第一章-2012-王洪伟

1ENGINEERINGFLUIDMECHANICSSchoolofJetPropulsion20122Textbook:《气体动力学基础》……王新月，陆利蓬等《FluidMechanics》……FrankM.WhiteReferences:《气体动力学基础》……潘锦珊等Grades:Homework:20%Inclassdiscuss&quiz:10%Midtermexam:30%(Openbooks)Finalexam:40%(Closebooks)3ScheduleChapter1………Introduction(6hours)Chapter2………FluidStatics(4hours)Chapter3………IntegralRelations(12hours)MidtermExam(2hours)Chapter4………DifferentialRelations(12hours)Chapter5………BoundaryLayer(6hours)Summary(2hours)FinalExam4Chapter1Introduction§1.1PreliminaryRemarksWhenyouthinkaboutit,almosteverythingonthisplaneteitherisafluidormoveswithinornearafluid.--FrankM.White5Curvedshoot(Bananashoot)ForceonarotatingcylinderSomeexamplesKarmanVortexTacomaBridge6JupiterHumanplumeWingtipvortexTornadoSomeotherexamples7Howcananairplanefly?Airplanes8Aturbofan(涡扇)jetengine9WhatisFluidMechanics?FluidMechanicsisthestudyoffluideitherinmotion(FluidDynamics流体动力学)oratrest(FluidStatics流体静力学)andsubsequenteffectsofthefluidupontheboundaries,whichmaybeeithersolidsurfacesorinterfaceswithotherfluids.Whatisafluid?10TheconceptofafluidAsolidcanresistashearstress(剪切应力)byastaticdeformation.Afluidcannotresistashearstressbyastaticdeformation.Anyshearstressappliedtoafluid,nomatterhowsmall,willresultinmotionofthatfluid.Thefluidmovesanddeformscontinuouslyaslongastheshearisapplied.11HistoryandScopeofFluidMechanicsPre-history:Sailingshipswithoars(橹桨)andirrigationsystemwerebothknowninprehistory12Archimedes(285-212BC)ParallelogramlawforadditionofvectorsLawofbuoyancy曹冲（196-208）13LeonardodaVinci(1452-1519)Equationofconservationofmassinone-dimensionalsteadyflowExperimentalistTurbulence14IsaacNewton(1642-1727)LawsofmotionLawsofviscosityofnewtonianfluid1518thcenturyMathematicians：Euler（欧拉）：EulerequationBernoulli(伯努利)：BernoulliequationIdealflowsolutionsD’Alembert（达朗贝尔）：D’Alembertparadox（佯谬，疑题）Engineers：Hydraulics(水力学),relayingonexperimentChannels，Shipresistance，PipeflowsPitotVenturiTorricelliPoiseuille1619thcenturyNavier(1785-1836)&Stokes(1819-1905)N-SequationReynolds(1842-1912)TurbulenceFamousexperimentontransitionReynoldsNumber1720thcenturyLudwigPrandtl(1875-1953)钱学森(1911-2009)陆士嘉(1911-1986)Boundarylayertheory(1904)ThefatherofmodernfluidmechanicsVonKarman(1881-1963)18§1.2SomePropertiesoffluids(1)Viscosity(粘性)Whenafluidissheared（剪切）,itbeginstomove.Subsequently,apairofforcesappearontheshearsurface,whichresiststheshearmotionofthefluid.Thisiscalledviscosity.ThenatureofviscosityForliquiditiscohesion（结合力）(oil_00100.mov)Forgasitisthetransportofmomentum（动量输运）(Particle_flow.mov)19dudyVelocitygradientdudyNewtonianlawofviscosity(牛顿粘性定律，牛顿内摩擦定律)UUu(y)xyShearstressThevelocitygradientiscomparabletodeformation.ThiskindoflinearfluidiscalledNewtonianfluid.（牛顿流体）：CoefficientofviscosityDynamiccoefficientofviscosity(动力粘性系数)[N∙s/m2]Invisidflow,Idealflow20(2)Compressibility(压缩性)Incompressible(不可压):r=constMostliquidflowsaretreatedasincompressible.（Only1%increaseifpressureincreaseby220）Compressible（可压缩）:r=r(p,T)Gasescanalsobetreatedasincompressiblewhentheirvelocityislessthan0.3ManumbersErnstMach21(4)ThermalConductivity(热传导)TqknFourier’slawofheatconduction(3)StateRelationsforGasesR=287.06forairPerfect-gasLaw（理想气体状态方程）RTpr22§1.3TheFluidasaContinuum(连续介质）*vvmlimvrDensity(密度)Elementalvolume（流体微团/质点）*Largeenoughinmicroscope（微观）10-9mm3ofairatstandardconditionscontainsapproximately3×107molecules.Mostengineeringproblemsareconcernedwithphysicaldimensionsmuchlargerthanthislimitingvolume.23Suchafluidiscalledacontinuum,Whichsimplymeansthedifferentialcalculuscanbeusedtoanalyzethesubstance.*Smallenoughinmacroscope（宏观）.微观足够大，宏观足够小24§1.4Surfaceforce(表面力)andbodyforce（质量力，体积力）Surfaceforcesactcontinuouslyonthesidesurfacesoffluidelements.Pressure,Friction.ContactPerunitarea(单位面积)应力Bodyforcesactontheentiremassoftheelement.Gravity,Electromagnetic.NocontactPerunitmass(单位质量)gRXiYjZk25§1.5TwodifferentpointsofviewinanalyzingproblemsinmechanicsTheLagrangianview(拉格朗日法)TheLagrangianviewfollowsanindividualparticlemovingthroughtheflow,appropriatetosolidmechanics.ThecontrastoftwoframesTheEulerianviewisconcernedwiththefieldofflow,appropriatetofluidmechanics.TheEulerianview(欧拉法)26Flowclassification(流动分类)AccordingtoEulerianview,anypropertyfisfunctionofcoordinates（space）andtime.InCartesiansystem(直角坐标系)，itcanbeexpressedasf(x,y,z,t)x,y,z,t:Eulerianvariablecomponent(欧拉变数)f:Functionoftime~~unsteady(非定常)steady(定常)0tf0tff:Functionofspace~one-dimensional(1-D,一维),two-dimensional(2-D,二维),three-dimensional(3-D,三维)27OneTwodimensionalThreeSteadyUnsteadyCompressibleIncompressibleViscousInviscid“Threedimensionalunsteadycompressibleviscousflow”“Onedimensionalsteadyincompressibleinvisidflow”28Apathlineistheactualpathtraversedbyagivenfluidparticles.WhatisaPathline?§1.6Pathline(迹线),Streamline(流线)&Flowfield(流场)PathlinesinsteadyflowPathlinesinunsteadyflow29WhatisaStreamline?Astreamlineisthelineeverywheretangenttothevelocityvectoratagiveninstant.Forsteadyflow:Streamline=PathlineStreamlinesinsteadyflowStreamlinesinunsteadyflow30Streamsurface(流面),Streamtube(流管),Fl