粘性流體動力學wang chap1

ViscousFluidDynamics

SchoolofEnergyandPowerEngineering

Fall2015

Textbook:

《粘性流體動力學基礎》……陳懋章

“ViscousFluidFlow”……WhiteF.M.

References:

《我所理解的流體力學》……王洪偉

《湍流初級教程》……Tenneskes,Lumley

“InternalFlow-ConceptsandApplications”……GreitzerE.M.

Website:

Grades:

Assignments: 40%

Finalexam: 60%

Teachers:

陸利蓬，柳陽威，王洪偉

Schedule

Chapter1. Introduction(4hours)

Chapter2. EquationsofFlow(10hours)

Chapter3. LaminarFlow(6hours)

SolutionsofN‐SEquations(2hours);

LaminarBoundaryLayerFlow(2hours);

StabilityofLaminarFlow(2hours).

Chapter4. TurbulentFlow(14hours)

TurbulentBoundaryLayerFlow(6hours);

FreeTurbulence(2hours);

TurbulenceModeling(6hours).

SpecialTopic2

Seminar1

Seminar2

Specialtopics&Seminars

SpecialTopic1. Force,Motion,Work,andEnergy(2hours)

SpecialTopic2. Separation,DragsandLosses(2hours)

Seminar1. ExperimentsinFluids(2hours)

Seminar2. ComputationsinFluids(2hours)

Assignments

Eightassignments,5pointsforeach.

Plagiarismisstrictlyprohibited.

Theanswersmightbediversified.

Chapter1Introduction

§1.1TheTimelineofFluidMechanics

Continuityequationfor1‐Dflow.

A1V1A2V2 incompressible

Sketchesofjets,wakes,eddies…

LeonardodaVinci(1452-1519)

Inventionofthebarometer.

Causeofwind

Torricelli'sLaw

2gh

V Ifviscouseffectsarenegligible

d(mV)

EvangelistaTorricelli(1608–1647)

Lawsofmotion

F dt u

Lawsofviscosityofnewtonianfluid

Differentialcalculus

y

IsaacNewton(1642–1727) 6

Bernoulli’sequation

Euler’sequation Invisidflow

DanielBernoulli(1700–1782)

LeonhardEuler(1707–1783)

JosephLagrange1736-1813

Pierre-SimonLaplace1749-1827

Jeand'Alembert1717-1783

HenriPitot1695-1771

GiovanniVenturi1746-1822

Navier1785-1836

Cauchy1789-1857

Poisson1781-1840

Venant1797–1886

Stokes1819-1903

Navier‐Stokesequation(1845) Generalandrigorous

Boundarylayer

Notrigorous,yetuseful

Aerodynamics

Gasdynamics

LudwigPrandtl1875-1953

vonKármán1881-1963

Turbulentflow

OsborneReynolds1842-1912

LewisRichardson1881-1953

GeoffreyTaylor1886-1975

AndreyKolmogorov1903-1987

Experiment

Numericalsimulation

§1.2Viscosity

Afluidgeneratesshearstressinshearmotion,whichiscalledviscosity.

Ice Water Vapor

Allofthemgeneratesshearstressinmotion.

Connectedtightly

Connectedloosely

Notconnected

Fluidscannotgenerateshearstressinstatic.

Theshearforceinsideasolidiscalledelasticforceorplasticforce.

Theshearforcebetweentwosolidsiscalledfriction.

FN

Forliquids: Cohesion(結合力)

Similar(butnotsame)tothefrictionbetweentwosolids.

when T

Forgases: Transportofmomentum(動量輸運)

Moleculescollidewitheachother.

Doesviscosityvarywithpressureortemperature?

when T

SurfacetensionisNOTviscosity.

1(1-1) 12

Viscous

§1.3Turbulentflow FluidDynamics

ReVLVL Mainlyrefersto

turbulentviscosity.

ShearstressdoesNOTvanishwhenRegoestoinfinity.Onthecontrary,shearstressisgreatforlargeReflow.

ForlargeRe,shearstressisgeneratedmainlybyirregularmotionofflow––turbulence.

Laminarflowandturbulentflow

ReVL

Sinceviscosityissmallformostfluids,flowinrealityisalmostalwaysturbulent.

Laminar&TurbulentBoundaryLayer

Forturbulentflow:

LaminarDiffusion

TurbulentDiffusion

Re~

TimescaleofmolecularTimescaleofturbulence

§1.4ViscousEffectinFlow

Forincompressibleflows,theprimarycontrollingparameterofflowisReynoldsnumber,whichmeans:Howdoestheviscousforceinfluencetheflow?

Exampl

5 7 V2

Re10 ~10 1%~5%L 1%

2

Evenforturbulentflow,shearstressismuchsmallerthanpressureinhighRe.Therefore,viscouseffectcanbeneglectedforsomecase.

Increasingangleofattack

Exam

Re4000

TheKarmanvortexstreet

St