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Study

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Study

    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,whichareobtainedonthetestsetupplacedhori

    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.itisdicult

    ;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)Thetemperatureatvaporliquidinterfaceisthe

    ;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, ;aa,

    ;p(JdPa+g+

    ;Underzero-gravitation

    ;forceisignored,thenthe

    ;sumptions1,3)becomes,

    ;environment,theinertial ;momentumequation(as

    ;Separatelythecontinuityandenergyequationof

    ;theliquidfilmare:

    ;OuOv

    ;+0

    ;+=n

    ;=..u

    ;Equation(3)canprovethattemperature ;alongthethicknessofliquidfilmislinear.

    ;2)Momentumequationofflowvapor

;dP

    ;4Tvtd(p-u2)=…

    ;dxDNdx

    ;(2)

    ;(3)

    ;profile

    ;InEquation(4),term一锯istheinfluenceterm

    ;onpressuregradientduetothefrictionforcebetween ;vaporandliquidfilm,whiletermisthatdue

    ;tovaporinertia1force.z,whichistheshearingstress ;betweenvaporandliquidfilm,consistsoftwoparts: ;theone,isduetothevelocitydifferencebetween ;vaporandliquid,theotheroneq’misduetovapor

    ;condensation,whichleadstothemomentuIntransfer. ;T”lT|+Tm

    ;when”>Ul6,

    ;:Cs(Uv--Ul6),=qdxz6)(5a)

    ;

    ;

    ;quWeieta1.StudyonCharacteristicsofSteadyFlowCondensationHeatTran

    sferinaTubeunderZeroGravitation219

    ;when>Ul6,

;=一一

    ;,

    ;m=_qdx(面一z6)hm一一_”uZ6J

    ;.fg

    ;Inequation(5a)and(5b)qdis

    ;

    ;(5b)

    ;(5c)

    ;InEquation(4),DNisthediameterofvaporflow ;path,

    ;DN=D26(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,=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=

    ;[(

    ;Sothemeanvelocityofliquidfilmis, ;1/o’=1dP

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