Heat transfer to supercritical fluids flowing in c

NuclearEngineeringandDesign230(2004)69–91Heattransfertosupercriticalfluidsflowinginchannels—empiricalcorrelations(survey)IgorL.Pioro∗,HussamF.Khartabil1,RomneyB.Duffey2ChalkRiverLaboratories,AECL,ChalkRiver,Ont.,CanadaK0J1J0Received6May2003;receivedinrevisedform3October2003;accepted27October2003AbstractThisliteraturesurveyisdevotedtotheproblemofheattransferoffluidsatsupercriticalpressuresincludingnearcriticalregion.Theobjectivesaretoassesstheworkthatwasdoneintheareaofheattransferatsupercriticalpressures,tounderstandthespecificsofheattransferattheseconditions,tocomparedifferentpredictionmethodsforsupercriticalheattransferintubesandbundles,andtochoosethemostreliableones.Thecomparisonsshowedthereisasignificantdifferenceinheattransfercoefficientvaluescalculatedaccordingtovariouscorrelations.Onlysomecorrelationsshowsimilarresults,whicharequiteclosetotheexperimentaldatafornormalsupercriticalheattransferinwaterandcarbondioxide.Also,noonecorrelationcanaccuratelypredictthemagnitudeandonsetofdeterioratedheattransfer.Theexhaustiveliteraturesearch,whichincludedhundredsofpapers,showedthatthemajorityofcorrelationswereobtainedintubesandjustfewoftheminotherflowgeometriesincludingbundles.Thevariationsinthepredictionofsupercriticalheattransferarerelatedtothesignificantchangesinthermophysicalpropertiesnearthecriticalandpseudocriticalpoints.Therefore,adiscussiononthegeneraltrendsofvariousthermophysicalpropertiesatnearcriticalandpseudocriticalpointsisalsoincluded.Basedonseveralchosencorrelations,theheattransfercoefficientsandtemperatureprofilesintheCANDU-Xreactorcooledwithsupercriticalwaterwerecalculated.©2003ElsevierB.V.Allrightsreserved.1.IntroductionTheuseofsupercriticalfluidsindifferentprocessesisnotnew,andisactuallynotahumaninvention.(Strictlyspeaking,asupercriticalfluidisafluidat∗Correspondingauthor.Tel.:[phone]x4805;fax:[phone].E-mailaddresses:[e-mail](I.L.Pioro),[e-mail](H.F.Khartabil),[e-mail](R.B.Duffey).1Tel.:[phone]x4785;fax:[phone]Tel.:[phone]x6272;fax:[phone].pressuresandtemperaturesthatarehigherthanthethermodynamiccriticalvalues.Afluidthatisatapres-sureabovethecriticalpressurebutatatemperaturebelowthecriticaltemperatureisconsideredtobeacompressedfluid.However,inthepresentpaper,thetermsupercriticalfluidreferstobothasupercriticalfluidandacompressedfluid.)Naturehasbeenpro-cessingmineralsinaqueoussolutionsatnearorabovethecriticalpointofwaterforbillionsofyears(LeveltSengers,2000).(Thecriticalpointisthepointwherethedistinctionbetweenliquidandvaporregionsdis-appears.ThecriticalpointischaracterizedbythestateparametersTcr,Vcr,andpcr,whichhaveuniqueval-0029-5493/$–seefrontmatter©2003ElsevierB.V.Allrightsreserved.doi:10.1016/j.nucengdes.2003.10.01070I.L.Pioroetal./NuclearEngineeringandDesign230(2004)69–91NomenclatureCconstantcpspecificheatatconstantpressure,J/kgK¯cpaveragedovercross-sectionspecificheatatconstantpressure((Hw−Hb)/(Tw−Tb)),J/kgKDinsidediameter,mDhyhydraulic-equivalentdiameter,mGmassflux,kg/m2sgaccelerationduetogravity,m/s2Hspecificenthalpy,J/kghheattransfercoefficient,W/m2Kkthermalconductivity,W/mKLheatedlength,mmmassflowrate,kg/sppressure,MPaqheatflux,kW/m2Ttemperature,Kttemperature,◦CVvolume,m3xaxialcoordinate,mGreeklettersβvolumetricthermalexpansioncoefficient,1/Kµdynamicviscosity,Pasπreducedpressure(p/pcr)ρdensity,kg/m3ξfrictioncoefficientõkinematicviscosity(ν/ρ),m2/sDimensionlessnumbersGrGrashofnumber(gβ(1−(ρw/ρb))D3/υ2b)NuNusseltnumber(hD/k)PrPrandtlnumber(µcp/k)PrmodifiedPrandtlnumber((Hw−Hb)/(Tw−Tb)(µb/kb))ReReynoldsnumber(GD/µ)SubscriptsbbulkcrcriticaldhtdeterioratedheattransferffilmhyhydraulicininletminminimumpatconstantpressurepcpseudocriticalwwallAbbreviationsAECLAtomicEnergyofCanadaLimitedASMEAmericanSocietyofMechanicalEngineersCANDUCANadaDeuteriumUraniumreactorisaregisteredtrademarkofAECLCRLChalkRiverLaboratoriesDOEDepartmentofEnergyFBRfastbreederreactorNISTNationalInstituteofStandardsandTechnology(USA)NPPnuclearpowerplantPWRpressurizedwaterreactoruesforeachpuresubstanceandmustbedeterminedexperimentally.)Inthelate1800s,scientistsstartedtousethisnaturalprocessintheirlabsforcreatingvar-iouscrystals.Duringthelast50–60years,thispro-cess,calledhydrothermalprocessing(operatingpa-rameters:waterpressurefrom20to200MPaandtem-peraturesfrom300to500◦C),waswidelyusedtopro-ducehigh-qualitysinglecrystals(mainlygemstones)(LeveltSengers,2000).Thefirstworksdevotedtotheproblemofheattransferatsupercriticalpressuresstartedasearlyasthe1930s.Schmidtetal.(1946)investigatedfreeconvectionheattransferoffluidsatthenear-criticalpoint,withtheobjectiveofdevelopinganeweffec-tivecoolingsystemforturbinebladesinjetengines(Schmidt,1960).(Thenear-criticalpointisactuallyaregionaroundthecriticalpointwhereallthermophys-icalpropertiesofapurefluidexhibitrapidvariations.)Theyfoundthatthefreeconvectionheattransfercoef-ficientoffluidatthenear-criticalstatewasquitehigh,anddecidedtousethisadvantageinsingle-phasethermosyphonswiththeintermediateworkingfluidatthenear-criticalpoint(PioroandPioro,1997).Inthe195