlow Userguide
Guido Morgenthal Aerodynamic Analysis of Structures UsingHigh-resolution Vortex Particle Methods University of CambridgePhD Thesis October 2002 Pages 21-31 121-142
Wikipedia Savonius wind turbine The Wikimedia Foundation March2014 httpenwikipediaorgwikiSavonius_wind_turbine
David Gutierrez Rivera Aerodynamic Shape Optimization 53 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
References
John James Tomick On Convergence of the Nelder-Mead SimplexAlgorithm for Unconstrained Stochastic Optimization ThePennsylvania State University PhD Thesis May 1995httpwwwdticmildtictrfulltextu2a289453pdf
David Gutierrez Rivera Aerodynamic Shape Optimization 54 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
M4 Neath Viaduct Wind Shield Vertical-Axis Wind Turbine (VAWT)
Final Shape
David Gutierrez Rivera Aerodynamic Shape Optimization 45 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Final Remarks
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 46 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Final Remarks
The Vortex Particle Method is a
Relatively low computational cost and highly accurate simulation
A mesh-free numerical method
David Gutierrez Rivera Aerodynamic Shape Optimization 47 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Final Remarks
The Vortex Particle Method is a
Relatively low computational cost and highly accurate simulation
A mesh-free numerical method
David Gutierrez Rivera Aerodynamic Shape Optimization 47 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Final Remarks
The Vortex Particle Method is a
Relatively low computational cost and highly accurate simulation
A mesh-free numerical method
David Gutierrez Rivera Aerodynamic Shape Optimization 47 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Final Remarks
Some Recommendations
Tweak Local Optimization Algorithms
Run-Time Smoothing
Global Optimization Algorithms
Parallelization
David Gutierrez Rivera Aerodynamic Shape Optimization 48 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Final Remarks
Some Recommendations
Tweak Local Optimization Algorithms
Run-Time Smoothing
Global Optimization Algorithms
Parallelization
David Gutierrez Rivera Aerodynamic Shape Optimization 48 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Final Remarks
Some Recommendations
Tweak Local Optimization Algorithms
Run-Time Smoothing
Global Optimization Algorithms
Parallelization
David Gutierrez Rivera Aerodynamic Shape Optimization 48 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Final Remarks
Some Recommendations
Tweak Local Optimization Algorithms
Run-Time Smoothing
Global Optimization Algorithms
Parallelization
David Gutierrez Rivera Aerodynamic Shape Optimization 48 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Final Remarks
Some Recommendations
Tweak Local Optimization Algorithms
Run-Time Smoothing
Global Optimization Algorithms
Parallelization
David Gutierrez Rivera Aerodynamic Shape Optimization 48 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Future Research
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 49 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Future Research
Some ideas
Multi-Disciplinary Optimization (MDO)
Life-Cycle Design
Development of Optimization Algorithms
David Gutierrez Rivera Aerodynamic Shape Optimization 50 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Future Research
Some ideas
Multi-Disciplinary Optimization (MDO)
Life-Cycle Design
Development of Optimization Algorithms
David Gutierrez Rivera Aerodynamic Shape Optimization 50 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Future Research
Some ideas
Multi-Disciplinary Optimization (MDO)
Life-Cycle Design
Development of Optimization Algorithms
David Gutierrez Rivera Aerodynamic Shape Optimization 50 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Future Research
Some ideas
Multi-Disciplinary Optimization (MDO)
Life-Cycle Design
Development of Optimization Algorithms
David Gutierrez Rivera Aerodynamic Shape Optimization 50 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Acknowledgments
Many Thanks to
Prof Guido Morgenthal
MSc Khaled Ibrahim
MSc Benjamin Bendig
MSc Samir Chawdhury
Shanmugam Narayanan
David Gutierrez Rivera Aerodynamic Shape Optimization 51 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
References
Stephen Boyd and Lieven Vandenberghe Convex OptimizationCambridge University Press The Edinburgh Building Cambridge CB28RU UK 2004 Pages 1-11 455-496httpwwwstanfordedu~boydcvxbookbv_cvxbookpdf
Jorge Nocedal and Stephen J Wright Numerical Optimization Springer175 Fifth Avenue New York NY 10010 USA 1999 Pages 2-3 4-710-30
Igor Griva Stephen G Nash and Ariela Sofer Linear and NonlinearOptimization Siam 3600 Market Street 6th Floor Philadelphia PA19104-2688 USA 2nd edition 2009 Pages 35-40 54-58 355-450
David G Luenberger and Yinyu Ye Linear and Nonlinear ProgrammingSpringer 233 Spring Street New YorkNY 10013 USA 3rd edition2008 Pages 2-7 183-257
David Gutierrez Rivera Aerodynamic Shape Optimization 52 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
References
Florent Brunet Contributions to Parametric Image Registration and 3DSurface Reconstruction Universite drsquoAuvergne PhD ThesisNovember 2010 Chapter 2 Pages 27-44httpwwwbrnteupublicationsbrunet2010phdpdf
Prof DK Chaturvedi Advances in Evolutionary OptimizationTechniques YouTube November 2013httpswwwyoutubecomwatchv=ftxiiaHNweQ
David Gutierrez Rivera OptiFlow v061a Weimar Germany March2014 OptiFlow Userguide
Guido Morgenthal Aerodynamic Analysis of Structures UsingHigh-resolution Vortex Particle Methods University of CambridgePhD Thesis October 2002 Pages 21-31 121-142
Wikipedia Savonius wind turbine The Wikimedia Foundation March2014 httpenwikipediaorgwikiSavonius_wind_turbine
David Gutierrez Rivera Aerodynamic Shape Optimization 53 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
References
John James Tomick On Convergence of the Nelder-Mead SimplexAlgorithm for Unconstrained Stochastic Optimization ThePennsylvania State University PhD Thesis May 1995httpwwwdticmildtictrfulltextu2a289453pdf
David Gutierrez Rivera Aerodynamic Shape Optimization 54 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Final Remarks
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 46 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Final Remarks
The Vortex Particle Method is a
Relatively low computational cost and highly accurate simulation
A mesh-free numerical method
David Gutierrez Rivera Aerodynamic Shape Optimization 47 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Final Remarks
The Vortex Particle Method is a
Relatively low computational cost and highly accurate simulation
A mesh-free numerical method
David Gutierrez Rivera Aerodynamic Shape Optimization 47 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Final Remarks
The Vortex Particle Method is a
Relatively low computational cost and highly accurate simulation
A mesh-free numerical method
David Gutierrez Rivera Aerodynamic Shape Optimization 47 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Final Remarks
Some Recommendations
Tweak Local Optimization Algorithms
Run-Time Smoothing
Global Optimization Algorithms
Parallelization
David Gutierrez Rivera Aerodynamic Shape Optimization 48 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Final Remarks
Some Recommendations
Tweak Local Optimization Algorithms
Run-Time Smoothing
Global Optimization Algorithms
Parallelization
David Gutierrez Rivera Aerodynamic Shape Optimization 48 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Final Remarks
Some Recommendations
Tweak Local Optimization Algorithms
Run-Time Smoothing
Global Optimization Algorithms
Parallelization
David Gutierrez Rivera Aerodynamic Shape Optimization 48 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Final Remarks
Some Recommendations
Tweak Local Optimization Algorithms
Run-Time Smoothing
Global Optimization Algorithms
Parallelization
David Gutierrez Rivera Aerodynamic Shape Optimization 48 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Final Remarks
Some Recommendations
Tweak Local Optimization Algorithms
Run-Time Smoothing
Global Optimization Algorithms
Parallelization
David Gutierrez Rivera Aerodynamic Shape Optimization 48 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Future Research
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 49 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Future Research
Some ideas
Multi-Disciplinary Optimization (MDO)
Life-Cycle Design
Development of Optimization Algorithms
David Gutierrez Rivera Aerodynamic Shape Optimization 50 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Future Research
Some ideas
Multi-Disciplinary Optimization (MDO)
Life-Cycle Design
Development of Optimization Algorithms
David Gutierrez Rivera Aerodynamic Shape Optimization 50 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Future Research
Some ideas
Multi-Disciplinary Optimization (MDO)
Life-Cycle Design
Development of Optimization Algorithms
David Gutierrez Rivera Aerodynamic Shape Optimization 50 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Future Research
Some ideas
Multi-Disciplinary Optimization (MDO)
Life-Cycle Design
Development of Optimization Algorithms
David Gutierrez Rivera Aerodynamic Shape Optimization 50 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Acknowledgments
Many Thanks to
Prof Guido Morgenthal
MSc Khaled Ibrahim
MSc Benjamin Bendig
MSc Samir Chawdhury
Shanmugam Narayanan
David Gutierrez Rivera Aerodynamic Shape Optimization 51 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
References
Stephen Boyd and Lieven Vandenberghe Convex OptimizationCambridge University Press The Edinburgh Building Cambridge CB28RU UK 2004 Pages 1-11 455-496httpwwwstanfordedu~boydcvxbookbv_cvxbookpdf
Jorge Nocedal and Stephen J Wright Numerical Optimization Springer175 Fifth Avenue New York NY 10010 USA 1999 Pages 2-3 4-710-30
Igor Griva Stephen G Nash and Ariela Sofer Linear and NonlinearOptimization Siam 3600 Market Street 6th Floor Philadelphia PA19104-2688 USA 2nd edition 2009 Pages 35-40 54-58 355-450
David G Luenberger and Yinyu Ye Linear and Nonlinear ProgrammingSpringer 233 Spring Street New YorkNY 10013 USA 3rd edition2008 Pages 2-7 183-257
David Gutierrez Rivera Aerodynamic Shape Optimization 52 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
References
Florent Brunet Contributions to Parametric Image Registration and 3DSurface Reconstruction Universite drsquoAuvergne PhD ThesisNovember 2010 Chapter 2 Pages 27-44httpwwwbrnteupublicationsbrunet2010phdpdf
Prof DK Chaturvedi Advances in Evolutionary OptimizationTechniques YouTube November 2013httpswwwyoutubecomwatchv=ftxiiaHNweQ
David Gutierrez Rivera OptiFlow v061a Weimar Germany March2014 OptiFlow Userguide
Guido Morgenthal Aerodynamic Analysis of Structures UsingHigh-resolution Vortex Particle Methods University of CambridgePhD Thesis October 2002 Pages 21-31 121-142
Wikipedia Savonius wind turbine The Wikimedia Foundation March2014 httpenwikipediaorgwikiSavonius_wind_turbine
David Gutierrez Rivera Aerodynamic Shape Optimization 53 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
References
John James Tomick On Convergence of the Nelder-Mead SimplexAlgorithm for Unconstrained Stochastic Optimization ThePennsylvania State University PhD Thesis May 1995httpwwwdticmildtictrfulltextu2a289453pdf
David Gutierrez Rivera Aerodynamic Shape Optimization 54 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Final Remarks
The Vortex Particle Method is a
Relatively low computational cost and highly accurate simulation
A mesh-free numerical method
David Gutierrez Rivera Aerodynamic Shape Optimization 47 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Final Remarks
The Vortex Particle Method is a
Relatively low computational cost and highly accurate simulation
A mesh-free numerical method
David Gutierrez Rivera Aerodynamic Shape Optimization 47 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Final Remarks
The Vortex Particle Method is a
Relatively low computational cost and highly accurate simulation
A mesh-free numerical method
David Gutierrez Rivera Aerodynamic Shape Optimization 47 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Final Remarks
Some Recommendations
Tweak Local Optimization Algorithms
Run-Time Smoothing
Global Optimization Algorithms
Parallelization
David Gutierrez Rivera Aerodynamic Shape Optimization 48 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Final Remarks
Some Recommendations
Tweak Local Optimization Algorithms
Run-Time Smoothing
Global Optimization Algorithms
Parallelization
David Gutierrez Rivera Aerodynamic Shape Optimization 48 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Final Remarks
Some Recommendations
Tweak Local Optimization Algorithms
Run-Time Smoothing
Global Optimization Algorithms
Parallelization
David Gutierrez Rivera Aerodynamic Shape Optimization 48 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Final Remarks
Some Recommendations
Tweak Local Optimization Algorithms
Run-Time Smoothing
Global Optimization Algorithms
Parallelization
David Gutierrez Rivera Aerodynamic Shape Optimization 48 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Final Remarks
Some Recommendations
Tweak Local Optimization Algorithms
Run-Time Smoothing
Global Optimization Algorithms
Parallelization
David Gutierrez Rivera Aerodynamic Shape Optimization 48 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Future Research
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 49 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Future Research
Some ideas
Multi-Disciplinary Optimization (MDO)
Life-Cycle Design
Development of Optimization Algorithms
David Gutierrez Rivera Aerodynamic Shape Optimization 50 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Future Research
Some ideas
Multi-Disciplinary Optimization (MDO)
Life-Cycle Design
Development of Optimization Algorithms
David Gutierrez Rivera Aerodynamic Shape Optimization 50 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Future Research
Some ideas
Multi-Disciplinary Optimization (MDO)
Life-Cycle Design
Development of Optimization Algorithms
David Gutierrez Rivera Aerodynamic Shape Optimization 50 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Future Research
Some ideas
Multi-Disciplinary Optimization (MDO)
Life-Cycle Design
Development of Optimization Algorithms
David Gutierrez Rivera Aerodynamic Shape Optimization 50 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Acknowledgments
Many Thanks to
Prof Guido Morgenthal
MSc Khaled Ibrahim
MSc Benjamin Bendig
MSc Samir Chawdhury
Shanmugam Narayanan
David Gutierrez Rivera Aerodynamic Shape Optimization 51 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
References
Stephen Boyd and Lieven Vandenberghe Convex OptimizationCambridge University Press The Edinburgh Building Cambridge CB28RU UK 2004 Pages 1-11 455-496httpwwwstanfordedu~boydcvxbookbv_cvxbookpdf
Jorge Nocedal and Stephen J Wright Numerical Optimization Springer175 Fifth Avenue New York NY 10010 USA 1999 Pages 2-3 4-710-30
Igor Griva Stephen G Nash and Ariela Sofer Linear and NonlinearOptimization Siam 3600 Market Street 6th Floor Philadelphia PA19104-2688 USA 2nd edition 2009 Pages 35-40 54-58 355-450
David G Luenberger and Yinyu Ye Linear and Nonlinear ProgrammingSpringer 233 Spring Street New YorkNY 10013 USA 3rd edition2008 Pages 2-7 183-257
David Gutierrez Rivera Aerodynamic Shape Optimization 52 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
References
Florent Brunet Contributions to Parametric Image Registration and 3DSurface Reconstruction Universite drsquoAuvergne PhD ThesisNovember 2010 Chapter 2 Pages 27-44httpwwwbrnteupublicationsbrunet2010phdpdf
Prof DK Chaturvedi Advances in Evolutionary OptimizationTechniques YouTube November 2013httpswwwyoutubecomwatchv=ftxiiaHNweQ
David Gutierrez Rivera OptiFlow v061a Weimar Germany March2014 OptiFlow Userguide
Guido Morgenthal Aerodynamic Analysis of Structures UsingHigh-resolution Vortex Particle Methods University of CambridgePhD Thesis October 2002 Pages 21-31 121-142
Wikipedia Savonius wind turbine The Wikimedia Foundation March2014 httpenwikipediaorgwikiSavonius_wind_turbine
David Gutierrez Rivera Aerodynamic Shape Optimization 53 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
References
John James Tomick On Convergence of the Nelder-Mead SimplexAlgorithm for Unconstrained Stochastic Optimization ThePennsylvania State University PhD Thesis May 1995httpwwwdticmildtictrfulltextu2a289453pdf
David Gutierrez Rivera Aerodynamic Shape Optimization 54 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Final Remarks
The Vortex Particle Method is a
Relatively low computational cost and highly accurate simulation
A mesh-free numerical method
David Gutierrez Rivera Aerodynamic Shape Optimization 47 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Final Remarks
The Vortex Particle Method is a
Relatively low computational cost and highly accurate simulation
A mesh-free numerical method
David Gutierrez Rivera Aerodynamic Shape Optimization 47 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Final Remarks
Some Recommendations
Tweak Local Optimization Algorithms
Run-Time Smoothing
Global Optimization Algorithms
Parallelization
David Gutierrez Rivera Aerodynamic Shape Optimization 48 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Final Remarks
Some Recommendations
Tweak Local Optimization Algorithms
Run-Time Smoothing
Global Optimization Algorithms
Parallelization
David Gutierrez Rivera Aerodynamic Shape Optimization 48 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Final Remarks
Some Recommendations
Tweak Local Optimization Algorithms
Run-Time Smoothing
Global Optimization Algorithms
Parallelization
David Gutierrez Rivera Aerodynamic Shape Optimization 48 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Final Remarks
Some Recommendations
Tweak Local Optimization Algorithms
Run-Time Smoothing
Global Optimization Algorithms
Parallelization
David Gutierrez Rivera Aerodynamic Shape Optimization 48 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Final Remarks
Some Recommendations
Tweak Local Optimization Algorithms
Run-Time Smoothing
Global Optimization Algorithms
Parallelization
David Gutierrez Rivera Aerodynamic Shape Optimization 48 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Future Research
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 49 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Future Research
Some ideas
Multi-Disciplinary Optimization (MDO)
Life-Cycle Design
Development of Optimization Algorithms
David Gutierrez Rivera Aerodynamic Shape Optimization 50 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Future Research
Some ideas
Multi-Disciplinary Optimization (MDO)
Life-Cycle Design
Development of Optimization Algorithms
David Gutierrez Rivera Aerodynamic Shape Optimization 50 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Future Research
Some ideas
Multi-Disciplinary Optimization (MDO)
Life-Cycle Design
Development of Optimization Algorithms
David Gutierrez Rivera Aerodynamic Shape Optimization 50 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Future Research
Some ideas
Multi-Disciplinary Optimization (MDO)
Life-Cycle Design
Development of Optimization Algorithms
David Gutierrez Rivera Aerodynamic Shape Optimization 50 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Acknowledgments
Many Thanks to
Prof Guido Morgenthal
MSc Khaled Ibrahim
MSc Benjamin Bendig
MSc Samir Chawdhury
Shanmugam Narayanan
David Gutierrez Rivera Aerodynamic Shape Optimization 51 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
References
Stephen Boyd and Lieven Vandenberghe Convex OptimizationCambridge University Press The Edinburgh Building Cambridge CB28RU UK 2004 Pages 1-11 455-496httpwwwstanfordedu~boydcvxbookbv_cvxbookpdf
Jorge Nocedal and Stephen J Wright Numerical Optimization Springer175 Fifth Avenue New York NY 10010 USA 1999 Pages 2-3 4-710-30
Igor Griva Stephen G Nash and Ariela Sofer Linear and NonlinearOptimization Siam 3600 Market Street 6th Floor Philadelphia PA19104-2688 USA 2nd edition 2009 Pages 35-40 54-58 355-450
David G Luenberger and Yinyu Ye Linear and Nonlinear ProgrammingSpringer 233 Spring Street New YorkNY 10013 USA 3rd edition2008 Pages 2-7 183-257
David Gutierrez Rivera Aerodynamic Shape Optimization 52 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
References
Florent Brunet Contributions to Parametric Image Registration and 3DSurface Reconstruction Universite drsquoAuvergne PhD ThesisNovember 2010 Chapter 2 Pages 27-44httpwwwbrnteupublicationsbrunet2010phdpdf
Prof DK Chaturvedi Advances in Evolutionary OptimizationTechniques YouTube November 2013httpswwwyoutubecomwatchv=ftxiiaHNweQ
David Gutierrez Rivera OptiFlow v061a Weimar Germany March2014 OptiFlow Userguide
Guido Morgenthal Aerodynamic Analysis of Structures UsingHigh-resolution Vortex Particle Methods University of CambridgePhD Thesis October 2002 Pages 21-31 121-142
Wikipedia Savonius wind turbine The Wikimedia Foundation March2014 httpenwikipediaorgwikiSavonius_wind_turbine
David Gutierrez Rivera Aerodynamic Shape Optimization 53 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
References
John James Tomick On Convergence of the Nelder-Mead SimplexAlgorithm for Unconstrained Stochastic Optimization ThePennsylvania State University PhD Thesis May 1995httpwwwdticmildtictrfulltextu2a289453pdf
David Gutierrez Rivera Aerodynamic Shape Optimization 54 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Final Remarks
The Vortex Particle Method is a
Relatively low computational cost and highly accurate simulation
A mesh-free numerical method
David Gutierrez Rivera Aerodynamic Shape Optimization 47 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Final Remarks
Some Recommendations
Tweak Local Optimization Algorithms
Run-Time Smoothing
Global Optimization Algorithms
Parallelization
David Gutierrez Rivera Aerodynamic Shape Optimization 48 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Final Remarks
Some Recommendations
Tweak Local Optimization Algorithms
Run-Time Smoothing
Global Optimization Algorithms
Parallelization
David Gutierrez Rivera Aerodynamic Shape Optimization 48 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Final Remarks
Some Recommendations
Tweak Local Optimization Algorithms
Run-Time Smoothing
Global Optimization Algorithms
Parallelization
David Gutierrez Rivera Aerodynamic Shape Optimization 48 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Final Remarks
Some Recommendations
Tweak Local Optimization Algorithms
Run-Time Smoothing
Global Optimization Algorithms
Parallelization
David Gutierrez Rivera Aerodynamic Shape Optimization 48 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Final Remarks
Some Recommendations
Tweak Local Optimization Algorithms
Run-Time Smoothing
Global Optimization Algorithms
Parallelization
David Gutierrez Rivera Aerodynamic Shape Optimization 48 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Future Research
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 49 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Future Research
Some ideas
Multi-Disciplinary Optimization (MDO)
Life-Cycle Design
Development of Optimization Algorithms
David Gutierrez Rivera Aerodynamic Shape Optimization 50 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Future Research
Some ideas
Multi-Disciplinary Optimization (MDO)
Life-Cycle Design
Development of Optimization Algorithms
David Gutierrez Rivera Aerodynamic Shape Optimization 50 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Future Research
Some ideas
Multi-Disciplinary Optimization (MDO)
Life-Cycle Design
Development of Optimization Algorithms
David Gutierrez Rivera Aerodynamic Shape Optimization 50 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Future Research
Some ideas
Multi-Disciplinary Optimization (MDO)
Life-Cycle Design
Development of Optimization Algorithms
David Gutierrez Rivera Aerodynamic Shape Optimization 50 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Acknowledgments
Many Thanks to
Prof Guido Morgenthal
MSc Khaled Ibrahim
MSc Benjamin Bendig
MSc Samir Chawdhury
Shanmugam Narayanan
David Gutierrez Rivera Aerodynamic Shape Optimization 51 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
References
Stephen Boyd and Lieven Vandenberghe Convex OptimizationCambridge University Press The Edinburgh Building Cambridge CB28RU UK 2004 Pages 1-11 455-496httpwwwstanfordedu~boydcvxbookbv_cvxbookpdf
Jorge Nocedal and Stephen J Wright Numerical Optimization Springer175 Fifth Avenue New York NY 10010 USA 1999 Pages 2-3 4-710-30
Igor Griva Stephen G Nash and Ariela Sofer Linear and NonlinearOptimization Siam 3600 Market Street 6th Floor Philadelphia PA19104-2688 USA 2nd edition 2009 Pages 35-40 54-58 355-450
David G Luenberger and Yinyu Ye Linear and Nonlinear ProgrammingSpringer 233 Spring Street New YorkNY 10013 USA 3rd edition2008 Pages 2-7 183-257
David Gutierrez Rivera Aerodynamic Shape Optimization 52 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
References
Florent Brunet Contributions to Parametric Image Registration and 3DSurface Reconstruction Universite drsquoAuvergne PhD ThesisNovember 2010 Chapter 2 Pages 27-44httpwwwbrnteupublicationsbrunet2010phdpdf
Prof DK Chaturvedi Advances in Evolutionary OptimizationTechniques YouTube November 2013httpswwwyoutubecomwatchv=ftxiiaHNweQ
David Gutierrez Rivera OptiFlow v061a Weimar Germany March2014 OptiFlow Userguide
Guido Morgenthal Aerodynamic Analysis of Structures UsingHigh-resolution Vortex Particle Methods University of CambridgePhD Thesis October 2002 Pages 21-31 121-142
Wikipedia Savonius wind turbine The Wikimedia Foundation March2014 httpenwikipediaorgwikiSavonius_wind_turbine
David Gutierrez Rivera Aerodynamic Shape Optimization 53 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
References
John James Tomick On Convergence of the Nelder-Mead SimplexAlgorithm for Unconstrained Stochastic Optimization ThePennsylvania State University PhD Thesis May 1995httpwwwdticmildtictrfulltextu2a289453pdf
David Gutierrez Rivera Aerodynamic Shape Optimization 54 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Final Remarks
Some Recommendations
Tweak Local Optimization Algorithms
Run-Time Smoothing
Global Optimization Algorithms
Parallelization
David Gutierrez Rivera Aerodynamic Shape Optimization 48 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Final Remarks
Some Recommendations
Tweak Local Optimization Algorithms
Run-Time Smoothing
Global Optimization Algorithms
Parallelization
David Gutierrez Rivera Aerodynamic Shape Optimization 48 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Final Remarks
Some Recommendations
Tweak Local Optimization Algorithms
Run-Time Smoothing
Global Optimization Algorithms
Parallelization
David Gutierrez Rivera Aerodynamic Shape Optimization 48 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Final Remarks
Some Recommendations
Tweak Local Optimization Algorithms
Run-Time Smoothing
Global Optimization Algorithms
Parallelization
David Gutierrez Rivera Aerodynamic Shape Optimization 48 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Final Remarks
Some Recommendations
Tweak Local Optimization Algorithms
Run-Time Smoothing
Global Optimization Algorithms
Parallelization
David Gutierrez Rivera Aerodynamic Shape Optimization 48 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Future Research
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 49 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Future Research
Some ideas
Multi-Disciplinary Optimization (MDO)
Life-Cycle Design
Development of Optimization Algorithms
David Gutierrez Rivera Aerodynamic Shape Optimization 50 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Future Research
Some ideas
Multi-Disciplinary Optimization (MDO)
Life-Cycle Design
Development of Optimization Algorithms
David Gutierrez Rivera Aerodynamic Shape Optimization 50 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Future Research
Some ideas
Multi-Disciplinary Optimization (MDO)
Life-Cycle Design
Development of Optimization Algorithms
David Gutierrez Rivera Aerodynamic Shape Optimization 50 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Future Research
Some ideas
Multi-Disciplinary Optimization (MDO)
Life-Cycle Design
Development of Optimization Algorithms
David Gutierrez Rivera Aerodynamic Shape Optimization 50 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Acknowledgments
Many Thanks to
Prof Guido Morgenthal
MSc Khaled Ibrahim
MSc Benjamin Bendig
MSc Samir Chawdhury
Shanmugam Narayanan
David Gutierrez Rivera Aerodynamic Shape Optimization 51 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
References
Stephen Boyd and Lieven Vandenberghe Convex OptimizationCambridge University Press The Edinburgh Building Cambridge CB28RU UK 2004 Pages 1-11 455-496httpwwwstanfordedu~boydcvxbookbv_cvxbookpdf
Jorge Nocedal and Stephen J Wright Numerical Optimization Springer175 Fifth Avenue New York NY 10010 USA 1999 Pages 2-3 4-710-30
Igor Griva Stephen G Nash and Ariela Sofer Linear and NonlinearOptimization Siam 3600 Market Street 6th Floor Philadelphia PA19104-2688 USA 2nd edition 2009 Pages 35-40 54-58 355-450
David G Luenberger and Yinyu Ye Linear and Nonlinear ProgrammingSpringer 233 Spring Street New YorkNY 10013 USA 3rd edition2008 Pages 2-7 183-257
David Gutierrez Rivera Aerodynamic Shape Optimization 52 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
References
Florent Brunet Contributions to Parametric Image Registration and 3DSurface Reconstruction Universite drsquoAuvergne PhD ThesisNovember 2010 Chapter 2 Pages 27-44httpwwwbrnteupublicationsbrunet2010phdpdf
Prof DK Chaturvedi Advances in Evolutionary OptimizationTechniques YouTube November 2013httpswwwyoutubecomwatchv=ftxiiaHNweQ
David Gutierrez Rivera OptiFlow v061a Weimar Germany March2014 OptiFlow Userguide
Guido Morgenthal Aerodynamic Analysis of Structures UsingHigh-resolution Vortex Particle Methods University of CambridgePhD Thesis October 2002 Pages 21-31 121-142
Wikipedia Savonius wind turbine The Wikimedia Foundation March2014 httpenwikipediaorgwikiSavonius_wind_turbine
David Gutierrez Rivera Aerodynamic Shape Optimization 53 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
References
John James Tomick On Convergence of the Nelder-Mead SimplexAlgorithm for Unconstrained Stochastic Optimization ThePennsylvania State University PhD Thesis May 1995httpwwwdticmildtictrfulltextu2a289453pdf
David Gutierrez Rivera Aerodynamic Shape Optimization 54 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Final Remarks
Some Recommendations
Tweak Local Optimization Algorithms
Run-Time Smoothing
Global Optimization Algorithms
Parallelization
David Gutierrez Rivera Aerodynamic Shape Optimization 48 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Final Remarks
Some Recommendations
Tweak Local Optimization Algorithms
Run-Time Smoothing
Global Optimization Algorithms
Parallelization
David Gutierrez Rivera Aerodynamic Shape Optimization 48 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Final Remarks
Some Recommendations
Tweak Local Optimization Algorithms
Run-Time Smoothing
Global Optimization Algorithms
Parallelization
David Gutierrez Rivera Aerodynamic Shape Optimization 48 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Final Remarks
Some Recommendations
Tweak Local Optimization Algorithms
Run-Time Smoothing
Global Optimization Algorithms
Parallelization
David Gutierrez Rivera Aerodynamic Shape Optimization 48 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Future Research
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 49 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Future Research
Some ideas
Multi-Disciplinary Optimization (MDO)
Life-Cycle Design
Development of Optimization Algorithms
David Gutierrez Rivera Aerodynamic Shape Optimization 50 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Future Research
Some ideas
Multi-Disciplinary Optimization (MDO)
Life-Cycle Design
Development of Optimization Algorithms
David Gutierrez Rivera Aerodynamic Shape Optimization 50 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Future Research
Some ideas
Multi-Disciplinary Optimization (MDO)
Life-Cycle Design
Development of Optimization Algorithms
David Gutierrez Rivera Aerodynamic Shape Optimization 50 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Future Research
Some ideas
Multi-Disciplinary Optimization (MDO)
Life-Cycle Design
Development of Optimization Algorithms
David Gutierrez Rivera Aerodynamic Shape Optimization 50 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Acknowledgments
Many Thanks to
Prof Guido Morgenthal
MSc Khaled Ibrahim
MSc Benjamin Bendig
MSc Samir Chawdhury
Shanmugam Narayanan
David Gutierrez Rivera Aerodynamic Shape Optimization 51 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
References
Stephen Boyd and Lieven Vandenberghe Convex OptimizationCambridge University Press The Edinburgh Building Cambridge CB28RU UK 2004 Pages 1-11 455-496httpwwwstanfordedu~boydcvxbookbv_cvxbookpdf
Jorge Nocedal and Stephen J Wright Numerical Optimization Springer175 Fifth Avenue New York NY 10010 USA 1999 Pages 2-3 4-710-30
Igor Griva Stephen G Nash and Ariela Sofer Linear and NonlinearOptimization Siam 3600 Market Street 6th Floor Philadelphia PA19104-2688 USA 2nd edition 2009 Pages 35-40 54-58 355-450
David G Luenberger and Yinyu Ye Linear and Nonlinear ProgrammingSpringer 233 Spring Street New YorkNY 10013 USA 3rd edition2008 Pages 2-7 183-257
David Gutierrez Rivera Aerodynamic Shape Optimization 52 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
References
Florent Brunet Contributions to Parametric Image Registration and 3DSurface Reconstruction Universite drsquoAuvergne PhD ThesisNovember 2010 Chapter 2 Pages 27-44httpwwwbrnteupublicationsbrunet2010phdpdf
Prof DK Chaturvedi Advances in Evolutionary OptimizationTechniques YouTube November 2013httpswwwyoutubecomwatchv=ftxiiaHNweQ
David Gutierrez Rivera OptiFlow v061a Weimar Germany March2014 OptiFlow Userguide
Guido Morgenthal Aerodynamic Analysis of Structures UsingHigh-resolution Vortex Particle Methods University of CambridgePhD Thesis October 2002 Pages 21-31 121-142
Wikipedia Savonius wind turbine The Wikimedia Foundation March2014 httpenwikipediaorgwikiSavonius_wind_turbine
David Gutierrez Rivera Aerodynamic Shape Optimization 53 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
References
John James Tomick On Convergence of the Nelder-Mead SimplexAlgorithm for Unconstrained Stochastic Optimization ThePennsylvania State University PhD Thesis May 1995httpwwwdticmildtictrfulltextu2a289453pdf
David Gutierrez Rivera Aerodynamic Shape Optimization 54 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Final Remarks
Some Recommendations
Tweak Local Optimization Algorithms
Run-Time Smoothing
Global Optimization Algorithms
Parallelization
David Gutierrez Rivera Aerodynamic Shape Optimization 48 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Final Remarks
Some Recommendations
Tweak Local Optimization Algorithms
Run-Time Smoothing
Global Optimization Algorithms
Parallelization
David Gutierrez Rivera Aerodynamic Shape Optimization 48 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Final Remarks
Some Recommendations
Tweak Local Optimization Algorithms
Run-Time Smoothing
Global Optimization Algorithms
Parallelization
David Gutierrez Rivera Aerodynamic Shape Optimization 48 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Future Research
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 49 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Future Research
Some ideas
Multi-Disciplinary Optimization (MDO)
Life-Cycle Design
Development of Optimization Algorithms
David Gutierrez Rivera Aerodynamic Shape Optimization 50 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Future Research
Some ideas
Multi-Disciplinary Optimization (MDO)
Life-Cycle Design
Development of Optimization Algorithms
David Gutierrez Rivera Aerodynamic Shape Optimization 50 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Future Research
Some ideas
Multi-Disciplinary Optimization (MDO)
Life-Cycle Design
Development of Optimization Algorithms
David Gutierrez Rivera Aerodynamic Shape Optimization 50 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Future Research
Some ideas
Multi-Disciplinary Optimization (MDO)
Life-Cycle Design
Development of Optimization Algorithms
David Gutierrez Rivera Aerodynamic Shape Optimization 50 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Acknowledgments
Many Thanks to
Prof Guido Morgenthal
MSc Khaled Ibrahim
MSc Benjamin Bendig
MSc Samir Chawdhury
Shanmugam Narayanan
David Gutierrez Rivera Aerodynamic Shape Optimization 51 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
References
Stephen Boyd and Lieven Vandenberghe Convex OptimizationCambridge University Press The Edinburgh Building Cambridge CB28RU UK 2004 Pages 1-11 455-496httpwwwstanfordedu~boydcvxbookbv_cvxbookpdf
Jorge Nocedal and Stephen J Wright Numerical Optimization Springer175 Fifth Avenue New York NY 10010 USA 1999 Pages 2-3 4-710-30
Igor Griva Stephen G Nash and Ariela Sofer Linear and NonlinearOptimization Siam 3600 Market Street 6th Floor Philadelphia PA19104-2688 USA 2nd edition 2009 Pages 35-40 54-58 355-450
David G Luenberger and Yinyu Ye Linear and Nonlinear ProgrammingSpringer 233 Spring Street New YorkNY 10013 USA 3rd edition2008 Pages 2-7 183-257
David Gutierrez Rivera Aerodynamic Shape Optimization 52 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
References
Florent Brunet Contributions to Parametric Image Registration and 3DSurface Reconstruction Universite drsquoAuvergne PhD ThesisNovember 2010 Chapter 2 Pages 27-44httpwwwbrnteupublicationsbrunet2010phdpdf
Prof DK Chaturvedi Advances in Evolutionary OptimizationTechniques YouTube November 2013httpswwwyoutubecomwatchv=ftxiiaHNweQ
David Gutierrez Rivera OptiFlow v061a Weimar Germany March2014 OptiFlow Userguide
Guido Morgenthal Aerodynamic Analysis of Structures UsingHigh-resolution Vortex Particle Methods University of CambridgePhD Thesis October 2002 Pages 21-31 121-142
Wikipedia Savonius wind turbine The Wikimedia Foundation March2014 httpenwikipediaorgwikiSavonius_wind_turbine
David Gutierrez Rivera Aerodynamic Shape Optimization 53 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
References
John James Tomick On Convergence of the Nelder-Mead SimplexAlgorithm for Unconstrained Stochastic Optimization ThePennsylvania State University PhD Thesis May 1995httpwwwdticmildtictrfulltextu2a289453pdf
David Gutierrez Rivera Aerodynamic Shape Optimization 54 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Final Remarks
Some Recommendations
Tweak Local Optimization Algorithms
Run-Time Smoothing
Global Optimization Algorithms
Parallelization
David Gutierrez Rivera Aerodynamic Shape Optimization 48 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Final Remarks
Some Recommendations
Tweak Local Optimization Algorithms
Run-Time Smoothing
Global Optimization Algorithms
Parallelization
David Gutierrez Rivera Aerodynamic Shape Optimization 48 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Future Research
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 49 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Future Research
Some ideas
Multi-Disciplinary Optimization (MDO)
Life-Cycle Design
Development of Optimization Algorithms
David Gutierrez Rivera Aerodynamic Shape Optimization 50 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Future Research
Some ideas
Multi-Disciplinary Optimization (MDO)
Life-Cycle Design
Development of Optimization Algorithms
David Gutierrez Rivera Aerodynamic Shape Optimization 50 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Future Research
Some ideas
Multi-Disciplinary Optimization (MDO)
Life-Cycle Design
Development of Optimization Algorithms
David Gutierrez Rivera Aerodynamic Shape Optimization 50 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Future Research
Some ideas
Multi-Disciplinary Optimization (MDO)
Life-Cycle Design
Development of Optimization Algorithms
David Gutierrez Rivera Aerodynamic Shape Optimization 50 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Acknowledgments
Many Thanks to
Prof Guido Morgenthal
MSc Khaled Ibrahim
MSc Benjamin Bendig
MSc Samir Chawdhury
Shanmugam Narayanan
David Gutierrez Rivera Aerodynamic Shape Optimization 51 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
References
Stephen Boyd and Lieven Vandenberghe Convex OptimizationCambridge University Press The Edinburgh Building Cambridge CB28RU UK 2004 Pages 1-11 455-496httpwwwstanfordedu~boydcvxbookbv_cvxbookpdf
Jorge Nocedal and Stephen J Wright Numerical Optimization Springer175 Fifth Avenue New York NY 10010 USA 1999 Pages 2-3 4-710-30
Igor Griva Stephen G Nash and Ariela Sofer Linear and NonlinearOptimization Siam 3600 Market Street 6th Floor Philadelphia PA19104-2688 USA 2nd edition 2009 Pages 35-40 54-58 355-450
David G Luenberger and Yinyu Ye Linear and Nonlinear ProgrammingSpringer 233 Spring Street New YorkNY 10013 USA 3rd edition2008 Pages 2-7 183-257
David Gutierrez Rivera Aerodynamic Shape Optimization 52 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
References
Florent Brunet Contributions to Parametric Image Registration and 3DSurface Reconstruction Universite drsquoAuvergne PhD ThesisNovember 2010 Chapter 2 Pages 27-44httpwwwbrnteupublicationsbrunet2010phdpdf
Prof DK Chaturvedi Advances in Evolutionary OptimizationTechniques YouTube November 2013httpswwwyoutubecomwatchv=ftxiiaHNweQ
David Gutierrez Rivera OptiFlow v061a Weimar Germany March2014 OptiFlow Userguide
Guido Morgenthal Aerodynamic Analysis of Structures UsingHigh-resolution Vortex Particle Methods University of CambridgePhD Thesis October 2002 Pages 21-31 121-142
Wikipedia Savonius wind turbine The Wikimedia Foundation March2014 httpenwikipediaorgwikiSavonius_wind_turbine
David Gutierrez Rivera Aerodynamic Shape Optimization 53 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
References
John James Tomick On Convergence of the Nelder-Mead SimplexAlgorithm for Unconstrained Stochastic Optimization ThePennsylvania State University PhD Thesis May 1995httpwwwdticmildtictrfulltextu2a289453pdf
David Gutierrez Rivera Aerodynamic Shape Optimization 54 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Final Remarks
Some Recommendations
Tweak Local Optimization Algorithms
Run-Time Smoothing
Global Optimization Algorithms
Parallelization
David Gutierrez Rivera Aerodynamic Shape Optimization 48 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Future Research
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 49 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Future Research
Some ideas
Multi-Disciplinary Optimization (MDO)
Life-Cycle Design
Development of Optimization Algorithms
David Gutierrez Rivera Aerodynamic Shape Optimization 50 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Future Research
Some ideas
Multi-Disciplinary Optimization (MDO)
Life-Cycle Design
Development of Optimization Algorithms
David Gutierrez Rivera Aerodynamic Shape Optimization 50 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Future Research
Some ideas
Multi-Disciplinary Optimization (MDO)
Life-Cycle Design
Development of Optimization Algorithms
David Gutierrez Rivera Aerodynamic Shape Optimization 50 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Future Research
Some ideas
Multi-Disciplinary Optimization (MDO)
Life-Cycle Design
Development of Optimization Algorithms
David Gutierrez Rivera Aerodynamic Shape Optimization 50 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Acknowledgments
Many Thanks to
Prof Guido Morgenthal
MSc Khaled Ibrahim
MSc Benjamin Bendig
MSc Samir Chawdhury
Shanmugam Narayanan
David Gutierrez Rivera Aerodynamic Shape Optimization 51 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
References
Stephen Boyd and Lieven Vandenberghe Convex OptimizationCambridge University Press The Edinburgh Building Cambridge CB28RU UK 2004 Pages 1-11 455-496httpwwwstanfordedu~boydcvxbookbv_cvxbookpdf
Jorge Nocedal and Stephen J Wright Numerical Optimization Springer175 Fifth Avenue New York NY 10010 USA 1999 Pages 2-3 4-710-30
Igor Griva Stephen G Nash and Ariela Sofer Linear and NonlinearOptimization Siam 3600 Market Street 6th Floor Philadelphia PA19104-2688 USA 2nd edition 2009 Pages 35-40 54-58 355-450
David G Luenberger and Yinyu Ye Linear and Nonlinear ProgrammingSpringer 233 Spring Street New YorkNY 10013 USA 3rd edition2008 Pages 2-7 183-257
David Gutierrez Rivera Aerodynamic Shape Optimization 52 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
References
Florent Brunet Contributions to Parametric Image Registration and 3DSurface Reconstruction Universite drsquoAuvergne PhD ThesisNovember 2010 Chapter 2 Pages 27-44httpwwwbrnteupublicationsbrunet2010phdpdf
Prof DK Chaturvedi Advances in Evolutionary OptimizationTechniques YouTube November 2013httpswwwyoutubecomwatchv=ftxiiaHNweQ
David Gutierrez Rivera OptiFlow v061a Weimar Germany March2014 OptiFlow Userguide
Guido Morgenthal Aerodynamic Analysis of Structures UsingHigh-resolution Vortex Particle Methods University of CambridgePhD Thesis October 2002 Pages 21-31 121-142
Wikipedia Savonius wind turbine The Wikimedia Foundation March2014 httpenwikipediaorgwikiSavonius_wind_turbine
David Gutierrez Rivera Aerodynamic Shape Optimization 53 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
References
John James Tomick On Convergence of the Nelder-Mead SimplexAlgorithm for Unconstrained Stochastic Optimization ThePennsylvania State University PhD Thesis May 1995httpwwwdticmildtictrfulltextu2a289453pdf
David Gutierrez Rivera Aerodynamic Shape Optimization 54 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Future Research
1 IntroductionWhat is OptimizationBasics of Aerodynamics
2 Optimization AlgorithmsLocalGlobal
3 Shape OptimizationParametrizationObjective Functions
4 Data Gathering5 Black-Box Optimization6 Simulation-based Optimization7 OptiFlow8 Optimization Examples
M4 Neath Viaduct Wind ShieldVertical-Axis Wind Turbine (VAWT)
9 Final Remarks10 Future Research
David Gutierrez Rivera Aerodynamic Shape Optimization 49 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Future Research
Some ideas
Multi-Disciplinary Optimization (MDO)
Life-Cycle Design
Development of Optimization Algorithms
David Gutierrez Rivera Aerodynamic Shape Optimization 50 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Future Research
Some ideas
Multi-Disciplinary Optimization (MDO)
Life-Cycle Design
Development of Optimization Algorithms
David Gutierrez Rivera Aerodynamic Shape Optimization 50 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Future Research
Some ideas
Multi-Disciplinary Optimization (MDO)
Life-Cycle Design
Development of Optimization Algorithms
David Gutierrez Rivera Aerodynamic Shape Optimization 50 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Future Research
Some ideas
Multi-Disciplinary Optimization (MDO)
Life-Cycle Design
Development of Optimization Algorithms
David Gutierrez Rivera Aerodynamic Shape Optimization 50 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Acknowledgments
Many Thanks to
Prof Guido Morgenthal
MSc Khaled Ibrahim
MSc Benjamin Bendig
MSc Samir Chawdhury
Shanmugam Narayanan
David Gutierrez Rivera Aerodynamic Shape Optimization 51 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
References
Stephen Boyd and Lieven Vandenberghe Convex OptimizationCambridge University Press The Edinburgh Building Cambridge CB28RU UK 2004 Pages 1-11 455-496httpwwwstanfordedu~boydcvxbookbv_cvxbookpdf
Jorge Nocedal and Stephen J Wright Numerical Optimization Springer175 Fifth Avenue New York NY 10010 USA 1999 Pages 2-3 4-710-30
Igor Griva Stephen G Nash and Ariela Sofer Linear and NonlinearOptimization Siam 3600 Market Street 6th Floor Philadelphia PA19104-2688 USA 2nd edition 2009 Pages 35-40 54-58 355-450
David G Luenberger and Yinyu Ye Linear and Nonlinear ProgrammingSpringer 233 Spring Street New YorkNY 10013 USA 3rd edition2008 Pages 2-7 183-257
David Gutierrez Rivera Aerodynamic Shape Optimization 52 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
References
Florent Brunet Contributions to Parametric Image Registration and 3DSurface Reconstruction Universite drsquoAuvergne PhD ThesisNovember 2010 Chapter 2 Pages 27-44httpwwwbrnteupublicationsbrunet2010phdpdf
Prof DK Chaturvedi Advances in Evolutionary OptimizationTechniques YouTube November 2013httpswwwyoutubecomwatchv=ftxiiaHNweQ
David Gutierrez Rivera OptiFlow v061a Weimar Germany March2014 OptiFlow Userguide
Guido Morgenthal Aerodynamic Analysis of Structures UsingHigh-resolution Vortex Particle Methods University of CambridgePhD Thesis October 2002 Pages 21-31 121-142
Wikipedia Savonius wind turbine The Wikimedia Foundation March2014 httpenwikipediaorgwikiSavonius_wind_turbine
David Gutierrez Rivera Aerodynamic Shape Optimization 53 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
References
John James Tomick On Convergence of the Nelder-Mead SimplexAlgorithm for Unconstrained Stochastic Optimization ThePennsylvania State University PhD Thesis May 1995httpwwwdticmildtictrfulltextu2a289453pdf
David Gutierrez Rivera Aerodynamic Shape Optimization 54 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Future Research
Some ideas
Multi-Disciplinary Optimization (MDO)
Life-Cycle Design
Development of Optimization Algorithms
David Gutierrez Rivera Aerodynamic Shape Optimization 50 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Future Research
Some ideas
Multi-Disciplinary Optimization (MDO)
Life-Cycle Design
Development of Optimization Algorithms
David Gutierrez Rivera Aerodynamic Shape Optimization 50 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Future Research
Some ideas
Multi-Disciplinary Optimization (MDO)
Life-Cycle Design
Development of Optimization Algorithms
David Gutierrez Rivera Aerodynamic Shape Optimization 50 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Future Research
Some ideas
Multi-Disciplinary Optimization (MDO)
Life-Cycle Design
Development of Optimization Algorithms
David Gutierrez Rivera Aerodynamic Shape Optimization 50 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Acknowledgments
Many Thanks to
Prof Guido Morgenthal
MSc Khaled Ibrahim
MSc Benjamin Bendig
MSc Samir Chawdhury
Shanmugam Narayanan
David Gutierrez Rivera Aerodynamic Shape Optimization 51 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
References
Stephen Boyd and Lieven Vandenberghe Convex OptimizationCambridge University Press The Edinburgh Building Cambridge CB28RU UK 2004 Pages 1-11 455-496httpwwwstanfordedu~boydcvxbookbv_cvxbookpdf
Jorge Nocedal and Stephen J Wright Numerical Optimization Springer175 Fifth Avenue New York NY 10010 USA 1999 Pages 2-3 4-710-30
Igor Griva Stephen G Nash and Ariela Sofer Linear and NonlinearOptimization Siam 3600 Market Street 6th Floor Philadelphia PA19104-2688 USA 2nd edition 2009 Pages 35-40 54-58 355-450
David G Luenberger and Yinyu Ye Linear and Nonlinear ProgrammingSpringer 233 Spring Street New YorkNY 10013 USA 3rd edition2008 Pages 2-7 183-257
David Gutierrez Rivera Aerodynamic Shape Optimization 52 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
References
Florent Brunet Contributions to Parametric Image Registration and 3DSurface Reconstruction Universite drsquoAuvergne PhD ThesisNovember 2010 Chapter 2 Pages 27-44httpwwwbrnteupublicationsbrunet2010phdpdf
Prof DK Chaturvedi Advances in Evolutionary OptimizationTechniques YouTube November 2013httpswwwyoutubecomwatchv=ftxiiaHNweQ
David Gutierrez Rivera OptiFlow v061a Weimar Germany March2014 OptiFlow Userguide
Guido Morgenthal Aerodynamic Analysis of Structures UsingHigh-resolution Vortex Particle Methods University of CambridgePhD Thesis October 2002 Pages 21-31 121-142
Wikipedia Savonius wind turbine The Wikimedia Foundation March2014 httpenwikipediaorgwikiSavonius_wind_turbine
David Gutierrez Rivera Aerodynamic Shape Optimization 53 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
References
John James Tomick On Convergence of the Nelder-Mead SimplexAlgorithm for Unconstrained Stochastic Optimization ThePennsylvania State University PhD Thesis May 1995httpwwwdticmildtictrfulltextu2a289453pdf
David Gutierrez Rivera Aerodynamic Shape Optimization 54 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Future Research
Some ideas
Multi-Disciplinary Optimization (MDO)
Life-Cycle Design
Development of Optimization Algorithms
David Gutierrez Rivera Aerodynamic Shape Optimization 50 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Future Research
Some ideas
Multi-Disciplinary Optimization (MDO)
Life-Cycle Design
Development of Optimization Algorithms
David Gutierrez Rivera Aerodynamic Shape Optimization 50 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Future Research
Some ideas
Multi-Disciplinary Optimization (MDO)
Life-Cycle Design
Development of Optimization Algorithms
David Gutierrez Rivera Aerodynamic Shape Optimization 50 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Acknowledgments
Many Thanks to
Prof Guido Morgenthal
MSc Khaled Ibrahim
MSc Benjamin Bendig
MSc Samir Chawdhury
Shanmugam Narayanan
David Gutierrez Rivera Aerodynamic Shape Optimization 51 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
References
Stephen Boyd and Lieven Vandenberghe Convex OptimizationCambridge University Press The Edinburgh Building Cambridge CB28RU UK 2004 Pages 1-11 455-496httpwwwstanfordedu~boydcvxbookbv_cvxbookpdf
Jorge Nocedal and Stephen J Wright Numerical Optimization Springer175 Fifth Avenue New York NY 10010 USA 1999 Pages 2-3 4-710-30
Igor Griva Stephen G Nash and Ariela Sofer Linear and NonlinearOptimization Siam 3600 Market Street 6th Floor Philadelphia PA19104-2688 USA 2nd edition 2009 Pages 35-40 54-58 355-450
David G Luenberger and Yinyu Ye Linear and Nonlinear ProgrammingSpringer 233 Spring Street New YorkNY 10013 USA 3rd edition2008 Pages 2-7 183-257
David Gutierrez Rivera Aerodynamic Shape Optimization 52 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
References
Florent Brunet Contributions to Parametric Image Registration and 3DSurface Reconstruction Universite drsquoAuvergne PhD ThesisNovember 2010 Chapter 2 Pages 27-44httpwwwbrnteupublicationsbrunet2010phdpdf
Prof DK Chaturvedi Advances in Evolutionary OptimizationTechniques YouTube November 2013httpswwwyoutubecomwatchv=ftxiiaHNweQ
David Gutierrez Rivera OptiFlow v061a Weimar Germany March2014 OptiFlow Userguide
Guido Morgenthal Aerodynamic Analysis of Structures UsingHigh-resolution Vortex Particle Methods University of CambridgePhD Thesis October 2002 Pages 21-31 121-142
Wikipedia Savonius wind turbine The Wikimedia Foundation March2014 httpenwikipediaorgwikiSavonius_wind_turbine
David Gutierrez Rivera Aerodynamic Shape Optimization 53 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
References
John James Tomick On Convergence of the Nelder-Mead SimplexAlgorithm for Unconstrained Stochastic Optimization ThePennsylvania State University PhD Thesis May 1995httpwwwdticmildtictrfulltextu2a289453pdf
David Gutierrez Rivera Aerodynamic Shape Optimization 54 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Future Research
Some ideas
Multi-Disciplinary Optimization (MDO)
Life-Cycle Design
Development of Optimization Algorithms
David Gutierrez Rivera Aerodynamic Shape Optimization 50 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Future Research
Some ideas
Multi-Disciplinary Optimization (MDO)
Life-Cycle Design
Development of Optimization Algorithms
David Gutierrez Rivera Aerodynamic Shape Optimization 50 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Acknowledgments
Many Thanks to
Prof Guido Morgenthal
MSc Khaled Ibrahim
MSc Benjamin Bendig
MSc Samir Chawdhury
Shanmugam Narayanan
David Gutierrez Rivera Aerodynamic Shape Optimization 51 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
References
Stephen Boyd and Lieven Vandenberghe Convex OptimizationCambridge University Press The Edinburgh Building Cambridge CB28RU UK 2004 Pages 1-11 455-496httpwwwstanfordedu~boydcvxbookbv_cvxbookpdf
Jorge Nocedal and Stephen J Wright Numerical Optimization Springer175 Fifth Avenue New York NY 10010 USA 1999 Pages 2-3 4-710-30
Igor Griva Stephen G Nash and Ariela Sofer Linear and NonlinearOptimization Siam 3600 Market Street 6th Floor Philadelphia PA19104-2688 USA 2nd edition 2009 Pages 35-40 54-58 355-450
David G Luenberger and Yinyu Ye Linear and Nonlinear ProgrammingSpringer 233 Spring Street New YorkNY 10013 USA 3rd edition2008 Pages 2-7 183-257
David Gutierrez Rivera Aerodynamic Shape Optimization 52 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
References
Florent Brunet Contributions to Parametric Image Registration and 3DSurface Reconstruction Universite drsquoAuvergne PhD ThesisNovember 2010 Chapter 2 Pages 27-44httpwwwbrnteupublicationsbrunet2010phdpdf
Prof DK Chaturvedi Advances in Evolutionary OptimizationTechniques YouTube November 2013httpswwwyoutubecomwatchv=ftxiiaHNweQ
David Gutierrez Rivera OptiFlow v061a Weimar Germany March2014 OptiFlow Userguide
Guido Morgenthal Aerodynamic Analysis of Structures UsingHigh-resolution Vortex Particle Methods University of CambridgePhD Thesis October 2002 Pages 21-31 121-142
Wikipedia Savonius wind turbine The Wikimedia Foundation March2014 httpenwikipediaorgwikiSavonius_wind_turbine
David Gutierrez Rivera Aerodynamic Shape Optimization 53 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
References
John James Tomick On Convergence of the Nelder-Mead SimplexAlgorithm for Unconstrained Stochastic Optimization ThePennsylvania State University PhD Thesis May 1995httpwwwdticmildtictrfulltextu2a289453pdf
David Gutierrez Rivera Aerodynamic Shape Optimization 54 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Future Research
Some ideas
Multi-Disciplinary Optimization (MDO)
Life-Cycle Design
Development of Optimization Algorithms
David Gutierrez Rivera Aerodynamic Shape Optimization 50 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Acknowledgments
Many Thanks to
Prof Guido Morgenthal
MSc Khaled Ibrahim
MSc Benjamin Bendig
MSc Samir Chawdhury
Shanmugam Narayanan
David Gutierrez Rivera Aerodynamic Shape Optimization 51 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
References
Stephen Boyd and Lieven Vandenberghe Convex OptimizationCambridge University Press The Edinburgh Building Cambridge CB28RU UK 2004 Pages 1-11 455-496httpwwwstanfordedu~boydcvxbookbv_cvxbookpdf
Jorge Nocedal and Stephen J Wright Numerical Optimization Springer175 Fifth Avenue New York NY 10010 USA 1999 Pages 2-3 4-710-30
Igor Griva Stephen G Nash and Ariela Sofer Linear and NonlinearOptimization Siam 3600 Market Street 6th Floor Philadelphia PA19104-2688 USA 2nd edition 2009 Pages 35-40 54-58 355-450
David G Luenberger and Yinyu Ye Linear and Nonlinear ProgrammingSpringer 233 Spring Street New YorkNY 10013 USA 3rd edition2008 Pages 2-7 183-257
David Gutierrez Rivera Aerodynamic Shape Optimization 52 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
References
Florent Brunet Contributions to Parametric Image Registration and 3DSurface Reconstruction Universite drsquoAuvergne PhD ThesisNovember 2010 Chapter 2 Pages 27-44httpwwwbrnteupublicationsbrunet2010phdpdf
Prof DK Chaturvedi Advances in Evolutionary OptimizationTechniques YouTube November 2013httpswwwyoutubecomwatchv=ftxiiaHNweQ
David Gutierrez Rivera OptiFlow v061a Weimar Germany March2014 OptiFlow Userguide
Guido Morgenthal Aerodynamic Analysis of Structures UsingHigh-resolution Vortex Particle Methods University of CambridgePhD Thesis October 2002 Pages 21-31 121-142
Wikipedia Savonius wind turbine The Wikimedia Foundation March2014 httpenwikipediaorgwikiSavonius_wind_turbine
David Gutierrez Rivera Aerodynamic Shape Optimization 53 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
References
John James Tomick On Convergence of the Nelder-Mead SimplexAlgorithm for Unconstrained Stochastic Optimization ThePennsylvania State University PhD Thesis May 1995httpwwwdticmildtictrfulltextu2a289453pdf
David Gutierrez Rivera Aerodynamic Shape Optimization 54 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
Acknowledgments
Many Thanks to
Prof Guido Morgenthal
MSc Khaled Ibrahim
MSc Benjamin Bendig
MSc Samir Chawdhury
Shanmugam Narayanan
David Gutierrez Rivera Aerodynamic Shape Optimization 51 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
References
Stephen Boyd and Lieven Vandenberghe Convex OptimizationCambridge University Press The Edinburgh Building Cambridge CB28RU UK 2004 Pages 1-11 455-496httpwwwstanfordedu~boydcvxbookbv_cvxbookpdf
Jorge Nocedal and Stephen J Wright Numerical Optimization Springer175 Fifth Avenue New York NY 10010 USA 1999 Pages 2-3 4-710-30
Igor Griva Stephen G Nash and Ariela Sofer Linear and NonlinearOptimization Siam 3600 Market Street 6th Floor Philadelphia PA19104-2688 USA 2nd edition 2009 Pages 35-40 54-58 355-450
David G Luenberger and Yinyu Ye Linear and Nonlinear ProgrammingSpringer 233 Spring Street New YorkNY 10013 USA 3rd edition2008 Pages 2-7 183-257
David Gutierrez Rivera Aerodynamic Shape Optimization 52 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
References
Florent Brunet Contributions to Parametric Image Registration and 3DSurface Reconstruction Universite drsquoAuvergne PhD ThesisNovember 2010 Chapter 2 Pages 27-44httpwwwbrnteupublicationsbrunet2010phdpdf
Prof DK Chaturvedi Advances in Evolutionary OptimizationTechniques YouTube November 2013httpswwwyoutubecomwatchv=ftxiiaHNweQ
David Gutierrez Rivera OptiFlow v061a Weimar Germany March2014 OptiFlow Userguide
Guido Morgenthal Aerodynamic Analysis of Structures UsingHigh-resolution Vortex Particle Methods University of CambridgePhD Thesis October 2002 Pages 21-31 121-142
Wikipedia Savonius wind turbine The Wikimedia Foundation March2014 httpenwikipediaorgwikiSavonius_wind_turbine
David Gutierrez Rivera Aerodynamic Shape Optimization 53 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
References
John James Tomick On Convergence of the Nelder-Mead SimplexAlgorithm for Unconstrained Stochastic Optimization ThePennsylvania State University PhD Thesis May 1995httpwwwdticmildtictrfulltextu2a289453pdf
David Gutierrez Rivera Aerodynamic Shape Optimization 54 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
References
Stephen Boyd and Lieven Vandenberghe Convex OptimizationCambridge University Press The Edinburgh Building Cambridge CB28RU UK 2004 Pages 1-11 455-496httpwwwstanfordedu~boydcvxbookbv_cvxbookpdf
Jorge Nocedal and Stephen J Wright Numerical Optimization Springer175 Fifth Avenue New York NY 10010 USA 1999 Pages 2-3 4-710-30
Igor Griva Stephen G Nash and Ariela Sofer Linear and NonlinearOptimization Siam 3600 Market Street 6th Floor Philadelphia PA19104-2688 USA 2nd edition 2009 Pages 35-40 54-58 355-450
David G Luenberger and Yinyu Ye Linear and Nonlinear ProgrammingSpringer 233 Spring Street New YorkNY 10013 USA 3rd edition2008 Pages 2-7 183-257
David Gutierrez Rivera Aerodynamic Shape Optimization 52 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
References
Florent Brunet Contributions to Parametric Image Registration and 3DSurface Reconstruction Universite drsquoAuvergne PhD ThesisNovember 2010 Chapter 2 Pages 27-44httpwwwbrnteupublicationsbrunet2010phdpdf
Prof DK Chaturvedi Advances in Evolutionary OptimizationTechniques YouTube November 2013httpswwwyoutubecomwatchv=ftxiiaHNweQ
David Gutierrez Rivera OptiFlow v061a Weimar Germany March2014 OptiFlow Userguide
Guido Morgenthal Aerodynamic Analysis of Structures UsingHigh-resolution Vortex Particle Methods University of CambridgePhD Thesis October 2002 Pages 21-31 121-142
Wikipedia Savonius wind turbine The Wikimedia Foundation March2014 httpenwikipediaorgwikiSavonius_wind_turbine
David Gutierrez Rivera Aerodynamic Shape Optimization 53 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
References
John James Tomick On Convergence of the Nelder-Mead SimplexAlgorithm for Unconstrained Stochastic Optimization ThePennsylvania State University PhD Thesis May 1995httpwwwdticmildtictrfulltextu2a289453pdf
David Gutierrez Rivera Aerodynamic Shape Optimization 54 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
References
Florent Brunet Contributions to Parametric Image Registration and 3DSurface Reconstruction Universite drsquoAuvergne PhD ThesisNovember 2010 Chapter 2 Pages 27-44httpwwwbrnteupublicationsbrunet2010phdpdf
Prof DK Chaturvedi Advances in Evolutionary OptimizationTechniques YouTube November 2013httpswwwyoutubecomwatchv=ftxiiaHNweQ
David Gutierrez Rivera OptiFlow v061a Weimar Germany March2014 OptiFlow Userguide
Guido Morgenthal Aerodynamic Analysis of Structures UsingHigh-resolution Vortex Particle Methods University of CambridgePhD Thesis October 2002 Pages 21-31 121-142
Wikipedia Savonius wind turbine The Wikimedia Foundation March2014 httpenwikipediaorgwikiSavonius_wind_turbine
David Gutierrez Rivera Aerodynamic Shape Optimization 53 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
References
John James Tomick On Convergence of the Nelder-Mead SimplexAlgorithm for Unconstrained Stochastic Optimization ThePennsylvania State University PhD Thesis May 1995httpwwwdticmildtictrfulltextu2a289453pdf
David Gutierrez Rivera Aerodynamic Shape Optimization 54 54
IntroductionOptimization Algorithms
Shape OptimizationData Gathering
Black-Box OptimizationSimulation-based Optimization
OptiFlowOptimization Examples
Final RemarksFuture Research
AcknowledgmentsReferences
References
John James Tomick On Convergence of the Nelder-Mead SimplexAlgorithm for Unconstrained Stochastic Optimization ThePennsylvania State University PhD Thesis May 1995httpwwwdticmildtictrfulltextu2a289453pdf
David Gutierrez Rivera Aerodynamic Shape Optimization 54 54
