potentiellewww.tl222666.com
www.tl222666.com 时间:2021-03-18 阅读:()
OnTheCOMSOLSoftwareAbilityOnStudyingTransitionFlowsForLowPrandtlNumberFluidsH.
Jamai1,A.
Elamari1,M.
ElGanaoui2,F.
S.
Oueslati1,B.
Pateyron2etH.
Sammouda31LETTM,Departementofphysics,F.
S.
T,Tunisia.
2SPCTSUMR6638CNRS,FaculteofSciences,87000Limoges,France.
3ESST-H.
Sousse,Tunisiehanene_jamai@yahoo.
frAbstract:COMSOLindustrialsoftwareisofferinganimportantalternativetohomecodesformodelingandsimulationofcomplexproblemswithincludingcoupledeffectsonHeatandMasseTransfers.
ThepresentworkfocusesonlowPrandtlnumberfluidmeltssubjecttosymmetrybreakingandtransitiontounsteadyregimes.
TheseconfigurationsareforpracticalinterestincrystalgrowthindustrynamelytheBridgmanconfigurationiswidelyusedtoproducesinglecrystalsofcompoundsemi-conductorsand2Denclosuresprovideabasicmodelforstudyinghydrodynamicregimeoccurringonsuchprocesses.
Afirststepinthisworkistostudytheeffectofmagneticfieldonliquidmetalflowandheattransferoccurringinanannularcavity.
Keywords:Naturalconvection,magneto-convection,moltenmetal(fluidsonlowPrandtlnumber),annularcavityNomenclatureΤAspectratioDiensionlessmagneticvector(tesla)GravitationalvectoraccelerationΤ)Cylinderheight(m)ElectricVectordensityΤRatioofraysDimonsionlesspressiontime(s)Differenceofrays(m)TDimensionlesstemperaturr,zDimensionlessradialandaxialcoordinatesu,wRadialandaxialvelocityvectorcomponentsGrecsLettersThermaldiffusivity(m2/s)Thermalexpansioncoefficient(1/k)Density(kg/m3)Dynamicviscosity,(kg/m.
s)ElectricConductivity(S/m)ElectricpotentielleFonction1.
IntroductionLiquidsmetals,inthepresenceofamagneticfield(magneto-convection)havearethesubjectofagreatnumberofresearches.
Theinterestoftheseflowsliesintheirpresenceinmanynaturalandappliedphenomena.
Inthesameway,metallurgicalindustry,coolingenginesinnuclearindustry,crystallinegrowthfortheindustryofthesemiconductorsgenerateseveralquestionsforcontrollingthestabilityoftheseflows[1,2,3].
Theappearanceoftheconvectionduringcrystalgrowthcanproduceinhomogenuitieswhichleadtostriationsandwhichaffectthequalityoftheobtainedcrystals[4].
Inthesecases,theapplicationofmagneticfieldtothethermalconvectionappearsofgreatimportanceforthecontrolofthestabilityoftheseflowsandtheheattransferswhileresulting.
Ourstudyrelatestotheconvectiveflow,ofafluidoflowPrandtlnumberinanannularandverticalcavityformedbytwocoaxialcylinders,differentiallyheatedinthepresenceofaconstantmagneticfield[5,6].
2.
MathematicalModelThesystemconsideredinthispaperisshownschematicallyinfig.
1Boussinesqapproximationisadopted,thatthedensityoffluidisgivenby:001TTT(1)Thedimensionlessequationswhichdescribetheproblem,arerespectivelyequationsof,continuity,conservationofthemomentum,theOhmlawandtheenergyconservationequation:Figure1.
Geometricalconfiguration0uuwrrz(1)22222221PrPr.
.
BruuuvPuuuuuwHajeutrzrrrrrzr(2)222221PrPrPr.
.
BzwwwPwwwuwRaTHajeutrzzrrrz(3)()BjVe(4)22221TTTTTTuwtrzrrrz(6)WithBeistheunitvectorinthedirectionofmagneticfieldB3RagTl,.
.
HalB,andPraretheRayleigh,HartmannandPrandtlnumbers,whicharethedimensionlessnumbersgoverningtheproblem.
TheboundaryconditionsTheboundaryconditionsadoptedfortheresolutionoftheproblemare:HydrodynamicCondition:zerovelocityonthewalls.
u=w=0ThermalCondition:1122:,:,0,1:0rRTTrRTTzTzElectricalconditions:electricalinsulationonthewalls.
0jnThegoverningequationsalongwiththeboundaryconditionsaresolvednumericallyusingtheCOMSOLcodewhichbasedonthefiniteelementmethod,allowingacouplingbetweenthedynamic,thermalandelectricproblems.
Totestandassessgridindependenceofthenumericalscheme,variousmeshesareexamined.
Veryfinenouniformgridsclosetothewallsareadopted.
Weassumethatthesolutionisconvergedwhentheerrorislessthan10-6.
3.
TheeffectofanaxialmagneticfieldInthispart,themagneticfieldissupposedaccordingtothezdirectionandweneglecttheelectrictermintheforceofLaplace.
WepresentonFigure2,theStreamlines,theisothermsandvelocityprofilesforRa=104andtheaspectratioA=1forvariousvaluesoftheHartmannnumber.
Intheabsenceofmagneticfield(Ha=0,Fig.
2(a)),theflowexhibitsasimplecirculatingpatternrisingalongthehotwallanddescendingalongthecoldwallofthecavity.
Itisinterestingtonotethatasthestrengthofthemagneticfieldincreases(Ha=40),thecentralstreamlinesareelongatedhorizontallyandthetemperaturestratificationinthecorediminishes(Fig.
2(b)).
AsHartmannnumberisfurtherincreased(Ha=100),theisothermsarealmostparallelandarenearlyconductionlike(Fig.
2(c))andthisisduetothesuppressionofconvectionbythemagneticfield.
Alsoitcanbeseenthattheflowfieldbecomesbicellularasstrengthofthemagneticfieldisincreased.
Itcanalsobeseenfromthefigure3(aandb)thattheflowoscillationinshallowcavityissuppressedmoreeffectivelybytheaxialmagneticfieldthantheradialmagneticfield.
'r'zBguruzu2TR1R2T1T2'r(a)Ha=0(b)Ha=40(c)Ha=100theStreamlinestheisothermvelocityprofilesFigure2:dynamics,thermalsFieldsandvelocityfromvariousvaluesofHartmann,A=1,k=2,Ra=104and=/2.
Thisbehaviorisconsistentwiththefactthatthemagneticfieldsuppressestheflowmoreeffectivelywhenthemagneticfieldisimposedperpendiculartothedirectionoftheflow.
1.
01.
52.
0-20-15-10-5051015wrHa=0Ha=20Ha=40Ha=60Ha=80Ha=100Ha=200-a-0,00,51,0-20-1001020uzHa=0Ha=20Ha=40Ha=60Ha=80Ha=100Ha=200-b-Figure3:Vertical(a)andhorizontal(b)velocityatmidheightfor,A=1,k=2,Ra=104and=/2.
4.
HeatTransferQuantitativeheattransferresultsarepresentedintermsofaverageNusseltnumber.
TheeffectofmagneticfieldontheheattransferrateisshowninFig.
4.
Asexpected,foragivenvalueofRaitcanbeseenthatNuisadecreasingfunctionofHa.
ThisisduetothefactthatwiththeincreaseinHartmannnumbertheconvectionisprogressivelyreducedbythemagneticdrag,resultinginalowerheattransfer.
102103104105106110__NuRaHa=020406080100Figure4:LocalheattransferratefordeferentvaluesofHaandRa5.
ConclusionThenumericalresultsindicatethatthemagneticfieldsuppressestheconvectiveflowandeliminatestheflowoscillations.
QuantitativeresultsarepresentedintermsofthelocalandaverageNusseltnumber.
TheheattransferrateincreaseswithradiiratioanddecreaseswiththeHartmannnumbers.
Thedirectionofmagneticfieldplaysanimportantroleinsuppressingtheconvectiveflows.
Themagneticfieldismoreeffectivewhenitisperpendiculartothedirectionoftheprimaryflow.
Thisphenomenonhasaseriousimplicationonthedesignofmagneticsystemsforstabilizingorweakeningtheconvectiveeffects.
Thenumericalresultsofthepresentstudyareingoodagreementwiththeexistingnumericalstudies,intheabsenceofmagneticfield.
BibliographicReferences1.
R.
Mhner,U.
Müller,1999,Anumericalinvestigationofthreedimensionalmagnetoconvectioninrectangularcavities.
Int.
J.
HeatMassTransfer42,1111-1121.
2.
BednarzT.
,FornalikE.
,TagawaT.
,OzoeH.
,SzmydJ.
S.
,2005,Experimentalandnumericalanalysesofmagneticconvectionofparamagneticfluidinacubeheatedandcooledfromopposingverticalswalls.
Int.
J.
ThermalSc.
,44,933-943.
3.
J.
S.
Walkera,D.
Henry,H.
BenHadid,2002,Magneticstabilizationofthebuoyantconvectionintheliquid-encapsulatedCzochralskiprocess.
J.
ofCrystalGrowth243108–116.
4.
KrakovM.
S.
,NikiforovI.
V.
,ReksA.
G.
,2005,Influenceoftheuniformmagneticfieldonnaturalconvectionincubicenclosure:experimentandnumericalsimulation.
J.
Magn.
Mater.
,289,272-274.
5.
Y.
Inatomi,2006,BuoyancyconvectionincylindricalconductingmeltwithlowGrashofnumberunderuniformstaticmagneticfield.
Int.
J.
HeatMassTransfer494821–4830.
6.
M.
Sankar,M.
Venkatachalappa,I.
S.
Shivakumara,2006,Effectofmagneticfieldonnaturalconvectioninaverticalcylindricalannulus.
Int.
J.
Eng.
Sci.
441556–1570.
Jamai1,A.
Elamari1,M.
ElGanaoui2,F.
S.
Oueslati1,B.
Pateyron2etH.
Sammouda31LETTM,Departementofphysics,F.
S.
T,Tunisia.
2SPCTSUMR6638CNRS,FaculteofSciences,87000Limoges,France.
3ESST-H.
Sousse,Tunisiehanene_jamai@yahoo.
frAbstract:COMSOLindustrialsoftwareisofferinganimportantalternativetohomecodesformodelingandsimulationofcomplexproblemswithincludingcoupledeffectsonHeatandMasseTransfers.
ThepresentworkfocusesonlowPrandtlnumberfluidmeltssubjecttosymmetrybreakingandtransitiontounsteadyregimes.
TheseconfigurationsareforpracticalinterestincrystalgrowthindustrynamelytheBridgmanconfigurationiswidelyusedtoproducesinglecrystalsofcompoundsemi-conductorsand2Denclosuresprovideabasicmodelforstudyinghydrodynamicregimeoccurringonsuchprocesses.
Afirststepinthisworkistostudytheeffectofmagneticfieldonliquidmetalflowandheattransferoccurringinanannularcavity.
Keywords:Naturalconvection,magneto-convection,moltenmetal(fluidsonlowPrandtlnumber),annularcavityNomenclatureΤAspectratioDiensionlessmagneticvector(tesla)GravitationalvectoraccelerationΤ)Cylinderheight(m)ElectricVectordensityΤRatioofraysDimonsionlesspressiontime(s)Differenceofrays(m)TDimensionlesstemperaturr,zDimensionlessradialandaxialcoordinatesu,wRadialandaxialvelocityvectorcomponentsGrecsLettersThermaldiffusivity(m2/s)Thermalexpansioncoefficient(1/k)Density(kg/m3)Dynamicviscosity,(kg/m.
s)ElectricConductivity(S/m)ElectricpotentielleFonction1.
IntroductionLiquidsmetals,inthepresenceofamagneticfield(magneto-convection)havearethesubjectofagreatnumberofresearches.
Theinterestoftheseflowsliesintheirpresenceinmanynaturalandappliedphenomena.
Inthesameway,metallurgicalindustry,coolingenginesinnuclearindustry,crystallinegrowthfortheindustryofthesemiconductorsgenerateseveralquestionsforcontrollingthestabilityoftheseflows[1,2,3].
Theappearanceoftheconvectionduringcrystalgrowthcanproduceinhomogenuitieswhichleadtostriationsandwhichaffectthequalityoftheobtainedcrystals[4].
Inthesecases,theapplicationofmagneticfieldtothethermalconvectionappearsofgreatimportanceforthecontrolofthestabilityoftheseflowsandtheheattransferswhileresulting.
Ourstudyrelatestotheconvectiveflow,ofafluidoflowPrandtlnumberinanannularandverticalcavityformedbytwocoaxialcylinders,differentiallyheatedinthepresenceofaconstantmagneticfield[5,6].
2.
MathematicalModelThesystemconsideredinthispaperisshownschematicallyinfig.
1Boussinesqapproximationisadopted,thatthedensityoffluidisgivenby:001TTT(1)Thedimensionlessequationswhichdescribetheproblem,arerespectivelyequationsof,continuity,conservationofthemomentum,theOhmlawandtheenergyconservationequation:Figure1.
Geometricalconfiguration0uuwrrz(1)22222221PrPr.
.
BruuuvPuuuuuwHajeutrzrrrrrzr(2)222221PrPrPr.
.
BzwwwPwwwuwRaTHajeutrzzrrrz(3)()BjVe(4)22221TTTTTTuwtrzrrrz(6)WithBeistheunitvectorinthedirectionofmagneticfieldB3RagTl,.
.
HalB,andPraretheRayleigh,HartmannandPrandtlnumbers,whicharethedimensionlessnumbersgoverningtheproblem.
TheboundaryconditionsTheboundaryconditionsadoptedfortheresolutionoftheproblemare:HydrodynamicCondition:zerovelocityonthewalls.
u=w=0ThermalCondition:1122:,:,0,1:0rRTTrRTTzTzElectricalconditions:electricalinsulationonthewalls.
0jnThegoverningequationsalongwiththeboundaryconditionsaresolvednumericallyusingtheCOMSOLcodewhichbasedonthefiniteelementmethod,allowingacouplingbetweenthedynamic,thermalandelectricproblems.
Totestandassessgridindependenceofthenumericalscheme,variousmeshesareexamined.
Veryfinenouniformgridsclosetothewallsareadopted.
Weassumethatthesolutionisconvergedwhentheerrorislessthan10-6.
3.
TheeffectofanaxialmagneticfieldInthispart,themagneticfieldissupposedaccordingtothezdirectionandweneglecttheelectrictermintheforceofLaplace.
WepresentonFigure2,theStreamlines,theisothermsandvelocityprofilesforRa=104andtheaspectratioA=1forvariousvaluesoftheHartmannnumber.
Intheabsenceofmagneticfield(Ha=0,Fig.
2(a)),theflowexhibitsasimplecirculatingpatternrisingalongthehotwallanddescendingalongthecoldwallofthecavity.
Itisinterestingtonotethatasthestrengthofthemagneticfieldincreases(Ha=40),thecentralstreamlinesareelongatedhorizontallyandthetemperaturestratificationinthecorediminishes(Fig.
2(b)).
AsHartmannnumberisfurtherincreased(Ha=100),theisothermsarealmostparallelandarenearlyconductionlike(Fig.
2(c))andthisisduetothesuppressionofconvectionbythemagneticfield.
Alsoitcanbeseenthattheflowfieldbecomesbicellularasstrengthofthemagneticfieldisincreased.
Itcanalsobeseenfromthefigure3(aandb)thattheflowoscillationinshallowcavityissuppressedmoreeffectivelybytheaxialmagneticfieldthantheradialmagneticfield.
'r'zBguruzu2TR1R2T1T2'r(a)Ha=0(b)Ha=40(c)Ha=100theStreamlinestheisothermvelocityprofilesFigure2:dynamics,thermalsFieldsandvelocityfromvariousvaluesofHartmann,A=1,k=2,Ra=104and=/2.
Thisbehaviorisconsistentwiththefactthatthemagneticfieldsuppressestheflowmoreeffectivelywhenthemagneticfieldisimposedperpendiculartothedirectionoftheflow.
1.
01.
52.
0-20-15-10-5051015wrHa=0Ha=20Ha=40Ha=60Ha=80Ha=100Ha=200-a-0,00,51,0-20-1001020uzHa=0Ha=20Ha=40Ha=60Ha=80Ha=100Ha=200-b-Figure3:Vertical(a)andhorizontal(b)velocityatmidheightfor,A=1,k=2,Ra=104and=/2.
4.
HeatTransferQuantitativeheattransferresultsarepresentedintermsofaverageNusseltnumber.
TheeffectofmagneticfieldontheheattransferrateisshowninFig.
4.
Asexpected,foragivenvalueofRaitcanbeseenthatNuisadecreasingfunctionofHa.
ThisisduetothefactthatwiththeincreaseinHartmannnumbertheconvectionisprogressivelyreducedbythemagneticdrag,resultinginalowerheattransfer.
102103104105106110__NuRaHa=020406080100Figure4:LocalheattransferratefordeferentvaluesofHaandRa5.
ConclusionThenumericalresultsindicatethatthemagneticfieldsuppressestheconvectiveflowandeliminatestheflowoscillations.
QuantitativeresultsarepresentedintermsofthelocalandaverageNusseltnumber.
TheheattransferrateincreaseswithradiiratioanddecreaseswiththeHartmannnumbers.
Thedirectionofmagneticfieldplaysanimportantroleinsuppressingtheconvectiveflows.
Themagneticfieldismoreeffectivewhenitisperpendiculartothedirectionoftheprimaryflow.
Thisphenomenonhasaseriousimplicationonthedesignofmagneticsystemsforstabilizingorweakeningtheconvectiveeffects.
Thenumericalresultsofthepresentstudyareingoodagreementwiththeexistingnumericalstudies,intheabsenceofmagneticfield.
BibliographicReferences1.
R.
Mhner,U.
Müller,1999,Anumericalinvestigationofthreedimensionalmagnetoconvectioninrectangularcavities.
Int.
J.
HeatMassTransfer42,1111-1121.
2.
BednarzT.
,FornalikE.
,TagawaT.
,OzoeH.
,SzmydJ.
S.
,2005,Experimentalandnumericalanalysesofmagneticconvectionofparamagneticfluidinacubeheatedandcooledfromopposingverticalswalls.
Int.
J.
ThermalSc.
,44,933-943.
3.
J.
S.
Walkera,D.
Henry,H.
BenHadid,2002,Magneticstabilizationofthebuoyantconvectionintheliquid-encapsulatedCzochralskiprocess.
J.
ofCrystalGrowth243108–116.
4.
KrakovM.
S.
,NikiforovI.
V.
,ReksA.
G.
,2005,Influenceoftheuniformmagneticfieldonnaturalconvectionincubicenclosure:experimentandnumericalsimulation.
J.
Magn.
Mater.
,289,272-274.
5.
Y.
Inatomi,2006,BuoyancyconvectionincylindricalconductingmeltwithlowGrashofnumberunderuniformstaticmagneticfield.
Int.
J.
HeatMassTransfer494821–4830.
6.
M.
Sankar,M.
Venkatachalappa,I.
S.
Shivakumara,2006,Effectofmagneticfieldonnaturalconvectioninaverticalcylindricalannulus.
Int.
J.
Eng.
Sci.
441556–1570.
- potentiellewww.tl222666.com相关文档
- Releasewww.tl222666.com
- PIC32MX250F128C-50I/TL
- occurrencewww.tl222666.com
- disputeswww.tl222666.com
- rieurwww.tl222666.com
- 接收器www.tl222666.com
inlicloud48元/月，云主机,2核1G/200Mbps，可选安徽/上海联通/广州移动/江门移动NAT
inlicloud怎么样?inlicloud(引力主机)主要产品为国内NAT系列VPS，目前主要有：上海联通NAT(200Mbps带宽)、宿州联通NAT(200Mbps带宽)、广州移动NAT(200Mbps带宽)。根据官方的说法国内的NAT系列VPS不要求备案、不要求实名、对中转要求也不严格，但是，禁止任何形式的回国!安徽nat/上海联通/广州移动/江门移动nat云主机,2核1G/200Mbps仅...
建站选择网站域名和IP主机地址之间关系和注意要点
今天中午的时候有网友联系到在选择网站域名建站和主机的时候问到域名和IP地址有没有关联，或者需要注意的问题。毕竟我们在需要建站的时候，我们需要选择网站域名和主机，而主机有虚拟主机，包括共享和独立IP，同时还有云服务器、独立服务器、站群服务器等形式。通过这篇文章，简单的梳理关于网站域名和IP之间的关系。第一、什么是域名所谓网站域名，就是我们看到的类似"www.laozuo.org"，我们可以通过直接记...
VoLLcloud6折限量,香港CMI云服务器三网直连-200M带宽
vollcloud LLC首次推出6折促销，本次促销福利主要感恩与回馈广大用户对于我们的信任与支持，我们将继续稳步前行，为广大用户们提供更好的产品和服务，另外，本次促销码共限制使用30个，个人不限购，用完活动结束，同时所有vps产品支持3日内无条件退款和提供免费试用。需要了解更多产品可前往官网查看!vollcloud优惠码：VoLLcloud终生6折促销码：Y5C0V7R0YW商品名称CPU内存S...
www.tl222666.com为你推荐
-
今日油条油条晚上炸好定型明天可再复炸吗？百度关键词工具常见百度关键词挖掘方法分别是什么请列举？mole.61.com摩尔庄园RK的秘密是什么？mole.61.com摩尔大陆？？？？？广告法广告法有什么字不能用javlibrary.comImage Library Sell Photos Digital Photos Photo Sharing Photo Restoration Digital Photos Photo Albumswww.toutoulu.comWWW【toutoulu】cOM怎么搜不到了？到哪里能看到toutoulu视频？龚如敏请问这张图片出自哪里？月风随笔散文校园月色600字初中作文ename.com做自己的网站、在哪里买域名啊？