Computational Fluid Dynamics (CFD)U7AEA29

Dr. S. Senthil KumarAssociate ProfessorDept. of Aeronautical EngineeringVel Tech Dr. RR & Dr. SR Technical UniversityAvadi, Chennai.

*Outline

What is CFD?Why use CFD?Where is CFD used?PhysicsModelingNumericsCFD processResources

*What is CFD?What is CFD and its objective?

Computational Fluid DynamicsHistorically Analytical Fluid Dynamics (AFD) and EFD (Experimental Fluid Dynamics) was used. CFD has become feasible due to the advent of high speed digital computers.Computer simulation for prediction of fluid-flow phenomena. The objective of CFD is to model the continuous fluids with Partial Differential Equations (PDEs) and discretize PDEs into an algebra problem (Taylor series), solve it, validate it and achieve simulation based design.

*Why use CFD?Why use CFD?Analysis and DesignSimulation-based design instead of build & testMore cost effectively and more rapidly than with experimentsCFD solution provides high-fidelity database for interrogation of flow fieldSimulation of physical fluid phenomena that are difficult to be measured by experimentsScale simulations (e.g., full-scale ships, airplanes)Hazards (e.g., explosions, radiation, pollution)Physics (e.g., weather prediction, planetary boundary layer, stellar evolution)Knowledge and exploration of flow physics

*Where is CFD used? (Aerospace)Where is CFD used?AerospaceAppliancesAutomotiveBiomedicalChemical ProcessingHVAC&RHydraulicsMarineOil & GasPower GenerationSportsF18 Store Separation

Wing-Body Interaction

Hypersonic Launch Vehicle

*

*Where is CFD used? (Appliances)Where is CFD used?AerospaceAppliancesAutomotiveBiomedicalChemical ProcessingHVAC&RHydraulicsMarineOil & GasPower GenerationSports

Surface-heat-flux plots of the No-Frost refrigerator and freezer compartments helped BOSCH-SIEMENS engineers to optimize the location of air inlets.

*Where is CFD used? (Automotive)Where is CFD used?AerospaceAppliancesAutomotiveBiomedicalChemical ProcessingHVAC&RHydraulicsMarineOil & GasPower GenerationSportsExternal Aerodynamics

Undercarriage Aerodynamics

Interior Ventilation

Engine Cooling

*Where is CFD used? (Biomedical)Where is CFD used?AerospaceAppliancesAutomotiveBiomedicalChemical ProcessingHVAC&RHydraulicsMarineOil & GasPower GenerationSports

Temperature and natural convection currents in the eye following laser heating.

Medtronic Blood Pump

*Where is CFD used? (Chemical Processing)Where is CFD used?AerospaceAppliancesAutomotiveBiomedicalChemical ProcessingHVAC&RHydraulicsMarineOil & GasPower GenerationSports

Polymerization reactor vessel - prediction of flow separation and residence time effects.

Shear rate distribution in twin-screw extruder simulation

Twin-screw extruder modeling

*Where is CFD used? (HVAC&R)Where is CFD used?AerospaceAppliancesAutomotiveBiomedicalChemical ProcessingHVAC&RHydraulicsMarineOil & GasPower GenerationSports

Flow pathlines colored by pressure quantify head loss in ductwork

*Where is CFD used? (Hydraulics)Where is CFD used?AerospaceAppliancesAutomotiveBiomedicalChemical ProcessingHVAC&RHydraulicsMarineOil & GasPower GenerationSports

*Where is CFD used? (Marine)Where is CFD used?AerospaceAppliancesAutomotiveBiomedicalChemical ProcessingHVAC&RHydraulicsMarineOil & GasPower GenerationSports

*Where is CFD used? (Oil & Gas)Where is CFD used?AerospaceAppliancesAutomotiveBiomedicalChemical ProcessingHVAC&RHydraulicsMarineOil & GasPower GenerationSports

Flow vectors and pressure distribution on an offshore oil rigFlow of lubricating mud over drill bitVolume fraction of water Volume fraction of oilVolume fraction of gasAnalysis of multiphase separator

*Where is CFD used? (Power Generation)Where is CFD used?AerospaceAppliancesAutomotiveBiomedicalChemical ProcessingHVAC&RHydraulicsMarineOil & GasPower GenerationSportsFlow pattern through a water turbine. Flow around cooling towersPathlines from the inlet colored by temperature during standard operating conditions

*Where is CFD used? (Sports)Where is CFD used?AerospaceAppliancesAutomotiveBiomedicalChemical ProcessingHVAC&RHydraulicsMarineOil & GasPower GenerationSports

*PhysicsCFD codes typically designed for representation of specific flow phenomenonViscous vs. inviscid (no viscous forces) (Re)Turbulent vs. laminar (Re)Incompressible vs. compressible (Ma)Single- vs. multi-phase (Ca)Thermal/density effects and energy equation (Pr, g, Gr, Ec)Free-surface flow and surface tension (Fr, We)Chemical reactions, mass transferetc

*PhysicsFluid MechanicsInviscidViscousLaminarTurbulenceInternal(pipe,valve)External(airfoil, ship)Compressible(air, acoustic)Incompressible(water)Components of Fluid Mechanics

*Claude-Louis NavierGeorge Gabriel StokesNavier-Stokes Equation

*ModelingMathematical representation of the physical problemSome problems are exact (e.g., laminar pipe flow)Exact solutions only exist for some simple cases. In these cases nonlinear terms can be dropped from the N-S equations which allow analytical solution.Most cases require models for flow behavior [e.g., Reynolds Averaged Navier Stokes equations (RANS) or Large Eddy Simulation (LES) for turbulent flow]Initial Boundary Value Problem (IBVP), include: governing Partial Differential Equations (PDEs), Initial Conditions (ICs) and Boundary Conditions (BCs)

*Governing Equations (B,S,& L)Continuityx - Equation of motion(Equations based on average velocity)

*Numerics / DiscretizationComputational solution of the IBVPMethod dependent upon the model equations and physicsSeveral components to formulationDiscretization and linearizationAssembly of system of algebraic equationsSolve the system and get approximate solutions

*Finite DifferencesMethods of SolutionDirect methodsIterative methodsCramers Rule, Gauss eliminationLU decompositionJacobi method, Gauss-SeidelMethod, SOR methodFinite differencerepresentationTruncation error

*Numeric Solution (Finite Differences)oxii+1i-1j+1jj-1imaxjmaxTaylors Series Expansion u i,j = velocity of fluidDiscrete Grid Points

*CFD processGeometry descriptionSpecification of flow conditions and propertiesSelection of modelsSpecification of initial and boundary conditionsGrid generation and transformationSpecification of numerical parametersFlow solutionPost processing: Analysis, and visualization

*Geometry descriptionTypical approaches Make assumptions and simplificationsCAD/CAE integrationEngineering drawingsCoordinates include Cartesian system (x,y,z), cylindrical system (r, , z), and spherical system(r, , )

*Selection of models for flow fieldDirect Numerical Simulations (DNS) is to solve the N-S equations directly without any modeling. Grid must be fine enough to resolve all flow scales. Applied for laminar flow and rare be used in turbulent flow.Reynolds Averaged Navier-Stokes (NS) equations (RANS) is to perform averaging of NS equations and establishing turbulent models for the eddy viscosity. Too many averaging might damping vortical structures in turbulent flowsLarge Eddy Simulation (LES), Smagorinsky constant model and dynamic model. Provide more instantaneous information than RANS did. Instability in complex geometriesDetached Eddy Simulation (DES) is to use one single formulation to combine the advantages of RANS and LES.

*Domain for bottle filling problem.Filling NozzleBottleCFD - how it worksAnalysis begins with a mathematical model of a physical problem.Conservation of matter, momentum, and energy must be satisfied throughout the region of interest.Fluid properties are modeled empirically.Simplifying assumptions are made in order to make the problem tractable (e.g., steady-state, incompressible, inviscid, two-dimensional).Provide appropriate initial and boundary conditions for the problem.

*Mesh for bottle filling problem.CFD - how it works (2)CFD applies numerical methods (called discretization) to develop approximations of the governing equations of fluid mechanics in the fluid region of interest.Governing differential equations: algebraic.The collection of cells is called the grid. The set of algebraic equations are solved numerically (on a computer) for the flow field variables at each node or cell.System of equations are solved simultaneously to provide solution.The solution is post-processed to extract quantities of interest (e.g. lift, drag, torque, heat transfer, separation, pressure loss, etc.).

*DiscretizationDomain is discretized into a finite set of control volumes or cells. The discretized domain is called the grid or the mesh.General conservation (transport) equations for mass, momentum, energy, etc., are discretized into algebraic equations.All equations are solved to render flow field.

control volume

*Design and create the gridShould you use a quad/hex grid, a tri/tet grid, a hybrid grid, or a non-conformal grid?What degree of grid resolution is required in each region of the domain?How many cells are required for the problem?Will you use adaption to add resolution?Do you have sufficient computer memory?arbitrary polyhedron

*Tri/tet vs. quad/hex meshesFor simple geometries, quad/hex meshes can provide high-quality solutions with fewer cells than a comparable tri/tet mesh.

For complex geometries, quad/hex meshes show no numerical advantage, and you can save meshing effort by using a tri/tet mesh.

*Hybrid mesh exampleValve port grid.Specific regions can be meshed with different cell types.Both efficiency and accuracy are enhanced relative to a hexahedral or tetrahedral mesh alone.

*Dinosaur mesh example

*Set up the numerical modelFor a given problem, you will need to:Select appropriate physical models.Turbulence, combustion, multiphase, etc.Define material properties.Fluid. Solid.Mixture.Prescribe operating conditions.Prescribe boundary conditions at all boundary zones.Provide an initial solution.Set up solver controls.Set up convergence monitors.

*Initial and boundary conditionsFor steady/unsteady flow IC should not affect final solution, only convergence path, i.e. iteration numbers needed to get the converged solution.Robust codes should start most problems from very crude IC, . But more reasonable guess can speed up the convergence.Boundary conditionsNo-slip or slip-free on the wall, periodic, inlet (velocity inlet, mass flow rate, constant pressure, etc.), outlet (constant pressure, velocity convective, buffer zone, zero-gradient), and non-reflecting (compressible flows, such as acoustics), etc.

*Compute the solutionThe discretized conservation equations are solved iteratively. A number of iterations are usually required to reach a converged solution.Convergence is reached when:Changes in solution variables from one iteration to the next are negligible.Residuals provide a mechanism to help monitor this trend.Overall property conservation is achieved.The accuracy of a converged solution is dependent upon:Appropriateness and accuracy of the physical models.Grid resolution and independence.Problem setup.

*Numerical parameters & flow solution Typical time history of residuals The closer the flow field to the converged solution, the smaller the speed of the residuals decreasing.Solution converged, residuals do not change after more iterations

*Post-processingAnalysis, and visualizationCalculation of derived variablesVorticityWall shear stress Calculation of integral parameters: forces, momentsVisualization (usually with commercial software)Simple X-Y plotsSimple 2D contours3D contour carpet plotsVector plots and streamlines (streamlines are the lines whose tangent direction is the same as the velocity vectors)Animations (dozens of sample pictures in a series of time were shown continuously)

*Examine the resultsVisualization can be used to answer such questions as:What is the overall flow pattern?Is there separation?Where do shocks, shear layers, etc. form?Are key flow features being resolved?Are physical models and boundary conditions appropriate?Numerical reporting tools can be used to calculate quantitative results, e.g:Lift, drag, and torque.Average heat transfer coefficients.Surface-averaged quantities.

*Velocity vectors around a dinosaur

*Velocity magnitude (0-6 m/s) on a dinosaur

*Pressure field on a dinosaur

*Advantages of CFDRelatively low cost.Using physical experiments and tests to get essential engineering data for design can be expensive.CFD simulations are relatively inexpensive, and costs are likely to decrease as computers become more powerful.Speed.CFD simulations can be executed in a short period of time.Quick turnaround means engineering data can be introduced early in the design process.Ability to simulate real conditions.Many flow and heat transfer processes can not be (easily) tested, e.g. hypersonic flow.CFD provides the ability to theoretically simulate any physical condition.

*Limitations of CFDPhysical models. CFD solutions rely upon physical models of real world processes (e.g. turbulence, compressibility, chemistry, multiphase flow, etc.).The CFD solutions can only be as accurate as the physical models on which they are based.Numerical errors.Solving equations on a computer invariably introduces numerical errors.Round-off error: due to finite word size available on the computer. Round-off errors will always exist (though they can be small in most cases).Truncation error: due to approximations in the numerical models. Truncation errors will go to zero as the grid is refined. Mesh refinement is one way to deal with truncation error.

*Limitations of CFD (2)Boundary conditions.As with physical models, the accuracy of the CFD solution is only as good as the initial/boundary conditions provided to the numerical model.Example: flow in a duct with sudden expansion. If flow is supplied to domain by a pipe, you should use a fully-developed profile for velocity rather than assume uniform conditions.

*Software and resourcesCFD software was built upon physics, modeling, numerics.Two types of available softwareCommercial (e.g., FLUENT, CFX, Star-CD)Research (e.g., CFDSHIP-IOWA, U2RANS)More information on CFD can be got on the following website:CFD Online: http://www.cfd-online.com/CFD softwareFLUENT: http://www.fluent.com/CFDRC: http://www.cfdrc.com/Computational Dynamics: http://www.cd.co.uk/CFX/AEA: http://www.software.aeat.com/cfx/Grid generation softwareGridgen: http://www.pointwise.comGridPro: http://www.gridpro.com/HypermeshVisualization softwareTecplot: http://www.amtec.com/Fieldview: http://www.ilight.com/

THANK YOU*

********************************************