工程流体力学英文版第七章pdf_.pdf
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Chapter7SimilitudeandDimensionalAnalysis?
Similitude:
HowtodesignexperimentalmodelModelPrototype(similitudeoffluidmotion)Dimensionalanalysis:
Howtooperateanexperimentandanalysisexperimentaldate)Preface1.Whatissimilitudeandwhatisdimensionalanalysis?
a.TheneedfordevelopingFluidMechanicsFM:
TheoreticalFMExperimentalFMComputationalFMb.Theneedofengineeringpractice2.Whyneedwestudy?
1.DynamicSimilitudeofFluidMotion?
2.SimilitudePrinciples?
3.DimensionalAnalysis,RayleighMehtod,Buchingham?
Method?
4.ModelExperiment3.Contents:
?
1.DynamicSimilitudeofFluidMotionDynamicSimilitudeofFluidMotion:
Atanytime,alltheparametersofthemodelandprototypeareinthesameratiothroughouttheentireflowfield:
Geometricsimilitude(basic)Motionsimilitude(result)Dynamicsimilitude(condition)prototypemodel1.Geometricsimilitude(basicandthemostobviousrequirement)Themodelisanexactgeometricreplicaoftheprototype.Allthelineardimensionsofthemodelandprototypeareinthesameratioscaleratiobetweenmodelandprototype1212lmmmlldClld=prototypemodelscaleratio:
ratioofarea:
ratioofvolume:
1212lmmmlldClld=222AlmmAlCCAl=333lmmlCCl=prototypemodel2.MotionSimilitude(result)Velocityofthemodelandtheprototypeareinthesameratiothroughouttheentireflowfield.ratioofvelocity312123VmmmVVVCVVV=prototypemodelratiooftime:
ltmmmVCVltCVltC=ratioofacceleration:
ratioofvolumerate:
ratioofkinematicviscosity:
ratioofrotation:
lVmmmtCltVCVltC=2VVammmtlCCVtaCaVtCC=3323lQlVmtmmCltQCCCQClt=222llVmtmmCltCCCClt=VmmmlCVlCVlC=3.Dynamicsimilitude(condition)Alltheforcesthatactoncorrespondingmassesinthemodelandtheprototypeareinthesameratiothroughouttheentireflowfield.312123FmmmFFFCFFF=prototypemodel22FmalVmmmaCCCCCCma=4.RelationshipGeometricsimilitude(basicandthemostobviousrequirement)MotionSimilitude(result)Dynamicsimilitude(condition)return?
2.SimilitudePrinciples(?
2.1NewtonSimilitudePrinciples2.2Eulernumber,Froudnumber,Reynoldsnumber,Machnumber2.1NewtonSimilitudePrinciplesOr:
DynamicSimilitudeNeequals22FlVmmmmmmVtmaCCCCmaVt=221FlVCCCC=2222mmmmFFNelVlV=2.2Eulernumber,Froudnumber,Reynoldsnumber,Machnumber22FNelV=()2222plpEulVV=22FNelV=()()2pFpApl=3gFmgglg=1.SimilitudePrincipleofflowactedbypressureforcePressureforce?
22mmmppEuVV=2.SimilitudePrincipleofflowactedbygravityGravity:
mmmVVFrglgl=Eulernumber:
Froudnumber:
22FNelV=RemmmmVlVl=22mmmVVCaEE=2dddduuFAAlyy?
=?
2sFEAEl=Viscousforce?
3.SimilitudePrincipleofflowactedbyviscousforce4.SimilitudePrincipleofflowactedbyelasticforceElasticforce?
aE=2222VVCaaa=()12VMCaa=Reynoldsnumber:
Forfluid:
2Ea=Machnumber:
?
3.DimensionalAnalysisDimension:
UnittypesofphysicalvariablesFundamentaldimension:
thedimensionoftimeT(hour,minute,second)thedimensionoflengthL(m,cm,mm)thedimensionofmassM(ton,kilogram,gram)thedimensionoftemperature?
(oC,K)1.PrincipleofidenticaldimensionsforphysicalequationsDeriveddimension:
velocity:
LT-1acceleration:
LT-2density:
ML-3force:
MLT-2pressure:
ML-1T-2dynamicviscosity:
ML-1T-1kinematicviscosity:
L2T-1HgVgpZ=+22LLLLPrincipleofidenticaldimensionsforphysicalequations:
Aprocessinvolves:
y,x1,x2,x3,xnTherelationshipbetweenyandy,x1,x2,x3,xncanbeexpressed:
example2.IndicialMehtod(RayleighMethod)312123.aaaannykxxxx=Thenumberofindependentdimensionlessgroupsofvariablesneededtocorrelatethevariablesinagivenprocessisequalton-m,wherenisthenumberofvariablesinvolvedandmisthenumberdimensionsincludedinthevariables.example3.BuckinghamMethod(groupMethod)()123,0nxxxx=()123,0mf=312123.iiaaaamimiiixxxxx+=?
4.ModelexperimentGeometricsimilitude(basic)Motionsimilitude(result)Dynamicsimilitude(condition)Similitudeofinitialandboundaryconditionprototypemodel1.ConditionofSimilitudeOnetypeofflowGeometricsimilitudeSimilitudeofinitialandboundaryconditionThesamesimilitudedimensionlessnumberdifficult:
a.Geometricsimilitude=LLDD2.Howtodesign:
b.Thesamesimilitudedimensionlessnumber(Fr,Re,Eu,Ca,Ma)Re=LVVLLgVgLV=if=,kkLV1=gg=Generally:
1/2VLkk=1=kkLV?
=1=kkkLV12/1=kkkLL2/3kkL=if101=kL,6231110123.k/v=?
=*themostimportantforce(dimensionlessnumber)*laminarorcompleteturbulenceroughzone3.Modelexperiment