Study
J.ofThermalScienceVo1.5,No.3
;StudyonCharacteristicsofSteadyFlowCondensation
;HeatTransferinaTubeunderZero-Gravitation
;QuWei
;HarbinInstituteofTechnology,Harbin150001China
;HouZengqiZhangJiaxun
;ChineseAcademyofSpaceTechnology,Beijing100086,China
;I?
thispapertheannularflow.modelforin-tubecompletedcondensationisemployedtopredictthe
;steadYflowcondensationheattransfercharacteristicsinatubeunderzero-gravitation.Inthiscase,lt
;isproposedthatvaporcondensesontheliquidfilmsurface.Duetotheeffectofsurfacetension,the
;liquidexistsintheformofliquidfilmringcontactingwall;whenthevelocityofvaporcoredecreases
;tozero,thecondensationprocessends.PuttingforwardthelC’hysicalandmathematicalmodels,the
;Droblemissolvedandthemulti-orderequationofthethicknessofliquidfilmis
obtained,whichin—
;cludestermsofthepressuregradientalongaxialdirection,thefrictionforcebetweenvaporandliquid
;oninterface.Bycomputationalcalculation,thismodelcanbeusednotonlytopredictthethickness
;ofliquidfilm.thecondensationpressuregradientalongtheaxialdirection,butalsotodeterminethe
;Nusseltnumber,thecondensationlengthandthetotalflowpressuredropofcondensationetc.At
;theend,thecalculationresultsofthenecessarycondensationlengtharecomparedapproximatelywith
;thosefromtheexperiments,whichareobtainedonthetestset—upplacedhori
zontallyingravitation
;field,andthedeviationisanalyzed.
;Keywords:zero-gravitation,theannularflowmodelforin-tubecompletedcondensation,thick—
;nessofliquidfilm,condensationpressuregradient,Nusseltnumber,totalflowpressuredropof
;condensation,condensationlength.
;INTRoDUCTIoN
;Withtherapiddevelopmentofspacetechnology,it
;isurgenttodevelopanewtypetwophaseheatsystem,
;whichshouldbesmaller,fighterandcantransfermore ;heatfor1ongerdistance.Insuchasystemtheconden- ;sationheattransferprocessmustbeincluded.Soin ;zero-gravitationfielditisveryimportanttopredict ;thecharacteristicsofsteadyflowcondensationhealt ;transfer1engthinsideacondensationtube. ;Inthispaper,itisbefievedthatvaporcondenses ;attheliquidfilmsurfaceunderzero-gravitationen- ;vironment,duetotheeffectofgurfacetension,the ;liquidcan’tleavethevapor-liquidinterfaceintothe
;ReceivedAugust,1995
;vaporcore.Fromzero,thethicknessofliquidfilmin- ;creasesgraduallyalongtheflowdirection,whenthe ;velocityofvaporcoredecreasestozero,thethickness ;of1iquidfilmwillincreasetotheradiusofcondensa- ;tiontube.thenthecondensationheattrailsferiscorn—
;pleted.Thatis.atsteadystatethecondensationheat ;trailsferinatubeconsistsoftheflowingliquidfilm ;ringcontactingwallandtheflowingvaporcorewhich ;velocitychangesgraduallytozero,afterwardsthere ;willbesingle-phase1iquidflowheattransfer.The ;threeterms,thatisthethicknessofliquidfilm,the
;axialpressuregradient,thefrictionforcebetweenva- ;porandliquid,arecomprehensivelyconsideredalong ;theentirecondensationprocess.Fromtheequilibrium ;equationsofmomentam,energyandmass,themulti—
;
;218
;ordercontrolequationof1iquidfilmthicknessisob—
;tained,incladingtermsofpressuregradientandshear—
;ingstress.Whencalculatingthethicknessofliquid ;filmandthepressuregradient,theNusseltnumber, ;theaxialcondensation1engthandtheflowpressure ;dropcanbesimultaneouslyobtained.
;Inthispaper.itisspecia1thatthe1iquidfilmthick—
;nessisn’tconsideredassmallterm,andthepressure
;gradientisn’tneglected.Theleadingconclusionfrom
;thishassignificancefordesigningcondenserinzero——
;gravity:itisnotsuitabletouse1argerdiametercon—
;densationtube,thisdifiersfromthestudiesofcon—
;densationheattransferinmicro-gravitation[1,5,61. ;Usingthismodel,itiscalculatedtofindthatthereis ;aconcaveturningpointofliquidfilmthicknessalong ;theaxialdirection,theconcavedirectsdowninthe
;beginning,anditwillturnupwardsneartheendofva—
;porcondensation.In1-gravitationfield.itisdi毋cult
;tofindthechangeofconcavedirection[5,71.Accord—
;ingtothemodelproposed,theconcavedirectionwill ;changeinzero-gravitationspaceenvironment,which ;willmakethecondensationcharacteristicschangedif- ;ferentlybetweenl_gandO-genvironments. ;PHYSICALMoDEL
;CALMoDEL
;ANDMATHEMATI.
;PhysicalModel(showninFig.1)
;1)Theworkingfluidhasconstantpropertiesand ;thecondensationtubeworksinzero-gravitationenvi—
;ronment;
;2)Inacondensationtubethereisonlypureva—
;porandflowingliquidfilmring.i.e.thereisnonon—
;condensablegas;
;3)Theinertialforcetermofliquidfilminthemo—
;mentumequationisignored,soistheconvectionterm ;inenergyequation:
;=0
;waIIpor..re
;fliwringofliquidfilm
;(a)
;ofvaporandliquid
;(b)
;Fig.1Theannularflowmodelforin-tubecompleted ;condensationunderzero--genvironment ;JournalofThermalScience,V_01.5,No.3,1996 ;4)Thetemperatureatvapor—liquidinterfaceisthe
;saturationtemperatureTs,andthereisnotemper—
;aturedifference,thewallofcondensationtubekeeps ;constanttemperatureT:
;5)Thepressureofliquidfilmandvaporcoreateach ;crosssectionishomogeneous;
;6)Thesurfaceoftheliquidfilmisinidealstate, ;thereisnooscillation;
;7)Whenthevelocityofvaporcoredecreasestozero, ;thecondensationends.?
;Co
;k
;nt
;m
;rolequati
;M
;on
;.
;quidfilm?1)ofliq’
;Whenflowvaporcondensesinatube,themomen—
;tumequationoftheliquidfilmis, ;厂aa,
;p(JdPa一+g+
;Underzero-gravitation
;forceisignored,thenthe
;sumptions1,3)becomes,
;environment,theinertial ;momentumequation(as—
;Separatelythecontinuityandenergyequationof
;theliquidfilmare:
;OuOv
;+0
;+=n
;斋=..u
;Equation(3)canprovethattemperature ;alongthethicknessofliquidfilmislinear.
;2)Momentumequationofflowvapor
;dP一
;4Tvtd(p-u2)一=…一
;dxDNdx
;(2)
;(3)
;profile
;InEquation(4),term一锯istheinfluenceterm
;onpressuregradientduetothefrictionforcebetween ;vaporandliquidfilm,whileterm一isthatdue
;tovaporinertia1force.z,whichistheshearingstress ;betweenvaporandliquidfilm,consistsoftwoparts: ;theone丁,isduetothevelocitydifferencebetween ;vaporandliquid,theotheroneq’misduetovapor
;condensation,whichleadstothemomentuIntransfer. ;T”lT|+Tm
;when面”>Ul6,
;:Cs(Uv--Ul6),=qdx一z6)(5a)
;如
;
;quWeieta1.StudyonCharacteristicsofSteadyFlowCondensationHeatTran
sferinaTubeunderZero—Gravitation219
;when面>Ul6,
;=一一
;,
;m=一_qdx(面一z6)hm一一_”一uZ6J
;.fg
;Inequation(5a)and(5b)qdis
;‰
;(5b)
;(5c)
;InEquation(4),DNisthediameterofvaporflow ;path,
;DN=D一26(6)
;3)Massflowrateandheattransferequation ;Accordingtotheequilibriumofmass,oneachcross ;sectionofthecondensationtube,thesumofliquid ;filmmassflowraterhzlandthevapormassflowrate ;rhzequalstotheentrancevapormassflowraterh., ;rhzl+rhzrh.
;rhzlmustsatisfytheheattransferequationofeach ;cylindricalsurfaceY=6/2from0to,theconden—
;sationheatquantityconductsthroughtheliquidfilm: ;Q0-.=D-5),qdzdx=hjg(8)
;rhlmustalsosatisfytheliquidfilmintegralmassflow
;rate:
;=D-2y
;4)Boundaryconditions
;when=0,U=0
;when=c,札=0
;whenY=0,Ul=0,T=
;(10a)
;(10b)
;(10c)
;when=6,z~yly=6:z(1Od)
;Inequation(10b),whenU=0,=isthelength ;variabletobesolved.
;SOLVINGTHEMATHEMATICALMODEL
;TOGETTHECONTROLEQUATIONS
;SolvingtheVelocityFieldofLiquidFilm ;Integrateequation(1)twice,determinetheintegral
;constantsusingequation(10),thevelocityofliquid
;filmis,
;z=
;[篆(
;Sothemeanvelocityofliquidfilmis, ;1/o’=去1dP