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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Figure2:ContoursofStaticPressure(SteadyState)
Figure3:ContoursofVelocityMagnitude(SteadyState)
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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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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.
5
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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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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(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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Figure8:SpectralAnalysisofConvergenceHistoryofStaticPressureonPoint-1
Figure9:SpectralAnalysisofConvergenceHistoryofStaticPressureonPoint-2
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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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Figure11:SpectralAnalysisofConvergencehistoryofStaticPressure
Thedeviationofsoundpressurelevelbetweenthefirsttwomaximumpeaks(50Hzand132Hz)isquitesmall.Thepostprocessingfunctionmagnitudeinfouriertransformpanelissimilartotherootmeansquarevalue(RMS)ofthestaticpressureatthesefrequencies.WecanusetheRMSvaluetoderivetheamplitudeofthepressurefluctuationwhichisresponsiblefortheSPL-peak.Theresolutionoffrequencyspectraislimitedbythetemporaldiscretization.Withthetemporaldiscretization,themaximumfrequencyis
fmax=
12t
(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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