《微机电糸统分析》PPT课件.ppt

1,微機電糸統分析期末報告(二)Inkjet授課教師:李旺龍學生:李聰瑞Q28961038,2,InkjetModel,Inkjetprintersareattractivetoolsforprintingtextandimagesbecauseoftheirlowcost,highresolution,andacceptablespeed.Theworkingprinciplebehindinkjettechnologyistoejectsmalldropletsofliquidfromanozzleontoasheetofpaper.Importantpropertiesofaprinterareitsspeedandtheresolutionofthefinalimages.Designerscanvaryseveralparameterstomodifyaprintersperformance.Forinstance,theycanvarytheinkjetgeometryandthetypeofinktocreatedropletsofdifferentsizes.Thesizeandspeedoftheejecteddropletsarealsostronglydependentonthespeedatwhichinkisinjectedintothenozzle.Simulationscanbeveryusefultoimprovetheunderstandingofthefluidflowandtopredicttheoptimaldesignofaninkjetforaspecificapplication.Althoughinitiallyinventedtoproduceimagesonpaper,theinkjettechniquehassincebeenadoptedforotherapplicationareas.Instrumentsfortheprecisedepositionofmicrodropletsoftenemployinkjets.Theseinstrumentsareusedwithinthelifesciencesfordiagnosis,analysis,anddrugdiscovery.Inkjetshavealsobeenusedas3Dprinterstosynthesizetissuefromcellsandtomanufacturemicroelectronics.Foralloftheseapplicationsitisimportanttobeabletoaccuratelycontroltheinkjetsperformance.ThisexampledemonstrateshowtouseCOMSOLMultiphysicstomodelthefluidflowwithinaninkjet.ThemodelusestheNavierStokesequationstodescribethemomentumtransportandconservationofmass.Surfacetensionisincludedinthemomentumequations.Areinitialized,conservativelevelsetmethodrepresentsandmovestheinterfacebetweentheairandink.,3,Figure4-61showsthegeometryoftheinkjetstudiedinthisexample.Becauseofitssymmetryyoucanuseanaxisymmetric2Dmodel.Initially,thespacebetweentheinletandthenozzleisfilledwithink.Additionalinkisinjectedthroughtheinletduringaperiodof10s,anditconsequentlyforcesinktoflowoutofthenozzle.Whentheinjectionstops,adropletofinksnapsoffandcontinuestotraveluntilithitsthetarget.,ModelDefinition,Figure4-61:Geometryoftheinkjet,4,TransportofMassandMomentum,TheNavier-Stokesequationsdescribethetransportofmassandmomentumforfluidsofconstantdensity.Itispossibletomodelbothinkandairasbeingincompressibleaslongasthefluidvelocityissmallcomparedtothespeedofsound.Inthismodel,youmustaddatermtoaccountforsurfacetension.TheNavier-Stokesequationswithsurfacetensionare,Here,denotesdensity(kg/m3),equalsthedynamicviscosity(Ns/m2),urepresentsthevelocity(m/s),andpdenotespressure(Pa).Fstisthesurfacetensionforce,whichis,whereIistheidentitymatrix,nistheinterfacenormal,equalsthesurfacetensioncoefficient(N/m),andequalsaDiracdeltafunctionbeingnonzeroonlyatthefluidinterface.InCOMSOLMultiphysics,theNavier-StokesequationsarealreadyformulatedintheIncompressibleNavier-Stokesapplicationmode,whichisavailableintheMEMSModule.Youmustaddonlythesurface-tensionforceexpressedincylindricalcoordinates.Thefollowingtablegivesthephysicalparametersofinkandair:,5,REPRESENTATIONANDCONVECTIONOFTHEFLUIDINTERFACE,Inthismodelyouuseareinitialized,conservativelevelsetmethodtodescribeandconvecttheinterface.The0.5contourofthelevelsetfunctiondefinestheinterface,whereequals0inairand1inink.Inatransitionlayerclosetotheinterface,goessmoothlyfrom0to1.Thenormaltotheinterfaceis,Theinterfacemoveswiththefluidvelocity,u,attheinterface.Thefollowingequationdescribesthereinitializedconvectionofthelevelsetfunction:,Thethicknessofthetransitionlayerisproportionalto.Forthismodelyoucanuse=2h,wherehisthemeshsize.Youthenobtainasharperinterfaceintheregionswherethemeshisfiner.Inthisexampleyouuseastructuredmesh.Forunstructuredmeshes,avoidlettingdependonh.,Theparameterdeterminestheamountofreinitialization.Ifthevelocitygradientsaresmallatthefluidinterfaceyoucanchoose=1.Inthisexamplethevelocitygradientsattheinterfacearesignificant,andyoumustthereforechoosealargervaluefortokeepthethicknessofthetransitionlayerconstant.,Youcanusethelevelsetfunctiontosmooththedensityandviscosityjumpacrosstheinterfacebyletting,Tosimplifythecalculationofthesurfacetensionforce,set,6,InitialConditions,Figure4-62showsatt=0,thatis,theinitialdistributionofinkandair.Thevelocityisinitially0.,Figure4-62:Initialdistributionofink.Blackcorrespondstoinkandwhitecorrespondstoair.,BoundaryConditions,Inlet,Theinletvelocityinthez-directionincreasesfrom0totheparabolicprofile,duringthefirst2s.Thevelocityisthenv(r)for10sandfinallydecreasesto0foranother2s.YoucanobtainthiseffectbyusingthesmoothstepfunctionH(t1,2),whichis0fort1+2asshowninFigure4-63.,7,Figure4-63:Smoothstepfunctionf(t)=H(t1,2).,Thetime-dependentvelocityprofileinthez-directioncanthenbedefinedas,Forthelevelsetequation,use=1astheboundarycondition.,Outlet,Setaconstantpressureattheoutlet.Thevalueofthepressuregivenhereisnotimportantbecausethevelocitydependsonlyonthepressuregradient.Youthusobtainthesamevelocityfieldregardlessofwhetherthepressureissetto1atmorto0.Useconvectivefluxastheboundaryconditionforthelevelsetequation.,8,Walls,Onallotherboundariesexceptthetarget,setnoslipconditions.Ifyouusethematthetarget,theinterfacecannotmovealongthisboundary.YoucanresolvethisproblembyreplacingthenoslipconditionwithaNavierslipcondition.Inthiscase,theNavierslipconditionforthevelocitycomponentinther-direction,u,isgivenby,whereisasmallparametercalledthesliplength.Notethatshouldbeofthesameorderasthesizeofthemesh.Useinsulation/symmetryastheboundaryconditionforthelevelsetequationonallwallsincludingthetarget.Thispreventsanyoutflowofwaterorinkthroughthewalls.,ResultsandDiscussion,Figure4-64andFigure4-65showtheinksurfaceandthevelocityfieldatdifferenttimes.Thedroplethitsthetargetafterapproximately160s.,9,Figure4-64:Positionofair/inkinterfaceandvelocityfieldatvarioustimes.,Figure4-65:Positionofair/inkinterfaceandvelocityfieldatvarioustimes.,10,Figure4-66illustratesthemassofinkthatisfurtherthanmfromtheinlet.Thefigureshowsthatthemassoftheejecteddropletisapproximatelykg.,Figure4-66:Amountofinkjustabovethenozzle.,Thisexamplestudiesonlyoneinkjetmodel,butitiseasytomodifythemodelinseveralways.Youcan,forexample,changepropertiessuchasthegeometryortheinletvelocityandstudytheinfluenceonthesizeandthespeedoftheejecteddroplets.Youcanalsoinvestigatehowtheinkjetwouldperformiftheinkwerereplacedbyadifferentfluid.Itisalsoeasytoaddforcessuchasgravitationtothemodel.,11,ModelinginCOMSOLMultiphysics,TosetupthemodelinCOMSOLMultiphysicsyouusetwo2Daxisymmetricapplicationmodes:IncompressibleNavier-Stokes,andConvectionandDiffusion.IntheNavier-Stokesequationsyoumustaddthesurface-tensionforce.YoumustalsomodifytheConvection/Diffusionequationtoobtainthelevelsetequation.Youuseastructuredmeshandrefineitintheregionswherethefluidinterfacepasses.Beforestartingthecalculations,youmustreinitializethelevelsetfunction.Dosobysolvingonlyforthelevelsetfunctionwithzerovelocity.Thenusetheresultingsolutionasinitialdata.Tocalculatethedropletsmassuseanintegrationcouplingvariable.Tovisualizethedropletin3D,revolvethe2Daxisymmetricsolutiontoa3Dgeometry.,References,Jyi-TyanYeh,“AVOF-FEMCoupledInkjetSimulation,”Proc.ASMEFEDSM01,NewOrleans,Louisiana,2001.2.E.OlssonandG.Kreiss,“AConservativeLevelSetMethodforTwoPhaseFlow,”J.Comput.Phys.,vol.210,pp.225-246,2005.,12,ModelingUsingtheGraphicalUserInterface,ModelNavigator,13,GeometryModeling,1FromtheDrawmenuselectSpecifyObjectsLine2SelectClosedpolyline(solid)fromtheStylelist.3Inthereditfield,enter01e-41e-42.5e-52.5e-51e-41e-42e-42e-40,andinthezeditfield002e-45.75e-46e-46e-41.5e-31.5e-31.6e-31.6e-3.4ClickOK.5ClicktheZoomExtentsbuttonontheMaintoolbar.6Shift-clicktheRectangle/SquarebuttonontheDrawtoolbar.Enter1e-4intheWidtheditfield,2e-4intheHeighteditfield,and0inboththerfieldandthezfields.MakesureCornerisselectedintheBaselist.ClickOK.7Repeatthepreviousstepthreetimestospecifythreemorerectanglesaccordingtothefollowingtable:,14,OPTIONSANDSETTINGS,1FromtheOptionsmenuselectConstants.2Enterthefollowingconstantsettings:,3ClickOK.4FromtheOptionsmenuselectExpressionsScalarExpressions.5Insertthefollowingexpressions:6ClickOK.,15,16,BoundaryConditionsIncompressibleNavier-Stokes,1IntheModelTree,right-clickIncompressibleNavier-Stokes(mmglf)andselectBoundarySettings.2PressCtrlandselectalltheboundariesatthesymmetryline,thatis,Boundaries1,3,5,7,and9.SelectAxialSymmetryfromtheBoundaryconditionlist.3Selecttheinlet(Boundary2)andselecttheboundaryconditionInflow/Outflowvelocity.Typeinletvelinthez-velocityeditfield.4SelectBoundary24(theoutlet)andspecifytheboundaryconditionOutflow/Pressure.5SelectBoundaries11,18,and23(thetarget).SelecttheboundaryconditionInflow/Outflowvelocityandtypelambdaslip*uzinther-velocityeditfield.6Verifythattheboundaryconditionfortheremainingboundaries(12,13,15,19,20,and22)isNoslip.7ClickOK.,17,18,19,SubdomainSettingsConvectionandDiffusion,1IntheModelTreewindow,right-clickConvectionandDiffusion(cd)andselectSubdomainSettings.2Makesurethatallthesubdomainsareselected.3Enter0intheDiffusioncoefficienteditfield,uinther-velocityeditfield,andvinthez-velocityeditfield.4ClicktheInittabandenterphi0intheeditfield.5ClicktheElementtabandselectLagrangeLinearinthePredefinedelementslist.6ClickOK.,20,Adjusttheconvection/diffusionequationtoobtaintheconservativelevelsetequation:1SelectPhysicsEquationSystemSubdomainSettings.Clicktheftab.2Replacetheexpressioninthefourthrowwith0.3Clickthetab.4Replacetheexpressioninthefirstcolumn,fourthrowwithr*u_phi_cd*phi+gamma*(r*phi*(1-phi)*normr-2*h*r*phir).Replacetheexpressioninthesecondcolumn,fourthrowwithr*v_phi_cd*phi+gamma*(r*phi*(1-phi)*normz-2*h*r*phiz).5ClickOK.,21,BoundaryConditionsConvectionandDiffusion,1IntheModelBrowser,right-clickConvectionandDiffusionandselectBoundarySettings.2SelectBoundaries1,3,5,7,and9,thenselectAxialsymmetryintheBoundaryconditionlist.3Selecttheinlet(Boundary2)andsetConcentrationastheboundarycondition.Enter1intheConcentrationeditfield.4Selecttheoutlet(Boundary24)andsetConvectivefluxastheboundarycondition.5ThedefaultboundaryconditionInsulation/Symmetryholdsforallotherboundaries.6ClickOK.,22,MeshGeneration,1FromtheMeshmenuselectMappedMeshParameters.2ClicktheBoundarytab.3SelectBoundaries1,2,3,5,7,9,15,and22,thenselecttheConstrainededgeelementdistributioncheckbox.NextselecteachboundaryseparatelyandspecifytheNumberofedgeelementsaccordingtothistable:4ClickRemeshandthenclickOK.,23,ComputingtheSolution,Firstreinitializetoobtainthecorrectshapeofinthetransitionlayer.1FromtheSolvemenuselectSolverParameters.2ClicktheGeneraltabandenter02e-6intheTimeseditfield.ClickOK.3SelectSolveSolverManager.4ClicktheSolveFortab.SelectConvectionandDiffusion(cd).ClickOK.5SelectSolveSolveProblem.Thiscreatesagoodinitialsolutiontothelevelsetfunction.6Tovisualizetheinitiallevelsetfunction,clickthePlotParametersbuttonontheMaintoolbar.ClicktheSurfacetab,thenselectConvectionandDiffusionConcentration,phifromthePredefinedquantitieslist.ClickOK.,Usetheobtainedsolutionasaninitialconditiontothesimulationofthedropletmotion.1ClicktheSolverManagerbuttonontheMaintoolbar.ClicktheInitialValuetab.2ClicktheStoreSolutionbutton.Selectthetime2e-6.ClickOK.3IntheInitialvalueareaselectStoredsolution.4Select2e-6fromtheSolutionattimelist.5ClicktheSolveFortab.ClickGeom1(2D)toselectallthevariables.ClickOK.6FromtheSolvemenuselectSolverParameters.7ClicktheGeneraltab,thenenter0:1e-5:2e-4intheTimeseditfield.ClickOK.8ClicktheSolvebuttonontheMaintoolbar.,24,PostprocessingandVisualization,Tovisualizetheinkjetsurfacein3D,performthesesteps:1FromtheDrawmenuselectRevolve.2IntheObjectstorevolvelistselectalltheelements(selectanyoneandthenpressCtrl+A).ClickOK.3IntheModelTreeclickGeom1toreturntothe2Dmodel.4SelectOptionsExtrusionCouplingVariablesSubdomainVariables.5SelectanysubdomainandthenpressCtrl+Atoselectallthesubdomains.6Enterphi3dintheNamefieldandphiintheExpressionfield.7ClicktheGeneraltransformationoptionbutton.8Locatethesecondrow,thenentervel3dintheNamefieldandsqrt(u2+v2)intheExpressionfield.9SelectGeneraltransformationforthisvariable.10ClicktheDestinationtab.IntheGeometrylistselectGeom2.IntheLevellistselectSubdomain.11SelectanysubdomainandpressCtrl+Atoselectallthesubdomains.12SelecttheUseselectedsubdomainsasdestinationcheckbox.13Entersqrt(x2+z2)inthexeditfield,thenclickOK.14Selectphi3dfromtheVariablelist.15SelecttheUseselectedsubdomainsasdestinationcheckboxandentersqrt(x2+z2)inthexeditfield.ClickOK.16FromtheSolvemenuselectUpdateModel.17ClickthePlotParametersbuttonontheMainmenu.18SelecttheGeneraltab