Chapter1 MainInthischapter,wefocusonthefollowingconceptsandDefinitionofaContinuumUnitsandBasic ysisTechniques,controlvolumeandEulerianandLagrangianThermodynamicpropertiesofaViscosityandothersecondaryproperties(Newtonian/non-Newtonian;no-slipcondition,turbulence;surfacetension)FlowVisualizationFlowpatterns--Streamlines,streaklines, DefinitionofaFluidisasubstancethatdeforms變形)continuouslyundertheapplicationofashear(tangential)stressnomatterhowsmallorlargetheshearstressmaybe.3Figure1.1Behaviorof(a)solidand(b)fluid,undertheactionofaconstantshear 與時間有4MaindifferencesbetweenthebehaviorofsolidsandfluidsunderanappliedforceForasolidthestrain（應(yīng)變）ordeformationisafunctionoftheappliedstressandindependentofthetimeoverwhichtheforceisapplied,providingthattheelasticlimitisnotForafluid,thedeformationisdependentonForasolid,iftheelasticlimitisnotexceeded,thedeformationdisappearswhentheforceisremoved;Afluidcontinuestoflowaslongastheforceisappliedandwillnotrecoveritsoriginalformwhentheforceisremoved.5Fluidsunderashearstressmustbeinakindof Howtokeepthefluidatrest (FWFluidtakesshapeofContinuum連續(xù)介質(zhì)概Allfluidsarecomposedofmoleculesinconstantmotion.Howeverinmostengineeringapplicationsweareinterestedintheaverageormacroscopiceffectsthatweordinarilyperceiveandmeasure.Wethustreatafluidasaninfini ydivisiblesubstance,acontinuum,thusfrommacropointofview,wedonotneedtoconcernwiththebehaviorofindividualmolecules.Thisistheso-calledcontinuumconceptinclassicalfluidmechanics.在經(jīng)典流體力學(xué)中，只考慮分子平均或作用，不考慮單獨分子的性能 ValidityofcontinuumTheconceptofacontinuumisthebasisofclassicalfluidmechanics.Thecontinuumassumptionisvalidintreatingthebehavioroffluidsundernormalconditions.Itbreaksdownwheneverthemeanfreepathofthemolecules（

7 esthesameorderasthesmallestsignificantcharacteristicdimension(特征長度)oftheproblem.Forrarefiedgasflow稀薄氣體(e.g.,asencounteredinflightsintotheupperreachesoftheatmosphere);micro-scalechannelflows(inMEMSandevenNEMS,etc.8HowtorepresentflowpropertyatapointinaForexample,thedensityatpointWhenVisshrank(收縮)toaverysmallsize,itthenwillrepresentafluidparticle/element,andthisvolumeistermedelementalvolume. CCVV Inacontinuum,volumeofafluidparticleorelementsatisfy(連續(xù)介質(zhì)中的流體質(zhì)點、流體微團滿足下Largeenoughinmicroscope（微觀足夠大Smallenoughinmacroscope（宏觀足夠小）,i.e.109

ofairatstandardconditions y

SignificanceofcontinuumAsaconsequenceofthecontinuumassumption,eachfluidpropertyisassumedtohaveadefinitevalueateverypointinspace.Thereforefluidpropertiessuchasdensity,temperature,velocity,andsoon,areconsideredtobecontinuousfunctionsofpositionandtime,andthisleadtoafield*descriptionoffluidflow.InparticularthevelocityfieldisgivenbyrrNOTE:稀薄微小空間(尺度)“Continuumconcept”breaksdownwheneverthemeanfreepathofthemolecules（分子自由行程） esthesamemagnitudeorder(相同數(shù)量級)asthesmallestsignificantcharacteristicdimension(特征長度)oftheproblem.若連續(xù)介質(zhì)不適用，應(yīng)如何處理呢？Dimensionand單位與量Dimensionsarepropertiesthatcanbemeasured,e.g.length,velocity,area,volume,accelerationetc.可以測量的性質(zhì)叫Unitsarethestandardelementsweuse (量化thesedimensionssuchasameter,afoot用來量化量綱的標(biāo)Itisnotedthat“dimension’isnotapropertyoftheindividualunits,butit lswhattheunitrepresentsAllmeasurable tiescanbedividedintotwogroups: tiesandsecondary PrimaryunitprimarydimensionMLTMMSITL ty–orsecondarydimensionorsecondary ThePrincipleofDimensional量綱一致性additivemustbedimensionallyhomogeneousandsimultaneouslybeconsistentinunitsDifferentsystemsandconversionBritishGravitationalunitsChineseEngineeringUnits（中國工程單位）.metricSIsystem公制或國際單位制TheSISEEpage850–AppendixC:Conversion1.41.4Basicysiscontrolvolumeandsystem,EulerianLagrangianBasic ysisTherearethreedifferentwaystotackleafluidflow ysis(積分分析lookingatgrosseffectoffluidparticlesincontrolvolumeorsystem–ToobtainsomeintegralDifferentialysis（微分分析）lookingatinfinitesimal(極微小的)systemorcontrolvolume(localindividualbehaviour)–Toobtaindifferentialequations ysis（量綱分析）isusedinexperimentalstudyoffluidflowtorearrangeflowparametersandobtaindimensionlessparametergroups,suchasRe,Ma,etc.throughwhichwecannotobtainanexactflowsolution.ControlvolumeandTheabovementionedflow ysiscanbecarriedoutforafluidsystemoracontrolvolume.Asystemisdefinedasafixed tyandfixedidentityofmass;thesystemboundariesseparatethesystemfromthesurroundings.Theboundariesofthesystemmaybefixedormovable,butthereisnomasstransferacrossthesystemboundaries.Piston-cylinderAfluidsystemfixedmassandfixedidentityofItisnotedalltheequationsareestablishedforafixedmassintegrity.DifficultyarisesfortreatingafluidInfact,weveryoftenconcernedwiththeflowoffluidsthroughadevice,suchascompressor,turbines,pipelines,nozzles.Inthesecases,itisdifficulttofocusourattentiononafixedidentifiable tyofmass.Itismuchmoreconvenientto yzingavolumeinspacethroughwhichthefluidflows.Controlvolumeisanarbitraryvolumeinspace,chosenby yst,withopenboundariesthroughwhichmass,momentum,andenergyareallowedtocross.ItsboundaryiscalledcontrolPPipFlowFluidflowthroughaItisnotedThecontrolvolumemaybefixed,movingordeformable(固定、運動、變形).Controlvolumecanbebothfiniteand ysisisusedforafinitevolume,whiledifferential usedforaninfinitesimalvolumeCanweusetheconservationequations(suchasenergyconservationequation,momentumconservationequation)introducedinpreviouscoursesdirectlytoacontrolvolume?Itisnotedthatallconservationequationsthatyoulearnedinpreviouscoursesareestablishedforasystem(afixedmassintegrity), suchasNewton’slaw,lawsofthermodynamics,etc.;theseequationscannotbedirectlyusedforacontrolvolume.Sincethecontrolvolumedoesnothaveafixed tyandidentityofmass!3Lagrangian&EulerTherearetwodistinctwaystodescribefluidflow(toestablishtheequationsofmotion),andtheyareLarangianandEulerianmethod.Lagrangianapproachwedealwithasystemandapplybasicequationstoa tyandidentityofmass(namelysystemasdefinedabove),forinstance,theapplicationofNewton’ssecondlawtoaparticleoffixedmass.SuchaapproachisoftentermedLagrangianapproach.Indifferential ysis,Lagrangianapproachfocusesona tyofmass,andtracethehistoryofpropertyforindividualfluidparticles(orelementalbodyofmassFrvtr(rr)rrrardd2rdrr(a,b,c)v.r(a,b,rrV a,andrrrSincea,V a,andrrr

ItisnotedthatinLagrangianframe(在日框架下)，flowparametersareexpressedasrV(a,b,c,t)P(a,b,c,t)(a,b,c,t)Wherea,b,&careconstants,andtheyrepresentinitialposition初始位置ofthefluidApplicationofLagrangianLagrangianapproachspecifieshistoryofpropertiesforindividualfluidparticles.Forexample,itisusedtotrackdiscreteparticlesanddroplets(離散粒子和液滴)inacontinuousfluid.Lagrangianapproachtracesallparticles(e.g.1,2,and3…..N)atinitialandsuccessivetimeinstant(a1,b1,c1,

,

,

,particle particle3

(a3,b3,c3,ty

t2Eulerapproach-focusesonflowpropertiesatagivenpointinspaceoragivenfinitecontrolvolume(throughwhichdifferentfluidparticlesmaypassatdifferenttimeinstants.)Itisnotedthatinanintegral ysisweshouldconsiderafinitecontrolvolumewithfixedboundary,whileinadifferential ysisweshouldconsideraninfinitesimalcontrolvolumeofagivenpointinspace.EulerEulerapproachfordifferential ysisfocusingonflowpropertyatanarbitrarypoint(ofaninfinitesimalcontrolvolume，微小的容積).ItisnotedthatinEulerframe(在框架下vv(x,y,z,tp(x,y,z,t(x,y,z,trTheapproachisbasedonfieldIngeneral,velocityisavectorfunctionofpositionandthushasthreecomponents,u,v,andw,andwritten 3Eulerapproachforintegral ysisfocusingonafinitecontrolvolume(有限大容積)withfixed3PPipControlFlowFluidflowthroughaThermodynamicpropertiesofaVelocityarethemostimportantfluidproperty,anditinteractscloselywiththethermodynamicpropertiesofthefluid.Thefollowing9tiesarethermodynamicpropertiesdeterminedbythermodynamicconditionorstate.Basic(intensive) OtherintensivePressureDensityTransportCoefficientofviscosity

Enthalpyh=?p/Entropy

weightVgg limmVV'(g)liquidV(V1000(g)gasV( 1.205Specificgravity(SG,)比引力或比（waterat（airat20°C&Internal,PotentialandKineticInternalmolecularbondingPotential

molecularactivityKineticfludmechanicssumofthree e?1/2V2 Wedefinezasupward,

gr

andwee?1/2V2Viscosityandothersecondary tiessuchaspressure,temperature,anddensityareprimarythermodynamicproperties(variables).Certainsecondaryproperties(variables)alsocharacterizespecificfluidmechanicalbehavior.Viscosityisthemostimportantsecondaryproperty,whichrelatesthelocalstressestothestrainrateofthemovingfluidelement.Itisa tativemeasureofafluid's toflow,inparticular,itdeterminesthefluidstrainrategeneratedbyagivenappliedshearViscosityisthepropertyofafluid,duetocohesionandinteractionbetweenmolecules,whichoffers sheardeformation.粘DifferentfluidsdeformatdifferentratesunderthesameshearTherelationshipamongstress,strainordeformationrate,viscosityisdifferentfordifferentDeformationofa 平板作用于流體上的切應(yīng)力 A0 ）流體的變形率（deformation）

limt0MM'之間的距 l lu故t 流體的變形率（deformationdd

Evenamongfluids,therecarewidedifferencesinthebehaviorunderstress.Accordingtotherelationbetweentheappliedshearstress,andtherateofdeformation,fluidsareclassifiedintoNewtonianandnon-newtonian流體與 NewtonianFluidsinwhichappliedshearstressisdirectlyproportionalto(正比于)rateofdeformationaretermedNewtonianfluids.

SuchapropertyoffluidsisaconstantforallNewtonianfluids,termeddynamicviscosity(動力粘性)/orabsoluteviscosity Newton’slawofviscosity（內(nèi)摩擦定律 Dynamicviscosityorabsolute

m2//Non-Newtonianfluids(非流體non-NewtonianfluidsdonotsatisfyNewton’slawofviscosity. Fornon-Newtonianfluids,theviscositycommonlyisnotaconstant. Figure1.9Rheologicalbehaviorofvariousmaterials:(a)Stressversusstrainrate--Comparisonsofnewtonianand newtonianfluids;(b)Effectoftimeonappliedstress--Tomaintainaconstantstrainratewithtime,thestressrequiredisdifferentforcommonfluids,rehopecticfluids,andthixotropicfluidsViscosityvarieswith

粘性隨壓力的變TheviscosityofNewtonianfluidsisatruethermodynamicpropertyandvarieswithtemperatureandGenerallyspeaking,theviscosityofafluidincreasesonlyweaklywithpressure.Forinstance,increasingpfrom1atmto50atmwillincreaseμofaironly10%.Itiscustomaryinmostengineeringworktoneglecttheinfluenceofpressurevariationonviscosityoffluids.Viscositymainlyvarieswith粘性隨溫度變Viscosityofgasesincreaseswithtemperature,whereasforliquids,viscositydecreaseswithincreasingThereasonisthatviscosityresultsfromthecombinedeffectofinteractionandcohesionofmolecules,andtheyplaydifferentrolesingasesandliquids.Forgases--Themoleculesofgasesareonlyweaklykeptinpositionbymolecularcohesion(astheyaresofarapart).Asadjacentlayersmovebyeachotherthereisacontinuousexchangeofmomentum.Moleculesofaslowerlayermovetofasterlayerscausingdrag,whilemoleculesmovingtheotherwayexertanaccelerationforce.氣體聚合力小，分子動量交換強,間動量交換Iftemperatureofagasincreasesthemomentumexchangebetweenlayerswillincreasethusincreasingviscosity.Forliquids--Thoughthereissomemolecularinteraction,butasthemoleculesaresomuchcloserthaningases,thecohesiveforceholdthemoleculesinplacemuchmorerigidly.Thiscohesionplaysanimportantroleintheviscosityofliquids.Increasingthetemperatureofaliquidreducesthecohesiveforcesandthen todeformationdecreases,thusdecreasingviscosity.Deceasingthetemperatureofaliquidincreasecohesiveforcesthusincreasingviscosity.NotionsrelatedtoNo-slip

i.e.atsolidboundary,

Turbulent

Withoutviscosity,therewouldnotbeanyturbulentflowatall!Figure1.15:VelocityNo-slipconditioninwaterflowpastathinfixedLaminarSurfacetension表面張Surfacetensionisgeneratedattheinterface界面AmoleculeIintheinteriorofaliquidisunderattractiveforces(i.e.cohesion)inalldirectionsandthevectorsumoftheseforcesiszero.ButamoleculeSatthesurfaceofaliquidisactedbyanetinwardcohesiveforcethatisperpendiculartothesurface.Hencetheinterfacerequiresworktomovemoleculestothesurfaceagainstthisopposing(cohesion)force,andsurfacemoleculeshavemoreenergythaninteriorones

ofliquidsandSurfacetensionofaliquidistheworkthatmustbedonetobringenoughmoleculesfrominsidetheliquidtothesurfacetoformoneunitareaofthatsurface(J/m2=N/m).SurfacetensionmustsatisfyminimumenergySurfacetensionleadingtocapillarity毛細(xì)管現(xiàn)象Surfacetensioncausesdropsofliquidtotendtotakeasphericalshape.Thisisresponsibleforcapillaryactionandcausesaliquidtoriseordropinafinetubewhenitslowerendisinvertedinaliquid.ExampleExampleFigureRiseorLiquidsriseintubesiftheyadhesionofsolidsurface(粘附力)>cohesion(聚合力)andfallintubesifcohesion>adhesionNote:Whenuseacolumnofliquidtomeasurepressure,oneshouldremembertocorrecthis/herreadingerrorsresultedfromcapillarity!!FlowpatternsStreamlines,streaklines,andpathlinesForFlowVisualizationFlowpatternscanbevisualizedindifferentways,wecansketchesandphotographstodescribetheflowqualitativelyandFourbasictypesofline'spatternsareusedtovisualizethe1Pathline(跡線isatra