Physical hydrodynamics

547 Pages·2015·20.38 MB·English

by  Etienne Guyon, Jean-Pierre Hulin, Luc Petit, Catalin D. Mitescu

PHYSICAL HYDRODYNAMICS

Physical Hydrodynamics
Second Edition
Etienne Guyon
HonorarydirectorofEcolenormalesupérieure.EcolesupérieuredePhysiqueetChimie(Paris)
Jean-Pierre Hulin
SeniorCNRSResearchScientist,Emeritus,FASTLaboratory,Paris-SaclayUniversity.
Luc Petit
ProfessorofPhysics,ILMLaboratory,UniversitéClaudeBernard-Lyon1
Catalin D. Mitescu
ProfessorofPhysics,EmeritusatPomonaCollege
3
3
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TranslatedwithrevisionsandextensionsfromtheFrenchlanguageeditionof:
Hydrodynamiquephysique–3eédition
DeEtienneGuyon,Jean-PierreHulinetLucPetit
©2012EditionsEDPSciences
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Foreword
Fluid mechanics is a subject with a long history, but yet is young with regard to recent
discoveries,andhasmanyapplicationswhichaffecteverydaylife.Itshistoryisaparadeof
thegreatnamesofscience:fromtheeighteenthcenturytheBernoullis,EulerandLagrange;
fromthenineteenthcenturyCauchy,Navier,Stokes,Helmholtz,Rayleigh,Reynoldsand
Lamb;andfromthetwentiethcenturyCouette,Prandtl,G.I.TaylorandKolmogorov.
Inthenaturalenvironment,wecannowrelyonthe5-dayweatherforecastsandtornado
warnings; early success in predicting tides is today applied to automated tsunami warn-
ings;understandingthecirculationintheoceansandatmosphereisappliedtopollution,
theozoneholeandclimatechange.Intheinterioroftheearth,fluidmechanicsisimpor-
tantinmantleconvection,volcanoesandtheirdustclouds,oilreservoirsandpossibleCO2
sequestration.
Fluid mechanics is central to many industries. The design of aircraft developed from
simpleideasintheearlytwentiethcenturytolow-dragformsofwingswithwingletsattheir
tipsandimprovedbodyprofilesbytheendofthecentury.Atthesametime,jet-noisewas
dramaticallyreducedwiththeintroductionofwideentrancebypassfanswhichshieldthe
fastjet.Simpleandcomplexfluidsareprocessedinvariousmanufacturingindustries:for
glassandothermaterials,chemicalengineeringandfoodprocessing.
Recentresearchinfluidmechanicsincludes:microfluidicsatthemicronscalewiththe
possibility of multiple simultaneous tests of small biological samples; similar scales and
effects of wettability in ink-jet-printing; the ideas of convection allowing the design of
energy-efficientbuildingsbyusingnaturalconvection;andthecontrolofinstabilitiesand
turbulence.
Withsuchawealthofideasandapplications,thereisamajorchallengeofhowtoteach
thesubject.SomematerialisbestlefttospecializedMasterscourses.Butthebasiccorehas
tobetaughtinawaytohelpstudents’progresstotheadvancedtopics,currentandfuture.
Theauthorsofthisbookhaveadoptedinmyopinionanapproachandstylewhichshould
interestandeducatestudents,preparingthemforthefuture.Ifearthatsomealternative
approachesfailonthis:someengineeringcourseshaveanover-relianceonComputational
FluidDynamics,whichcanbeunsafeinnovelapplications;somemathematicalcoursesare
lost in the enormous difficulty of proving the governing equations have, or do not have,
solutionsinthesimplestofsituations,anopenClayprizeproblem.Theapproachinthis
bookisgroundedinexperimentandreality.Thechosenstructureofthepresentationhelps
studentscometodeepinsightsintothesubject.
In my opinion, the subject of fluid mechanics has benefited in the last 30 years from
the contributions of French physicists such as the authors of this book, bringing a fresh
approachtothesubjectalongwithnovelexperimentaltechniquesandanappreciationof
practicalities.
JohnHinch
UniversityofCambridge

Contents
Introduction xv
1 ThePhysicsofFluids 1
1.1 Theliquidstate 1
1.1.1 Thedifferentstatesofmatter:modelsystemsandrealmedia 2
1.1.2 Thesolid–liquidtransition:asometimesnebulousboundary 5
1.2 Macroscopictransportcoefficients 5
1.2.1 Thermalconductivity 6
1.2.2 Massdiffusion 11
1.3 Microscopicmodelsfortransportphenomena 13
1.3.1 Therandomwalk 13
1.3.2 Transportcoefficientsforidealgases 15
1.3.3 Diffusivetransportphenomenainliquids 19
1.4 Surfaceeffectsandsurfacetension 21
1.4.1 Surfacetension 21
1.4.2 Pressuredifferencesassociatedwithsurfacetension 23
1.4.3 Spreadingofdropsonasurface–theideaofwetting 25
1.4.4 Influenceofgravity 27
1.4.5 Somemethodsformeasuringthesurfacetension 29
1.4.6 TheRayleigh–Taylorinstability 31
1.5 Scatteringofelectromagneticwavesandparticlesinfluids 33
1.5.1 Someprobesofthestructureofliquids 33
1.5.2 Elasticandinelasticscattering 34
1.5.3 Elasticandquasielasticscatteringoflight:atoolforstudyingthestructureanddiffusivetransportinliquids 37
1.5.4 Inelasticscatteringoflightinliquids 40
1A Appendix-Transportcoefficientsinfluids 42
2 MomentumTransportUnderVariousFlowConditions 43
2.1 Diffusiveandconvectivetransportofmomentuminflowingfluids 43
2.1.1 Diffusionandconvectionofmomentum:twoillustrativeexperiments 43
2.1.2 Momentumtransportinashearflow–introductionoftheviscosity 45
2.2 Microscopicmodelsoftheviscosity 48
2.2.1 Viscosityofgases 48
2.2.2 Viscosityofliquids 49
2.2.3 Numericalsimulationofmoleculartrajectoriesinaflow 51
2.3 Comparisonbetweendiffusionandconvectionmechanisms 52
2.3.1 TheReynoldsnumber 52
2.3.2 Convectiveanddiffusivemass,orthermalenergy,transport 53
2.4 Descriptionofvariousflowregimes 55
2.4.1 Flowsinacylindricaltube:Reynolds’experiment 56
2.4.2 Variousflowregimesinthewakeofacylinder 57
2.4.3 Flowbehindasphere 58
viii Contents
3 KinematicsofFluids 60
3.1 Descriptionofthemotionofafluid 60
3.1.1 Characteristiclinearscalesandthehypothesisofcontinuity 60
3.1.2 EulerianandLagrangiandescriptionsoffluidmotion 61
3.1.3 Accelerationofaparticleoffluid 61
3.1.4 Streamlinesandstream-tubes,trajectoriesandstreaklines 63
3.2 Deformationsinflows 64
3.2.1 Localcomponentsofthevelocitygradientfield 64
3.2.2 Analysisofthesymmetriccomponentoftherateofstraintensor:purestrain 65
3.2.3 Antisymmetriccomponentofthetensoroftherateofdeformation:purerotation 68
3.2.4 Application 70
3.2.5 Caseoflargedeformations 71
3.3 Conservationofmassinamovingfluid 72
3.3.1 Equationfortheconservationofmass 73
3.3.2 Conditionforanincompressiblefluid 73
3.3.3 Rotationalflows;potentialflows 75
3.4 Thestreamfunction 75
3.4.1 Introductionandsignificanceofthestreamfunction 75
3.4.2 Streamfunctionsfortwo-dimensionalflows 77
3.4.3 Streamfunctionsforaxiallysymmetricflows 79
3.5 Visualizationandmeasurementofthevelocityandofthevelocitygradientsinflows 80
3.5.1 Visualizationofflows 81
3.5.2 Concentrationmeasurements 83
3.5.3 Afewmethodsformeasuringthelocalvelocityinafluid 83
3.5.4 Measurementsofthevelocityfieldandofvelocity–gradientsinaflowingfluid 86
4 Dynamicsofviscousfluids:rheologyandparallelflows 90
4.1 Surfaceforces 90
4.1.1 Generalexpressionforthesurfaceforces:stressesinafluid 90
4.1.2 Characteristicsoftheviscousshearstresstensor 92
4.1.3 Theviscousshear-stresstensorforaNewtonianfluid 93
4.2 Equationofmotionforafluid 95
4.2.1 Generalequationforthedynamicsofafluid 95
4.2.2 Navier–StokesequationofmotionforaNewtonianfluid 97
4.2.3 Euler’sequationofmotionforanidealfluid 97
4.2.4 DimensionlessformoftheNavier–Stokesequation 98
4.3 Boundaryconditionsforfluidflow 98
4.3.1 Boundaryconditionatasolidwall 98
4.3.2 Boundaryconditionsattheinterfacebetweentwofluids:surfacetensioneffects 99
4.4 Non-Newtonianfluids 101
4.4.1 Measurementofrheologicalcharacteristics 101
4.4.2 Time-independentnon-Newtonianfluids 102
4.4.3 Non-Newtoniantime-dependentfluids 106
4.4.4 Complexviscosityandelasticityofviscoelasticfluids 108
4.4.5 Anisotropicnormalstresses 111
4.4.6 Elongationalviscosity 113
4.4.7 Summaryoftheprincipalkindsofnon-Newtonianfluids 114
4.5 One-dimensionalflowofviscousNewtonianfluids 115
4.5.1 Navier–Stokesequationforone-dimensionalflow 115
Contents ix
4.5.2 Couetteflowbetweenparallelplanes 116
4.5.3 Poiseuille-typeflows 117
4.5.4 Oscillatingflowsinaviscousfluid 120
4.5.5 Parallelflowresultingfromahorizontaldensityvariation 124
4.5.6 CylindricalCouetteflow 125
4.6 Simpleone-dimensional,steadystateflowsofnon-Newtonianfluids 127
4.6.1 Steady-stateCouetteplaneflow 128
4.6.2 One-dimensionalflowbetweenfixedwalls 128
4.6.3 Velocityprofilesforsimplerheologicalbehavior 130
4.6.4 Flowofaviscoelasticfluidnearanoscillatingplane 132
4A Appendix-Representationoftheequationsoffluidmechanicsindifferentsystemsofcoordinates 134
4A.1 Representationofthestress-tensor,theequationofconservationofmassandtheNavier–Stokes
equationsinCartesiancoordinates(x,y,z) 134
4A.2 Representationofthestress-tensor,theequationofconservationofmass,andtheNavier–Stokes
equationsincylindricalcoordinates(r,ϕ,z) 134
4A.3 Representationofthestress-tensor,theequationofconservationofmass,andtheNavier–Stokes
equationsinsphericalpolarcoordinates(r,θ,ϕ) 135
Exercises 136
5 ConservationLaws 138
5.1 Equationofconservationofmass 138
5.2 Conservationofmomentum 139
5.2.1 Thelocalequation 139
5.2.2 Theintegralexpressionofthelawofconservationofmomentum 139
5.3 Theconservationofkineticenergy;Bernoulli’sEquation 142
5.3.1 Theconservationofenergyforaflowingincompressiblefluidwithorwithoutviscosity 143
5.3.2 Bernoulli’sequationanditsapplications 146
5.3.3 ApplicationsofBernoulli’sequation 147
5.4 Applicationsofthelawsofconservationofenergyandmomentum 152
5.4.1 Jetincidentontoaplane 152
5.4.2 Exitjetfromanopeninginareservoir 154
5.4.3 Forceonthewallsofanaxiallysymmetricconduitofvaryingcross-section 157
5.4.4 Liquidsheetsofvaryingthickness:thehydraulicjump 158
Exercises 164
6 PotentialFlow 166
6.1 Introduction 166
6.2 Definitions,propertiesandexamplesofpotentialflow 167
6.2.1 Characteristicsandexamplesofvelocitypotentials 167
6.2.2 Uniquenessofthevelocitypotential 168
6.2.3 Velocitypotentialsforsimpleflowsandcombinationsofpotentialfunctions 170
6.2.4 Examplesofsimplepotentialflows 174
6.3 Forcesactingonanobstacleinpotentialflow 180
6.3.1 Two-dimensionalflows 181
6.3.2 Addedmasseffectsforathree-dimensionalbodyundergoingaccelerationinanidealfluid 184
6.4 Linearsurfacewavesonanidealfluid 187
6.4.1 Swell,ripplesandbreakingwaves 187
6.4.2 Trajectoriesoffluidparticlesduringthepassageofawave 191
6.4.3 Solitons 192
6.4.4 Anotherexampleofpotentialflowinthepresenceofaninterface:theTaylorbubble 193