comsol涡流模块.docx

comsol涡流模块.docx

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comsol涡流模块

InductionCurrentsfromCircularCoils

Introduction

Atime-varyingcurrentinducesavaryingmagneticfield.Thisfieldinducescurrentsinneighboringconductors.Theinducedcurrentsarecallededdycurrents.Thefollowingmodelillustratesthisphenomenonbyatime-harmonicfieldsimulationaswellasatransientanalysis,whichprovidesastudyoftheeddycurrentsresultingfromswitchingonthesource.

Twocurrent-carryingcoilsareplacedaboveacopperplate.Theyaresurroundedbyair,andthereisasmallairgapbetweenthecoilsandthemetalplate.Apotentialdifferenceprovidestheexternalsource.Toobtainthetotalcurrentdensityinthecoilsyoumusttaketheinducedcurrentsintoaccount.Thetime-harmoniccaseshowstheskineffect,thatis,thatthecurrentdensityishighclosetothesurfaceanddecreasesrapidlyinsidetheconductor.

ModelDefinition

EQUATION

Tosolvetheproblem,useaquasi-staticequationforthemagneticpotentialA:

----------

σ-∂--A----+∇×（μ–1μ–1∇×A）=σVcoi-l

∂t0r

2πr

Hereμ0isthepermeabilityofvacuum,μrtherelativepermeability,σtheelectricconductivity,andVcoilthevoltageoveroneturninthecoil.Inthetime-harmoniccasetheequationreducesto

–1–1

V

coil

=-----------

jωσA+∇×（μ0μr

∇×A）

σ2πr

FORCES

ThetotalelectromagneticforceactingonregionofspaceΩcanbeobtainedbyintegratingMaxwell’sstresstensoronthedelimitingboundary∂Ω:

F=TndS

∂Ω

TheForceCalculationfeatureautomaticallyperformstheintegralalongtheboundariesofthedesiredregion,consideringalsotheaxisymmetricgeometryoftheproblem.Thecomputedforcewillbeavailableinresultsprocessingasaglobalvariable.

ResultsandDiscussion

Inthetime-harmonicregime,thevaryingmagneticfieldinduceselectricalcurrentsinthemetallicplate.Thecurrents,inturn,actassourcesofanopposingmagneticfield“shielding”theplatefromthemagneticfield.Asaresultofthisphenomenon,theregioninwhichelectricalcurrentsaregeneratedisconfinedinproximityofthesurfaceandreducesinsizewithincreasingfrequency.Figure1andFigure2showtheinducedcurrentdensityat10Hzand300Hz,respectively.

Inthismodel,atime-domainstudyisperformedtoinvestigatethestepresponseofthesystem.Figure3displaysasnapshotoftheinducedcurrentdensityandmagneticfluxdensityforthetransientsolutioninacombinedsurfaceandarrowplot.

Finally,Figure4showsthetotalaxialforcebetweenthecoilsandtheplateasafunctionoftimecomputedbytheForceCalculationfeature.Forthechosencurrentdirection,theforceisrepulsive（negative）.

Figure1:

Theϕcomponentoftheinducedcurrentdensityforthetime-harmonicsolutionplottedtogetherwithacontourplotofthemagneticvectorpotentialatafrequencyof

10Hz.

Figure2:

Plotofthesamequantitiesatafrequencyof300Hz.

Figure3:

Snapshotoftheinducedcurrentdensity（surfaceplot）andthemagneticfluxdensity（arrowplot）duringthetransientstudy.

Figure4:

Totalforceactingonthecopperplateplottedasafunctionoftime.

ModelLibrarypath:

ACDC_Module/Inductive_Devices_and_Coils/coil_above_plate

ModelingInstructions—FrequencyDomain

FromtheFilemenu,chooseNew.

NEW

1IntheNewwindow,clicktheModelWizardbutton.

MODELWIZARD

1IntheModelWizardwindow,clickthe2DAxisymmetricbutton.

2IntheSelectphysicstree,selectAC/DC>MagneticFields（mf）.

3ClicktheAddbutton.

4ClicktheStudybutton.

5Inthetree,selectPresetStudies>FrequencyDomain.

6ClicktheDonebutton.

GEOMETRY1

Square1

1IntheModelBuilderwindow,underComponent1right-clickGeometry1andchoose

Square.

2IntheSquaresettingswindow,locatetheSizesection.

3IntheSidelengtheditfield,type0.1.

4LocatethePositionsection.Inthezeditfield,type-0.05.

Rectangle1

1IntheModelBuilderwindow,right-clickGeometry1andchooseRectangle.

2IntheRectanglesettingswindow,locatetheSizesection.

3IntheWidtheditfield,type0.08.

4IntheHeighteditfield,type0.02.

5LocatethePositionsection.Inthezeditfield,type-0.021.

Circle1

1Right-clickGeometry1andchooseCircle.

2IntheCirclesettingswindow,locatetheSizeandShapesection.

3IntheRadiuseditfield,type0.0025.

4LocatethePositionsection.Inthereditfield,type0.0125.

5Inthezeditfield,type0.0025.

Circle2

1Right-clickGeometry1andchooseCircle.

2IntheCirclesettingswindow,locatetheSizeandShapesection.

3IntheRadiuseditfield,type0.0025.

4LocatethePositionsection.Inthereditfield,type0.0185.

5Inthezeditfield,type0.0025.

6ClicktheBuildAllObjectsbutton.Thegeometryisnowcomplete.

Next,addthematerialsrelevanttothemodel.

MATERIALS

OntheHometoolbar,clickAddMaterial.

ADDMATERIAL

1GototheAddMaterialwindow.

2Inthetree,selectBuilt-In>Air.

3IntheAddMaterialwindow,clickAddtoComponent.

MATERIALS

ADDMATERIAL

1GototheAddMaterialwindow.

2Inthetree,selectBuilt-In>Copper.

3IntheAddMaterialwindow,clickAddtoComponent.

4ClosetheAddMaterialwindow.

MATERIALS

Copper

1IntheModelBuilderwindow,underComponent1>MaterialsclickCopper.

2SelectDomains2–4only.

MAGNETICFIELDS

Single-TurnCoil1

1OnthePhysicstoolbar,clickDomainsandchooseSingle-TurnCoil.

2SelectDomains3and4only.

3IntheSingle-TurnCoilsettingswindow,locatetheSingle-TurnCoilsection.

4FromtheCoilexcitationlist,chooseVoltage.

5IntheVcoileditfield,type0.1[mV].

Withthissetting,theSingle-TurnCoilfeatureappliesaloopvoltageof0.1mVtoeachofthecoilloops.

Now,addaForceCalculationfeaturethatcomputesthetotalforceactingontheplate.

ForceCalculation1

1OnthePhysicstoolbar,clickDomainsandchooseForceCalculation.

2SelectDomain2only.

3IntheForceCalculationsettingswindow,locatetheForceCalculationsection.

4IntheForcenameeditfield,typeplate.

STUDY1

Step1:

FrequencyDomain

1IntheModelBuilderwindow,underStudy1clickStep1:

FrequencyDomain.

2IntheFrequencyDomainsettingswindow,locatetheStudySettingssection.

3IntheFrequencieseditfield,type10[Hz],100[Hz],300[Hz].Disabletheautomaticplotgeneration.

4IntheModelBuilderwindow,clickStudy1.

5IntheStudysettingswindow,locatetheStudySettingssection.

6CleartheGeneratedefaultplotscheckbox.

7OntheStudytoolbar,clickCompute.

Whenthesolutionprocessiscompleted,createplotgroupstovisualizetheresults.

RESULTS

2DPlotGroup1

1OntheResultstoolbar,click2DPlotGroup.

2Onthe2DPlotGroup1toolbar,clickSurface.

3IntheSurfacesettingswindow,clickReplaceExpressionintheupper-rightcorneroftheExpressionsection.Fromthemenu,chooseMagneticFields>Currentsandcharge>Inducedcurrentdensity>Inducedcurrentdensity,phicomponent（mf.Jiphi）.

Addacontourplottoshowthefieldlinesofthemagneticfluxdensity.Inaxialsymmetry,thoselinescanbeobtainedbyplottingtheisolinesofthemagneticvectorpotentialmultipliedbytheradialcoordinate,r.

4Onthe2DPlotGroup1toolbar,clickContour.

5IntheContoursettingswindow,locatetheExpressionsection.

6IntheExpressioneditfield,typeAphi*r.

7IntheModelBuilderwindow,click2DPlotGroup1.

8Inthe2DPlotGroupsettingswindow,locatetheDatasection.

9FromtheParametervalue（freq）list,choose10.

10Onthe2DPlotGroup1toolbar,clickPlot.

Theplotshowstheinducedcurrentdensityintheplate.Plottingtheothersolutionsshowshowtheregioninwhichthecurrentsareinduceddecreaseswithincreasingfrequency.

11FromtheParametervalue（freq）list,choose100,thenclickPlot.

12FromtheParametervalue（freq）list,choose300,thenclickPlot.

TransientAnalysis

Tosetupatime-dependentstudytoinvestigatethestepresponseofthesystemrequiresonlyafewadditionalsteps.TheInitialValuesfeatureautomaticallyincludedintheMagneticFieldsinterfacespecifiestheinitialvalueforthemagneticvectorpotential,defaultedtozero.Atthebeginningofthetransientsimulation（t=0）,a

0.1mVvoltageisappliedtothecoil.Thiscorrespondstoexcitingfromanunexcitedstatethesystemwithastepfunction.

1OntheStudytoolbar,clickAddStudy.

ADDSTUDY

1GototheAddStudywindow.

2FindtheStudiessubsection.Inthetree,selectPresetStudies>TimeDependent.

3IntheAddstudywindow,clickAddStudy.

4ClosetheAddStudywindow.

STUDY2

Step1:

TimeDependent

1IntheModelBuilderwindow,underStudy2clickStep1:

TimeDependent.

2IntheTimeDependentsettingswindow,locatetheStudySettingssection.

3IntheTimeseditfield,type0,10^（range（-4,1/3,-1））.

4SelecttheRelativetolerancecheckbox.

5Intheassociatededitfield,type0.001.

6IntheModelBuilderwindow,clickStudy2.

7IntheStudysettingswindow,locatetheStudySettingssection.

8CleartheGeneratedefaultplotscheckbox.

9OntheStudytoolbar,clickCompute.

RESULTS

2DPlotGroup2

1OntheResultstoolbar,click2DPlotGroup.

2Inthe2DPlotGroupsettingswindow,locatetheDatasection.

3FromtheDatasetlist,chooseSolution2.

4FromtheTime（s）list,choose0.002154.

5Onthe2DPlotGroup2toolbar,clickSurface.

6IntheSurfacesettingswindow,clickReplaceExpressionintheupper-rightcorneroftheExpressionsection.Fromthemenu,chooseMagneticFields>Currentsandcharge>Inducedcurrentdensity>Inducedcurrentdensity,phicomponent（mf.Jiphi）.

7IntheModelBuilde