Analysis and optimization of aerodynamic noise

JOURNALOFSOUNDANDVIBRATIONJournalofSoundandVibration289(2006)999–1018AnalysisandoptimizationofaerodynamicnoiseinacentrifugalcompressorHyosungSun
,HyungkiShin,SoogabLeeCenterforEnvironmentalNoiseandVibrationResearch,SchoolofMechanicalandAerospaceEngineering,SeoulNationalUniversity,San56-1,Shinlim-dong,Kwanak-gu,Seoul151-742,KoreaReceived18March2004;receivedinrevisedform18November2004;accepted7March2005Availableonline2June2005AbstractThenumericalmethodsfortheperformanceanalysisandthenoisepredictionofthecentrifugalcompressorimpelleraredeveloped,whicharecoupledwiththeoptimizationdesignmethodologyconsistingofresponsesurfacemethod,statisticalapproach,andgeneticalgorithm.Navier–Stokesequationswiththetwo-equation(k–o)turbulencemodelareappliedtocalculateimpelleraerodynamiccharacteristics,andFfowcsWilliams–Hawkingsformulationandboundaryelementmethodareusedtopredicttheimpelleraerodynamicnoiseonthebasisofimpellerflowfieldresults.Thecomputationalcodesareverifiedthroughthecomparisonofmeasureddata.ThequadraticresponsesurfacemodelwithD-optimalthree-levelfactorialexperimentaldesignpointsisconstructedtooptimizetheimpellergeometryfortheadvancedcentrifugalcompressor,anditisshownthatthequadraticmodelexhibitsareasonablefittingqualityresultingintheimpellerbladedesignwiththehighperformanceandthelowfar-fieldnoiselevel.Theinfluencesofselecteddesignvariablesandtheirmutualinteractionsaswellastheeffectsofvariousobjectivefunctionsandconstraintsontheimpellerperformanceandtheimpellernoisearealsoexaminedasaresultoftheoptimizationprocess.r2005ElsevierLtd.Allrightsreserved.ARTICLEINPRESS:10.1016/j.jsv.2005.03.004
Correspondingauthor.Tel.:[phone];fax:[phone].E-mailaddress:[e-mail](H.Sun).1.IntroductionTheacousticconsiderationofthecentrifugalcompressorhasbecomeimperativeduetoregulationsandtheubiquitouscallforenvironment-friendlyproducts.Thecentrifugalcompressorimpellerdesignershavereliedheavilyontheirexperienceorpredictioncodesthatsupplyonlyaroughestimationtoconsiderthenoiseperformanceasaparameterfromthedesignprocess.Owingtotheadvancesincomputationalfluiddynamics(CFD)andnoisepredictiontools,however,theaerodynamic/acousticshapedesignoptimizationoftheimpellerbladehasbeeninitiated.Theautomationoftheaerodynamic/acousticshapedesignbycouplingnumericalmethodswiththedesignframeworkenablestheoveralldesigncosttobereduced.Sincevariousshapescanbetestedinanumericalenvironment,thedesignresultcanbeimproveddrasticallycomparedwiththatobtainedbyman-in-loopactivities.Fromthispointofview,thepresentresearchisfocusedonsuggestingacomprehensiveoptimizationtoolthatincorporatesthelatestdevelopmentsinfluiddynamics,aeroacoustics,andoptimizationtechnique.Responsesurfacemethod(hereafter,RSM)isacollectionofstatisticalandmathematicaltechniquesusefulfordevelopingandimprovingtheoptimizationprocess[1,2].RSMhasdrawnmuchattentionbecauseofitsefficiencyandadvantages:(1)Itsmoothesoutthehigh-frequencynoiseoftheobjectivefunctionandisexpectedtofindasolutionneartheglobaloptimum.(2)Variousobjectivesandconstraintscanbeattemptedinthedesignprocesswithoutadditionalnumericalcomputations.(3)Itcanbeeffectivelyappliedtomulti-disciplinarydesignoptimization(MDO)problemswithmanyobjectivesandconstraints.(4)Itdoesnotrequireamodificationinanalysiscodes.However,therearesomedrawbackstoRSM.Therangeofdesignparametershighlyaffectsthefittingcapabilitiesoftheresponsemodel.Thewiderangemayincreasepredictionerrorssuchthatthepredictedperformancecannotbeexactlyobtained.RSMhasalimitationonthenumberofdesignvariables,becausethecomputationtimeforconstructingtheresponsemodelisproportionaltothesquareofthenumberofdesignparameters.Navier–Stokessolverisemployedtocomputetheimpellerperformance,andthefrequencydomainapproachofFfowcsWilliams–Hawkings(hereafter,FW–H)formulationapplicabletotheimpellerbladedesignischosenasthegoverningequationforthenoiseprediction.Theoptimizationprocedureisexplainedindetailwiththeadditionaldiscussionabouttheexperimentalpointselectionmethod.Sincetheoptimizationmethodinvolvesstatistics,somediscussionsofregressioncoefficientsappearinginstatisticalanalysisaregiven.Thedevelopednumericalmethodisappliedtothecentrifugalcompressorimpellershapedesignandthedesignvariableshavingadominanteffectontheperformanceandthenoisearealsoanalyzed.2.FlowsolverThegoverningequationsare3D,unsteady,compressibleNavier–StokesequationsandcanbewritteninconservationlawformasqrqtþqqxjðrujÞ¼0,ARTICLEINPRESSH.Sunetal./JournalofSoundandVibration289(2006)999–10181000qqtðruiÞþqqxjðruiujÞ¼
qpqxiþq^tijqxj,qreqtþqqxjðreujÞ¼
qpujqxjþqqxj½ui^tij
qj,(1)whereristhedensity,tisthetime,xjð¼x;y;zÞaretheCartesiancoordinates,ujð¼u;v;wÞaretheCartesiancomponentsofthevelocity,pisthestaticpressure,eisthetotalenergy,and^tijiscomposedofthemolecularandReynoldsstressesdefinedas^tij¼2mðSij
Skkdij=3Þþtij,tij¼2mTðSij
Skkdij=3Þ
2rkdij=3,Sij¼12quiqxjþqujqxi
,(2)wheremisthelaminarviscosity,mTistheturbulenteddyviscosity,dijistheKroneckerdelta,Sijisthemeanstrain-rateten