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info@engys.com | Tel: +44 (0)20 32393041 | Fax: +44 (0)20 3357 3123 | www.engys.com
NOFUN 2014
24th September 2014
Braunschweig, Germany
Georgios Karpouzas, Engys Ltd. – NTUA
Eugene De Villiers, Engys Ltd.
Thomas Schumacher, Engys UG
“Adjoint Optimization with HELYX”
2
Contents
• Introduction
• Topology Optimization
• Shape Optimization
• Adjoint Coupled Solver
• Summary
© 2014 Engys Ltd.
3
Introduction | Continuous Adjoint
© 2014 Engys Ltd.
• Gradient based optimization method
• Used to calculate sensitivities w.r.t. user defined objective functions
• Cost doesn’t increase with the number of parameters
• The calculation of the sensitivity derivatives is approximately equivalent with the solution of one primal problem
• Avoid calculating the computationally expensive terms (δU/δb, δp/δb) by making their multipliers (adjoint equations+BCs) zero
C.Othmer. Adjoint methods for car aerodynamics. Journal of Mathematics in Industry 2014 4:6.
G.K. Karpouzas, E. De Villiers, “Level-set based topology optimization using the Continuous Adjoint Method". OPTi2014 - International Conference on Engineering and Applied Sciences Optimization, June 4-6 2014, Kos, Greece.
I.S Kavvadias, G.K. Karpouzas, E.M. Papoutsis-Kiachagias, D.I. Papadimitriou, K.C. Giannakoglou: “Optimal Flow Control and Topology Optimization Using the Continuous Adjoint Method in Unsteady Flows”, EUROGEN 2013
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Introduction | HELYX Adjoint Features
© 2014 Engys Ltd.
• “One-shot” primal/adjoint/topology update
• Incompressible & compressible flows
• Adjoint MRF and porous media support
• Level-set immersed boundary for interface tracking
• 2nd order accuracy
• Multi-objective:
forces & moments, uniformity, pressure loss, massflow split,
swirl, wall shear stress, etc.
• No expert operator knowledge required
5
Contents
• Introduction
• Topology Optimization
Simple Duct
HVAC duct
Gear pump
• Shape Optimization
• Adjoint Coupled Solver
• Summary
© 2014 Engys Ltd.
6
Topology Optimization | Overview
© 2014 Engys Ltd.
• Specify design space and inlet/outlet interfaces
• Define optimization objectives
• Run single simulation till geometry converges
Iteration: Primal Adjoint Geometry update
• Output optimized shape
7
Contents
• Introduction
• Topology Optimization
Simple Duct
HVAC duct
Gear pump
• Shape Optimization
• Adjoint Coupled Solver
• Summary
© 2014 Engys Ltd.
8
Topology Optimization | Simple Duct
© 2014 Engys Ltd.
• Topology Optimization
• Pressure loss minimization
• Design space with obstacles
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Topology Optimization | Simple Duct
© 2014 Engys Ltd.
• 50% Pressure Loss improvement
• Optimized shape:
11
Contents
• Introduction
• Topology Optimization
Simple Duct
HVAC duct
Gear pump
• Shape Optimization
• Adjoint Coupled Solver
• Summary
© 2014 Engys Ltd.
12 © 2014 Engys Ltd.
• Multiple objective functions employed
Minimize pressure loss in domain
Maximize flow uniformity through porous media
Target flow split through outlets 3x33%
Topology Optimization | HVAC Duct
14 © 2014 Engys Ltd.
• Final shape
• 30% reduction in pressure loss achieved
• Other objectives unchanged
Topology Optimization | HVAC Duct
15
Contents
• Introduction
• Topology Optimization
Simple Duct
HVAC duct
Gear pump
• Shape Optimization
• Adjoint Coupled Solver
• Summary
© 2014 Engys Ltd.
16
Topology Optimization | Gear pump
© 2014 Engys Ltd.
Inlet Port Outlet Port
Gear
• Geometry provided by Aisin AW
• Case separated into two parts: Inlet port (low pressure)
Outlet port (high pressure)
• Objective: minimization of power losses
17
Topology Optimization | Gear pump
© 2014 Engys Ltd.
Power Losses Inport Outport Gear Pump
Baseline 2.208 W 31.017 W 33.325 W
Optimized 1.635 W 25.379 W 27.013 W
Percentage 29.17 % 18.18 % 18.94 %
18
Contents
• Introduction
• Topology Optimization
• Shape Optimization
• Adjoint Coupled Solver
• Summary
© 2014 Engys Ltd.
20
Shape Optimization | DRIVAER
© 2014 Engys Ltd.
• Comparison of 2nd order accuracy (top) with former 1st order (bottom) results
21
Contents
• Introduction
• Topology Optimization
• Shape Optimization
• Adjoint Coupled Solver
• Summary
© 2014 Engys Ltd.
22
Adjoint Coupled Solver
© 2014 Engys Ltd.
• Block coupled adjoint solver
• Fully implicit ATC term
• Speedup ~x4
23
Adjoint Coupled Solver
© 2014 Engys Ltd.
• Top: segregated volumetric sensitivities
• Bottom: block volumetric sensitivities
24
Contents
• Introduction
• Topology Optimization
• Shape Optimization
• Adjoint Coupled Solver
• Summary
© 2014 Engys Ltd.
25
Summary
© 2014 Engys Ltd.
• Proven methodology Robust implementation
2nd order accurate adjoint
Many successful industrial applications
• Unique Level-Set immersed boundary technology Better control of the optimization
More manufacturable final shape
Improved primal accuracy due to IB
• Coupled solver > ~x4 speed up
Implicit ATC more robust
26
Looking Ahead
© 2014 Engys Ltd.
• GUI support to enable routine use
• Integrated shape morphing
CARAT++ from FEMopt
Harmonic coordinates (IODA ITN 7)
• Algorithmic improvements
Enhanced immersed boundaries
Composite objectives (e.g. Lift/Drag, Pump efficiency)
Multipoint optimization (pseudo-transient & transient)
Adjoint thermal and species
Integration with Coupled Primal Solver
27
Acknowledgements
© 2014 Engys Ltd.
• Aboutflow ITN
• Adjoint-Based optimization of industrial and unsteady flows
• http://aboutflow.sems.qmul.ac.uk
“This project has received funding from the European
Union’s Seventh Framework Programme for research,
technological development and demonstration under
grant agreement no [317006]”.
• Volkswagen Research: C. Othmer, M.M. Gregersen
• Volkswagen Methods Development: D. Schreader
• Volkswagen Engine Developement: W. Py
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