Critical Flashing Flow in ConvergentDivergent nozzles with Initially Subcooled Liquid.docx
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CriticalFlashingFlowinConvergentDivergentnozzleswithInitiallySubcooledLiquid
CriticalFlashingFlowinConvergent-DivergentNozzleswithInitiallySubcooledLiquid
JinghuiLiua*,JiangpingChenb,ZhijiuChenc
a,b,cSchoolofMechanicalEngineering,ShanghaiJiaotongUniversity,ShanghaiChina200240
Abstract:
Aone-dimensionalnumericalanalysisofcriticalflashingflowofinitiallysubcooledwaterinconvergent-divergentnozzlesiscarriedoutinthispaper.Amodelisdevelopedtoinvestigatetheperformanceofconvergent-divergentnozzles.Inthismodel,thesuddenphasechangeimmediatelydownstreamthethroatismodeledasanobliqueevaporationwave,andthevelocitydirectionchangeofthesupersonicflowdownstreamtheobliqueevaporationwaveismodeledasanobliqueshockwave.Next,thefurtherfluidexpansioninthedivergentsectionisregardedinIsentropicHomogeneousEquilibrium(IHE).Theresultsshowthatthepressureimmediatelydownstreamthethroatpredictedbythismodelisveryclosetotheexperimentalresult,about4%deviationfromAKGAWA’stestedvalue.Non-homogeneousequilibriumregionexistsnearthethroatinthedivergentsection.Thelengthofthenon-homogeneousequilibriumregionisincreasedastheinitiallyinletsubcooleddegreeisincreased.ThepressureprofilepredictedbythemodelagreesverywellwiththetestedprofileofAKGAWAexceptinthenon-homogeneousequilibriumregionnearthethroatinthedivergentsection.
Keywords:
convergent-divergentnozzle;criticalflow;evaporationwave;flashingflow;mestableliquid
1.Introduction
Inmanysituations,apressurizedliquidmayrapidlyexpandintoalowpressureenvironment.Forexample,refrigerantsflowingthroughexpansiondevices(suchasvalve,capillary,shorttube,nozzle,etc.)inrefrigerationsystemsanddisastrousindustrialrupturingaccidentsofpressurizedliquefiedgasstoragetank.Iftheenvironmentalpressureislowenough,theliquidwillundergoafastphasetransitionprocess.Manyprecedentedinvestigations[1-9]haverevealedthatrapidexpansionofinitiallysubcooledliquidwillmaketheevaporationdelayed,andtheliquidwillbecomesuperheatedbeforeevaporation.
SeveralreviewsoftheliteraturepertainingtocriticaldischargeofflashingflowsexistincludingthosebyHutmacher[10],Hsu[11],Saha[12],andIsbin[13].Ithasbeengenerallyfoundthatmodelsbasedonassumptionsofhomogeneousequilibriumunder-predictthecriticaldischargerate.Thedifferencesareattributedtothepresenceofnon-equilibriumresultinginthesuperheatedliquid.Inordertoaccountforthiseffect,Alamgir,M.D.etal.[1]investigatedtherapidblowdowndepressurizedhotwaterandsuggestedasemi-empiricalformulatopredictthepressureundershoot(ortheliquidsuperheateddegree)beforeevaporationoccurrence.OnthebasisofAlamgirM.D.etal.,O.C.Jr.,Jones[2]suggestedanequationtopredictthepressureundershootatthethroatofconvergent-divergentnozzles.Further,N.Abuafetal.[3]improvedO.C.Jr.,Jones’sequationandsuggestedaunifiedtheoryforthecalculationofcriticalmassflux,whoseaccuracyiswithin5%.
Thebehavioroffluidinnozzlesisverycomplicated.Schrock,V.Eetal.[4]suggestedatwo-stepmodeltoinvestigatedthepressureprofileintheconvergent-divergentnozzles,andfoundthatitonlycouldgivethepressureprofileinthedivergentsectionwithtrendandmagnitudessimilartothetesteddata.Onthebasisofthemass,momentum,andenergyconservationlaws,E.EliasandP.L.Chambre[14],H.JRichter[15],K.H.Ardron[16],T.S.ShinandO.C.Jones[17],andV.N.Blinkovetal.[18]separatelyestablisheddifferenttwo-phasefluidmodeltoinvestigatethecriticalflowinnozzlesorpipes.Thesemodelsareallbasedonthestepproceedingmethod.Theselectionofthebubblegrowthmodelwilldistinctivelyinfluencetheresults.Thesemodelscannotexplicitlyexplainthebehaviorsoffluidflashinginnozzles.
Nowthatflashingisdelayedwheninitiallysubcooledliquidflowsthroughconvergent-divergentnozzles,whereistheflashinginceptionlocated?
Schrock,V.E.etal.[4]investigatedtheflashinginceptionpointofinitiallysubcooledwaterinconvergent-divergentnozzles,andfoundthattheflashinginceptionpointislocatedimmediatelyupstreamthethroatandnearlyhasnothingtodowiththeinitiallyinletsubcooleddegree.N.Abuafetal.[3]provedthattheflashinginceptionislocatedattheminimalareaplane(throat)oftheconvergent-divergentnozzlewhentheflowisstable.Althoughthereexistsevidencesthatthebubblesarecreatedinfrontofthenozzlethroat[9][17],theresultofT.S.ShinandO.C.Jones[14]showsthatthecomputedmaximumthroatvoidfractionislessthan1%,whichsupportsN.Abuaf’sresult.
Superheatedliquidwillexplosivelyevaporateinanarrowandobservableregion,i.e.evaporat