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AnInvestigationonTurbochargerTurbinePerformanceParametersUnderInletPulsatingFlow

TabatabaeiHamidreza

DepartmentofMechanicandAerospaceEngineering,ScienceandResearchBranch,IslamicAzadUniversity,P.O.Box14155-4933,Hesarak,Tehran,Irane-mail:

h.tabatabaei@iaukashan.ac.ir

BoroomandMasoud

DepartmentofAerospaceEngineering,AmirkabirUniversityofTechnology,HafezAvenue,P.O.Box15875-4413,Tehran,Irane-mail:

boromand@aut.ac.ir

TaeibiRahniMohammad

DepartmentofAerospaceEngineering,SharifUniversityofTechnology,AzadiAvenue,P.O.Box11365-11155,Tehran,Irane-mail:

taeibi@sharif.ac.ir

Three-dimensionalsteadyandunsteady（pulsating）compressibleflowsinavane-lessturbochargerturbineofa1.7literSIenginearesimulatednumerically,andtheresultsarevalidatedexperimentallyusingaturbochargedon-enginetestcell.Simulationsarecarriedoutfora720_enginecycleatthreeenginespeeds,andthecompleteformsofvoluteandrotorvanesaremodeled.Twowaysformodelingtherotatingwheel,multiplereferenceframes（MRF）,andslidingmesh（SM）techniquesarealsoexamined.Finally,theeffectsofpulsatingflowontheturbochargerturbineperformanceparameters（TTPP）suchastheinletstaticpressure,reducedmassflowrate,andefficiencyareobtainedandcomparedwiththeirvaluesundersteadyflow.TheresultsshowthattheaccuracyofsteadycharacteristicmaptoestimatetheTTPPshassomesourceofambiguity,whichshouldbeconsideredfordetailedanalysis.TTPPvaluesundersteadyflowconditionsarefoundtobesignificantlydeviatedfromtheunsteadyresults.Thesedeviationsaredecreasedastheenginespeedincreases.

Keywords:

computationalfluiddynamics,unsteadyflow,compressibleflow,SI-engine,simulation

1Introduction

Theusualpulsatingflowintheexhaustgasofanautomotivepowertrainsystemcausesanunsteadyflowattheinlettotheturbochargerturbine.Inafourcylinderfourstrokeengine,thepulsefrequencyvariesbetween30to166Hz,whichisequivalenttoanenginespeedof900to5000rpm.TheturbochargerturbineisusuallytestedundersteadyflowbymanufacturersandcharacteristiccurvesofturbinesdonotmatchwiththeTTPPsbecausethemassflowrate,pressures,andtemperaturesvarywithtime.ThereareseveralwaystoevaluatetheTTPPs:

（i）Theexperimentalmethod,whichisveryexpensiveandlengthyandisrecommendedonlyforvalidationofcalculations.（ii）The1Dunsteadyflowsimulation,whichusesthesteadyflowcharacteristicmapoftheturbineandrequiresconsiderableattentioninmodelingreal3Dphenomenaina1Denvironment.（iii）The3Dsteadyflowsimulation,whichignoresthepulsatingfloweffects.（iv）Finally,the3Dunsteady（pulsating）flowsimulation,whichismorepracticalcomparedwiththeabovementionedmethods,asitwillbeshowninthisreport.

Severalinvestigationshavebeenperformedabouttheturbineperformanceunderinletpulsatingflow.CapobiancoandGambarotta[1]usedasmallturbochargerengineandmeasuredthepowerofturbineunderthepulsatingflowandconcludedthattheefficiencywas15–20%higherthanthatundersteadyflow.Arcoumanisetal.[2]showedthatthepulse-turbochargedsystemsproducingaturbineoperatingenvironmentisdominatedbyunsteadyflowandthatthemechanicalinertiaoftheshaftandwheelsservestoholdrotationalspeednearlyconstant.Chenetal.[3]indicatedthattheunsteadymodelisbetterforpredictingtheturbineflowbehaviorthanaquasi-studymodel.Elrich[4]performedextensivemeasurementsonasixcylinderdieselenginetoanalyzetheonengineturbineperformance.Theexperimentsshowedthattheflowvelocity,temperature,andpressurewithintheexhaustmanifoldandturbinepropagatewithdifferentvelocities.Arcoumanisetal.[5]derivedinstantaneousefficiencyforamixed-flowturbineusingtwodifferentmethodsofphaseshifting.Resultsshowedthatthemethodusedforphaseshiftinghasasignificanteffectonthederivedinstantaneousefficiency,andthecycleaveragedisentropicefficiencieswerehigherforamixed-flowturbinecomparedtoaradialturbine.HuandLawless[6]developedaturbinemodel,butwerenotabletoshowanyrelationshipbetweenthesimulationsandEhrlich’smeasurements.Lametal.[7]didacomplete3DCFDcalculationofunsteadyflowinaradialturbochargerturbine.Theyshowedthatthepulseamplitudeisdampedquiteheavilythroughthevoluteandnozzlevanes.Costalletal.[8]andRajooandMartinez-Botas[9]studiedtheinstantaneousefficiencyofamixedflowturbineunderpulsatingflowandpresentedagoodcorrelationbetweenthepressuresmeasuredatdifferentlocationsoftheturbine.HellstromandFuchs[10]modeledpulsatingandnonpulsating3DflowsintheturbinepartoftheradialturbochargerusingReynoldsaveragedNavier-Stokes（RANS）andlargeeddysimulations（LES）.CapobiancoandMarelli[11]carriedoutanexperimentalinvestigationintoasmallturbochargerturbinefittedwithawaste-gatevalve.Theturbineperformancewasmeasuredunderbothsteadyandunsteadyflowoperation.Particularattentionwasgiventopulsatingflowperformanceevaluatedusingtheinstantaneousparameters.Theeffectofflowunsteadinessonturbinebehaviorwasanalyzed.Copelandetal.[12]presentedtheexperimentalperformanceevaluationofacircumferentiallydivided,double-entryturbochargerturbine.Oneoftheprincipalobjectiveswastoassessthedegreetowhichtheunsteadyperformancediffersfromthequasi-steadyassumption.Chiongetal.[13]presentedtheappropriateinletboundaryconditionmsettingsforturbochargerturbineunsteadyperformancepredictionusing1Dmodelingwithoutthefullaccesstopulsatingengineexhaustflowparameter.Allboundaryconditionsshowedacceptableunsteadyturbinenondimensionalparameterprediction,particularlythehysteresisofunsteadyturbineswallowingcapacityperformance.MacekandVitek[14]developedatoolimprovingtheaccuracyofturbochargerturbinesimulationduringmatchingofaturbochargertoanengine.RajooandMartinez-Botas[15]showedaturbochargerturbinewithanozzlebehavingdifferentlyfromanozzle-lessturbineunderpulsatingflow.

Thepresentreportisfocusedonthesimulationoftheturbineperformanceunder3Dsteadyandunsteadycompressibleflow,andtheresultsarevalidatedexperimentally.Therotatingwheelismodeledusingmultiplereferenceframesandslidingmeshtechniques.

2ModelSetup

2.1TurbineGeometry.Avane-lessturbochargerturbineofa1.7literSIengineismodeledatthreeoperatingenginespeedsof998,2500,and5000rpm.Table1showsthemaingeometricparametersoftheturbine.

TheCADmodeloftheturbochargerturbine,whichwaspreparedbyCatiaVersion5R18andmodifiedbyAnsysDesignModelerV12.0,isshowninFig.1.Theturbineiscomprisedofbothsolid（turbineblades）andfluidregions.Thegapbetweentheturbinerotorvanesandtheshroudisneglected.

2.2TurbineEfficiencyCalculations.Theinstantaneousturbineefficiencyisvariedandbecomespulsatingattheturbineinletandisdefinedas

（1.1）

Andthemeanefficiencyoftheturbineisdefinedas

（1.2）

Theinstantaneousactualpowerisdefinedas

（2）

Theinstantaneousisentropicturbinepowerisdefinedas

（3）

Themeanvaluesof

and

arecalculatedasaveragevaluesfortheworkingtemperaturerangeoftheturbine.

Themeanvaluesofactualandisentropicturbinepowersaredefinedas

（4）

（5）

3NumericalModeling

3.1GoverningEquations.Theunsteadyconservationformofmass,momentum,andenergyequationsinstationaryframeofreferenceareasfollows:

（6）

（7）

（8）

Wherethestresstensorisrelatedtothestrainratesby

（9）

Andthesourcetermofmomentum,is

expressedby

Thesourceofthemomentumequationcontainstwoaccelerationterms:

theCoriolisacceleration--

andthecentripetalacceleration--

.Where

and

arethelocationvector,therelativeframevelocity（thatis,therotatingframevelocityforarotatingframeofreference）,andtheangularvelocity,respectively.

3.2TurbulenceModeling.Oneofthemostprominentturbulencemodels,the

model,hasbeenimplementedinmostgeneralpurposeCFDcodesandisconsideredasastandardmodelinmanyflowsimulationcasesbecauseofitsstability,numericalrobustness,anditswellestablishedregimeofpredictivecapability.Previousinvestigationshaveshownthatthismodelwithallitscapabilitiesmaynotbesuitableforapplicationssuchasrotatingfluidflowinaturbinewhereasuddenchangeinstrainmayoccur[16,17].Forthisreason,theRNG

modelrecommendedbysomeresearchers[4,7,18]hasbeenused.

3.3GridGeneration.Intheproposedsimulation,theuseofanunstructuredtetrahedralgridhasbeendecidedonduetoitsgreateradaptationtothegeometry.Innear-wallregions,boundarylayereffectsgiverisetovelocitygradients,whichhavethegreatestnormaltothemeshface.Computationallyefficientmeshesintheseregionsrequirethattheelementshavehighaspectratios.Iftetrahedralmeshesareused,thenaprohibitivelyfinesurfacemeshmayberequiredtoavoidgeneratinghighlydistortedtetrahedralelementsatthemeshface.So,sixinflationlayersnearthewallsaredefined.Figure2showstheunstructuredtetrahedralmeshesontheturbinecasingandtheturbineblades.

3.4BoundaryConditions.Unfortunately,thetestcellcannotmeasuretheunsteadymassflowrateandthestagnationtemperature,so1DflowsimulationisdoneusingtheGT-SuiteV6.0commercialsoftwarefromGamma-Technologiestopreparetheboundaryconditionsfor3Dflowsimulations.

Figure3showstheschematicdiagramfora1