Theintroductionofprinciples
Asmanymekaaniset tiedotusvälineet.Kuiten.The ExperimentalResultSareOnlyApplicableToCertSpecificConditionSandarenoTofuniversalsificance.Siksi jopa, että itisdiffultoreVealthEphysicalNaturefenomenononanandDescribetherelationshipBetweventHeVariousquanties.Säännöllinen suhteet.ThereArtemanphenomenethatarenotsuctablefordirectexperimentation.Faresxample, theairplaneistoolargeToDirectlyStudeThEflightProblemofTheAirLaneProTypeNewindTUnNel;.WePreferTousedceDAirPlanemodelSorenlargeDInSectModelSForResearch.Thenthequestionwearemostconcernedaboutiswhetherthephysicalphenomenondescribedfromtheexperimentalresultsofthemodelcantrulyreproducetheoriginalphysicalphenomenon?Iftheaccuratequantitativedataobtainedfromthemodelexperimentcanaccuratelyrepresenttheflowphenomenonofthecorrespondingprototype,thefollowingsamanlainenitiesmustbesatisfiedbetweenthemodelandtheprototype.
Samankaltaisuuskatsaus
(1)Geometricsamanlainenity
Geometriset samanlaisuusmuodot, ettäThemodelhasthesameshapeAsitsprototyyppi, butthesizecanbebefferent, andallcorrespondinglineardimensionsarproportionals.Thelinedimensionsherekanbediametri, pituus, karheus jne.Jos
Thelineaariset suhteet
TheareaproportionalconstantCanbeexpresseDasca = ap/am = cl^2
ThevolumeratioConstantCanbeexpresseDascv = vp/vm = cl^3
(2)Similarmotion
SimilarmotionMeansThatfordifferentFlowfenomena, vastaava vastaava jaAccelerationDirectionsAtAllCorResponingpointSintheflowfieldareconsistent, andtheratiosareequal, se, joka on twoflowswithsamanlainenmotion, heidän streamlinesandLinedflowspocraaregeomethersamanlainent..
ThespeedProportionalConstantCanbeexPresseDascv = VP/VM;
SininediDIimensionOftTimeisl/V, theTimeproportionalConstantisct = tp/tm = (lp/vp)/(lm/vm) = cl/cv
TheaccelationProportionalConstantCa = Ap/Am = cv/ct = ci/ct^2
(3)PowersamanlainenityPowersamanlainenitymeansthatthevariousforcesactingondifferentflowphenomenaatcorrespondingpositionsonthefluid,Forexample,gravity,pressure,viscousforce,elasticforce,etc., heidän directionscorrespondTothesame, ja valmistaja, jotka ovat twoflowswithsamanlainendynamics, theforcepolygonformedbyeachforceactingthecorrespestionpositiononthefluidisgeometricsamanlainen.
Yleisesti ottaminen, forcesactingonthefluidElementCleagravityfg, painePPP, ViscousforceFV, ElasticForceFeandsUrfaceSentenstTht.IfthefluidismonvingAtaccelation (hidastuvuus), jälkikäteenTheinertialforcefi, theaboveforcesWillFormForMaforcePolygon, SOFG+FP+FV+Fe+Ft+Fi = 0.
Tietysti, inmanypracticalproblems, Theabove-MagnedForcesarenoTequalyScortTant.SomeimessomeforcesMaynotexistoraresosmallthattheyareneglicheo, Suchasfeandft, AsshownThefigure.IftwoflowfenomenasasfyinggeometricalSimilemilementArefg, fp, fv, fi, fi, jne.., sitten, josFeSeforcesMeetthefollowingConditions, thetwofenomenaAaresAidTobedynamics.samanlainen.
POWERPROPORTALCONSTANTCANBEEXPRESTEDAS: CF = FGP/FGM = FPP/FPM = FVP/FVM = FIP/FIM =…
Whentheabovesamanlainenconditionsaremet,twoflowphenomena(Orflowfield)issamanlaineninmechanics.Amongthethreesamanlainenconditions,geometricsamanlainenityistheprerequisiteandbasisformotionsamanlainenityanddynamicsamanlainenity,dynamicsamanlainenityistheleadingfactorofflowsamanlainenity,andmotionsamanlainenityisonlyarepresentationofgeometricsamanlainenityanddynamicsamanlainenity;thethreearecloselyrelated,andoneismissing.Ei mahdollista.
Samankaltaisuuskriteeri
Inteory, AnyflowisUniquelyDeterMedByTheBasicDifferentialEquation,.Fortwosamanlainenflowphenomena,inordertoensurethattheyfollowthesameobjectivelaw,theirdifferentialequationsshouldbethesame.Thisisageneralsolutionforsamanlainenflows;inaddition,aspecificsolutionforaspecificflowisrequired,anditssingle-valuedconditionmustalsoberequired.samankaltaisuus.NämäUniquEconditions sisältää:
(1)Initialconditions,whichrefertothedistributionofphysicalquantitiessuchasflowvelocityandpressureatthebeginningoftheunsteadyflowproblem;Thisconditionisnotrequiredforsteadyflow.
(2)Boundaryconditions,refertothephysicalquantitiessuchasflowvelocityandpressureontheboundaryofthestudiedsystem(suchasinlet,outletandwall,etc.) Jakauma.
(3)Geometricconditions,refertothegeometricshape,positionandsurfaceroughnessofthesystemsurface.
(4)Physicalconditions,refertothetypeandphysicalpropertiesofthefluidinthesystem,suchasdensity,viscosity,etc.
Therefore,ifthetwoflowsaresamanlainen,theyareconsideredasthesingularityconditions.TheratioftheInertialforceactingonthetwosystemsTheotherforcessHeuldBecorrespest Equal -arvoinen.Inthefluidmechanicsproblem,ifthereareallthesixforcesmentionedabove,andthedynamicsaresamanlainen,theproportionsofthefollowingforcesmustbeequal.
TheratioofinertialForcetoPressure (Orpressuredifference): FI/FP
Theratioofinertialforcetogravity: fi/fg
Inertiaalisen voiman ja kitkavoiman suhde: for/TV: lle
TheratioofinertialforceeelasticForce: fi/fe
Inertiaalisen voiman suhde pintajännitykseen:/ft
TheaboveFiveFormulasRespectiveSInTroDuceFiveDIntensionNernNumbers, Whatareinorder:
1)EulernumberEu=2Δp/(ρ·V^2),forexample,laterOftenusedtoexpressthepressurecoefficientofthesurfacepressuredistribution,aswellastheliftcoefficientanddragcoefficient.Fyysisesti euler'snumberResentsTheMagnituderatiobetweentheinertialforceandhepressuregradient.
2)FroudenumberFr=V/sqrt(l·g),inphysics,Froudenumberrepresentsthemagnituderatiobetweeninertialforceandgravity,Isadimensionlessquantitythatcharacterizestheflowrate.
3)ReynoldsnumberRe=Vl/υ,inphysics,theReynoldsnumberrepresentsthemagnituderatiobetweentheinertialforceandtheviscousforceinasamanlainenflow,theflowRenumberSmall,meansthatthemagnitudeofviscousfrictionismuchlargerthanthatofinertialforce,sotheeffectofinertialforcecanbeignored;conversely,alargeRenumbermeansthatinertialforceplaysamajorrole,soitcanberegardedasnon-viscousFluidhandling.
4)MachnumberMa=V/c,inphysics,Machnumberrepresentsthemagnituderatiobetweeninertialforceandelasticforce,andisameasureofgascompressibility,Usuallyusedtoindicatetheflyingspeedoftheaircraftortheflowspeedoftheairflow.
5)WebernumberWe,physically,theWebernumberrepresentsthemagnituderatiobetweeninertialforceandsurfacetension.
ItcanbeseenthatEu,Fr,Re,MaandWearealldimensionlessnumbers,whicharecalledsamanlainenitycriterionorsamanlainenitycriterioninthesamanlainenitytheory.b>,theyarethebasisforjudgingwhethertwophenomenaaresamanlainen.Therefore,forphenomenathataresamanlainentoeachother,thevalueofthesamanlainenitycriterionofthesamenamemustbeequal.Conversely,iftwoflowingsingle-valueconditionsaresamanlainen,andthevaluesofthesamanlainenitycriteriaofthesamenamecomposedofsingle-valuedconditionsareequal,thetwophenomenamustbesamanlainen.
Detailedsamanlainenityprinciple
Thefirsttheoremofsamanlainenity
Twosamanlainenflowphenomenabelongtothesametypeofphysicalphenomenon,andtheyshouldDescribedbythesamemathematicalandphysicalequations.TheGeometricConditionsOftHeflowfenomenon (theboundaryShapeandsizeftheflowfield), fyysiset ehdot (fluiddensiteetti, viskositeetti jne..), rajakonnedit (jakelufysikaalisetquantitiesontheflowfieldboundary, subasevelocityDistribution, painostuksen jakelu jne..)Thereareinitialconditions(thephysicalquantitydistributionateachpointintheflowfieldattheinitialtimeoftheselectedstudy)mustbesamanlainen.TheseconditionSareCollectiivisesti.Asmentionedabove,thetwoflowphenomenaaremechanicallysamanlainen,andthephysicalquantitiesatthecorrespondingpointsinspaceandthecorrespondinginstantaneousphysicalquantitiesareincertainproportionstoeachother,andthesephysicalquantitiesmustsatisfythesamedifferentialequations.Siksi suhteettomat käsittely-.
Tosumup,theconclusioncanbedrawn:Physicalphenomenathataresamanlainentoeachothermustobeythesameobjectivelaws.Ifthelawscanbeexpressedbyequations,thephysicalequationsmustbeexactlythesameandcorrespondingSimilarcriteriaThevaluesmustbeequal.Thisissamanlainentothefirsttheorem.Itisworthpointingoutthatthesamanlainenitycriterionofaphysicalphenomenonatdifferentmomentsanddifferentspatiallocationshasdifferentvalues,whilephysicalphenomenathataresamanlainentoeachotherhavethesamevaluesamanlainenitycriterionatthecorrespondingtimeandatthecorrespondingpoint.Therefore,samanlainenityThecriterionisnotconstant.
Thesecondtheoremofsamanlainenity
Onlywhentheexperimentalmodelissamanlainentotheresearchobjectitsimulatescantheresultsoftheexperimentbeappliedtotheresearchobject.Tojudgewhethertwophenomenaaresamanlainen,itisoftenimpossibletojudgewhetherthedistributionofthephysicalquantityinthecorrespondingtimeandspacemaintainsthesameratio.Forexample,theflowfieldofamodelairplaneinawindtunnelissamanlainentotheflowfieldofanactualflyingairplane.Usein vainTheAncomingFlowvelocityintHefarfrontOftHEAIRPLANEISKNOWNOWN, BUTHEFLOWFIELDILTIONTIONNEARTHEAIRPLANEISNOTNOTTON.Therefore,thetwocannotbejudgedbasedonsamanlainendefinitions.Aretheysamanlainen.
Twophysicalphenomenaaresamanlainenandmustbethesamekindofphysicalphenomena.Siksi TheDifferentialEquationsDescripfysicalfenomenamustbethesame.Thisisthefirstnecessaryconditionforsamanlainenphenomena.
Similarsinglevalueconditionsarethesecondnecessaryconditionforsamanlainenphysicalphenomena.Becausetherearemanysamanlainenphenomenathatobeythesamedifferentialequations,single-valuedconditionscansinglelydistinguishtheresearchobjectfromcountlessmultiplephenomena.Matemaattisesti ItSTheDefinitesolutionConditionHatmaKestheDifferentialEquationsHaveaUniquesolution.
Thesamanlainenitycriterioncomposedofphysicalquantitiesinthesinglevalueconditionisequaltothephenomenonofsamanlainenitythethirdnecessarycondition.
Converselyspeaking,whentheybelongtothesametypeofphysicalphenomenonandthesinglevalueconditionsaresamanlainen,thetwophenomenahavethecorrespondingrelationshipbetweentimeandspaceandthesamephysicalquantityconnectedwithtimeandspace.Ifthecorrespondingsamanlainenitycriteriaareequal,Andmaintainthesameratioofphysicalquantitiesatthecorrespondingtimeandspacepoints,whichalsoensuresthesamanlainenityofthetwophysicalphenomena.
Tosumup,samanlainenconditionscanbeexpressedas:Forthesametypeofphysicalphenomenon,whensinglevaluetheconditionsaresamanlainenandconsistofsinglevalueWhenthesamanlainenitycriterionofthephysicalquantitycompositionintheconditioncorrespondstothesame,thenthesephenomenamustbesamanlainen.Thisisthesecondtheoremofsamanlainenity,whichisasufficientandnecessaryconditionforjudgingwhethertwophysicalphenomenaaresamanlainen.
Periaatteet
SamankaltaisetPrinciplesandDimensismymethodShavesolveDaseriesOfproblemsInModelexperiments.
Tocarryoutamodeltest,firstencounterhowtodesignthemodelandhowtochoosethemediumintheflowofthemodeltoensurethatitissamanlainentotheprototype(physical)flow.Accordingtothesecondtheoremofsamanlainenity,thedesignmodelandtheselectionmediummustmakethesingle-valuedconditionssamanlainen,andthesamanlainenitycriteriacomposedofthephysicalquantitiesinthesingle-valuedconditionsareequalinvalue.
Whatphysicalquantitiesneedtobemeasuredduringthetestandhowtodealwiththetestdatainordertoreflecttheobjectiveessence?Thefirsttheoremofsamanlainenitystatesthatphenomenathataresamanlainentoeachothermusthaveasamanlainenitycriterionofequalvalues.Therefore,somephysicalquantitiescontainedineachsamanlainenitycriterionshouldbedeterminedintheexperiment,andtheyshouldbesortedintosamanlainenitycriterion.
Howtoorganizethemodeltestresultstofindtheregularity,sothatitcanbepromotedandappliedtotheprototypeflow?ItcanbeseenfromtheΠtheoremthattherelationshipbetweenvariousvariablesdescribingacertainphysicalphenomenoncanbeexpressedasarelativelysmallnumberofdimensionlessΠexpressions,andeachdimensionlessΠhasdifferentsamanlainenitycriteria,andthefunctionalrelationshipbetweenthemisalsocalledIsthecriterionequation.Forphenomenasamanlainentoeachother,theircriterionequationsarealsothesame.Therefore,thetestresultsshouldbesortedintotherelationshipbetweensamanlainencriteria,whichcanbepromotedandappliedtotheprototype.
Reynoldsnumbersamanlainenitymethod
Inordertobetterexplaintheapplicationofthesamanlainenityprinciple,thefollowingintroducesanapproximatemodelmethod:Reynoldsnumbersamanlainenitymethod
Kohdepracticalflow, HeReMainyAffectedByviscousforce, PressureanDinertialForce.Forexample,ifthefluidflowsinapipewithafullcross-section,sincethereisnofreesurface,thereisnosurfacetensioneffect,sotheWesamanlainenitycriterioncanbeignored;gravitydoesnotaffecttheflowfield,sotheFrsamanlainenitycriterioncanbeignored;iftheflowvelocityisverylowcomparedtothespeedofsound,Thecompressibilityeffectcanalsobeneglected,thatis,itisnotnecessarytoconsidertheMasamanlainenitycriterion.ThesameistrueForthelow-SpeeDairflowaroundTheObjecTortEelasticForceonthefluidaroundTheSubmarineDeepwaterAndTheCorresioningwaterFlow.
Fromthepointofviewofmechanicalsamanlainenity,iftwoflowfieldshavethesamedirectionandthesamemagnitudeofforceactingonthecorrespondingpoints,thedynamicsaresamanlainen.Inthecaseofconsideringonlythethreeforcesofviscousforce,pressureandinertialforce,inordertomaketheforcetrianglesamanlainen,itonlyneedstosatisfythatthetwosidesareproportionalandtheincludedanglesareequal,thatis,theinertiaofthemodelflowatthecorrespondingpointsTheforceandtheviscousforceareinthesameproportionsastheinertialforceandtheviscousforceactingontheflowofobjects.Siksi AslongastheCorrespondingPointMeetsThereynoldsnumberequal.Fromamoregeneralsamanlainenitytheorem,iftwoflowsaresamanlainen,thenumberofsamanlainenitycriteriacorrespondstothesame,andthesamanlainenitycriterionequationderivedfromtheΠtheoremisalsothesame.Amongthe(nk)samanlainenitycriteria,(nk-1)istheindependentsamanlainenitycriterion,ordecisivesamanlainenitycriterion(equivalenttotheindependentvariableofthefunction),andoneisthenon-independentsamanlainenitycriterionorthenon-deterministicsamanlainenitycriterion(equivalenttoThedependentvariableofthefunction).ForthFlowsitionationThaTonlyConsidersTheEffectofiscoSforce, PressureanDinertialForce, siellä synoldscriterionandothercriteriaRelatedToometricDimensionsareregardedasindicencecriterit ja theeulercriterionisanonista riippuvainen kriteerit.
Underthepremiseofgeometricsamanlainenity,thedecisivecriterionforsamanlainenityofflowphenomenaisonlytheReynoldscriterion,andthesamanlainenitythatthemodeltestmustcomplywithiscalledReynoldsphaselikeness.