06传热学第六章(英文)

2020/7/51CHAPTER6ExperimentalCorrelationsofSinglePhaseConvection2020/7/52§6.1SimilarityPrincipleandDimensionalAnalysis1.SimilarityofPhysicalPhenomenonIftwophysicalphenomenahavethesamedimensionlessformsofgoverningdifferentialequationsandboundaryconditions,theyaresimilarphenomena.※similarconditionsMustbethesamekindphenomenaPhysicalquantitiesareproportionaltocorrespondingphysicalquantitiesreduceexperimenttimes＆obtaingenerallawThespacialdistributionofphysicalquantitiesaresimilaratthesametimeinunsteadystateSamedifferentialequationsdescribesimilarphysicalquantitieswithuniformdimensionlessfield2.ContentofSimilarityPrinciple（1）equivalenceofsamecharacteristicparameter0)(yfwyttth0)/()/()(yfwwlytttthl21hlhl21NuNu（2）numberandrelationofsililarcharacteristicparameterΠtheorem：m=n-rn:numberofindependentphysicalquantitiesinequationr:numberofbasicdimensionsinequationm:numberofdimensionlessparametersincorrelation（3）necessaryandsufficientconditionsofsimilarphenomena※samedeterminedcharacteristicnumberscomposedbyknownquantitiesareequal※conditionofuniquesolutionaresimilarinitialconditionboundaryconditiongeometryconditionphysicalcondition2020/7/553.DerivationofSimilarCharacteristicParameter（1）similaritymethod(※nondimensionalizationofparameters)22xa0,0xxhxx,0,022)/()(xFo0)/(,0xxBixx)/(,11,0FoxBiFof,,charateristicparameterequation6introducingproportionalcoefficient0''''''yytth0yytthlthCyyCttCChh'''',,,0ylhytthCCC1CCClh'''yhyh'''lhlh'NuNucharateristicparametersofconvectionincommonuse：Re,Pr,Nu,Gr2020/7/57（2）dimensionalanalyticalmethodbasicdimensionse.g.forcedconvectioninapipe),,,,,(pcdufhkg、s、m、K、mol、A、cdsm/u1LTdmLsPa11TML3/mkg3MLpc)/(KkgJ122TL)/(KmW13MLTtimeTlengthLmassMtemperaturen=7r=4h)/(2KmW13MT2020/7/59setupthreedimensionlessparameters11111dcbadhu22222dcbadu33333dcbapduc331111111111111dimcdacdcdcbaTMLNuhddhu01101Re2udPr3pcPr)(Re,fNu2020/7/510Similarly,forothercases,Pr),Gr(NufNaturalconvectionheattransfer,Mixedconvectionheattransfer,Pr),Gr(Re,NufNu—tobedetermined（containsh,unknown）Re，Pr，Gr—determinedPr)Re,,/(NuPr)(Re,Nulxffx；Forforcedconvectionheattransfer,§6.2ApplicationofSimilarityPrinciple1.GuidanceofExperimentArrangementandDataProcessing※individualexperimentresultscanrepresententiregroup※commonformofexperimentalcorrelation（characteristicparameterequation)PrRe,fNunCNuRemnCNuPrReorC,n,maredeterminedbyexperiments2020/7/512（1）determinenCNuReRelglglgnCNuYabXbXaYYX······bXaY2020/7/513（2）determinemnCNuPrReⅰconstRePrlgRelglgmCNunY'bXⅱRelglgPrlgnCNumY''a''b'aXYX······XbaY''YX······XbaY''''2020/7/5142.GuidanceofSimulationExperimentsimulationexperiment:experimenttostudythephysicalprocessinanactualdevicewithareducedscalemodel.Adoptsimilarityprinciple,onlyrequiresomecriticalconditionssatisfyingsimilarityprinciple,suchasB.C,G.C,Re,Pretc,otherconditionscanbeapproximate.2020/7/515在一台缩小成为实物1/8的模型中，用20oC的空气来模拟实物中平均温度为200oC空气的加热过程。实物中空气的平均流速为6.03m/s，问模型中的流速应为若干？若模型中的平均表面传热系数为195W/(m2·K)，求相应实物中的值。在这一实验中，模型与实物中流体的Pr数并不严格相等，你认为这样的模化试验有无实用价值？例题：2020/7/516解：21ReRe222111lulusmlluu/85.2011222121NuNu222111lhlh)/(99.362112212KmWhllh2020/7/5173、应用特征数方程应注意问题（1）特征长度应按该准则式规定的方式选取（2）特征速度应按规定方式计算（3）定性温度应按该准则式规定的方式选取（4）准则方程不能任意推广到得到该方程的实验参数范围以外使用3.AccuracyofExperimentCorrelationsconvectionheattransferisaverycomplexphenomenoncalculationerrorderivedfromrestrictionofdeterminationconditioncontinuousrenewal,betteraccuracyrefinedcalculationsshouldemployspecificcorrelationsPrRe,PrRe,PrRe,fjfStfNu2020/7/519§6.3Forced-convectionCorrelationsofInternalFlow1.CharacteristicsofInternalForced-convectionFlowandHeatTransfer※twoflowregimes：laminarflow＆turbulentflowRec=2300Re2300laminarflow2300Re10000transitionalflowRe10000turbulentflowexternalflow:freedevelopingofB.Linternalflow:passagewallimposerestrictionsondevelopingofB.L※entranceregion＆fullydevelopedregionentrylengthoflaminarflowturbulentflow,if,entrylengthhasnoimpactonaverageh.PrRe05.0dlx60dl2020/7/521※typicalthermalboundary(T.B.)conditionsuniformheatfluxuniformwalltemperature2020/7/522※meanfluidtemperatureandmeantemperaturebetweenfluidandwallfwmttt)('ffpmmmttcqtAhⅱmeantemperaturedifferenceinequationofNewton’sCoolingLawForuniformheatflux，fullydevelopedregionForuniformwalltemperature，localtemperaturedifferenceatcrosssectionchangescontinuously.ⅰreferencetemperatureisthemeantemperatureoffluidatcrosssection(orinlet,outletcrosssection).''lnfwfwffmttttttt2.ForcedConvectionTurbulentFlowCorrelationsinTubes※conventionalfluid（Pr0.6）ⅰDittus–BoelterequationnfffNuPrRe023.08.0characteristiclength：internaldiameter（orhydraulicdiameter）referencetemperature：'''21ffmtttrangeofapplication：54102.1~10Ref7.0Prf～12060dlsuitableforlowtemperaturedifferencebetweenfluidandwallheatingn=0.4coolingn=0.3turbulentflowregion2020/7/524Correctionsforcasesbelo