锅炉设计外文翻译边缘冷却的不稳定效果.docx
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锅炉设计外文翻译边缘冷却的不稳定效果.docx
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锅炉设计外文翻译边缘冷却的不稳定效果
附录
附录A英文资料原文
UnsteadyEffectsonTrailingEdgeCooling
MechanicalEngineeringDepartment,StanfordUniversity,Stanford,CA
(Received:
January21,2003;revised:
November8,2004)
Itisshownhownaturalandforcedunsteadinessplayamajorroleinturbinebladetrailingedgecoolingflows.Reynoldsaveragedsimulationsarepresentedforasurfacejetincoflow,resemblingthegeometryofthepressuresidebreakoutonaturbineblade.Steadycomputationsshowveryeffectivecooling;however,whennatural—orevenmoreso,forced—unsteadinessisallowed,theadiabaticeffectivenessdecreasessubstantially.Streamwisevorticesinthemeanflowarefoundtobethecauseoftheincreasedheattransfer.
Introduction
Thetrailingedgesofhigh-pressureturbinebladesaresubjectedtosubstantialheatloads.Forthisreasoncoolingairisblownfrombreakoutsonthepressureside,jettingtowardthetrailingedge.Acomputationalanalysishastendedtosignificantlyoverestimatethecoolingeffectivenessofthesejets.Indeed,adiabaticeffectiveness,
isfoundtobenearly1tothetrailingedge;atleast,thatissowhenthepredictionsinquestionaresteady,Reynolds-averaged(RANS)computations.Unfortunately,labtestsshowthattheeffectivenessstartstodropafteraboutfourjetnozzlediameters,andmightfalltoabout0.5nearthetrailingedge,attypicalblowingratios.Ithasbeensuggestedthatthediscrepancybetweenpredictionandobservationmightbeduetocoherentunsteadiness.
Inthepresentpaper,wedescribeunsteadyRANScomputationsofaflowthatisrepresentativeofthepressure-side,trailingedge.Someinterestingphenomenologyisobserved.Itisthis,notappliedpredictionmethods,thatisthesubjectofthisarticle.Wefindthatnaturalunsteadinessdoesarise,duetothree-dimensionalvortexsheddingfromtheupperlipofthebreakout(Fig.2,later).Thismeanflowunsteadinesscausessomeextramixing,andcausesthetime-averaged
todecreasenoticeablybelow1;however,itdoesnotseemtodropasmuchaslabtestsleadonetoexpect.Pulsationsaddedtotheupstreamplenumcauseamoresubstantialdropin
.Adiabaticeffectivenessthenmimicsthatobservedexperimentally.Itisunclearwhetherthepulsationshaveanyanalogytoconditionsthatoccurinlabtests;sotheyarepresentedheresimplyasastudyintheeffectofforcing.Afascinatingchangeinthemeanvorticalstructureisseenundertheimpositionofperiodicforcing.Theshedvorticesbecomemorethree-dimensional,formingintoloops,whicharethecauseofgreatlyenhancedmixing.
Figure2.
TherationaleforunsteadyRANSissometimesacauseofconfusion.Thereisnoinconsistencybetweenrepresentingturbulentmixingbyastatisticalclosure,whilecomputinganunsteadymeanflow.Inthepresenceofcoherent,periodicunsteadiness,theenergyspectrumwilllooklikeFig.1.Mixingduetothebroadbandportionofthespectrumisrepresentedbytheclosuremodel.Thespikeisduetomeanflowunsteadiness.Thismustbecomputedbyanunsteadysimulation.Itisasourceofadditionalmixing—mixingthatisnotduetoturbulence,butrather,tovorticesinthemeanflow.
Figure1.
Hollowayetal.havepreviouslysuggestedaroleofunsteadinessinthepressure-sidebleedproblem.Indeed,thepresentisafollow-ontotheirstudy,andismotivatedbythesameexperiments.ThoseexperimentsaredescribedinHollowayetal..ThepapersbyHollowayetal.appearbetheonlypreviouscomputationalstudiesofcoherentunsteadinessinexternaltrailingedgefilmcooling.ComputationsaddressingthepassagesinternaltothetrailingedgearediscussedinRigbyandBunker.ArecentarticlebyMartiniandShultzdescribesexperimentsandcomputationsofatrailingedgegeometry,cooledbyarowofjets,withoutlands.Theyfoundunsteadinessduetorandomcoalescencebetweenthejets.However,unsteadinesswasnotimportantintheirCFDanalysis.Theirgeometrydifferssubstantiallyfromthepresent,becauseofthelands.
Computations
Thecommercialcode,CFX,wasusedforthepresentsimulations.Second-ordertimesteppingmustbeusedforthiscodetocapturethecoherentunsteadiness.Withthatswitchedon,weconductedanumberofgrid-andtime-steprefinementstobeconvincedthattheobservedunsteadinessisnotanumericalartifact.Infact,weranafewsimulationswithadifferentcode,Star-CD,withsimilarresults.Hence,thenumericalaccuracyappearstobesufficientforthetaskathand.
ThepresentcomputationsinvoketheSSTmodel,asimplementedinCFX.Thebroadfeaturesofthesesimulationsareinsensitivetotheparticularsoftheturbulenceclosure;similarresultswereseenwiththetwo-layerRNGandChenk–
models.
Figure2showsthecomputationaldomain.Itconsistsofanupstreamplenum,alandthatchannelstheflowintojets,andanexternalregionofcoflowingfluid.Atthebreakouttheinternalflowexitsthrougharectangularnozzle.Thethicknessoftheupperlipofthenozzleisequaltotheheightofthejet.Thelandprotrudesdownstreamfromthenozzle,inawedgeshape,tothetrailingedge.ThelowerpartofFig.2showsageometryconstructedfromfourimagesofthedomain.
Theflowisfromlefttoright,intwostreams:
thewalljetexitsfromtheplenumandischanneledbytheland;theexternalflowentersintheupperportion.Generally,thetwostreamshavedifferentbulkvelocities;theirratio,Ujet/Ufree-streamistheblowingratio,sinceweconsiderconstantdensity,incompressibleflow.Afewcompressiblesimulationsshowedthesamevorticalflowcomponentsandheattransferthataredescribedherein.
Thegeometryissubjecttoasymmetryconditionontheleftandtherightlateralsidesofthedomain.Thisemulatesaseriesofjets,blowingtowardthetrailingedge.Thecomputationaldomaincontainsonlyone-halfofthejetexit;hencethesecondsymmetryconditionisatthecenterofthejet.Computationswithafulljetcrosssectionproducedverysimilarresultstothoseshownherein.Inthepresenceofforcing,theflowbecomesquitecomplex.Thatwastheprimarymotivefortestingthevalidityofthesymmetryassumption.Thepresentforcingwasplanewave;hence,itisconsistentwiththesymmetry,butitwasuncertainwhethertheflowrespectsthatsymmetry—itappearsthatitdoes.Therefore,wepresentresultsonlyforthegeometryofFig.2.TheReynoldsnumberbasedonfree-streamvelocityandnozzlelipthicknessis5×104.
Thefinalgridconsistedof0.75millioncells,inablockstructuredform.Thesolvertreatsitasfullyunstructured,butblockstructuredgriddingproducedasmoothgrid,withgoodresolutionnearsurfacesandinthewakeoftheuppernozzlelip.Agridrefinementstudywasconducted,withaspecialfocusonthegridblocksinthesheddingregion.Theresolutioninthoseblockswassuccessivelydoubledinthestreamwiseandspanwisedirection.Thefinestgridhad1.25millioncells.Coarseningthegridinthesamemannerledtoalossofaccuracyforgridswithapproximately0.25millioncells.The0.75millioncellmeshwasdesignedfromthesestudies,toprovidegridinsensitivity.
Forthetime-accuratecomputations,thetimestepwasadjustedtoprovideabout50
tperperiod.Inthenaturalcase,noforcingwasapplied.Theflowwasallowedtodevelopaself-sustainedunsteadiness.Alargenumberofsimulations,notreportedherein,wereconductedatvariousblowingratios.Itwasfoundthatcoherentunsteadinessdevelopedspontaneouslyforallsimulationswithablowingratiolargerthan0.35(simulationsforverylowblowingratioswerenotperformed).Forblowingratioslargerthan1.5,theunsteadinesswasdampeddownandtheflowbecamesteady.Toconfirmthecomputationalresults,labtestswereconductedontherigdescribedinHollowayetal.solelytodeterminewhetherornotcoherentunsteadinessoccurred.Theresultswerepositive:
afrequencywasseencorrespondingtoaStrouhalnumberofabout0.2.
Results
Observationswillbesummarizedforsteady,unsteady,andforcedsimulations.Toanextent,weareusingaRANSsimulationtounderstandtheaveragedmixingprocessesofthepressure-sidecoolingjets.
Temperaturecontoursinaverticalsectionthroughthemidplaneofthenozzleshowshowalayerofcoolfluidliesnexttothewallinthesteadyflowcalculation:
seeFig.3.Thesamemidplanesectionthroughanunsteadycomputationshowsvortexsheddingfromtheuppernozzlelip:
seeFig.4.
Figure3.
Figure4.
Comparingthetemperaturecontoursfromthesteady(Fig.3)andunsteadysolutions(Fig.4)showsthatthemeanflowvorticescausesubstantialadditionalmixing.However,alayerofcoolairpersistsnexttothewallforadistanceofabouteightjetheights.Thecoolingeffectiveness,
dependsonlyontheadiabaticsurfacetemperature.Despitetheenhancedmixingawayfromthewall,intheunsteadysimulation
remainsnearunityuntilnearthetrailingedge.
Intheseincompressiblecomputations,temperatureisapassivescalar.Thecontourlevelsinthefigurescouldberegardedasrangingfrom0inthecoolantstreamto1inthegasstream.Darkregionsshowwherethetemperatureislow.
TheplanforminFig.4illustratesthismorecompletely.Hotfluidisseenontopoftheland.Thisiscarriedovertheland,andisnotcooledbymixingwiththejet;butthelowersurface,betweenthelands,remainsnearthejettemperaturetothetrailingedge.Hotfluidbeginstoimpingeneartheverticalwallsoftheland.
Timehistoriesoftemperaturenearthelowerwallshowthestrictperiodicity.Thisdemonstratesthatthecomputationhasconvergedtoalimitcycle.SpectracontainasharppeakataStrouhalnumberof0.2basedon
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