换热器性能分析新方法_柳雄斌

＊柳雄斌　过增元(,　100084)(20081025;20081120)　　,,,,..,(),.,-().:,,,PACC:4425,8630R,4490＊(973)(:2007CB206901).,E-mail:[e-mail]1.引言,:-[1,2].U,A,,﹒Q=UAΔTM,(1)﹒Q,ΔTM.ΔTM=ΔTa-ΔTbln(ΔTaΔTb)=ΔTLM,(2)ΔTLM(logarithmicmeantemperaturedifference,LMTD),ΔTa,ΔTb.,,,Bowman[3],,.F≤1,F,.UA,,,.,.,,.-KaysLondon[4],,,.,ε=1-exp[-Ntu(1+C)]1+C,　(),(3a)ε=1-exp[-Ntu(1-C)]1-Cexp[-Ntu(1-C)],　(),(3b)Ntu=UA/Cmin,,C=CminCmax.,[5].,,(),,.,().Bejan[6],,587200971000-3290200958(07)4766-06　　　ACTAPHYSICASINICAVol.58,No.7,July,2009c2009Chin.Phys.Soc..,01,.0,Ntu,ε,,,,“”[7].Hesselgreaves[8]Bejan.Shah[9]18,,()、.Shah,,.[10,11],、,.,,,..2.换热器中的耗散与当量热阻2.1.[10]　　[10,11],“”:E=12QvhT,(4)Qvh,T.,().,,,,.,.[10,11]Rh=﹒E﹒Q2,(5)﹒Q,﹒E=∫ΨKdTdn2dΨ,Ψ.,,Re=﹒EeI22.2.　　1,、CdT(x)dx=-q·(x),(6)C,,q·(x).1　(6)T,CT(x)dT(x)dx=-T(x)q·(x),(7),.(7),Ehi-Eho=12ChT2hi-12ChT2ho=∫outinq·(x)Th(x)dx,(8a)Ch,Thi,Tho、,Ehi,Eho、.Eco-Eci=12CcT2co-12CcT2ci=∫outinq·(x)Tc(x)dx,(8b)Cc,Tci,Tco、,Eci,Eco、.,﹒E=﹒Ei-﹒Eo=12ChT2hi+12CcT2ci　-12ChT2ho+12CcT2co.(9a)47677:　　,﹒E=∫Lq·(x)Th(x)-Tc(x)dx=∫LU(x)ΔT(x)2dx.(9b)　　(9a)(9b),,.(9a)、,(9b),.,Rex=﹒E﹒Q2,(10)﹒Q=∫Sq·dS,S.ΔTex=﹒E﹒Q=Rex﹒Q.(11)　　(9a)ΔTex=12ChT2hi-12ChT2hoCh(Thi-Tho)-12CcT2co-12CcT2ciCc(Tco-Tci)=12(Thi+Tho)-12(Tco+Tci)=ΔTAM,(12),,Rex=ΔTex﹒Q=ΔTAM﹒Q.(13)　　((1)),Rconv=(UA)-1=ΔTM﹒Q,(14)Rex=Rconv·ΔTAMΔTM=(1UA)ΔTAMΔTM,(15)ΔTAMΔTM=f≥1,,1,f=1,,1,,f:、1.,,.3.有效度-热导(热阻)法　　(2)(15),()Rex=1UAΔTAMΔTM=1UAUACmin(Tco-Tci)Thi+Tho2-Tci+Tco2=(Thi-Tci)-Thi-Tho2+Tco-Tci2Cmin(Tco-Tci)=1Cmin1ε-12CminCmax+1.(16)　　,,“”,,;UA;ΔTMΔTAM,Rex=Rex(Cmin)-1=1ε-12CminCmax+1.(17)　　Nex=Rex-1=UACminΔTMΔTAM=NtuΔTMΔTAM.(18)　　Nex=1ε-12CminCmax+1-1.(19)(17)(19)ε=22Rex+(1+C),(20)ε=2Nex2+Nex(1+C),(21)C=CminCmax.(21),,.:1),C=1,Nex=Ntu.(21)4768　　　　　　58ε=2Nex2+2Nex=Ntu1+Ntu.(22)　　.2),,C=1,Ntu※∞,ΔTLM※0,ε=Nex1+Nex=0.5,(23)Nex=NtuΔTLMΔTAM=1.(24)　　3),,C※0,Ntu※∞,ΔTLM※0,ε=2Nex2+Nex=1,(25)Nex=NtuΔTLMΔTAM=2.(26)　　(21)2.2C=1aNtu※∞(Nex=1),Nex1,εmax=0.5;C=0.5,εmax=0.66(b);C=0,εmax=1(c).(C≠0)1,εmax=1.-():1),.2)ε-Ntu,(21)2,(),.:,().,,,.3),ε-Ntu、,(10),.-():,(),,.2　Cε-Nex4.关于熵产悖论问题　　Bejan[6]NS=﹒SCmin=ln1-ε1-T2T11+εT1T2-1.(27)3　NS-ε　　,,47697:.3,,Ntu,ε,NS,ε∈[0,0.5],Ntu,,ε∈[0,0.5]ε“”.Shah[9],ε-NS.,ε-NS4　,NS.,,4,(),,,,.5.结论1.(),(),.2.-,-(),.3.,ε∈(0,1),,.[1]RohsenowWM,HartnettJP,ChoYI1998HandbookofHeatTransfer(NewYork:McGraw-Hill)[2]HolmanJP2002HeatTransfer(ninthed.)(McGraw-Hill)[3]BowmanRA,MuellerAC,NagleWM1940Trans.Am.Soc.Mech.Engrs.62283[4]KaysWM,LondonAL1955CompactHeatExchangers(NewYork:McGraw-Hill)[5]ParkerJD,BoggsJH,BlickEF1969IntroductiontoFluidMechanicsandHeatTransfer(Addison-Wesley)[6]BejanA1977J.HeatTransfer99374[7]BejanA1998AdvancedEngineeringThermodynamics(NewYork:Wiley)[8]HesselgreavesJE2000Int.J.HeatMassTransfer434189[9]ShahRK,SkiepkoT2004J.HeatTransfer126994[10]GuoZY,LiangXG,ZhuHY2006Prog.Nat.Sci.161288(inChinese)[、、2006161228][11]GuoZY,ZhuHY,LiangXG2007Int.J.HeatMassTransfer5025454770　　　　　　58Anovelmethodforheatexchangeranalysis＊LiuXiong-Bin　GuoZeng-Yuan(DepartmentofEngineeringMechanics,TsinghuaUniversity,Beijing　100084,China)(Received25October2008;revisedmanuscriptreceived20November2008)AbstractSincetheheattransferirreversibilityofaheatingorcoolingprocessshouldbemeasuredbytheentransydissipationrate,anequivalentthermalresistanceforaheatexchangerwasdefinedbasedontheentransydissipationrateoftheheatexchanger.Theequivalentthermalresistanceincludesboththeoverallheattransferresistanceandtheextrathermalresistancecausedbythenon-counter-flowarrangementandthenon-equilibriumheatcapacityrateratioofaheatexchanger.Thereciprocaloftheequivalentthermalresistancewasdefinedastheequivalentthermalconductance.Therelationshipisestablishedbetweentheheattransferirreversibilityandtheeffectivenessofaheatexchangerintermsoftheequivalentthermalresistance.Finally,aformuladescribingtherelationamongtheeffectiveness,theequivalentthermalresistanceandtheheatcapacityrateratioisobtainedwhichdoesnotdependonthedifferentflowarrangements.Thereforetheeffectiveness-thermalresistance(conductance)methodismoresuitablefortheperformancecomparisonofdifferentheatexchangers.Keywords:heatexchanger,thermalresistance,entransydissipation,entropyPACC:4425,8630R,4490＊ProjectsupportedbytheStateKeyDevelopmentProgramforBasicResearchofChina(GrantNo.2007CB206901).Correspondingauthor.E-mail:[e-mail]47717: