heat transfer in vertical upward and downward supe

ExperimentalinvestigationofheattransferinverticalupwardanddownwardsupercriticalCO2flowinacirculartubeDongEokKim,Moo-HwanKim⇑DepartmentofMechanicalEngineering,PohangUniversityofScienceandTechnology,San31,Hyoja-dong,Namgu,Pohang,Kyungbuk790-784,RepublicofKoreaarticleinfoArticlehistory:Received29March2010Receivedinrevisedform1September2010Accepted3September2010AvailableonlinexxxxKeywords:SupercriticalCO2LocalheattransferBuoyancyFlowaccelerationCorrelationabstractAnexperimentalinvestigationofturbulentheattransferinverticalupwardanddownwardsupercriticalCO2flowwasconductedinacirculartubewithaninnerdiameterof4.5mm.Theexperimentswereper-formedforbulkfluidtemperaturesfrom29to115C,pressuresfrom74.6to102.6bar,localwallheatfluxesfrom38to234kW/m2,andmassfluxesfrom208to874kg/m2s.Atamoderatewallheatfluxandlowmassflux,thewalltemperaturehadanoticeablepeakvalueforverticalupwardflow,butincreasedmonotonicallyalongtheflowdirectionwithoutapeakvaluefordownwardflow.TheratiosoftheexperimentalNusseltnumbertothevalueobtainedfromareferencecorrelationwerecomparedwithBoandq+distributionstoobservethebuoyancyandflow-accelerationeffectsonheattransfer.Intheexperimentalrangeofthisstudy,theflowaccelerationpredominantlyaffectedtheheat-transferphe-nomena.Basedonananalysisoftheshear-stressdistributionintheturbulentboundarylayerandthesig-nificantvariationofthespecificheatacrosstheturbulentboundarylayer,anewheat-transfercorrelationforverticalupwardanddownwardflowofsupercriticalpressurizedfluidwasdeveloped;thiscorrelationagreedwithvariousexperimentaldatasetswithin±30%.2010ElsevierInc.Allrightsreserved.1.IntroductionSupercriticalfluidshavebeendrawingattentionasheat-trans-fermediaforpowerplanttechnologyandforrefrigerationandair-conditioningapplications.Theheat-transfercharacteristicsofsupercriticalfluidsarekeyparametersforthesesystemapplica-tions.Inparticular,heattransferatsupercriticalpressureisinflu-encedbythesignificantchangesinthermophysicalproperties(thermalconductivity,density,viscosity,specificheat,volumeexpansioncoefficient,etc.).Nearthecriticalpoint,thephysicalpropertiesoffluidsvaryrapidlywithtemperatureandpressure(Fig.1a–f),soheattransferatsupercriticalpressureistotallydiffer-entfromthatatsubcriticalpressure.Thepseudo-criticaltempera-ture(Tpc)isatemperaturepointatwhichthespecificheatofafluidatacriticalpressurereachesapeakvalue.Inmostheat-transferphenomena,thediffusionofheat(bybothmolecularandturbulentmotion)canbesignificantlyaffectedbyvariationsofthermalcon-ductivity,specificheat,andviscositywithtemperature(Eq.(1))(Winterton,1998).Nub¼hDkb¼0:023Re0:8bPr0:4bh¼0:028_m0:8D1:8l0:4bk0:6bc0:4p;b:ð1ÞIninternalheat-transferphenomenanearthethermodynamiccriticalpoint,thephysicalpropertiesoffluidsvarysignificantlybothacrossandalongthefluidflowdirection.Inparticular,se-verevariationsindensitybetweenbulkandwallpositionsandalongtheflowdirectioncanchangetheflowstructureandaffecttheturbulenceintheflowduetotheinfluencesofbuoyancyandflowacceleration.Thischangeinturbulenceinturnaffectstherateofheattransferbyturbulentenergytransport.Whenthebuoyancyandflow-accelerationeffectsareextreme,thevelocityprofileatacross-sectionalareaoftheflowcanchangefromaparabolicshapetoan‘M’shape(seeFig.2)(KurganovandZeigarnik,2005).Thischangeofflowstructurecansignificantlyaffecttheturbulentshear-stressdistributionandturbulenteddydiffusivity.Eventually,achangeintheturbulentflowstructurecanexertastronginfluenceontheturbulentheat-transferphenomena.McEligotetal.(1970)studiedheattransferduringthetransi-tionfromturbulenttolaminarflow.Theyclaimedthatthisphe-nomenonwascausedbyflowaccelerationduetostrongheating.Hall(1971)triedtopresentaphysicalmechanismforthelocaldeteriorationintheheat-transfercoefficientofsupercriticalfluidflow.Hereportedthattheturbulentdiffusivitywasreducedinupwardflowwhenthelowdensitylayerbecamethickenoughtoreducetheshearstressintheregionwhereenergyisnormallyfedintotheturbulence,andthatthisreducedthediffusivityforheatandthustheheat-transfercoefficient.Tanakaetal.(1973)0142-727X/$-seefrontmatter2010ElsevierInc.Allrightsreserved.doi:10.1016/j.ijheatfluidflow.2010.09.001⇑Correspondingauthor.E-mailaddress:[e-mail](M.-H.Kim).InternationalJournalofHeatandFluidFlowxxx(2010)xxx–xxxContentslistsavailableatScienceDirectInternationalJournalofHeatandFluidFlowjournalhomepage::Kim,D.E.,Kim,M.-H.ExperimentalinvestigationofheattransferinverticalupwardanddownwardsupercriticalCO2flowinacirculartube.Int.J.HeatFluidFlow(2010),doi:10.1016/j.ijheatfluidflow.2010.09.001studiedtheshear-stressdistributioninaverticaltubebytakingintoconsiderationthebuoyancyforceaswellastheinertiaforceduetoacceleration.Byexamininghowthevelocityprofilede-pendedupontheshear-stressgradientatthewall,theydeducedcriteriafortheprominenteffectsofbuoyancyandacceleration.Petukhovetal.(1972)investigatedexperimentallytheworseningheat-transferconditionsforCO2turbulentflowatsupercriticalpressure.Intheirexperiments,atlowandmoderatemassflowrates,thelocalworseningofheattransferwasclearlyobserved,butatahighmassflowra