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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 Q289610381Inkjet ModelInkjetprintersareattractivetoolsforprintingtextandimagesbecauseoftheirlowcost,highresolution,andacceptablespeed.Theworkingprinciplebehindinkjettechnologyistoejectsmalldropletsofliquidfromanozzleontoasheetofpaper.Importantpropertiesofaprint
2、erareitsspeedandtheresolutionofthefinalimages.Designerscanvaryseveralparameterstomodifyaprintersperformance.Forinstance,theycanvarytheinkjetgeometryandthetypeofinktocreatedropletsofdifferentsizes.Thesizeandspeedoftheejecteddropletsarealsostronglydependentonthespeedatwhichinkisinjectedintothenozzle.S
3、imulationscanbeveryusefultoimprovetheunderstandingofthefluidflowandtopredicttheoptimaldesignofaninkjetforaspecificapplication.Althoughinitiallyinventedtoproduceimagesonpaper,theinkjettechniquehassincebeenadoptedforotherapplicationareas.Instrumentsfortheprecisedepositionofmicrodropletsoftenemployinkj
4、ets.Theseinstrumentsareusedwithinthelifesciencesfordiagnosis,analysis,anddrugdiscovery.Inkjetshavealsobeenusedas3Dprinterstosynthesizetissuefromcellsandtomanufacturemicroelectronics.Foralloftheseapplicationsitisimportanttobeabletoaccuratelycontroltheinkjetsperformance.Thisexampledemonstrateshowtouse
5、COMSOLMultiphysicstomodelthefluidflowwithinaninkjet.ThemodelusestheNavierStokesequationstodescribethemomentumtransportandconservationofmass.Surfacetensionisincludedinthemomentumequations.Areinitialized,conservativelevelsetmethodrepresentsandmovestheinterfacebetweentheairandink.2Figure4-61showsthegeo
6、metryoftheinkjetstudiedinthisexample.Becauseofitssymmetryyoucanuseanaxisymmetric2Dmodel.Initially,thespacebetweentheinletandthenozzleisfilledwithink.Additionalinkisinjectedthroughtheinletduringaperiodof10s,anditconsequentlyforcesinktoflowoutofthenozzle.Whentheinjectionstops,adropletofinksnapsoffandc
7、ontinuestotraveluntilithitsthetarget. Model DefinitionFigure 4-61: Geometry of the inkjet3REPRESENTATION AND CONVECTION OF THE FLUID INTERFACEInthismodelyouuseareinitialized,conservativelevelsetmethodtodescribeandconvecttheinterface.The0.5contourofthelevelsetfunctiondefinestheinterface,whereequals0i
8、nairand1inink.Inatransitionlayerclosetotheinterface,goessmoothlyfrom0to1.ThenormaltotheinterfaceisTheinterfacemoveswiththefluidvelocity,u,attheinterface.Thefollowingequationdescribesthereinitializedconvectionofthelevelsetfunction: Thethicknessofthetransitionlayerisproportionalto.Forthismodelyoucanus
9、e=2h,wherehisthemeshsize.Youthenobtainasharperinterfaceintheregionswherethemeshisfiner.Inthisexampleyouuseastructuredmesh.Forunstructuredmeshes,avoidlettingdependonh.Theparameterdeterminestheamountofreinitialization.Ifthevelocitygradientsaresmallatthefluidinterfaceyoucanchoose=1.Inthisexamplethevelo
10、citygradientsattheinterfacearesignificant,andyoumustthereforechoosealargervaluefortokeepthethicknessofthetransitionlayerconstant.YoucanusethelevelsetfunctiontosmooththedensityandviscosityjumpacrosstheinterfacebylettingTosimplifythecalculationofthesurfacetensionforce,set5Initial ConditionsFigure4-62s
11、howsatt=0,thatis,theinitialdistributionofinkandair.Thevelocityisinitially0.Figure 4-62: Initial distribution of ink.Black corresponds to ink and white corresponds to air.BoundaryConditions InletTheinletvelocityinthez-directionincreasesfrom0totheparabolicprofile duringthefirst2s.Thevelocityisthenv(r)
12、for10sandfinallydecreasesto0foranother2s.YoucanobtainthiseffectbyusingthesmoothstepfunctionH(t 1,2), whichis0fort1+2asshowninFigure4-63.6Figure 4-63: Smooth step function f(t) = H(t 1,2).Thetime-dependentvelocityprofileinthez-directioncanthenbedefinedasForthelevelsetequation,use=1astheboundarycondit
13、ion.OutletSetaconstantpressureattheoutlet.Thevalueofthepressuregivenhereisnotimportantbecausethevelocitydependsonlyonthepressuregradient.Youthusobtainthesamevelocityfieldregardlessofwhetherthepressureissetto1atmorto0.Useconvectivefluxastheboundaryconditionforthelevelsetequation.7WallsOnallotherbound
14、ariesexceptthetarget,setnoslipconditions.Ifyouusethematthetarget,theinterfacecannotmovealongthisboundary.YoucanresolvethisproblembyreplacingthenoslipconditionwithaNavierslipcondition.Inthiscase,theNavierslipconditionforthevelocitycomponentinther-direction,u,isgivenbywhereisasmallparametercalledthesl
15、ip length.Notethatshouldbeofthesameorderasthesizeofthemesh.Useinsulation/symmetryastheboundaryconditionforthelevelsetequationonallwallsincludingthetarget.Thispreventsanyoutflowofwaterorinkthroughthewalls.Results and DiscussionFigure4-64andFigure4-65showtheinksurfaceandthevelocityfieldatdifferenttime
16、s.Thedroplethitsthetargetafterapproximately160s.8Figure 4-64: Position of air/ink interface and velocity field at various times.Figure 4-65: Position of air/ink interface and velocity field at various times.9Figure4-66illustratesthemassofinkthatisfurtherthanmfromtheinlet.Thefigureshowsthatthemassoftheejecteddropletisapproximatelykg.Figure 4-66: Amount of ink just above the nozzle.Thisexamplestudiesonlyoneinkjetmodel,butitiseasytomodifythemodelinseveralways.Youcan,forexample,changepropertiessucha
