three-dimensional unsteady turbomachinery flow analysis

8/12/2019 Three-Dimensional Unsteady Turbomachinery Flow Analysis

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DISTRIBUTIONST AT EMENT A Approved fo rPublicReleaseDistributionUnlimitedISABE99-7283

Three-DimensionalUnsteadyTurbomachineryFlow AnalysisS.H .Chen(Associate Professor),andL.C.Lee Research Assistant)InstituteofAeronautics an d Astronautics,NationalCheng Kung University,Tainan,Taiwan,RepublicofChina

ABSTRACTALooselyCoupleBladeRowLCBR)umerical

methodsevelopedonalyzehensteadylowfieldfhree-dimensionalulti-blade-row turbomachinery problem.Thismethodallowstheus eof initialbladenumbersfo runsteady calculationan donlyneladehannelerladeowssed.Circumferentialveragepproachobtainconvergedteadyolutionshenitialonditionsadoptedornsteadyalculation.elatively,totonlymaintainshe ladeonfiguration,utslso computationallyor efficient.heumericalmethodusedis compressible iscousinitevolumealgorithmolvingReynoldsveragedNavier-Stokesequations.rtificial issipationermsimilartothatused by Jamesonisadopted tosuppressth enumericaloscillations.Four-StageRunge-Kuttachemesse dtodvancehelowquationsnime.esidualsmoothing an d multi-gridechniquesareemployed toaccelerateheonvergence.aldwinndomaxalgebraicurbulentmodels sedorhealculation ofeddy iscosity.TheU TRCUnitedTechnologiesResearchCenter)argecaleurbinesse der esth ees tcase.Thensteadylo w redictedorrelateswellwithdata.The resultsndicatethattheunsteadyturbomachinerylowfieldaneolvedwithingleflowchannelofunequalpitch on each bladero w 1.INTRODUCTION

Multistageurbomachineryalculationsav ebecomingopularinceid0's.hewoain streamsreircumferentialveragealculationsnd unsteadyalculations.mongheircumferentialaveragemethods,epresentativesstudiesarefromNi[1989],Adamczyk[1990],Denton[1992]nd Dawes[1992].Thesemethodshavebeensedtoreplacethetraditionalow-by-rowesignethodsse dnindustry formany years.However, these type of

methodsenerallygnorehensteadynteractionsbetweenladeows.espitehisindfmethodignoresruensteadynteractionffectsetweenbladeows,tllowshengineersoesignnd optimize multi-stageurbomachinewithin muchshorterime.hedvantagefunningcircumferentialveragemethodssmorebvioussthenumber ofblade rows is increased.

Thensteadyressureluctuationsnladesurfacesca nbesignificantespecially fo rmodernhighloadingladeesignsithmallerap setweenbladerows.As result,othermeansocalculatehe fluctuatingpressureson thebladesmustbeoundinorderossureheesignatigueife.Anpproachusinghree-dimensionaluasi-steadyethodology wasstudied by Chenan dLe e1998].tdoesprovidepressureluctuationatabtainedro mhi smethodan dismoreeconmomicalthanfullunsteady analysis.Howeverhisannl yeonsideredsnintermediatepproach.heimulationfullycouplednsteadyotor-statornteractionsllowshetotalnderstandingofhelowhysics.hehree-dimensionalullyouplednsteadyotor-statorinteractionimulationtartsfromRa i1987]withanoverlaidatchedridystem.therethodsthereaftere.g.ah1992])or eresssehesimilarpproach.heiralculationsrequentlymodifiedheotorndtatorumberso implearithmeticatioike :3 r:1.Thehangeofbladenumberwasccompaniedby changeofbladeizeinrderoaintaintsolidityr lockage.hishoweverbiasedhehysical roblem.The redictedamplitudean d frequency in th erotor-stator interaction ar elso iased.oreover,hesemethodsreer ycomputationalostly.s esult,he yweremostlyusednheinalesignerificationrhe nproblemoccurs.Erdoset al.1977]proposed aphase-laggedethodorunsteadynalysis.hi sethodusesnlyneladeitchorac hladeow .t

86DTICQUALITY DiGPBGTEDI


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requirestostore theunsteadyflow dataoveran entireperiodoha theladesaneeleriodicalexcitationsro meighboringladeows.he memoryequirementshu sremendous.hissituationwillecomeworsesheumberofbladerows is large.Aimplifiedooselyoupledpproachor unsteadyurbomachinerylowfieldredictionsasinvestigatedyodson1985]ndond Lakshminarayana1998].he yimplyodelhe upstreamnsteadyisturbancesithnncomingwakes.The wakesca nbe calculatedseparatelyfromasteadytateolutionro mnpstream ladeow .Dorneytl.1996]evelopednteratedooselycoupled ladeowmethodndppliedto wo -dimensionalurbinetage.nheirpproach,he perturbationsetweenwodjacentbladeow swereiteratedto updatedvaluesuntilconvergence.Itshowsthatheooselyoupledalculationanredictunsteadinessuitewellutsnorderofmagnitudeinomputationalfficiencyomparedith ullycoupleunsteadyanalysisinatwo-dimensionalsense.H oandLakshminarayana'sthree-dimensionalooselycouplednalysisodifiedheotor/statorladenumbersro m2:40o0:40onqualitchchannelor stationary an drotating bladerowsca nbeused.Bladesizewerescaledtomaintainits blockageeffect.Dorney et al.modified thestator/rotor numbersfrom 22:28to 21:28so an 3: 4bladeratios ca nbe usedtoav eeriodicoundaryonditionatisfied.Neitheroftheboveooselyoupledmethodvoidthebladegeometry modification.

The purposeofthe resenttudysoevelopmethodha tanolve urbomachinerynsteadyflowfield,utlsoasheollowingistinctadvantages:senlyneladehannelorcalculationhileeepingheladeonfigurationunchanged.Thenumericalmethod used in thepresentstudysompressibleiscousiniteolumealgorithmolvingReynoldsveragedNavier-Stokesequations.hertificial issipationermsimilartothatse dyamesonsdoptedouppresshenumericalscillations.our-stageunge-Kuttascheme isused toadvance theflowequationsintime.Residualmoothing techniqueisemployed tourtheraccelerateonvergence.aldwinndomaxalgebraicurbulentodel1978]sse dorhe calculationofeddy iscosity.TheU TRCargecaleturbinees tataerese doalidateheFD calculations.

2.UMERICALMETHOD The governing three-dimensional,compressible

Navier-Stoke equations in integralformca nbe written as:

dtwhere

an d

\WdV+ Fc-dA= Fv-dA+\HdV1)FC=E7+Fj+GkFv=Ri+Sj+Tk

~p pu' 'pv pw'pu pun'+p puv puw'pv E= pvii F= pvv'+p G = pvWpw pwu' pwv pww' pe en' +pit evpv ew ' pw

0 0 0 0rXX ryx Tzx 0r*y 5= Tyy T= *zy H=Q pw*xz V Tzz -pvIAJ y. kJ 0

where e is the total energy per unit volume,v =(u',v',w')sheelativevelocity,tselationshipwith theabsolutevelocityVs:

v =v-Six?Q .=Q .i=(x,y,z)

Thelgebraicwo-layer,dd yiscosityurbulencemodelderivedbyBaldwinan dLomaxisusedfo r thecalculationofturbulenteddyviscosity.

Th ehysicalomainsdividedntomanymallcontrolvolumes.The discretization formofeq .(1 ) is

-(hw)+Qc+Qv=hHdt

where h is thevolumeofgrid,an d

(2 )


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Qc=ZFck-Sk

Qv=^

vk -s

kkwherek=1-6, Sstheurfaceareaon eachsideofcontrolvolume.

Equation2)solvedsingentralifferencingschemewhichsecondorderccuratenpace.norderoam pheumericalscillationssociatedwithcentraldifferencingscheme,artificialdissipation termsimilaroha tse dyameson1981]reconsidered.Eq.(2) ca nbewrittenas:

wherea=2/3D Atps the time step in the^-direction.Itca nbe approximated as:

AsAfe==6r (9 )

Four-stageRunge-Kuttachemesusedodvanceth eflow equation(3 )in time.ofurtheraccelerate convergencendllowargerim etepsesed,implicitesidualmoothingechniquesse dominimizeumericalnstability.heesiduecalculatedaboveissmoothed aftereachRunge-Kuttastage by :

(hw)+Q c+Qv-D=hH3)dtwhereD is thedissipative term:

/)=(*+Z)^+D/-)w4)The direction operator isgivenby :> W=C^ V 2Wgg -K4VC)5)

The termsnd Are givenby 26V 1=t2mzx(vi Vvi,vi_xK 4=max(0,//42) (6 )

visexpressedasvJi+\-lPi+Pi-\\?)

Pi+l+2Pi+Pi-lThealuesf2>PArehosens.5nd .0 5respectively. sacoefficientthatha san impacton thetabilityndccuracyfheolution.ominimize issipationwithin iscousoundaryayer,CPscalculatedfrom:

Af Atq Atg'

l-eg5^ \ -SJJSJJJJXI- rSrr)R=R (10)where feAn /T are standard secondrderdifferencingperator, an d smoothingarametersc= 7 7 = Er=0.5re chosen Thensteadyalculationtartsro mteadytate

solutionsromacircumferentialveragealculation.Inheircumferentialveragealculation,nl ynebladehannel er bladeows sed.Thealculated exitonditionofhe tatoror mhenletnsteadyboundaryonditionorhedownstreamotor laderow.On the therwayround,henonuniforminletfloworheotoralculatedromircumferentialaverageolutionormshetatorunsteadyconditionathexit.hensteadynteractionetweenhe rotatingan dstationary bladerowsareperturbedwithrespect to themeanvalues(thesteadystatesolutions).Theperturbedflow quantityat thestatorexitca nthenbe expressedas:

t s= < t > j < ? / < / > (11)wherej > jsthestatorsteadystatesolution(obtained fromircumferentialveragealculation),pshe stator pitchwisemean value.he flow quantityat therotornletwould eheteadyotoralueddhe perturbationro mhetatorxitequalsotorpitchwiseea nultipliedytatorxit perturbation),

t r=( )r+((*)/ -0s (12).


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Similarily,he flowquantityathetatorexitanbe expressedsheteadytatorxitaluelushe pertubationfrom therotor inlet,

< > s=(j)s+(


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1 ststator 1st rotor 2n dstatorbladenumber 22 28 22 chord(m ) 0.151 0.161 0.164hu b radius(m ) 0.610 0.610 0.610tip radius(m ) 0.762 0.762 0.762

Th e ridystem fo rtheurbines enerated singthenteractive rideneration rocedureevelopedby Leetl.1995].The ridystemisheam esthatusedinapreviousstudy[Chenan dLe e(1998)].A two-dimensionalview oft he thegridsystem fo r the1.5tageurbineshownnig..Th e ridystemha s9x33x25ridsorheirsttator,5x33x25gridsfo r th erotor,an d99x33x25 gridsfo r th esecondstator.Theotalumberofgridss25,225.Fo rthepresenttudy,nl yhetatorndotorridsreconsidered.oo drthogonality,moothnessnd clusternessareachieved.The circumferentialaveragesolution isused astheinitialonditionornsteadyalculations.ig .showsheircumferentialverageolutionorhestatorro mearheuboea rea rheip.he resultsomparedellithheataDringtl.(1982)].ig . howsheircumferentialveragesolution fo rthe rotor.So m euncertainty in thedata fo rtherotorisshowninthefigure.Againtheagreementisgood.Fig. isthepressuredistributions atvarioustimetepsorhetatorndotortmidspan.he circlesinthefigurearethetimeaverageresultsoveron e ladeassingeriod.heim everageesultsbecomeheewteadytateolution.heinalconvergedteadytateolutionsteveralladeheightsrehownnigs. nd.The solutionsor bothhenitialircumferentialverageolutionnd theinalim everagedteadytateolutionsresimilarlthoughom e iscrepanciesreoundea rth ehu band the tip.

The pressuresat6 locations(3nearstator exitan d3ea rotornlethownnig.)remonitoredomakesuretheunsteady pressuresdo reachperiodicalsolutions.Noteha theigureslottedfqualpitchusedintheothercalculations)Fig. showstheunsteady pressuresat these6monitorpoints.Itca nbeseenthattheunsteady pressuresreachnearperiodicalconditioneryuicklyfternlyne lade assingperiod.

Th etatorxitelocitiestheidspanixingplaneboundaryar eshownin fig.7 fo ron erotorbladepassing period.Thestatorwake at pitch=0.9ha ssomesignificantvelocityfluctuation du e to interaction withth eownstreamrotor.The lobalwavemovesrom

pitch=loitch=0ueootorotion.heim eaveragevelocityattatorexitmixingplaneisshowninfig..tshouldbe pointedou tthatthecalculatedresultasee nhiftedangentiallynrderocomparegainstheriginaleasurementata.Although thepredictedwake velocity deficit is larger,theoveralltrendagreesquitewellwithdata.Fig.9istheotornletelocitiestheixinglaneboundary.lobalerturbationav eotionsmovingnpposite irectionelativeoha tnhestator.Thestatorviscouswakeinfluenceon therotoris obviousasitmoveswithwith theglobalwave.The resultsho wha theotornfluencenhehe upstreamtatorsbasically otentialffect.nd ,thestator influenceon therotorboth thepotentialan dviscouswakeeffectsareimportant.The timeaveragevelocitytotorinletmixing laneshownnig. 10 .The fluctuation is larger than thatdu e to thestatorwake (fig.8).

Theressureluctuationmplitudesorheunsteadyalculationsrehownnig.1.he predictionsagreedquitewellwiththedataespecially th emaximumamplitudeandtrendat thecriticalareas(trailingdg eoftatorndeadingdg efotor),althoughom eoverpredictionnheuctionurfaceofstator an d underpredictionon thesuctionsurfaceofrotor.

Thenalysishowsha three-dimensionalunsteadynalysissinginglenequalitchorturbinetageaneuccessfulfhenteractionsbetweenhetationaryndotating ladeow sreproperlyodeled.heiggestdvantagefsingthispproachsomputationalfficiencynd maintainheladeonfigurationntact.hus,he predictedlowfieldouldeor eealistic.he computationsereerformednEC-8400machine.Roughly50 0timetepsperstatorpassingperiod,nd 3ubiterationspe rtimetepswereused.On entirensteadyalculationincludingnitialcircumferentialaveragecalculation)ofabout10 statorpassingperiods(orroughly3otorpassingperiods)took about6days in C PU.5.CONCLUSIONS

Aooselyoupled ladeownalysisethodsusedn hree-dimensionalingletageurbineunsteady analysis.Unlike theother looselycoupled orfullycoupled methods, thepresentapproach usesonlyon e ladepitchorac hbladeowwhilehe ladeconfigurationisunmodified.Circumferentialverageanalysisresult singth eam eomputationaldomain


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issedshenitialonditionorunsteadyanalysis.Thesefircumferentialverageolutionshe startingpointmakesthepredictedunsteadyperiodicalsolutionca nearlybechievedfteronlyon ebladepassingeriod.heteadytateolutions im eaverageresultve racompletebladeassingperiod.Basicallyot hteadytateolutionnd circumferentialverageolutiongreeel lithmeasuredata,lthoughom eifferencesxistbetweenhewoolutions.heredictednsteadysolutionsho whwha thensteadynteraction betweenwodjacent ladeow saneeasonablywellimulated.tisclearthattheinfluencero m thedownstream bladerowbasicallysdu eoapotentialeffectan dtheinfluencefrom theupstreambladero wisueot hoiscousak endotentialffects.Despiteheresentpproachsonsideredsnapproximateolutionomparedwith ullycoupledunsteady calculation,theresult is veryencouraging.6.ACKNOWLEDGEMENT

TheresenttudysupportedyheationalScienceouncilN S C )fheepublicfhinaunder thecontr ctnumberNSC87-0210-D-006-003. 7.REFERENCES1 .Adamczyk,J.J.,Celestina,M.L.,Beach,T.A.and Barnett, M. Simulation ofThree-Dimensional V iscousFlow within aMultistageTurbine ASMEJ.ofTurbomachinery,V ol112,p370-376,19902.Baldwin,B.S.and Lomax,H ., ThinLayerApproximationand AlgebraicModelfo rSeparationTurbulent Flows AIAA6t hAerospace SciencesMeeting1978,78-257.3.Chen,S. H., Th eFlow AnalysisofAThree-DimensionalMultistageTurbomachinery BladeDesign ,Proceedings ofthe6t h InternationalSymposium on TransportPhenomena an d DynamicsofRotatingMachinery,Vo l .2,996,pp.277-286.4.Chen,S.H. an d Lee,L.C, Three-DimensionalMulti-Blade-Row TurbomachineryFlow Analysis,7th ISRO MAC,February1998.5.Dawes,W.N., Toward Improved Through-flow Capability: theus eofThree-Dimensional V iscousFlow Solvers in aMultistageEnvironment J.ofTurbomachinery,V ol14p8-17,January,992.6.Denton,J.D., Th eCalculationofThree-DimensionalV iscousFlow Through MultistageTurbomachines J.ofTurbomachinery,V ol14pp 18-26,January,1992.7.orney,D. J.,Davis,R.L.an dSharma,O.P .,

UnsteadyMultistage AnalysisUsing aLoosely

Couple BladeRow Approach, J.ofPropulsion andPower,V o l .2,No .2,March1996.8.ring,R.P .,Joslyn,H. P ., Hardin,L.W., an dWagner, J.H. , Turbine Rotor-StatorInteraction , J.ofEngineering fo rPower,V o l .04 ,No .0. ,1982,pp.729-742.9.Dring,R.P.,Blair,M. F. ,Joslyn,H. D. ,Power,G .D. ,an d V erd on, J.M., The EffectsofInletTurbulentan d Rotor/StatorInteractionson theAerodynamicsand HeatTransferofaLarge-ScaleRotating TurbineModel ,Part I,FinalReport,N A S AContracteportCR4079,M ay 1986.10 .Dring,R.P .,Joslyn,H. D.,Blair,M. F. , Th eEffects ofInletTurbulentan d Rotor/StatorInteractions on theAerodynamicsan d HeatTransferofaLarge-Scale Rotating TurbineModel ,PartIV ,AerodynamicDataTabulation,N A S A ContractReportCR179496, M ay 1988.11. Erdos, J.I., Alzner,E.an d McNally,W .,

NumericalSolution ofPeriodicTransonic FlowThroughaFa nStage, AIAA Journal,V o l .5, N o.Il,pp.l559~1568,977.12. Hah,C, Navier-Stokes AnalysisofThree-Dimensional Unsteady Flows insideTurbineStages ,AIAApapern o.92-3211,28thJointPropulsionConference, July1992.13.H o,Y .H. and Lakshminarayana, B. , A LooselyCoupledUnsteady Flow Simulation ofaSingleStageCompressor , IJCFD,Vo l .10,1998,pp.73-89.14. Hodson,H. P., An InviscidBlade-to-BladePredictionofWake-GeneratedUnsteady Flow ,JournalofEngineering fo rG as Turbines an d Power,Vo l .07 ,April1985,pp.337-344.15. Jameson,A. ,Schmidt,W .,an d Trkei,E. ,

NumericalSolutions oftheEulerEquations by FiniteV o lu m eMethodsUsingRunge-KuttaTime-Stepping Schemes ,AIAApaper81-1259, June1981.16. Lee,LC,Chen,S .H .,Shu,S. B. ,an d Hsu,W.Y ., Interactive Grid Generation fo rTurbomachineryApplications ,TheChineseThirdCF D Conference,August1995.17. Ni ,R.H.an d Bogoian,J.C., Predictionof3D MultistageTurbineFlow Field UsingaMultipleGrid EulerSolver AIAA paperno .89-0203,January1989.18. Rai,M.M., Unsteady Three-DimesnioalNavier-StokesSimulationsofTurbineRotor-StatorInteracton AIAA-87-2058,1987.


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Fig. Gridsystem fo rU TRC turbine calculation.STATOR(22/28)[12.5%SPAN)

00.5 00.s ROTOR{ 2 2 B) (12.5% S P A N )ROTOfl t2 2 /2 B)(50.0*S P A N )00.5R O T O R [ 22/28)


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ROTOR(22/28) 50.0%SPAN

O TIMEAVERAGE

(1 )

(2 )

STATOR (22/2B)50.0%SPAN

,}-W

0 TIMEAVERAGE

Fig.4Midspan pressuredistributions fo rStatoran drotorat different time steps.

Fig.5Monitorpoint locations.

(5 )

Fig.6Pressure variations at 6 monitorpoints.


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VtlOCtTY ATSTATOflE)UT[UID-3PAN).T.O 1-S 20 **~-_ ~N .- *'

CTCT ,> IX)e. s

'O li 4 J tl M U

VELOCITYATSTATORBCTHHOJPANJ.T.IM

VELOCITY ATSTATOflEWTTMO-BPAWJOS ID V(L0CITATSTAT0fHXIT(MI0SPANJ,T.I7S Ut ^ - - ^ _ _

CTOT 1.5 v/1A0-t0. B B ' 61 6.4 tu U i

VELOCITY AT3TATOAEXIT(MO-5PAN).T- VELOCITYAT STATOfl EXIT UlD.SPAN).T-MO

VEIOOTYAT STATOREX1T M0-SPAN).T.TS Fig.7Unsteady velocity atstator exit.

VELOCITYAT STATOBEXrT[MD-SPAMl.T.10O

O M P U T E O MEA S URE

WLOCTTYAT STATOflXrT|MO-SPAN).T-12S

Fig.8Timeaveragevelocityat statorexit.


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RELATIVVELOCTYATROTORNLETIMO-SAN.T.ORSIATIVE VELOCITYAT ROTORNLET(MO- MN).T-174

RELATIVEVELOCITYAT ROTORNLET(MD-SPAN),T-2S RELATIVEVE L OCTTY ATROTORMLET(MI^SFANJ.T-IM

10 RELATIVEVELOCITYATROTORWLET[MD-S,A N) ,T SO

10 . . ^ * " * WTOTU

l.O

on DO

RSLATtVEVELOCITYAT ROTORiNLET(WO-SPAN).T-aS5

~ti*1o M RELATIVVELOCITYATROTORLETp.lO-SMNVT.TSl.S10 ^ _ _ ^ _ _ _ _ ~ ~ " ~ * ^ ^

WTOT.J

O.S 0-0 06 o.i oj

Fig.9Unsteady relativevelocityat rotorexit.

RELATIVEVE LOOTTATROTORM.ET|UO-SPAN).T>IOO

-53TRCLATIVEVCLOCJTTATROTOR MtJT|MCMFAH).T>lll

Fig.0Timeaveragerelativevelocity atrotorexit.

10


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Pressure AmplitudeDistr ibutionat Midspan(22/28) (Stator) Compute O Measure

pressuresfde

Pressure Amplitude Distr ibutiona t Midspan3 (Rotor)

2. 5 : Compute O Measure 2

Suct ionSide /1.5 /

o0 PressureSide0.5

o o~_ ~ 0 Lead ingEdge V

Fig.1Unsteady pressure fluctuation amplitudes.

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three-dimensional unsteady turbomachinery flow analysis

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