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Lesson2

FluidFlow

LiQiongCollegeofArchitectureEngineeringNorthChinaInstituteofScienceandtechnologyVersion:2012-2013Content2.1Fluidproperties2.2Basicrelationsoffluid2.3BasicflowprocessLesson2

FluidFlowFlowingfluidsinHVAC&Rsystemscan

transfer

heat,massandmomentum.Thischapterintroducesthebasicsoffluidmechanicsthatare

relatedtoHVACprocess,reviewpertinent

flowprocess.Lesson2

FluidFlow2.1FluidpropertiesFluids

differfrom

solidsintheirreactiontoshearing.Whenplacedunder

shearstress,asoliddeformsonlyafiniteamount,whereasafluiddeformscontinuouslyforaslongastheshearisapplied.Lesson2

FluidFlowBothliquidsandgasesarefluids.Althoughliquidsandgasesdifferstrongly

inthenatureof

molecularactions,theirprimarymechanicaldifferencesareinthedegreeofcompressibility

andliquidformationofafreesurface

(interface)Fluidmotioncanusuallybedescribedby

oneofseveral

simplifiedmodes

ofactionormodels.Thesimplestistheideal-fluidmodel,whichassumesnoresistancetoshearing.(许多简单运行形式或模型通常可以描述流体移动.)Lesson2

FluidFlowMostfluidsinHVACapplicationscanbetreatedas

Newtonian,wheretherateofdeformation

isdirectlyproportionaltotheshearingstress.Turbulencecomplicatesfluidsbehavior,andviscosity

influencesthenatureoftheturbulentflow.Turbulence,whichcomplicatesfluidbehavior,andviscositydoestendtoinfluenceturbulence.Lesson2

FluidFlowFluidpropertiesDensity

(密度),kg/m3Thedensitiesofairandwater

atstandardindoorconditionsof20oCand101.325Pa

(sealevelatmosphericpressure)areair=1.20kg/m3 water=998kg/m3Viscosity(粘性),Ns/m2

Absoluteviscosityordynamicviscosity(绝对粘度,动力粘度)Differentialequation:Lesson2

FluidFlowThevelocitygradientassociatedwithviscousshearforasimplecaseinvolvingflowvelocityinthexdirectionbutofvaryingmagnitudeintheydirectionisillustratedinFigure1B.Lesson2

FluidFlow

Absoluteviscositydependsprimarilyontemperature.Forgases,viscosityincreaseswith

thesquarerootoftheabsolutetemperature.Liquidviscositydecreaseswith

increasingtemperature.Shearingstress(切应力),NKinematicviscosity(运动粘度),m2/sTheratioofabsoluteviscositytodensity.Velocitygradient(速度梯度)Lesson2

FluidFlow2.2

Basicrelationsoffluiddynamics

Thissectionconsidershomogeneous,

constant-property,incompressiblefluids

andintroducesfluiddynamic

considerationsusedinmostanalyses.Continuity(连续性)

ConservationofmatterappliedtofluidflowinaconduitrequiresthatLesson2

FluidFlowBothandvmayvaryoverthecrosssectionAoftheconduit.Ifbothandvareconstantoverthecross-sectionalareanormaltotheflow,thenFortheideal-fluidmodel,flowpatternsaroundbodies(orinconduitsectionchanges)resultfromplacementeffects.Anobstructioninafluidstream,suchasastrutinafloworabumpontheconduitwall,pushestheflowsmoothlyoutoftheway,sothatbehindtheobstruction,theflowbecomesuniformagain.Theeffectoffluidinertia(density)appearsonlyinpressurechanges.Lesson2

FluidFlowPressureVariationAcrossFlowPressurevariationinfluidflowisimportantandcanbeeasilymeasured.Variationacrossstreamlinesinvolvesfluidrotation(vorticity).Thisrelationexplainsthepressuredifferencefoundbetweentheinsideandoutsidewallsofabendandnearotherregionsofconduitsectionchange.Italsostatesthatpressurevariationishydrostaticacrossanyconduitwherestreamlinesareparallel.Lesson2

FluidFlowBernoulliequationandpressurevariation

alongflowAbasictooloffluidflowanalysisistheBernoullirelation,whichinvolvestheprincipleofenergyconservation

alongastreamline.Thefirstlawofthermodynamics

canbeappliedtomechanicalflowenergies(kineticandpotential)andthermalenergies:heatisaformofenergy

and

energyisconserved.Thechangeinenergycontent

Eperunitmassofflowingmaterialis

a

resultfrom

the

workWdoneonthesystemplustheheatQabsorbed:Lesson2

FluidFlow

Fluidenergyiscomposedofkinetic,potential(duetoelevationz),andinternal

(u)energies.Per

unitmassoffluid,theaboveenergychangerelationbetweentwosectionsofthesystemistheexternalworkfromafluidmachinethepressureorflowworkLesson2

FluidFlowRearranging,theenergyequationcanbewrittenasthegeneralizedBernoulliequation:Lesson2

FluidFlowLaminarflow

Forsteady,fullydevelopedlaminarflow

inaparallel-walledconduit,theshearstressvarieslinearlywith

distanceyfromthecenterlineParabolicvelocityprofile(抛物线速度分布)Lesson2

FluidFlowTurbulenceTurbulencecanbequantified

bystatisticalfactors.Thus,thevelocitymostoftenusedinvelocityprofilesisthetemporalaveragevelocity

v,andthestrengthoftheturbulence

ischaracterizedbyroot-mean-square

oftheinstantaneousvariationinvelocityaboutthismean.Theeffectsofturbulencecausethefluidtodiffusemomentum,heat,andmassveryrapidlyacrosstheflow.Lesson2

FluidFlowReynoldsnumberRe,adimensionlessquantity,givestherelativeratioofinertialtoviscousforces;Inflowthroughroundpipesandtubes,thecharacteristiclengthisthediameter.Generally,laminarflowinpipescanbeexpectediftheReynoldsnumber,whichisbasedonthepipediameter,islessthanabout2300;Lesson2

FluidFlowFullyturbulentflow

existswhenRe>10000;Between2300and10000,theflowisintransitionstate.Inothergeometries,differentcriteria

fortheReynoldsnumberexist.Lesson2

FluidFlowHydraulicdiameter(水力直径)wettedperimeterthecross-sectionalareaofthepipeLesson2

FluidFlow2.3

BasicflowprocessWallfriction(壁面摩擦力)Attheboundaryofreal-fluidflow,therelativetangentialvelocity

atthefluidsurfaceiszero;Sometimesinturbulentstudies,velocityatthewallmayappearfinite,implyingafluidslipatthewall.However,thisisnotthecase.Lesson2

FluidFlowZerovelocityleadstoahighshearstressnearthewallboundaryandaslowingdownofadjacentfluidlayers.Avelocityprofilesdevelopsnearawall,withthevelocityincreasing

fromzeroatthewalltoanexteriorvalue

withinafinitelateraldistanceLaminarandturbulentflowdiffersignificantly

intheir

velocityprofiles.Lesson2

FluidFlowTurbulentflowprofilesareflatcomparedto

themorepointedprofilesoflaminarflow.Nearthewall,velocitiesof

theturbulentprofilesmustdroptozeromorerapidlythan

thoseof

thelaminarprofile,sotheshearstressandfrictionaremuchgreaterintheturbulentflowcase.Lesson2

FluidFlowFullydevelopedconduitflow

maybecharacterizedbythe

pipefactor,whichistheratioofaverage

tomaximumvelocity.BoundarylayerInmostflows,thefrictionofaboundingwallonthefluidflowisevidencedbya

boundarylayerTheboundarylayeristheregioncloseto

thewallwher

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