Introdukční PRINCIPLES
AsmanyMechanicalProblemSaredifficultToSlollosovebyMathematicaltHods, oni mustestuDiedThroughExperiments.TheDiRectExperimentalMethodhasgreatlimatitace však.ExperimentálníresultsareonlyApplicableTecoreCecificConditionSandarenotoFuniversalssignicance.Proto, dokonce ifTheCostishuge, itisdifficultToreVealhysicalNatureofThePhenomenoNanddescreatherelationshipBetweenthevariousquanties.Regularlationship.ThereMeranyphenomeNathatatarenotsuitablefordFirecTexperimentation.Forexample,theairplaneistoolargetodirectlystudytheflightproblemoftheairplaneprototypeinthewindtunnel;andtheprototypeoftheinsectistoosmalltoconductdirectexperimentsinthewindtunnel;besides,directexperimentationThemethodcanonlyderivetheregularrelationshipbetweenindividualquantities,anditisdifficulttograsptheessenceofthephenomenon.WepreferTosereDereDiredplaneModelsOrenLargedInSectModelsforresearch.Thenthequestionwearemostconcernedaboutiswhetherthephysicalphenomenondescribedfromtheexperimentalresultsofthemodelcantrulyreproducetheoriginalphysicalphenomenon?Iftheaccuratequantitativedataobtainedfromthemodelexperimentcanaccuratelyrepresenttheflowphenomenonofthecorrespondingprototype,thefollowingpodobnýitiesmustbesatisfiedbetweenthemodelandtheprototype.
Přehled podobnosti
(1)Geometricpodobnýity
GeometricIlilarityMeansThatthemodelhasthesameshapeasitsprototype, butthesizecanberifferent, allcoreresponspondingLineardimensionsionsionsionsAProportional.Thelineardimensionsherecanbediameter, délka, drsnost atd..IfThesubscriptsPandMareusedSorePresentThototypeandthemodelreslesive, pak
TheLinearProportionConstantCanBeexpresseDascl = LP/LM
TheAreaPorportionConstantcanBeexpressAsca = ap/am = cl^2
TheVolumeratioConstantCanBeexpresseDassv = VP/VM = cl^3
(2)Similarmotion
Similarmotionmeansthatfordifferentflowphenomena,thecorrespondingvelocityandaccelerationdirectionsatallcorrespondingpointsintheflowfieldareconsistent,Andtheratiosareequal,thatistosay,twoflowswithpodobnýmotion,theirstreamlinesandflowspectraaregeometricallypodobný.
ThespeedProportionalCanBeexpresseDassv = VP/VM;
SinCethedimensionOftimeIsl/V, thetimeProportionConstantisct = tp/tm = (lp/vp)/(lm/vm) = cl/cv
TheAccelerationProportionConstantca = AP/AM = CV/CT = CI/CT^2
(3)PowerpodobnýityPowerpodobnýitymeansthatthevariousforcesactingondifferentflowphenomenaatcorrespondingpositionsonthefluid,Forexample,gravity,pressure,viscousforce,elasticforce,etc.,theirdirectionscorrespondtothesame,andtheratioofmagnitudesisequal,thatistosay,twoflowswithpodobnýdynamics,theforcepolygonformedbyeachforceactingatthecorrespondingpositiononthefluidisgeometricpodobný.
Obecně řečeno, TheForcesActingonthefluidelemenTinCludeGravityfg, Putypp, Viscousforcefv, ElasticforceFeandsurfacetensionft.IfThefluidismingingataCceleration (zpomalení), afterdingtheInTialForcefi, Theaboveforceswillformforcepolygon, sofg+fp+fv+fe+ft+fi = 0.
Samozřejmě, inmanypracticalproblems, theabove-intentiomedforcesarenotequally imrpartment.NěkdyssomeforcesMayNotexistoraresosmalltheyareneglobible, takové, ashowninthefigure.IfintWoflowPhenomenasatissinggeometricalpodobnýityandsiMiMiLarmotion, theForcesActingonanyfluidelementarefg, fp, fv, fi atd. Atd.., pak, ifthesForceMeetTheFollingConditions, thetwophenomenaaresaidtobedynamics.podobný.
ThePowerPorportionConstantCanBeexpressedas: CF = FGP/FGM = FPP/FPM = FVP/FVM = FIP/FIM =…
Whentheabovepodobnýconditionsaremet,twoflowphenomena(Orflowfield)ispodobnýinmechanics.Amongthethreepodobnýconditions,geometricpodobnýityistheprerequisiteandbasisformotionpodobnýityanddynamicpodobnýity,dynamicpodobnýityistheleadingfactorofflowpodobnýity,andmotionpodobnýityisonlyarepresentationofgeometricpodobnýityanddynamicpodobnýity;thethreearecloselyrelated,andoneismissing.Nemožné.
Kritérium podobnosti
Intheory, AnyflowiSuniquelyderindedBytheBasicferentiaLequationtheControlstHeflowandThoreDorespondingolutionConditions.Fortwopodobnýflowphenomena,inordertoensurethattheyfollowthesameobjectivelaw,theirdifferentialequationsshouldbethesame.Thisisageneralsolutionforpodobnýflows;inaddition,aspecificsolutionforaspecificflowisrequired,anditssingle-valuedconditionmustalsoberequired.podobnost.TheuniqueConditionSInclude:
(1)Initialconditions,whichrefertothedistributionofphysicalquantitiessuchasflowvelocityandpressureatthebeginningoftheunsteadyflowproblem;Thisconditionisnotrequiredforsteadyflow.
(2)Boundaryconditions,refertothephysicalquantitiessuchasflowvelocityandpressureontheboundaryofthestudiedsystem(suchasinlet,outletandwall,etc.)Rozdělení.
(3)Geometricconditions,refertothegeometricshape,positionandsurfaceroughnessofthesystemsurface.
(4)Physicalconditions,refertothetypeandphysicalpropertiesofthefluidinthesystem,suchasdensity,viscosity,etc.
Therefore,ifthetwoflowsarepodobný,theyareconsideredasthesingularityconditions.TheratiooftheInTialForceActingonthetwosystemstothetrotherForcessHouldBecordinglyedlyplyal.Inthefluidmechanicsproblem,ifthereareallthesixforcesmentionedabove,andthedynamicsarepodobný,theproportionsofthefollowingforcesmustbeequal.
TheratiooFinerTialForcetopressure (Orpressuredurediferife): Fi/FP
TheratioofinerTialForcetogravita: Fi/FG
Poměr inerciální síly a síly tření: pro/TV
TheratioofinerTialForceelasticforce: fi/fe
Poměr inerciální síly k povrchu napětí: to/ft
TheaboveFiveformresrespectivelectivelyInntroducefidemensionlessNessnumbers, které jsou uvedeny:
1)EulernumberEu=2Δp/(ρ·V^2),forexample,laterOftenusedtoexpressthepressurecoefficientofthesurfacepressuredistribution,aswellastheliftcoefficientanddragcoefficient.Fyzicky, Euler'sNumberrepresentsThemagnituderatiobetweentheinertialForceandthepressureGradiant.
2)FroudenumberFr=V/sqrt(l·g),inphysics,Froudenumberrepresentsthemagnituderatiobetweeninertialforceandgravity,Isadimensionlessquantitythatcharacterizestheflowrate.
3)ReynoldsnumberRe=Vl/υ,inphysics,theReynoldsnumberrepresentsthemagnituderatiobetweentheinertialforceandtheviscousforceinapodobnýflow,theflowRenumberSmall,meansthatthemagnitudeofviscousfrictionismuchlargerthanthatofinertialforce,sotheeffectofinertialforcecanbeignored;conversely,alargeRenumbermeansthatinertialforceplaysamajorrole,soitcanberegardedasnon-viscousFluidhandling.
4)MachnumberMa=V/c,inphysics,Machnumberrepresentsthemagnituderatiobetweeninertialforceandelasticforce,andisameasureofgascompressibility,Usuallyusedtoindicatetheflyingspeedoftheaircraftortheflowspeedoftheairflow.
5)WebernumberWe,physically,theWebernumberrepresentsthemagnituderatiobetweeninertialforceandsurfacetension.
ItcanbeseenthatEu,Fr,Re,MaandWearealldimensionlessnumbers,whicharecalledpodobnýitycriterionorpodobnýitycriterioninthepodobnýitytheory.b>,theyarethebasisforjudgingwhethertwophenomenaarepodobný.Therefore,forphenomenathatarepodobnýtoeachother,thevalueofthepodobnýitycriterionofthesamenamemustbeequal.Conversely,iftwoflowingsingle-valueconditionsarepodobný,andthevaluesofthepodobnýitycriteriaofthesamenamecomposedofsingle-valuedconditionsareequal,thetwophenomenamustbepodobný.
Detailedpodobnýityprinciple
Thefirsttheoremofpodobnýity
Twopodobnýflowphenomenabelongtothesametypeofphysicalphenomenon,andtheyshouldDescribedbythesamemathematicalandphysicalequations.TheGeometricconditionSofTheflowfenomenon (TheBoundaryshapeandsizeofTheflowfield), fyzikální kondice (tekuta, viskozita atd..), hranice (distribucephysicalquantitiesStheflowfieldBoundary, takové distribuce, tlak atd..)Thereareinitialconditions(thephysicalquantitydistributionateachpointintheflowfieldattheinitialtimeoftheselectedstudy)mustbepodobný.TheSeconditionSareCollectivelyReferredToAslAslValueConditions.Asmentionedabove,thetwoflowphenomenaaremechanicallypodobný,andthephysicalquantitiesatthecorrespondingpointsinspaceandthecorrespondinginstantaneousphysicalquantitiesareincertainproportionstoeachother,andthesephysicalquantitiesmustsatisfythesamedifferentialequations.Proto je protokortionalcoefficientiesfthequantitiesaresiMilarMultriplescannotbearbitrary, butrestrictotherotherother.
Tosumup,theconclusioncanbedrawn:Physicalphenomenathatarepodobnýtoeachothermustobeythesameobjectivelaws.Ifthelawscanbeexpressedbyequations,thephysicalequationsmustbeexactlythesameandcorrespondingSimilarcriteriaThevaluesmustbeequal.Thisispodobnýtothefirsttheorem.Itisworthpointingoutthatthepodobnýitycriterionofaphysicalphenomenonatdifferentmomentsanddifferentspatiallocationshasdifferentvalues,whilephysicalphenomenathatarepodobnýtoeachotherhavethesamevaluepodobnýitycriterionatthecorrespondingtimeandatthecorrespondingpoint.Therefore,podobnýityThecriterionisnotconstant.
Thesecondtheoremofpodobnýity
Onlywhentheexperimentalmodelispodobnýtotheresearchobjectitsimulatescantheresultsoftheexperimentbeappliedtotheresearchobject.Tojudgewhethertwophenomenaarepodobný,itisoftenimpossibletojudgewhetherthedistributionofthephysicalquantityinthecorrespondingtimeandspacemaintainsthesameratio.Forexample,theflowfieldofamodelairplaneinawindtunnelispodobnýtotheflowfieldofanactualflyingairplane.Často často, že jsou to dojetí, které je třeba.Therefore,thetwocannotbejudgedbasedonpodobnýdefinitions.Aretheypodobný.
Twophysicalphenomenaarepodobnýandmustbethesamekindofphysicalphenomena.Proto theDifferentialequationsDescrippingphysicalphenomenamustbethesame.Thisisthefirstnecessaryconditionforpodobnýphenomena.
Similarsinglevalueconditionsarethesecondnecessaryconditionforpodobnýphysicalphenomena.Becausetherearemanypodobnýphenomenathatobeythesamedifferentialequations,single-valuedconditionscansinglelydistinguishtheresearchobjectfromcountlessmultiplephenomena.Matematicky, itisthedefinitesolutionConditionTomakeSthedifferentialequationShaveauniqueSolution.
Thepodobnýitycriterioncomposedofphysicalquantitiesinthesinglevalueconditionisequaltothephenomenonofpodobnýitythethirdnecessarycondition.
Converselyspeaking,whentheybelongtothesametypeofphysicalphenomenonandthesinglevalueconditionsarepodobný,thetwophenomenahavethecorrespondingrelationshipbetweentimeandspaceandthesamephysicalquantityconnectedwithtimeandspace.Ifthecorrespondingpodobnýitycriteriaareequal,Andmaintainthesameratioofphysicalquantitiesatthecorrespondingtimeandspacepoints,whichalsoensuresthepodobnýityofthetwophysicalphenomena.
Tosumup,podobnýconditionscanbeexpressedas:Forthesametypeofphysicalphenomenon,whensinglevaluetheconditionsarepodobnýandconsistofsinglevalueWhenthepodobnýitycriterionofthephysicalquantitycompositionintheconditioncorrespondstothesame,thenthesephenomenamustbepodobný.Thisisthesecondtheoremofpodobnýity,whichisasufficientandnecessaryconditionforjudgingwhethertwophysicalphenomenaarepodobný.
Principysandexperiments
Podobné principlessanddimensimensionAlalysisMethodshavesolvedaserieriesOfproblemSInModelexperiments.
Tocarryoutamodeltest,firstencounterhowtodesignthemodelandhowtochoosethemediumintheflowofthemodeltoensurethatitispodobnýtotheprototype(physical)flow.Accordingtothesecondtheoremofpodobnýity,thedesignmodelandtheselectionmediummustmakethesingle-valuedconditionspodobný,andthepodobnýitycriteriacomposedofthephysicalquantitiesinthesingle-valuedconditionsareequalinvalue.
Whatphysicalquantitiesneedtobemeasuredduringthetestandhowtodealwiththetestdatainordertoreflecttheobjectiveessence?Thefirsttheoremofpodobnýitystatesthatphenomenathatarepodobnýtoeachothermusthaveapodobnýitycriterionofequalvalues.Therefore,somephysicalquantitiescontainedineachpodobnýitycriterionshouldbedeterminedintheexperiment,andtheyshouldbesortedintopodobnýitycriterion.
Howtoorganizethemodeltestresultstofindtheregularity,sothatitcanbepromotedandappliedtotheprototypeflow?ItcanbeseenfromtheΠtheoremthattherelationshipbetweenvariousvariablesdescribingacertainphysicalphenomenoncanbeexpressedasarelativelysmallnumberofdimensionlessΠexpressions,andeachdimensionlessΠhasdifferentpodobnýitycriteria,andthefunctionalrelationshipbetweenthemisalsocalledIsthecriterionequation.Forphenomenapodobnýtoeachother,theircriterionequationsarealsothesame.Therefore,thetestresultsshouldbesortedintotherelationshipbetweenpodobnýcriteria,whichcanbepromotedandappliedtotheprototype.
Reynoldsnumberpodobnýitymethod
Inordertobetterexplaintheapplicationofthepodobnýityprinciple,thefollowingintroducesanapproximatemodelmethod:Reynoldsnumberpodobnýitymethod
ThereMeranyPracticalflow, theremainlyainlyAptedByvissousforce, pressureandinertialforce.Forexample,ifthefluidflowsinapipewithafullcross-section,sincethereisnofreesurface,thereisnosurfacetensioneffect,sotheWepodobnýitycriterioncanbeignored;gravitydoesnotaffecttheflowfield,sotheFrpodobnýitycriterioncanbeignored;iftheflowvelocityisverylowcomparedtothespeedofsound,Thecompressibilityeffectcanalsobeneglected,thatis,itisnotnecessarytoconsidertheMapodobnýitycriterion.TheSameistrueforthelow-SpeedairflowaroundtheObjectOrtheelasticforceonthefluidaroundesUbMarineidEepwaterandtherespondingWaterflow (thisNosurfaceWaveFormationAtThistime).
Fromthepointofviewofmechanicalpodobnýity,iftwoflowfieldshavethesamedirectionandthesamemagnitudeofforceactingonthecorrespondingpoints,thedynamicsarepodobný.Inthecaseofconsideringonlythethreeforcesofviscousforce,pressureandinertialforce,inordertomaketheforcetrianglepodobný,itonlyneedstosatisfythatthetwosidesareproportionalandtheincludedanglesareequal,thatis,theinertiaofthemodelflowatthecorrespondingpointsTheforceandtheviscousforceareinthesameproportionsastheinertialforceandtheviscousforceactingontheflowofobjects.Proto aslongasthecorespondingPointMeetsTherenoldsNumbequal.Fromamoregeneralpodobnýitytheorem,iftwoflowsarepodobný,thenumberofpodobnýitycriteriacorrespondstothesame,andthepodobnýitycriterionequationderivedfromtheΠtheoremisalsothesame.Amongthe(nk)podobnýitycriteria,(nk-1)istheindependentpodobnýitycriterion,ordecisivepodobnýitycriterion(equivalenttotheindependentvariableofthefunction),andoneisthenon-independentpodobnýitycriterionorthenon-deterministicpodobnýitycriterion(equivalenttoThedependentvariableofthefunction).OutEfLowsituationThatonlyConSidersheeffectofViscoUsforce, pressureanDinerTialforce, eynoldscriteriondotercriteriaredtoometricdimensinsionsionsionsionsionsionsionsionsionsionsionsionsionsionsionsinsionsionsionsionsionsionsionsionsionsionsionsionsionSaregardedAsIndependentCriteria a atheeulercriterianon-nezávislými třpytkami.
Underthepremiseofgeometricpodobnýity,thedecisivecriterionforpodobnýityofflowphenomenaisonlytheReynoldscriterion,andthepodobnýitythatthemodeltestmustcomplywithiscalledReynoldsphaselikeness.