CFD-Lecture-(Introduction-to-CFD)-CFD經(jīng)典課件完整版

IntroductiontoComputationalFluidDynamics(CFD)TaoXing,ShantiBhushanandFredSternIIHR—Hydroscience&EngineeringC.MaxwellStanleyHydraulicsLaboratoryTheUniversityofIowa57:020MechanicsofFluidsandTransportProcesses/~fluids/Ocrtober7,20092Outline1.What,whyandwhereofCFD?2.Modeling3.Numericalmethods4.TypesofCFDcodes5.CFDEducationalInterface6.CFDProcess7.ExampleofCFDProcess8.57:020CFDLabs3WhatisCFD?CFDisthesimulationoffluidsengineeringsystemsusingmodeling(mathematicalphysicalproblemformulation)andnumericalmethods(discretizationmethods,solvers,numericalparameters,andgridgenerations,etc.)HistoricallyonlyAnalyticalFluidDynamics(AFD)andExperimentalFluidDynamics(EFD).CFDmadepossiblebytheadventofdigitalcomputerandadvancingwithimprovementsofcomputerresources(500flops,194720teraflops,20031.3pentaflops,RoadrunneratLasAlamosNationalLab,2009.)4WhyuseCFD?AnalysisandDesign1.Simulation-baseddesigninsteadof“build&test”MorecosteffectiveandmorerapidthanEFDCFDprovideshigh-fidelitydatabasefordiagnosingflowfield2.SimulationofphysicalfluidphenomenathataredifficultforexperimentsFullscalesimulations(e.g.,shipsandairplanes)Environmentaleffects(wind,weather,etc.)Hazards(e.g.,explosions,radiation,pollution)Physics(e.g.,planetaryboundarylayer,stellarevolution)Knowledgeandexplorationofflowphysics5WhereisCFDused?WhereisCFDused?AerospaceAutomotiveBiomedicalChemicalProcessingHVACHydraulicsMarineOil&GasPowerGenerationSportsF18StoreSeparationTemperatureandnaturalconvectioncurrentsintheeyefollowinglaserheating.AerospaceAutomotiveBiomedical6WhereisCFDused?Polymerizationreactorvessel-predictionofflowseparationandresidencetimeeffects.StreamlinesforworkstationventilationWhereisCFDused?AerospaceeAutomotiveBiomedicalChemicalProcessingHVACHydraulicsMarineOil&GasPowerGenerationSportsHVACChemicalProcessingHydraulics7WhereisCFDused?WhereisCFDused?AerospaceAutomotiveBiomedicalChemicalProcessingHVACHydraulicsMarineOil&GasPowerGenerationSportsFlowoflubricatingmudoverdrillbitFlowaroundcoolingtowersMarine(movie)Oil&GasSportsPowerGeneration8ModelingModelingisthemathematicalphysicsproblemformulationintermsofacontinuousinitialboundaryvalueproblem(IBVP)IBVPisintheformofPartialDifferentialEquations(PDEs)withappropriateboundaryconditionsandinitialconditions.Modelingincludes:1.Geometryanddomain2.Coordinates3.Governingequations4.Flowconditions5.Initialandboundaryconditions6.Selectionofmodelsfordifferentapplications

9Modeling(geometryanddomain)Simplegeometriescanbeeasilycreatedbyfewgeometricparameters(e.g.circularpipe)Complexgeometriesmustbecreatedbythepartialdifferentialequationsorimportingthedatabaseofthegeometry(e.g.airfoil)intocommercialsoftwareDomain:sizeandshape

TypicalapproachesGeometryapproximationCAD/CAEintegration:useofindustrystandardssuchasParasolid,ACIS,STEP,orIGES,etc.Thethreecoordinates:Cartesiansystem(x,y,z),cylindricalsystem(r,θ,z),andsphericalsystem(r,θ,Φ)shouldbeappropriatelychosenforabetterresolutionofthegeometry(e.g.cylindricalforcircularpipe).10Modeling(coordinates)xyzxyzxyz(r,,z)zr(r,,)r(x,y,z)CartesianCylindricalSphericalGeneralCurvilinearCoordinatesGeneralorthogonalCoordinates11Modeling(governingequations)Navier-Stokesequations(3DinCartesiancoordinates)ConvectionPiezometricpressuregradientViscoustermsLocalaccelerationContinuityequationEquationofstateRayleighEquation12Modeling(flowconditions)Basedonthephysicsofthefluidsphenomena,CFDcanbedistinguishedintodifferentcategoriesusingdifferentcriteria

Viscousvs.inviscid(Re)Externalfloworinternalflow(wallboundedornot)Turbulentvs.laminar(Re)Ipressible(Ma)Single-vs.multi-phase(Ca)Thermal/densityeffects(Pr,g,Gr,Ec)Free-surfaceflow(Fr)andsurfacetension(We)Chemicalreactionsandcombustion(Pe,Da)etc…13Modeling(initialconditions)Initialconditions(ICS,steady/unsteadyflows)ICsshouldnotaffectfinalresultsandonlyaffectconvergencepath,i.e.numberofiterations(steady)ortimesteps(unsteady)needtoreachconvergedsolutions.MorereasonableguesscanspeeduptheconvergenceForcomplicatedunsteadyflowproblems,CFDcodesareusuallyruninthesteadymodeforafewiterationsforgettingabetterinitialconditions14Modeling(boundaryconditions)Boundaryconditions:No-sliporslip-freeonwalls,periodic,inlet(velocityinlet,massflowrate,constantpressure,etc.),outlet(constantpressure,velocityconvective,numericalbeach,zero-gradient),andnon-reflecting(forcompressibleflows,suchasacoustics),etc.No-slipwalls:u=0,v=0v=0,dp/dr=0,du/dr=0Inlet,u=c,v=0Outlet,p=cPeriodicboundaryconditioninspanwisedirectionofanairfoilorxAxisymmetric15Modeling(selectionofmodels)CFDcodestypicallydesignedforsolvingcertainfluidphenomenonbyapplyingdifferentmodels

Viscousvs.inviscid(Re)Turbulentvs.laminar(Re,Turbulentmodels)Ipressible(Ma,equationofstate)Single-vs.multi-phase(Ca,cavitationmodel,two-fluidmodel)Thermal/densityeffectsandenergyequation(Pr,g,Gr,Ec,conservationofenergy)Free-surfaceflow(Fr,level-set&surfacetrackingmodel)andsurfacetension(We,bubbledynamicmodel)Chemicalreactionsandcombustion(Chemicalreactionmodel)etc…16Modeling(Turbulenceandfreesurfacemodels)

Turbulentmodels:

DNS:mostaccuratelysolveNSequations,buttooexpensiveforturbulentflows

RANS:predictmeanflowstructures,efficientinsideBLbutexcessivediffusionintheseparatedregion.

LES:accurateinseparationregionandunaffordableforresolvingBL

DES:RANSinsideBL,LESinseparatedregions.

Free-surfacemodels:

Surface-trackingmethod:meshmovingtocapturefreesurface,limitedtosmallandmediumwaveslopes

Single/twophaselevel-setmethod:meshfixedandlevel-setfunctionusedtocapturethegas/liquidinterface,capableofstudyingsteeporbreakingwaves.

TurbulentflowsathighReusuallyinvolvebothlargeandsmallscalevorticalstructuresandverythinturbulentboundarylayer(BL)nearthewall17Examplesofmodeling(Turbulenceandfreesurfacemodels)DES,Re=105,Iso-surfaceofQcriterion(0.4)forturbulentflowaroundNACA12withangleofattack60degreesURANS,Re=105,contourofvorticityforturbulentflowaroundNACA12withangleofattack60degreesURANS,WigleyHullpitchingandheaving18NumericalmethodsThecontinuousInitialBoundaryValueProblems(IBVPs)arediscretizedintoalgebraicequationsusingnumericalmethods.AssemblethesystemofalgebraicequationsandsolvethesystemtogetapproximatesolutionsNumericalmethodsinclude:1.Discretizationmethods2.Solversandnumericalparameters3.Gridgenerationandtransformation4.HighPerformanceComputation(HPC)andpost-processing19DiscretizationmethodsFinitedifferencemethods(straightforwardtoapply,usuallyforregulargrid)andfinitevolumesandfiniteelementmethods(usuallyforirregularmeshes)Eachtypeofmethodsaboveyieldsthesamesolutionifthegridisfineenough.However,somemethodsaremoresuitabletosomecasesthanothersFinitedifferencemethodsforspatialderivativeswithdifferentorderofaccuraciescanbederivedusingTaylorexpansions,suchas2ndorderupwindscheme,centraldifferencesschemes,etc.HigherordernumericalmethodsusuallypredicthigherorderofaccuracyforCFD,butmorelikelyunstableduetolessnumericaldissipationTemporalderivativescanbeintegratedeitherbytheexplicitmethod(Euler,Runge-Kutta,etc.)orimplicitmethod(e.g.Beam-Warmingmethod)20Discretizationmethods(Cont’d)ExplicitmethodscanbeeasilyappliedbutyieldconditionallystableFiniteDifferentEquations(FDEs),whicharerestrictedbythetimestep;Implicitmethodsareunconditionallystable,butneedeffortsonefficiency.Usually,higher-ordertemporaldiscretizationisusedwhenthespatialdiscretizationisalsoofhigherorder.Stability:Adiscretizationmethodissaidtobestableifitdoesnotmagnifytheerrorsthatappearinthecourseofnumericalsolutionprocess.Pre-conditioningmethodisusedwhenthematrixofthelinearalgebraicsystemisill-posed,suchasmulti-phaseflows,flowswithabroadrangeofMachnumbers,etc.Selectionofdiscretizationmethodsshouldconsiderefficiency,accuracyandspecialrequirements,suchasshockwavetracking.21Discretizationmethods(example)2Dincompressiblelaminarflowboundarylayerm=0m=1L-1Lyxm=MMm=MM+1(L,m-1)(L,m)(L,m+1)(L-1,m)FDSign()<0BDSign()>02ndordercentraldifferencei.e.,theoreticalorderofaccuracyPkest=

2.1storderupwindscheme,i.e.,theoreticalorderofaccuracyPkest=122Discretizationmethods(example)B2B3B1B4SolveitusingThomasalgorithmTobestable,MatrixhastobeDiagonallydominant.23SolversandnumericalparametersSolvers

include:tridiagonal,pentadiagonalsolvers,PETSCsolver,solution-adaptivesolver,multi-gridsolvers,etc.Solverscanbeeitherdirect(Cramer’srule,Gausselimination,LUdecomposition)oriterative(Jacobimethod,Gauss-Seidelmethod,SORmethod)Numericalparametersneedtobespecifiedtocontrolthecalculation.Underrelaxationfactor,convergencelimit,etc.DifferentnumericalschemesMonitorresiduals(changeofresultsbetweeniterations)NumberofiterationsforsteadyflowornumberoftimestepsforunsteadyflowSingle/doubleprecisions24Numericalmethods(gridgeneration)Gridscaneitherbestructured(hexahedral)orunstructured(tetrahedral).DependsupontypeofdiscretizationschemeandapplicationSchemeFinitedifferences:structuredFinitevolumeorfiniteelement:structuredorunstructuredApplicationThinboundarylayersbestresolvedwithhighly-stretchedstructuredgridsUnstructuredgridsusefulforcomplexgeometriesUnstructuredgridspermitautomaticadaptiverefinementbasedonthepressuregradient,orregionsinterested(FLUENT)structuredunstructured25Numericalmethods(gridtransformation)yxooPhysicaldomainComputationaldomainTransformationbetweenphysical(x,y,z)andcomputational(x,h,z)domains,importantforbody-fittedgrids.Thepartialderivativesatthesetwodomainshavetherelationship(2Dasanexample)Transform26HighperformancecomputingCFDcomputations(e.g.3Dunsteadyflows)areusuallyveryexpensivewhichrequiresparallelhighperformancesupercomputers(e.g.IBM690)withtheuseofmulti-blocktechnique.Asrequiredbythemulti-blocktechnique,CFDcodesneedtobedevelopedusingtheMassagePassingInterface(MPI)Standardtotransferdatabetweendifferentblocks.Emphasisonimproving:Strongscalability,mainbottleneckpressurePoissonsolverforincompressibleflow.Weakscalability,limitedbythememoryrequirements.Figure:StrongscalabilityoftotaltimeswithoutI/OforCFDShip-IowaV6andV4onNAVOCrayXT5(Einstein)andIBMP6(DaVinci)arecomparedwithidealscaling.Figure:WeakscalabilityoftotaltimeswithoutI/OforCFDShip-IowaV6andV4onIBMP6(DaVinci)andSGIAltix(Hawk)arecomparedwithidealscaling.27Post-processing:1.VisualizetheCFDresults(contour,velocityvectors,streamlines,pathlines,streaklines,andiso-surfacein3D,etc.),and2.

CFDUA:verificationandvalidationusingEFDdata(moredetailslater)Post-processingusuallythroughusingcommercialsoftwarePost-ProcessingFigure:IsosurfaceofQ=300coloredusingpiezometricpressure,free=surfacecoloredusingzforfullyappendedAthena,Fr=0.25,Re=2.9×108.Tecplot360isusedforvisualization.28TypesofCFDcodesCommercialCFDcode:FLUENT,Star-CD,CFDRC,CFX/AEA,etc.ResearchCFDcode:CFDSHIP-IOWAPublicdomainsoftware(PHI3D,HYDRO,andWinpipeD,etc.)OtherCFDsoftwareincludestheGridgenerationsoftware(e.g.Gridgen,Gambit)andflowvisualizationsoftware(e.g.Tecplot,FieldView)CFDSHIPIOWA29CFDEducationalInterfaceLab1:PipeFlowLab2:AirfoilFlowLab3:DiffuserLab4:Ahmedcar1.Definitionof“CFDProcess”2.Boundaryconditions3.Iterativeerror4.Griderror5.Developinglengthoflaminarandturbulentpipeflows.6.VerificationusingAFD7.ValidationusingEFD1.Boundaryconditions2.Effectoforderofaccuracyonverificationresults3.Effectofgridgenerationtopology,“C”and“O”Meshes4.Effectofangleofattack/turbulentmodelsonflowfield5.VerificationandValidationusingEFD1.Meshinganditerativeconvergence2.Boundarylayerseparation3.Axialvelocityprofile4.Streamlines5.Effectofturbulencemodels6.EffectofexpansionangleandcomparisonwithLES,EFD,andRANS.1.Meshinganditerativeconvergence2.Boundarylayerseparation3.Axialvelocityprofile4.Streamlines5.EffectofslantangleandcomparisonwithLES,EFD,andRANS.30CFDprocessPurposesofCFDcodeswillbedifferentfordifferentapplications:investigationofbubble-fluidinteractionsforbubblyflows,studyofwaveinducedmassivelyseparatedflowsforfree-surface,etc.Dependonthespecificpurposeandflowconditionsoftheproblem,differentCFDcodescanbechosenfordifferentapplications(aerospace,marines,combustion,multi-phaseflows,etc.)OncepurposesandCFDcodeschosen,“CFDprocess”isthestepstosetuptheIBVPproblemandrunthecode:

1.Geometry2.Physics

3.Mesh

4.Solve

5.Reports

6.Postprocessing31CFDProcessViscousModelBoundaryConditionsInitialConditionsConvergentLimitContoursPrecisions(single/double)NumericalSchemeVectorsStreamlinesVerificationGeometrySelectGeometryGeometryParametersPhysicsMeshSolvePost-ProcessingCompressibleON/OFFFlowpropertiesUnstructured(automatic/manual)Steady/UnsteadyForcesReport(lift/drag,shearstress,etc)XYPlotDomainShapeandSizeHeatTransferON/OFFStructured(automatic/manual)Iterations/StepsValidationReports32GeometrySelectionofanappropriatecoordinateDeterminethedomainsizeandshapeAnysimplificationsneeded?Whatkindsofshapesneededtobeusedtobestresolvethegeometry?(lines,circular,ovals,etc.)Forcommercialcode,geometryisusuallycreatedusingcommercialsoftware(eitherseparatedfromthecommercialcodeitself,likeGambit,orcombinedtogether,likeFlowLab)Forresearchcode,commercialsoftware(e.g.Gridgen)isused.33PhysicsFlowconditionsandfluidproperties1.Flowconditions:inviscid,viscous,laminar,orturbulent,etc.2.Fluidproperties:density,viscosity,andthermalconductivity,etc.3.FlowconditionsandpropertiesusuallypresentedindimensionalforminindustrialcommercialCFDsoftware,whereasinnon-dimensionalvariablesforresearchcodes.Selectionofmodels:differentmodelsusuallyfixedbycodes,optionsforusertochooseInitialandBoundaryConditions:notfixedbycodes,userneedsspecifythemfordifferentapplications.34MeshMeshesshouldbewelldesignedtoresolveimportantflowfeatureswhicharedependentuponflowconditionparameters(e.g.,Re),suchasthegridrefinementinsidethewallboundarylayerMeshcanbegeneratedbyeithercommercialcodes(Gridgen,Gambit,etc.)orresearchcode(usingalgebraicvs.PDEbased,conformalmapping,etc.)Themesh,togetherwiththeboundaryconditionsneedtobeexportedfromcommercialsoftwareinacertainformatthatcanberecognizedbytheresearchCFDcodeorothercommercialCFDsoftware.35SolveSetupappropriatenumericalparametersChooseappropriateSolversSolutionprocedure(e.g.incompressibleflows)Solvethemomentum,pressurePoissonequationsandgetflowfieldquantities,suchasvelocity,turbulenceintensity,pressureandintegralquantities(lift,dragforces)36ReportsReportssavedthetimehistoryoftheresidualsofthevelocity,pressureandtemperature,etc.Reporttheintegralquantities,suchastotalpressuredrop,frictionfactor(pipeflow),liftanddragcoefficients(airfoilflow),etc.XYplotscouldpresentthecenterlinevelocity/pressuredistribution,frictionfactordistribution(pipeflow),pressurecoefficientdistribution(airfoilflow).AFDorEFDdatacanbeimportedandputontopoftheXYplotsforvalidation37Post-processingAnalysisandvisualizationCalculationofderivedvariablesVorticityWallshearstressCalculationofintegralparameters:forces,momentsVisualization(usuallywithcommercialsoftware)Simple2Dcontours3DcontourisosurfaceplotsVectorplotsandstreamlines(streamlinesarethelineswhosetangentdirectionisthesameasthevelocityvectors)Animations38Post-processing(UncertaintyAssessment)Simulationerror:thedifferencebetweenasimulationresultSandthetruthT(objectivereality),assumedcomposedofadditivemodelingδSMandnumericalδSN

errors:

Error:Uncertainty:Verification:processforassessingsimulationnumericaluncertaintiesUSNand,whenconditionspermit,estimatingthesignandmagnitudeDeltaδ*SNofthesimulationnumericalerroritselfandtheuncertaintiesinthaterrorestimateUSNI:Iterative,G:Grid,T:Timestep,P:InputparametersValidation:processforassessingsimulationmodelinguncertaintyUSMbyusingbenchmarkexperimentaldataand,whenconditionspermit,estimatingthesignandmagnitudeofthemodelingerrorδSMitself.D:EFDData;UV:ValidationUncertaintyValidationachieved39Post-processing(UA,Verification)Convergencestudies:Convergencestudiesrequireaminimumofm=3solutionstoevaluateconvergencewithrespectivetoinputparameters.Considerthesolutionscorrespondingtofine,medium,andcoarsemeshes(i).Monotonicconvergence:0<Rk<1(ii).OscillatoryConvergence:Rk<0;|Rk|<1(iii).Monotonicdivergence:Rk>1(iv).Oscillatorydivergence:Rk<0;|Rk|>1Gridrefinementratio:uniformratioofgridspacingbetweenmeshes.MonotonicConvergenceMonotonicDivergenceOscillatoryConvergence40Post-processing(Verification,RE)GeneralizedRichardsonExtrapolation(RE):Formonotonicconvergence,generalizedREisusedtoestimatetheerrorδ*kandorderofaccuracypkduetotheselectionofthekthinputparameter.Theerrorisexpandedinapowerseriesexpansionwithintegerpowersofxk

asafinitesum.Theaccuracyoftheestimatesdependsonhowmanytermsareretainedintheexpansion,themagnitude(importance)ofthehigher-orderterms,andthevalidityoftheassumptionsmadeinREtheory41Post-processing(Verification,RE)PowerseriesexpansionFinitesumforthekthparameterandmthsolutionorderofaccuracyfortheithtermThreeequationswiththreeunknownsεSNistheerrorintheestimateSCisthenumericalbenchmark42Post-processing(UA,Verification,cont’d)MonotonicConvergence:GeneralizedRichardsonExtrapolation

OscillatoryConvergence:Uncertaintiescanbeestimated,butwithoutsignsandmagnitudesoftheerrors.Divergence1.Correctionfactors2.GCIapproach

Inthiscourse,onlygriduncertaintiesstudied.So,allthevariableswithsubscribesymbolkwillbereplacedbyg,suchas“Uk”willbe“Ug”isthetheoreticalorderofaccuracy,2for2ndorderand1for1storderschemesistheuncertaintiesbasedonfinemeshsolution,istheuncertaintiesbasedonnumericalbenchmarkSCisthecorrectionfactorFS:FactorofSafety43AsymptoticRange:Forsufficientlysmallxk,thesolutionsareintheasymptoticrangesuchthathigher-ordertermsarenegligibleandtheassumptionthatandareindependentofxkisvalid.WhenAsymptoticRangereached,willbeclosetothetheoreticalvalue,andthecorrectionfactorwillbecloseto1.Toachievetheasymptoticrangeforpracticalgeometryandconditionsisusuallynotpossibleandnumberofgridsm>3isundesirablefromaresourcespointofviewPost-processing(Verification,AsymptoticRange)44Post-processing(UA,Verification,cont’d)VerificationforvelocityprofileusingAFD:Toavoidill-definedratios,L2normoftheG21and

G32areusedtodefineRGandPGNOTE:ForverificationusingAFDforaxialveloc