工程师流体力学（研究生教材）Fluidmechanicsforengineers摘要：本文为面向研究生的工程流体力学教材第五章积分守恒律内容，依托雷诺输运定理推导流体质量、线动量、角动量、能量四大积分守恒方程。结合控制体积法建立适用于叶轮机械、喷管、燃烧室等工程部件的求解模型，引入总焓、熵增与总压损失理论，分析不可逆流动损耗。系统推导涡轮、压气机级欧拉方程，定义流量系数、负荷系数、反应度等无量纲级参数，结合自由涡径向平衡理论阐述叶片展向流动分布，完整给出叶轮机械能量转换统一分析框架，为热力叶轮气动设计、性能评估提供基础理论工具。PrefaceThecontentsofthisbookcoversthematerialrequiredintheFluidMechanicsGraduateCoreCourse(MEEN-621)andinAdvancedFluidMechanics,aPh.D-levelelectivecourse(MEEN-622),bothofwhichIhavebeenteachingatTexasA&MUniversityforthepasttwodecades.Whiletherearenumerousundergraduatefluidmechanicstextsonthemarketforengineeringstudentsandinstructorstochoosefrom,thereareonlylimitedtextsthatcomprehensivelyaddresstheparticularneedsofgraduateengineeringfluidmechanicscourses.Tocomplementthelecturematerials,theinstructorsmoreoftenrecommendseveraltexts,eachofwhichtreatsspecialtopicsoffluidmechanics.Thiscircumstanceandtheneedtohaveatextbookthatcoversthematerialsneededintheabovecoursesgavetheimpetustoprovidethegraduateengineeringcommunitywithacoherenttextbookthatcomprehensivelyaddressestheirneedsforanadvancedfluidmechanicstext.Althoughthistextbookisprimarilyaimedatmechanicalengineeringstudents,itisequallysuitableforaerospaceengineering,civilengineering,otherengineeringdisciplines,andespeciallythosepracticingprofessionalswhoperformCFD-simulationonaroutinebasisandwouldliketoknowmoreabouttheunderlyingphysicsofthecommercialcodestheyuse.Furthermore,itissuitableforselfstudy,providedthatthereaderhasasufficientknowledgeofcalculusanddifferentialequations.Inthepast,becauseofthelackofadvancedcomputationalcapability,thesubjectoffluidmechanicswasartificiallysubdividedintoinviscid,viscous(laminar,turbulent),incompressible,compressible,subsonic,supersonicandhypersonicflows.Withtoday’sstateofcomputation,thereisnoneedforthissubdivision.ThemotionofafluidisaccuratelydescribedbytheNavier-Stokesequations.Theseequationsrequiremodelingoftherelationshipbetweenthestressanddeformationtensorforlinearandnonlinearfluidsonly.EffortsbymanyresearchersaroundtheglobeareaimedatdirectlysolvingtheNavier-Stokesequations(DNS)withoutintroducingtheReynoldsstresstensor,whichistheresultofanartificialdecompositionofthevelocityfieldintoameanandfluctuatingpart.TheuseofDNSforengineeringapplicationsseemstobeoutofreachbecausethecomputationtimeandresourcesrequiredtoperformaDNS-calculationareexcessiveatthistime.Consideringthisconstrainingcircumstance,engineershavetoresorttoNavier-StokessolversthatarebasedonReynoldsdecomposition.ItrequiresmodelingofthetransitionprocessandtheReynoldsstresstensortowhichthreechaptersofthisbookarededicated.Thebookisstructuredinsuchawaythatallconservationlaws,theirderivativesandrelatedequationsarewrittenincoordinateinvariantforms.ThistypeofstructureenablesthereadertouseCartesian,orthogonalcurvilinear,ornon-orthogonalbodyfittedcoordinatesystems.Thecoordinateinvariantequationsarethendecomposedintocomponentsbyutilizingtheindexnotationofthecorrespondingcoordinatesystems.Theuseofacoordinateinvariantformisparticularlyessentialinunderstandingtheunderlyingphysicsoftheturbulence,itsimplementationintotheNavier-Stokesequations,andthenecessarymathematicalmanipulationstoarriveatdifferentcorrelations.Theresultingcorrelationsarethebasisforthefollowingturbulencemodeling.Itisworthnotingthatinstandardtextbooksofturbulence,indexnotationsareusedthroughoutwithalmostnoexplanationofhowtheywerebroughtabout.Thiscircumstanceaddstothedifficultyinunderstandingthenatureofturbulencebyreaderswhoarefreshlyexposedtotheproblematicsofturbulence.Introducingthecoordinateinvariantapproachmakesiteasierforthereadertofollowstep-by-stepmathematicalmanipulations,arriveattheindexnotationandthecomponentdecomposition.This,however,requirestheknowledgeoftensoranalysis.Chapter2givesaconciseoverviewofthetensoranalysisessentialfordescribingtheconservationlawsincoordinateinvariantform,howtoaccomplishtheindexnotation,andthecomponentdecompositionintodifferentcoordinatesystems.UsingthetensoranalyticalknowledgegainedfromChapter2,itisrigorouslyappliedtothefollowingchapters.InChapter3,thatdealswiththekinematicsofflowmotion,theJacobiantransformationdescribesindetailhowatimedependentvolumeintegralistreated.InChapter4and5conservationlawsoffluidmechanicsandthermodynamicsaretreatedindifferentialandintegralforms.ThesechaptersarethebasisforwhatfollowsinChapters7,8,9,10and11whichexclusivelydealwithviscousflows.Beforediscussingthelatter,thespecialcaseofinviscidflowsispresentedwheretheorderofmagnitudeofaviscosityforcecomparedwiththeconvectiveforcesareneglected.Thepotentialflow,aspecialcaseofinviscidflowcharacterizedbyzerovorticityv-0,exhibitedamajortopicinfluidmechanicsinpre-CFDera.Inrecentyears,however,itsrelevancehasbeendiminished.Despitethisfact,Ipresenteditinthisbookfortworeasons.(1)Despiteitsmajorshortcomingstodescribetheflowpatterndirectlyclosetothesurface,becauseitdoesnotsatisfytheno-slipcondition,itreflectsareasonablygoodpictureoftheflowoutsidetheboundarylayer.(2)Combinedwiththeboundarylayercalculationprocedure,ithelpsacquiringareasonablyaccuratepictureoftheflowfieldoutsideandinsidetheboundarylayer.This,ofcourse,isvalidaslongastheboundarylayerisnotseparated.Forcalculatingthepotentialflows,conformaltransformationisusedwherethenecessarybasicsarepresentedinChapter6,whichisconcludedbydiscussingdifferentvorticitytheorems.ParticularissuesoflaminarflowatdifferentpressuregradientsassociatedwiththeflowseparationinconjunctionwiththewallcurvatureconstitutethecontentofChapter7whichseamlesslymergesintoChapter8thatstartswiththestabilityoflaminar,followedbylaminar-turbulenttransition,intermittencyfunctionanditsimplementationintoNavier-Stokes.AveragingtheNavier-StokesequationthatincludestheintermittencyfunctionleadingtotheReynoldsaveragedNavier-Stokesequation(RANS),concludesChapter8.IndiscussingtheRANS-equations,twoquantitieshavetobeaccuratelymodeled.Oneistheintermittencyfunction,andtheotheristheReynoldsstresstensorwithitsninecomponents.Inaccuratemodelingofthesetwoquantitiesleadstoamultiplicativeerroroftheirproduct.ThetransitionwasalreadydiscussedinChapter8buttheReynoldsstresstensorremainstobemodeled.This,however,requirestheknowledgeandunderstandingofturbulencebeforeattemptsaremadetomodelit.InChapter9,Itriedtopresentthequintessenceofturbulencerequiredforagraduatelevelmechanicalengineeringcourseandtocriticallydiscussseveraldifferentmodels.WhileChapter9predominantlydealswiththewallturbulence,Chapter10treatsdifferentaspectsoffreeturbulentflowsandtheirgeneralrelevanceinengineering.Amongdifferentfreeturbulentflows,theprocessofdevelopmentanddecayofwakesunderpositive,zero,andnegativepressuregradientsisofparticularengineeringrelevance.WiththeaidofthecharacteristicsdevelopedinChapter10,thisprocessofwakedevelopmentanddecaycanbedescribedaccurately.Chapter11isentirelydedicatedtothephysicsoflaminar,transitionalandturbulentboundarylayers.Thistopichasbeenofparticularrelevancetotheengineeringcommunity.Itistreatedinintegralanddifferentialformsandappliedtolaminar,transitional,turbulentboundarylayers,andheattransfer.Chapter12dealswiththecompressibleflow.Atfirstglance,thistopicseemstobedissonantwiththerestofthebook.Despitethis,Idecidedtointegrateitintothisbookfortworeasons:(1)Duetoacompletechangeoftheflowpatternfromsubsonictosupersonic,associatedwithasystemofobliqueshocksmakesitimperativetopresentthistopicinanadvancedengineeringfluidtext;(2)Unsteadycompressibleflowwithmovingshockwavesoccursfrequentlyinmanyenginessuchastransonicturbinesandcompressors,operatinginoff-designandevendesignconditions.Asimpleexampleistheshocktube,wheretheshockfronthitstheoneendofthetubetobereflectedtotheotherend.Asetofsteadystateconservationlawsdoesnotdescribethisunsteadyphenomenon.AnentiresetofunsteadydifferentialequationsmustbecalleduponwhichispresentedinChapter12.Arrivingatthispoint,thestudentsneedtoknowthebasicsofgasdynamics.Ihadtwooptions,eitherreferthereadertoexistinggasdynamicstextbooks,orpresentaconciseaccountofwhatismostessentialinfollowingthischapter.Idecidedonthesecondoption.Attheendofeachchapter,thereisasectionthatentailsproblemsandprojects.Inselectingtheproblems,IcarefullyselectedthosefromthebookFluidMechanicsProblemsandSolutionsbyProfessorSpurkofTechnischeUniversitätDarmstadtwhichItranslatedin1997.Thisbookcontainsanumberofhighlyadvancedproblemsfollowedbyverydetailedsolutions.Istronglyrecommendthisbooktothoseinstructorswhoareinchargeofteachinggraduatefluidmechanicsasasourceofadvancedproblems.MysincerethanksgotoProfessorSpurk,myformerCo-Advisor,forgivingmethepermission.Besidestheproblems,anumberofdemandingprojectsarepresentedthatareaimedatgettingthereadersinvolvedinsolvingCFD-typeofproblems.InthecourseofteachingtheadvancedFluidMechanicscourseMEEN-622,IinsistthatthestudentspresenttheprojectsolutionintheformofatechnicalpaperintheformatrequiredbyASMETransactions,JournalofFluidEngineering.Intypingseveralthousandequations,errorsmayoccur.Itriedhardtoeliminatetyping,spellingandothererrors,butIhavenodoubtthatsomeremaintobefoundbyreaders.Inthiscase,Isincerelyappreciatethereadernotifyingmeofanymistakesfound;theelectronicaddressisgivenbelow.Ialsowelcomeanycommentsorsuggestionsregardingtheimprovementoffutureeditionsofthebook.Mysincerethanksareduetomanyfineindividualsandinstitutions.Firstandforemost,IwouldliketothankthefacultyoftheTechnischeUniversitätDarmstadtfromwhomIreceivedmyentireengineeringeducation.IfinalizedmajorchaptersofthemanuscriptduringmysabbaticalinGermanywhereIreceivedtheAlexandervonHumboldtPrize.IamindebtedtotheAlexandervonHumboldtFoundationforthisPrizeandthematerialsupportformyresearchsabbaticalinGermany.MythanksareextendedtoProfessorBerndStoffel,ProfessorDitmarHennecke,andDipl.Ing.BerndMatyschokforprovidingmewithaverycongenialworkingenvironment.IamalsoindebtedtoTAMUadministrationforpartiallysupportingmysabbaticalwhichhelpedmeinfinalizingthebook.SpecialthanksareduetoMrs.MahaliaNixwhohelpedmeincross-referencingtheequationsandfiguresandrenderedothereditorialassistance.Last,butnotleast,myspecialthanksgotomyfamily,SusanandWilfriedfortheirsupportthroughoutthisendeavor.M.T.SchobeiriAugust2009CollegeStation,Texastschobeiri@mengr.tamu.eduNomenclature1IntroductionThestructureofthermo-fluidsciencesrestsonthreepillars,namelyfluidmechanics,thermodynamics,andheattransfer.Whilefluidmechanics’principlesareinvolvedinopensystemthermodynamicsprocesses,theyplayaprimaryroleineveryconvectiveheattransferproblem.Fluidmechanicsdealswiththemotionoffluidparticlesanddescribetheirbehaviorunderanydynamicconditionwheretheparticlevelocitymayrangefromlowsubsonictohypersonic.Italsoincludesthespecialcasetermedfluidstatics,wherethefluidvelocityapproacheszero.Fluidsareencounteredinvariousformsincludinghomogeneousliquids,unsaturated,saturated,andsuperheatedvapors,polymersandinhomogeneousliquidsandgases.Aswewillseeinthefollowingchapters,onlyafewequationsgovernthemotionofafluidthatconsistsofmolecules.Atmicroscopiclevel,themoleculescontinuouslyinteractwitheachothermovingwithrandomvelocities.Thedegreeofinteractionandthemutualexchangeofmomentumbetweenthemoleculesincreaseswithincreasingtemperature,thus,contributingtoanintensiveandrandommolecularmotion.1.1ContinuumHypothesisTherandommotionmentionedabove,however,doesnotallowtodefineamolecularvelocityatafixedspatialposition.Tocircumventthisdilemma,particularlyforgases,weconsiderthemasscontainedinavolumeelementvGwhichhasthesameorderofmagnitudeasthevolumespannedbythemeanfreepathofthegasmolecules.ThevolumeVGhasacomparableorderofmagnitudeforamoleculeofaliquidV.Thus,afluidcanbetreatedasacontinuumifthevolume8VGoccupiedbythemassdoesnotexperienceexcessivechanges.ThisimpliesthattheratiodoesnotdependuponthevolumevG.Thisisknownasthecontinuumhypothesisthatholdsforsystems,whosedimensionsaremuchlargerthanthemeanfreepathofthemolecules.Acceptingthishypothesis,onemaythinkofafluidparticleasacollectionofmoleculesthatmoveswithavelocitythatisequaltotheaveragevelocityofallmoleculesthatarecontainedinthefluidparticle.Withthisassumption,thedensitydefinedinEq.(1.1)isconsideredasapointfunctionthatcanbedealtwithasathermodynamicpropertyofthesystem.Ifthep-v-T-behaviorofafluidisgiven,thedensityatanypositionvectorxandtimetcanimmediatelybedeterminedbyprovidinganinformationabouttwootherthermodynamicproperties.Forfluidsthatarefrequentlyusedintechnicalapplications,thep-v-Tbehaviorisavailablefromexperimentsintheformofp-v,h-s,orT-stablesordiagrams.Forcomputationalpurposes,theexperimentalpointsarefittedwithaseriesofalgebraicequationsthatallowaquickdeterminationofdensitybyusingtwoarbitrarythermodynamicproperties.1.2MolecularViscosityMolecularviscosityisthefluidpropertythatcausesfriction.Fig.1.1givesaclearphysicalpictureofthefrictioninaviscousfluid.Aflatplateplacedatthetopofaparticularviscousfluidismovingwithauniformvelocityvi-Urelativetothestationarybottomwall.Thefollowingobservationsweremadeduringexperimentation:1)Inordertomovetheplate,acertainforceF1mustbeexertedinx1-direction.2)ThefluidstickstotheplatesurfacethatmoveswiththevelocityU.3)Thevelocitydifferencebetweenthestationarybottomwallandthemovingtopwallcausesavelocitychangewhichis,inthisparticularcase,linear.4)TheforceF1isdirectlyproportionaltothevelocitychangeandtheareaoftheplate.Theseobservationsleadtotheconclusionthatonemayset:Multiplyingtheproportionality(1.2)byafactorμwhichisthesubstancepropertyviscosity,resultsinanequationforthefrictionforceinx1-direction:ThesubsequentdivisionofEq.(1.3)bytheplateareaAgivestheshearstresscomponentτ21:Equation(1.4)istheNewton’sequationofviscosityforthisparticularcase.Thefirstsubscriptreferstotheplaneperpendiculartothex2-coordinate;thesecondreferstothedirectionofshearstress.Equation(1.4)isvalidforatwo-dimensionalflowofaparticularclassoffluids,theNewtonianFluids,whoseshearstressislinearlyproportionaltothevelocitychange.Thegeneralthree-dimensionalversionderivedanddiscussedinChapter4is:withDasthedeformationtensor.Thecoefficientλisgivenby,withμastheabsoluteviscosityandthebulkviscosity.InsertingEq.(1.5)intotheequationofmotion(seeChapter4),theresultingequationindependentlydevelopedbyNavier[1]andStokes[2]completelydescribesthemotionofaviscousfluid.InacoordinateinvariantformtheNavier-Stokesequationreads:AlthoughEq.(1.6)hasbeenknownsincethepublicationofthefamouspaperbyNavierin1823,withtheexceptionoffewspecialcases,itwasnotpossibletofindsolutionsforcasesofpracticalinterests.NeglectingtheviscositytermsignificantlyreducesthedegreeofdifficultyinfindingasolutionforEq.(1.6).Thissimplification,however,leadstoresultsthatdonotaccountfortheviscousnatureofthefluid,thereforetheydonotreflecttherealflowsituations.Thisisparticularlytruefortheflowregionsthatareclosetothesurface.ConsiderthesuctionsurfaceofawingsubjectedtoanairflowasshowninFig.1.2.Twoflowlayersaredistinguished:(1)averythinlayerclosetothesurface,calledtheboundarylayer,wheretheviscosityeffectispredominantand(2)anexternallayerwheretheviscositymaybeneglected.Asaresult,thefluidoutsidetheboundarylayermaybeconsideredinviscid.Inthiscase,theNavier-StokesequationisreducedtotheEulerequationofmotionthatcanbesolved.Prandtl[3]wasthefirsttoestablishaconceptthatcouplesthesolutionoftheexternalinviscidlayerwiththesolutionoftheviscousboundarylayerbydevelopingtheboundarylayertheory.Usingasetofassumptionsthatwerebasedonaseriesofcomprehensiveexperimentalstudies,Prandtl[3]andvonKármán[4]significantlysimplifiedthegoverningsystemofpartialdifferentialequationsandderivedanintegralmethodtosolveforboundarylayermomentumdeficiencythicknessforincompressiblesteadyflow.Althoughtheintegralmethodiscapableofprovidingusefulinformationabouttheboundarylayerintegralparameterssuchasmomentumthicknessorwallfriction,itisnotabletoprovidedetailinformationaboutthevelocitydistributionwithintheboundarylayer.Likewise,caseswithflowseparationcannotbetreated.Furthermore,itcontainsseveralempiricalcorrelationsthathavetobeadjustedfromcasetocase.Topartiallycircumventtheabovedeficiencies,theintegralmethodcanbereplacedbyadifferentialmethod.Althoughtheintroductionofboundarylayertheorywasamajorbreakthroughinfluidmechanics,itsfieldofapplicationsislimited.Withtheintroductionofpowerfulnumericalmethodsandhighspeedcomputers,itisnowpossibletosolvetheNavier-Stokesequationsforlaminar(seeSection1.3.1)flows.Tofindsolutionsforturbulent(seeSection1.3.1)flows,theequationsareaveragedleadingtoReynoldsaveragedNavier-Stokesequations(RANS).TheaveragingprocesscreatesanewsecondordertensorcalledtheReynoldsstresstensor,withnineunknowns.ThenumericalsolutionofRANS,however,requiresmodelingtheReynoldsstresstensor.Inthelastthreedecades,avarietyofturbulencemodelshavebeendevelopedincludingsinglealgebraicandmulti-equationmodels.Thetrendincomputationfluiddynamicsgoestowardadirectnumericalsimulation(DNS)ofNavier-Stokesequations,avoidingtimeaveragingandturbulencemodelingaltogether.原资料见附件免责声明：本页面/内容部分素材来源于互联网公开信息，旨在传递更多信息，不代表本平台立场。版权归原作者或机构所有，如涉及侵权，请通过平台联系我们，我们将在核实后第一时间处理。本平台对转载内容的真实性、准确性不作任何保证，用户需自行判断并承担使用风险。
