大涡模拟的FLUENT算例2D

Introduction

Thepurposeofthistutorialistoprovideguidelinesandrecommendationsforthebasicsetupandsolutionprocedureforatypicalaeroacousticapplicationusingcomputationalaeroacoustic(CAA)method.Inthistutorialyouwilllearnhowto:

•ModelaHelmholtzresonator.

•Usethetransientk-epsilonmodelandthelargeeddysimulation(LES)modelforaeroacousticapplication.•Setup,run,andperformpostprocessinginFLUENT.

Prerequisites

Thistutorialassumesthatyouarefamiliarwiththeuserinterface,basicsetupandsolutionproceduresinFLUENT.Thistutorialdoesnotcovermechanicsofusingacousticsmodel,butfocusesonsettinguptheproblemforHelmholtz-Resonatorandsolvingit.Italsoassumesthatyouhavebasicunderstandingofaeroacousticphysics.

IfyouhavenotusedFLUENTbefore,itwouldbehelpfultofirstreviewFLUENT6.3User’sGuideandFLUENT6.3TutorialGuide.

ProblemDescription

AHelmholtzresonatorconsistsofacavityinarigidstructurethatcommunicatesthroughanarrowneckorslittotheoutsideair.Thefrequencyofresonanceisdeterminedbythemassofairintheneckresonatinginconjunctionwiththecomplianceoftheairinthecavity.ThephysicsbehindtheHelmholtzresonatorissimilartowindnoiseapplicationslikesunroofbuffeting.

Weassumethatoutofthetwocavitiesthatarepresent,smalleroneistheresonator.Themotionofthefluidtakesplacebecauseoftheinletvelocityof27.78m/s(100km/h).Theflowseparatesintoahighlyunsteadymotionfromtheopeningtothesmallcavity.Thisunsteadymotionleadstoapressurefluctuations.Twomonitorpoints(Point-1andPoint-2)actasmicrophonepointstorecordthegeneratedsound.TheacousticsignaliscalculatedwithinFLUENT.Theflowexitsthedomainthroughthepressureoutlet.

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ModelingAeroacousticsforaHelmholtzResonatorUsingtheDirectMethod(CAA)

Preparation

1.Copythefilessteady.cas.gz,steady.dat.gz,execute-by-name.scm,stptmstp4.scm,ti-to-scm-jos.scmandstptmstp.txtintoyourworkingdirectory.2.Startthe2Ddoubleprecision(2ddp)versionofFLUENT.

SetupandSolution

Step1:Grid

1.Readtheinitialcaseanddatafilesforsteady-state(steady.cas.gzandsteady.dat.gz).

File−→Read−→Case&Data...

IgnorethewarningthatisdisplayedintheFLUENTconsolewhilereadingthesefiles.2.Keepdefaultscaleforthegrid.

Grid−→Scale...

3.Displaythegridandobservethelocationsofthetwomonitorpoints,Point-1andPoint-2(Figure1).

Figure1:GraphicsDisplayoftheGrid

4.Displayandobservethecontoursofstaticpressure(Figure2)andvelocitymagnitude(Figure3)fortheinitialsteady-statesolution.

Display−→Contours..

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ModelingAeroacousticsforaHelmholtzResonatorUsingtheDirectMethod(CAA)

Figure2:ContoursofStaticPressure(SteadyState)

Figure3:ContoursofVelocityMagnitude(SteadyState)

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ModelingAeroacousticsforaHelmholtzResonatorUsingtheDirectMethod(CAA)

Step2:Models

1.Selectunsteadysolver.

Define−→Models−→Solver...(a)SelectUnsteadyintheTimelist.

(b)Select2nd-order-implicitintheUnsteadyformulationlist.(c)Retainthedefaultsettingsforotherparameters.(d)ClickOKtoclosetheSolverpanel.2.Definetheviscousmodel.

Define−→Models−→Viscous...

(a)SelectNon-EquilibriumWallFunctionsintheNear-WallTreatmentlist.(b)Retainthedefaultsettignsforotherparameters.(c)ClickOKtoclosetheViscousModelpanel.

Near-WallTreatmentpredictsgoodseparationandre-attachmentpoints.Step3:MaterialsDefine−→Materials...

1.Selectideal-gasfromtheDensitydrop-downlist.2.Retainthedefaultvaluesforotherparameters.3.ClickChange/CreateandclosetheMaterialspanel.

Idealgaslawisgoodinpredictingthesmallchangesinthepressure.Step4:Solution

1.Monitorthestaticpressureonpoint-1andpoint-2.

Solve−→Monitors−→Surface...(a)Enter2fortheSurfaceMonitors.

(b)EnablePlotandPrintoptionsformonitor-1andmonitor-2.(c)SelectTimeStepfromtheWhenlist.

(d)ClickDefine...formonitor-1toopenDefineSurfaceMonitorpanel.

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ModelingAeroacousticsforaHelmholtzResonatorUsingtheDirectMethod(CAA)

i.SelectVertexAveragefromtheReportTypedrop-downlist.ii.SelectFlowTimefromtheXAxisdrop-downlist.iii.Enter1forPlotWindow.

iv.Selectpoint-1fromtheSurfacesselectionlist.

(e)Similarly,specifythesurfacemonitorparametersforpoint-2.2.Startthecalculationsusingthefollowingsettings.

Solve−→Iterate...

(a)Enter3e-04sforTimeStepSize.

Theexpectedtimestepsizeforthisproblemisofthesizeofabout1/10thofthetimeperiod.Thetimeperioddependsonthefrequency(f)whichiscalculatedusingthefollowingequation:

cf=

2π

where,

c=Speedofsound

S=AreaoftheorificeoftheresonatorV=Volumeoftheresonator

L=LengthoftheconnectionbetweentheresonatorandthefreeflowareaDh=Hydraulicdiameteroftheorifice

Forthisgeometry,theestimatedfrequencyisabout120Hz.(b)Enter250fortheNumberofTimeSteps.(c)Enter50forMaxIterationsperTimeStep.(d)ClickApply.

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󰀁

SDh

V[L+π2.2]

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ModelingAeroacousticsforaHelmholtzResonatorUsingtheDirectMethod(CAA)

(e)Readtheschemefile(stptmstp4.scm).

File−→Read−→Scheme...

Thisfileactivatesaalternativeconvergencecriteria.ForacousticsimulationswithCAAitisobligatorythatthepressureiscompletelyconvergedattherecieverposition.FLUENTcomparesthemonitorquantitieswithinthelastn-definedit-erationstojudgeifthedeviationissmallerthanay-defineddeviation.

(f)Specifythenumberofpreviousiterationsfromwhichmonitorvaluesofeach

quantityusedaresavedandcomparedtothecurrent(latest)value(includetheparanthesis):

(set!stptmstp-n5)

(g)Specifytherelative(thesmalleroftwovaluesinanycomparison)difference

bywhichanyoftheoldermonitorvalues(foraselectedmonitorqauntity)maydifferfromthenewestvalue:

(set!stptmstp-maxrelchng1.e-02)

(h)Definetheexecutecommands.

Solve−→ExecuteCommands

i.Enter(stptmstp-resetvalues)forthefirstcommandandselectTimeStepfromthedrop-downlist.ii.Enter(stptmstp-chckcnvrg\"/report/surface-integralsvertex-avgpoint-1()pressure\")andselectIterationfromthedrop-downlist.iii.ClickOK.

(i)ClickIteratetostartthecalculations.

Theiterationswilltakealongtimetocomplete.Youcanskipthissimulationaf-terfewtimestepsandreadthefiles(transient.cas.gzandtransient.dat.gz)providedwiththistutorial.Thesefilescontainthedatafortheflowtimeof0.22seconds.AsseeninFigures4and5,nopressurefluctuationsarepresentatthisstage.Theoscillationsofthestaticpressureatbothmonitorpointshasreachedaconstantvalue.

TheRANS-simulationisagoodstartingpointforLargeEddySimulation.IfyouchoosetousethesteadysolutionasinitialconditionforLES,usetheTUIcommand/solve/initialize/init-instantaneous-velprovidestogetamorerealisticinstantaneousvelocityfield.TheusageofLESforacousticsimulationsisobliga-tory.ThenexttwopicturescomparethestaticpressureobtainedwithRANSandLargeEddySimulationforacompletesimulationuntil0.525seconds.Obviously,thek-epsilonmodelunderpredictsthestrongpressureoscillationafterreachingadynamicallysteadystate(>0.3s)duetoitsdissipativecharacter.Under-predictedpressureoscillationsleadtounderpredictedsoundpressurelevelwhichmeanstheacousticnoiseismoregentle.

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Figure4:ConvergenceHistoryofStaticPressureonPoint-1(Transient)

Figure5:ConvergenceHistoryofStaticPressureonPoint-2(Transient)

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Step5:EnableLargeEddySimulation

1.EnterthefollowingTUIcommandintheFLUENTconsole:

(rpsetvar’les-2d?#t)

2.Enablelargeeddysimulationeffects.

Thek-epsilonmodelcannotresolveverysmallpressurefluctuationsforaeroacousticduetoitsdissipativecharacter.UseLargeEddySimulationtoovercomethisproblem.Define−→Models−→Viscous...

(a)EnableLargeEddySimulation(LES)intheModellist.(b)EnableWALEintheSubgrid-ScaleModellist.(c)ClickOKtoclosetheViscousModelpanel.

AnInformationpanelwillappear,warningaboutboundedcentral-deferencingbe-ingdefaultformomentumwithLES/DES.

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(d)ClickOKtoclosetheInformationpanel.

3.Retaindefaultdiscretizationschemesandunder-relaxationfactors.

Solve−→Controls−→Solution...

4.Enablewritingoftwosurfacemonitorsandspecifyfilenamesasmonitor-les-1.outandmonitor-les-2.outformonitorplotsofpoint-1andpoint-2respectively.

Solve−→Monitors−→Surface...

Toaccountforstochasticcomponentsoftheflow,FLUENTprovidestwoalgorithms.Thesealgorithmsmodelthefluctuatingvelocityatvelocityinlets.Withthespec-tralsynthesizerthefluctuatingvelocitycomponentsarecomputedbysynthesizingadivergence-freevelocity-vectorfieldfromthesummationofFourierharmonics.5.Enablethespectralsynthesizer.

Define−→BoundaryConditions...

(a)SelectinletintheZonelistandclickSet....

i.SelectSpectralSynthesizerfromtheFluctuatingVelocityAlgorithmdrop-downlist.ii.Retainthedefaultvaluesforotherparameters.iii.ClickOKtoclosetheVelocityInletpanel.(b)ClosetheBoundaryConditionspanel.

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ModelingAeroacousticsforaHelmholtzResonatorUsingtheDirectMethod(CAA)

Typicallyittakesalongtimetogetadynamicallysteadystate.Additionally,thesimulated(andrecordedforFFT)flowtimedependsontheminimumfrequencyinthefollowingrelationship:

flowtime=

10

minimumfrequency

(1)

Thestandardtransientscheme(iterativetimeadvancement)requiresaconsiderableamountofcomputaionaleffortduetoalargenumberofouteriterationsperformedforeachtime-step.Toacceleratethesimulation,theNITA(non-iterativetimeadvance-ment)schemeisanalternative.6.Setthesolverparameters.

Define−→Models−→Solver...

(a)EnableNon-IterativeTimeAdvancementintheTransientControlslist.(b)ClickOKtoclosetheSolverpanel.7.Setthesolutionparameters.

Solve−→Controls−→Solution...

(a)SelectFractionalStepfromthePressure-VelocityCouplingdrop-downlist.(b)ClickOKtoclosetheSolutionControlspanel.8.Disableboththeexecutecommands.

Solve−→ExecuteCommands...

9.Continuethesimulationwiththesametimestepsizefor1500timestepstogetadynamicallysteadysolution.10.Writethecaseanddatafiles(unsteady-final.cas.gzandunsteady-final.dat.gz).

File−→Write−→Case&Data...

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Figure6:ConvergenceHistoryofStaticPressureonPoint-1(Transient)

Figure7:ConvergenceHistoryofStaticPressureonPoint-2(Transient)

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ModelingAeroacousticsforaHelmholtzResonatorUsingtheDirectMethod(CAA)

Step6:Postprocessing

1.Displaythecontoursofstaticpressuretovisualizetheeddiesneartheorifice.2.Enabletheacousticsmodel.

Define−→Models−→Acoustics...

(a)EnableFfowcs-Williams&HawkingsfromtheModelselectionlist.(b)Retainthedefaultvalueof2e-05PaforReferenceAcousticPressure.

Tospecifyavaluefortheacousticreferencepressure,itisnecessarytoactivatetheacousticmodelbeforestartingpostprocessing.(c)Retaindefaultsettingsforotherparameters.(d)ClickOKtoacceptthesettings.

AWarningdialogboxappears.Thisisaninformativepanelandwillnotaffectthepostprocessingresults.

(e)ClickOKtoacknowledgetheinformationandclosetheWarningpanel.3.Plotthesoundpressurelevel(SPL).

Plot−→FFT...

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ModelingAeroacousticsforaHelmholtzResonatorUsingtheDirectMethod(CAA)

(a)ClickLoadInputFile...button.

(b)SelectmonitorplotfileforPoint-1(monitor-les-1.out).(c)ClickPlot/ModifyInputSignal....

i.SelectCliptoRange,intheOptionslist.

ii.Enter0.3forMinand0.5forMaxintheXAxisRangegroupbox.

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ModelingAeroacousticsforaHelmholtzResonatorUsingtheDirectMethod(CAA)

iii.SelectHanningintheWindowdrop-downlist.

Hanningshowsgoodperformanceinfrequencyresolution.Itcutsthetimerecordmoresmoothly,eliminatingdiscontinuitiesthatoccurwhendataiscutoff.

iv.ClickApply/PlotandclosethePlot/ModifyInputSignalpanel.(d)SelectSoundPressureLevel(dB)fromtheYAxisFunctiondrop-downlist.(e)SelectFrequency(Hz)intheXAxisFunctiondrop-downlist.(f)ClickPlotFFTtovisualizethefrequencydistributionatPoint-1.(g)SelectWriteFFTtoFileintheOptionslist.

Note:PlotFFTbuttonwillchangetoWriteFFT.

(h)ClickWriteFFTandspecifythenameoftheFFTfileintheresultingSelectFile

panel.(i)SimilarlywritetheFFTfileformonitorplotforpoint-2(Figure9).

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ModelingAeroacousticsforaHelmholtzResonatorUsingtheDirectMethod(CAA)

Figure8:SpectralAnalysisofConvergenceHistoryofStaticPressureonPoint-1

Figure9:SpectralAnalysisofConvergenceHistoryofStaticPressureonPoint-2

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ModelingAeroacousticsforaHelmholtzResonatorUsingtheDirectMethod(CAA)

InFigures8and9,thesoundpressurelevel(SPL)peakoccursat125Hzwhichisclosetotheanalyticalestimation.Consideringthatthistutorialusesaslightlylargetimestepanda2Dgeometry,theresultisfine.4.Comparethefrequencyspectraatpoint-1andpoint-2.

Plot−→File...

(a)ClickAdd...andselecttwoFFTfiles(point-1-fft.xyandpoint-2-fft.xy)

thatyouhavesavedinthepreviousstep.(b)ClickPlottovisualizebothspectrainthesamewindow(Figure10).

NotethatthepeakforPoint-1isalittlehigherthanforPoint-2.Thisisduetothedissipativebehaviourofthesoundinthedomain.Thebiggerthedistancebetweentherecieverpointandthenoisesource,thebiggeristhedissipationofsound.Thisisthereason,whyweuseCAAmethodonlyfornearfieldcalculations.

Figure10:ComparisonofFrequencySpectraatPoint-1andPoint-2

Asecondissueisthedissipationofsoundduetotheinfluenceofthegridsize.Thisappliesespeciallyforwhichthewavelengthsareveryshort.Thus,atoocoarsemeshisnotcapableofresolvinghighfrequenciescorrectly.Inthepresentexample,themeshisrathercoarseinthefar-field.Thus,thediscrepancybetweenbothspectraismoreevidentinthehighfrequencyrange.

ThisbehaviourcanbeseeninFigure11.

Forhighfrequencies,themonitorforPoint-1generatesmuchfewernoisethanmonitorforPoint-2duetocoarsegridresolution.16

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ModelingAeroacousticsforaHelmholtzResonatorUsingtheDirectMethod(CAA)

Figure11:SpectralAnalysisofConvergencehistoryofStaticPressure

Thedeviationofsoundpressurelevelbetweenthefirsttwomaximumpeaks(50Hzand132Hz)isquitesmall.Thepostprocessingfunctionmagnitudeinfouriertransformpanelissimilartotherootmeansquarevalue(RMS)ofthestaticpressureatthesefrequencies.WecanusetheRMSvaluetoderivetheamplitudeofthepressurefluctuationwhichisresponsiblefortheSPL-peak.Theresolutionoffrequencyspectraislimitedbythetemporaldiscretization.Withthetemporaldiscretization,themaximumfrequencyis

fmax=

12󰀄t

(2)

ThisfrequencyisdefinedasNyquistfrequency.Itisthemaximumeduciblefrequency.Toresolveuptofmaxthemaximumallowabletimestepsizeis

fmax=

12×fmax

(3)

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ModelingAeroacousticsforaHelmholtzResonatorUsingtheDirectMethod(CAA)

Figure12:SpectralAnalysisofConvergenceHistoryofStaticPressureonPoint-1

Aninstabilityofthefluidmotioncoupledwithanacousticresonanceofthecavity(helmholtzresonator)produceslargepressurefluctuations(at132Hz).Comparedtothisdominanthelmholtzresonancethepressurefluctuationat50Hzisquitesmall.

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Figure13:SpectralAnalysisofConvergenceHistoryofStaticPressureonPoint-2

Summary

AeroacousticsimulationofHelmholtzresonatorhasbeenperformedusingk-epsilonmodelandLargeEddySimulationmodel.TheadvantageofusingLESmodelhasbeendemon-strated.Youalsolearnedhowthesounddissipationoccursinthedomainbymonitoringsoundpressurelevelattwodifferentpointsinthedomain.TheimportanceofusingCAAmethodhasalsobeenexplained.

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