委培期间各种作业-工程热力学

Course#:SpringSemester,READINGREPORTFabianKock,HeinzHerwig,Localentropyproductioninturbulentshearflows:ahigh-Reynoldsnumbermodelwithwallfunctions,ArbeitsbereichTechnischeThermodynamik6-08TechnischeUniversitatHamburg-Harburg,Denickestrasse15,21073Hamburg,GermanyReceived19February2003;receivedinrevisedform18November2003/在湍流层中剪切流的局部熵产：带Secondlawysisofmomentumandheattransferinunitoperations，HeinzHerwig,TammoWenterodt，InstituteofThermo-FluidDynamics,HamburgUniversityofTechnology,Germany；Receivedinrevisedform4November2010/用热力学第二定律分析在单元操作中的动力和热量的传递Department/Institu能源科学与/先进动力/ rLocalentropyproductioninturbulentshearflows:ahigh-ReynoldsnumbermodelwithwallFabianKock,HeinzArbeitsbereichTechnischeThermodynamik(6-08),TechnischeUniversityatHamburg-Harburg,Denickestrasse15,21073Hamburg,GermanyDescriptionoftheTherearefourdifferentmechanismsofentropyproduction:dissipationinameanandfluctuatingvelocityfieldandheatfluxinameanandfluctuatingtemperaturefield.EntropyproductioninpressibleturbulentshearflowsofNewtonianfluidsisysedsystematicallyandincorporatedintoaCFDcode.Computationalfluiddynamics(CFD)has estateoftheartinthermalengineeringlikeinheat-exchangerdesign.However,alltheseCFDmodelsonlytakeaccountthelawofAnefficientuseofenergyisoneofthemajorobjectivesindesigningmodernthermalsystemslikecompactheatexchangersandpowerplants.Theamountofentropyproducedcanbeuseddirectlyasanefficiencyparameterofthesystem.SecondlawandentropyproductionysisinparticularhavebeenwidelyusedtoevaluatethesourcesofirreversibilitiesincomponentsandUnfortunay,whendesigningathermalapparatusimportantinformationinherentinthesolutionoftheturbulentmomentumandenergyequationsisneverlookedatnorusedbythedesigners.However,itcouldbeusedtocalculatetheamountofentropyproductionandhelptheCFDengineertoimprovetheperformanceofhisapparatus.InthisprresentmodelequationsforthecalculationofthelocalentropyproductioninturbulentshearflowsbyextendingtheReynolds-averagingproceduretotheentropyequation.Thisequationservestoidentifytheentropyproductionsources,withoutneedtosolvetheequationitself.ThemathematicalTransportequationforForasystematicderivationofamodelforentropyproductioninturbulentflows,westartwiththetransportequationforentropy(Cartesian pressiblefluid,single-phaseflow,Fourierheatconduction),

tuxv

divT

T ModelequationsforthelocalentropyForthatpurposeinformationalreadyavailableinak–εturbulenceclosureofthewholeofequationsshouldbeusedasfaraspossible.ItTT PRO

sothatthek–εmodelmightprovidethenecessaryinformationto Q PROT

PRO,DHerekisthevarianceofthetemperaturefluctuations,k=T^2/2andisitsdissipation.Suchmodelsexist,buttheyarenotincorporatedinstandardCFD-codes.Neverthelessitisworthwhiletohaveacloserlookatthekequation. kQtuxvywzTVDTTDTPROQ ternativeapproach,suggestedbyoneoftherefereesofthisp r,couldbetolinktothedissipationrateεviakk.Then,however,anextendedturbulencemodelisThemainAsystematicprocedurehasbeenpresentedtoderiveformulationsforthelocalentropyproductionratesinturbulentflowswithheat-transfer.TheprocedureisbasedontheReynolds-averagedtransportequationforentropy.Foursourcesofentropyproductioninturbulentflowswithheattransfercanbeidentified:Entropyproductionbydirectdissipation,byturbulentdissipation,byheattransferwithmeantemperaturegradientsandbyheattransferwithgradientsofthefluctuatingtemperature.Foreachentropyproductionrateamodelequationincombinationwiththestandardk-εmodelisderived.Itturnsout,thatpeakvaluesofentropyproductionoccurveryclosetoawall.Wethereforeintroducedsemi-empiricalwall-functionsfortheentropyproductiontermsonthebasisofasymptoticconsiderations.alevaluationofthe rwithfutureIthinkthatadoptingthepresentedmodelequations,localentropyproductioncanbecalculatedinthepost-processingphaseofaCFDysis.Nofurtherdifferential-ortransportequationneedstobesolved.Thus,thepresentedproceduredoesnotrequiremuchCPUtimeandcaneasilybeimplementedinexistingCFDcodes.Itisatooltoevaluatetheperformanceofanapparatusinthermalengineering. rSecond ysisofmomentumandheattransferinunitHeinzHerwig,TammoInstituteofThermo-FluidDynamics,HamburgUniversityofTechnology,DescriptionoftheMomentumandheattransferincomplexsystemsalwaysisthesumofsingleandsimpletransferelementsherecalledunitoperations.TheyareusuallycharacterisedbyheadlosscoefficientsandNusseltnumbersasfarastheflowandtheheattransferaspectisconcerned.Attheenergeticview,deviationsfromtheidealcyclesmaybeduetodeviationsintheprocessdesignbuttheydefiniywillbeduetotheirreversibilityofallrealprocesses.Thisficationoflossesinthewholethermodynamiccycleisdonebyintroducingefficiencyratiosandcoefficientsofperformance,whichquitegenerallyaretheratiooftwoglobaltiescharacterisingtherealandtheidealprocess.Sinceeachenergyorenergyfluxcanbedividedintotwocomplementarypartscalledexergyandanergy,amorespecificcharacterisationoftechnicalprocessescanbegivenintheseterms.Here,exergyisthe umtheoreticalworkobtainablefromtheenergyinteractingwiththeenvironmenttoequilibrium.Exergyisalsocalledavailablework.Anergy,sinceitisthecomplementarypartwithrespecttotheenergyasawhole,isjustallthatisnotexergy.IftheflowbehaviourischaracterizedbyaheadlosscoefficientKonlyandtheheattransferbyaNusseltnumberNuasthesoleassessmentparametersthesestandardsarenotfulfilled.OnthebackgroundofthisdeficiencyweysethecommonassessmentparameterswhicharetheheadlosscoefficientKandtheNusseltnumberNuandsuggesthowtheyshouldbecomplementedbyadditionalconsiderations.Insteadofgivingadetailedliteraturereviewaboutsimilarconsiderationsbasedonthesecondlawofthermodynamicswewilldiscussthemtogetherwithourownapproach.ThemathematicalMomentumandheattransferarethemostimportanttransferaspectsinthesinglecomponentsofcomplexsystemsthatrealizethermodynamiccycles.Intheseconduitcomponentstheunitoperationsofmomentumandheattransferoccur.Theycharacterisedbycertaincoefficientswhichfythe“transferquality”.TheytheheadlosscoefficientKofaconduitcomponentwhichcharacterizestheflowtheNusseltnumberNuinheattransferelementslikechannelsorpipeswhichcharacterisestheheattransferbehaviour.Bothoperationsaresubjecttolosseswhichfromathermodynamicspointofviewarelossesof paniedbyentropygeneration.Thelossofexergyoravailableworkisacommonandimportantaspectofbothunitoperations.Since,however,certainmassandheatflowratesmustbeachievedinthetransferelementsitisnotthelossitselfthatcountsbuttherelativei.e.thelossofavailableworkpertransferForflowassessment,acommonwaytoassessthe“flowbehavior”inaconduitcomponentisK u2introduceaheadlosscoefficientK.Itsgeneraldefinition (headlosswithPlossmasspecificdissipationofmechanicalenergyduetotheForheattransferassessment,Acommonwaytoassessthe“heattransferbehavior”inacomponentistointroduceaheattransfercoefficienth,ormoresystematicallyaNusseltNu=hL/k.Itsgeneraldefinition

qwT

hk(Nusseltnumber),withthewall

qwQ

andtheoperatingtemperature

T

TasthewtiesintheheattransferunitwForconvectiveheattransferassessment,part(a)ofthetablecollectstheparametersintheformoftheiroriginaldefinitionwhilepart(b)showsthelimitswithrespecttoanidealoperation,i.e.anoperationwithoutlossesofavailablework.Fromathermodynamicspointofviewthesearereversibleprocesses.ThemainThisprmainlywantstoysethecommonassessments