��sr!com.femlab.server.ModelFileHeader�D���%LtagstLcom/femlab/util/FlStringList;Ltypesq~LvrsntLcom/femlab/util/FlVersion;xpwsrcom.femlab.util.FlVersion��%�/B = IbuildImajorLdatetLjava/lang/String;Lextq~Lnameq~Lrcsq~L reactionExtq~L reactionNameq~L scriptExtq~L scriptNameq~xpwtCOMSOL Script 1.3tt#COMSOL Reaction Engineering Lab 1.5q~t COMSOL 3.5q~w�t $Name: $t$Date: 2008/09/19 16:09:48 $xur[Ljava.lang.String;��V��{Gxpt modelinfotxfemtguitfem0tg7tg12tg14tg15tg16tg17tg21tfem2213t fem2213.0q~q~tfem2221t fem2221.0q~q~t mfileinfouq~ q~t femstructt guistructq~ tdrawq~"q~"q~"q~"q~"q~"tgeomtmeshtsolutiontxmeshq~#q~$q~%q~&q~xsrcom.femlab.api.client.ModelInfo�^���%Ldescrq~LdocURLq~[imaget[Bxpwptpxuq~ t]sclear xfem clear vrsn vrsn.name = 'COMSOL 3.5'; vrsn.ext = ''; vrsn.major = 0; vrsn.build = 494; vrsn.rcs = '$Name: $'; vrsn.date = '$Date: 2008/09/19 16:09:48 $'; xfem.version = vrsn; xfem.id = 2210; xfem.geomdata = 'geom'; xfem.eqvars = 'on'; xfem.cplbndeq = 'on'; xfem.cplbndsh = 'off'; xfem.drawvalid = 'on'; xfem.geomvalid = 'on'; xfem.solvalid = 'on'; xfem.linshape = 'on'; xfem.linshapetol = 0.1; xfem.meshtime = 't'; clear appl appl.mode.class = 'PerpendicularCurrents'; appl.mode.type = 'cartesian'; appl.dim = {'Az','redAz'}; appl.sdim = {'x','y','z'}; appl.name = 'emqa'; appl.module = 'ACDC'; appl.shape = {'shlag(2,''Az'')'}; appl.gporder = 4; appl.cporder = 2; appl.sshape = 2; appl.border = 'off'; appl.assignsuffix = '_emqa'; clear prop prop.elemdefault='Lag2'; prop.analysis='transient'; prop.biasapplmode='none'; prop.solvefor='ATot'; prop.backgroundFieldSpec='A_external'; prop.frame='ref'; clear weakconstr weakconstr.value = 'off'; weakconstr.dim = {'lm1','lm2'}; prop.weakconstr = weakconstr; prop.constrtype='ideal'; appl.prop = prop; clear pnt pnt.I0 = {'0'}; pnt.style = {{{'0'},{'0','0','0'}}}; pnt.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; appl.pnt = pnt; clear bnd bnd.name = {'',''}; bnd.H0 = {{'0';'0'},{'0';'0'}}; bnd.Js0z = {'0','0'}; bnd.A0z = {'0','0'}; bnd.murbnd = {{'1','0';'0','1'},{'1','0';'0','1'}}; bnd.murext = {'1','1'}; bnd.epsilonrbnd = {'1','1'}; bnd.sigmabnd = {'0','0'}; bnd.eta = {'1','1'}; bnd.Esz = {'0','0'}; bnd.d = {'0','0'}; bnd.index = {'0','0'}; bnd.chsrcdst = {'0','0'}; bnd.pertype = {'sym','sym'}; bnd.nsect = {'2','2'}; bnd.type = {'A0','cont'}; bnd.style = {{{'0'},{'0','0','0'},{'solid'}},{{'0'},{'0','255','0'},{'solid'}}}; bnd.ind = [1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1]; appl.bnd = bnd; clear equ equ.shape = {[1],[1],[1],[1]}; equ.gporder = {{1},{1},{1},{1}}; equ.cporder = {{1},{1},{1},{1}}; equ.init = {{'0';'0'},{'0';'0'},{'0';'0'},{'0';'0'}}; equ.usage = {1,1,1,1}; equ.name = {'','','',''}; equ.mur = {{'1','0';'0','1'},{'mat3_MUR(normB_emqa[1/T])','0';'0','mat3_MUR(normB_emqa[1/T])'}, ... {'mat5_mur','0';'0','mat5_mur'},{'mat5_mur','0';'0','mat5_mur'}}; equ.elconstrel = {'epsr','epsr','epsr','epsr'}; equ.Pz = {'0','0','0','0'}; equ.Drz = {'0','0','0','0'}; equ.magconstrel = {'mur','mur','mur','mur'}; equ.M = {{'0';'0'},{'0';'0'},{'0';'0'},{'0';'0'}}; equ.Br = {{'0';'0'},{'0';'0'},{'0';'0'},{'0';'0'}}; equ.fH = {{'1/mu0_emqa*Bx_emqa';'1/mu0_emqa*By_emqa'},{'1/mu0_emqa*Bx_emqa'; ... '1/mu0_emqa*By_emqa'},{'1/mu0_emqa*Bx_emqa';'1/mu0_emqa*By_emqa'},{'1/mu0_emqa*Bx_emqa'; ... '1/mu0_emqa*By_emqa'}}; equ.normfH = {'1/mu0_emqa*normB_emqa','mat3_HB(normB_emqa[1/T])[A/m]','1/mu0_emqa*normB_emqa', ... '1/mu0_emqa*normB_emqa'}; equ.epsilonr = {'1','mat3_epsilonr','mat5_epsilonr','mat5_epsilonr'}; equ.sigma = {'mat2_sigma','mat3_sigma','mat5_sigma','mat5_sigma'}; equ.Jez = {'0','0','(1-flc2hs(t-0.2,0.1))*R','(flc2hs(t-0.2,0.1)-1)*R'}; equ.v = {{'0';'0'},{'0';'0'},{'0';'0'},{'0';'0'}}; equ.deltaV = {'0','0','0','0'}; equ.L = {'1','1','1','1'}; equ.maxwell = {{},{},{},{}}; equ.nTsrcpnt = {{{'0';'0'}},{{'0';'0'}},{{'0';'0'}},{{'0';'0'}}}; equ.Sd = {{'Sdx_guess_emqa';'Sdy_guess_emqa'},{'Sdx_guess_emqa';'Sdy_guess_emqa'}, ... {'Sdx_guess_emqa';'Sdy_guess_emqa'},{'Sdx_guess_emqa';'Sdy_guess_emqa'}}; equ.dr = {'dr_guess_emqa','dr_guess_emqa','dr_guess_emqa','dr_guess_emqa'}; equ.S0 = {{'S0x_guess_emqa';'S0y_guess_emqa'},{'S0x_guess_emqa';'S0y_guess_emqa'}, ... {'S0x_guess_emqa';'S0y_guess_emqa'},{'S0x_guess_emqa';'S0y_guess_emqa'}}; equ.R0 = {'R0_guess_emqa','R0_guess_emqa','R0_guess_emqa','R0_guess_emqa'}; equ.user = {{'0';'0'},{'0';'0'},{'0';'0'},{'0';'0'}}; equ.Stype = {'none','none','none','none'}; equ.coordOn = {{'0';'0'},{'0';'0'},{'0';'0'},{'0';'0'}}; equ.rOn = {'0','0','0','0'}; equ.srcpnt = {{'0';'0'},{'0';'0'},{'0';'0'},{'0';'0'}}; equ.srcaxis = {{'0';'0'},{'0';'0'},{'0';'0'},{'0';'0'}}; equ.style = {{{'0'},{'193','193','193'}},{{'0'},{'0','0','255'}},{{'0'},{'255', ... '0','255'}},{{'0'},{'0','255','255'}}}; equ.ind = [1,2,3,4,2,3,4]; appl.equ = equ; appl.var = {'epsilon0','8.854187817e-12', ... 'mu0','4*pi*1e-7'}; xfem.appl{1} = appl; xfem.geom = flbinary('fem2213','geom','2 coils, iron core.mph'); xfem.mesh = flbinary('fem2213.0','mesh','2 coils, iron core.mph'); xfem.sdim = {'x','y'}; xfem.frame = {'ref'}; xfem.shape = {'shlag(2,''Az'')'}; xfem.gporder = 4; xfem.cporder = 2; xfem.sshape = 2; xfem.simplify = 'on'; xfem.border = 1; xfem.form = 'coefficient'; clear units; units.basesystem = 'SI'; xfem.units = units; clear equ equ.shape = {[1],[1],[1],[1]}; equ.gporder = {{1},{1},{1},{1}}; equ.cporder = {{1},{1},{1},{1}}; equ.init = {{'0'},{'0'},{'0'},{'0'}}; equ.dinit = {{'0'},{'0'},{'0'},{'0'}}; equ.weak = {{'dVol_emqa*(Jz_emqa*test(depAz_emqa)-Hx_emqa*test(curlAx_emqa)-Hy_emqa*test(curlAy_emqa))'}, ... {'dVol_emqa*(Jz_emqa*test(depAz_emqa)-Hx_emqa*test(curlAx_emqa)-Hy_emqa*test(curlAy_emqa))'}, ... {'dVol_emqa*(Jz_emqa*test(depAz_emqa)-Hx_emqa*test(curlAx_emqa)-Hy_emqa*test(curlAy_emqa))'}, ... {'dVol_emqa*(Jz_emqa*test(depAz_emqa)-Hx_emqa*test(curlAx_emqa)-Hy_emqa*test(curlAy_emqa))'}}; equ.dweak = {{'0'},{'0'},{'0'},{'0'}}; equ.constr = {{'0'},{'0'},{'0'},{'0'}}; equ.constrf = {{'0'},{'0'},{'0'},{'0'}}; equ.c = {{{'0'}},{{'0'}},{{'0'}},{{'0'}}}; equ.a = {{'0'},{'0'},{'0'},{'0'}}; equ.f = {{'0'},{'0'},{'0'},{'0'}}; equ.ea = {{'0'},{'0'},{'0'},{'0'}}; equ.da = {{'0'},{'0'},{'0'},{'0'}}; equ.al = {{{'0';'0'}},{{'0';'0'}},{{'0';'0'}},{{'0';'0'}}}; equ.be = {{{'0';'0'}},{{'0';'0'}},{{'0';'0'}},{{'0';'0'}}}; equ.ga = {{{'0';'0'}},{{'0';'0'}},{{'0';'0'}},{{'0';'0'}}}; equ.sshape = {[1],[1],[1],[1]}; equ.sshapedim = {{1},{1},{1},{1}}; equ.ind = [1,2,3,4,2,3,4]; equ.dim = {'Az'}; equ.var = {'dr_guess_emqa',{'0','0','0','0'}, ... 'R0_guess_emqa',{'0','0','0','0'}, ... 'Sx_emqa',{'x','x','x','x'}, ... 'S0x_guess_emqa',{'0','0','0','0'}, ... 'Sdx_guess_emqa',{'0','0','0','0'}, ... 'Sy_emqa',{'y','y','y','y'}, ... 'S0y_guess_emqa',{'0','0','0','0'}, ... 'Sdy_guess_emqa',{'0','0','0','0'}, ... 'curlAx_emqa',{'Azy','Azy','Azy','Azy'}, ... 'curlAy_emqa',{'-Azx','-Azx','-Azx','-Azx'}, ... 'dVol_emqa',{'detJ_emqa','detJ_emqa','detJ_emqa','detJ_emqa'}, ... 'Bx_emqa',{'curlAx_emqa','curlAx_emqa','curlAx_emqa','curlAx_emqa'}, ... 'By_emqa',{'curlAy_emqa','curlAy_emqa','curlAy_emqa','curlAy_emqa'}, ... 'Hx_emqa',{'Bx_emqa/(mur_emqa*mu0_emqa)','Bx_emqa/(mur_emqa*mu0_emqa)', ... 'Bx_emqa/(mur_emqa*mu0_emqa)','Bx_emqa/(mur_emqa*mu0_emqa)'}, ... 'Hy_emqa',{'By_emqa/(mur_emqa*mu0_emqa)','By_emqa/(mur_emqa*mu0_emqa)', ... 'By_emqa/(mur_emqa*mu0_emqa)','By_emqa/(mur_emqa*mu0_emqa)'}, ... 'mu_emqa',{'mu0_emqa*mur_emqa','mu0_emqa*mur_emqa','mu0_emqa*mur_emqa', ... 'mu0_emqa*mur_emqa'}, ... 'muxx_emqa',{'mu0_emqa*murxx_emqa','mu0_emqa*murxx_emqa','mu0_emqa*murxx_emqa', ... 'mu0_emqa*murxx_emqa'}, ... 'muxy_emqa',{'mu0_emqa*murxy_emqa','mu0_emqa*murxy_emqa','mu0_emqa*murxy_emqa', ... 'mu0_emqa*murxy_emqa'}, ... 'muyx_emqa',{'mu0_emqa*muryx_emqa','mu0_emqa*muryx_emqa','mu0_emqa*muryx_emqa', ... 'mu0_emqa*muryx_emqa'}, ... 'muyy_emqa',{'mu0_emqa*muryy_emqa','mu0_emqa*muryy_emqa','mu0_emqa*muryy_emqa', ... 'mu0_emqa*muryy_emqa'}, ... 'Jpz_emqa',{'sigma_emqa*deltaV_emqa/L_emqa','sigma_emqa*deltaV_emqa/L_emqa', ... 'sigma_emqa*deltaV_emqa/L_emqa','sigma_emqa*deltaV_emqa/L_emqa'}, ... 'Ez_emqa',{'-diff(Az,t)','-diff(Az,t)','-diff(Az,t)','-diff(Az,t)'}, ... 'Jz_emqa',{'Jpz_emqa+Jiz_emqa+Jez_emqa','Jpz_emqa+Jiz_emqa+Jez_emqa', ... 'Jpz_emqa+Jiz_emqa+Jez_emqa','Jpz_emqa+Jiz_emqa+Jez_emqa'}, ... 'Pox_emqa',{'-Ez_emqa*Hy_emqa','-Ez_emqa*Hy_emqa','-Ez_emqa*Hy_emqa', ... '-Ez_emqa*Hy_emqa'}, ... 'Poy_emqa',{'Ez_emqa*Hx_emqa','Ez_emqa*Hx_emqa','Ez_emqa*Hx_emqa', ... 'Ez_emqa*Hx_emqa'}, ... 'normE_emqa',{'abs(Ez_emqa)','abs(Ez_emqa)','abs(Ez_emqa)','abs(Ez_emqa)'}, ... 'Jiz_emqa',{'sigma_emqa*Ez_emqa','sigma_emqa*Ez_emqa','sigma_emqa*Ez_emqa', ... 'sigma_emqa*Ez_emqa'}, ... 'Q_emqa',{'Jz_emqa*(Ez_emqa+deltaV_emqa/L_emqa+Jez_emqa/sigma_emqa)', ... 'Jz_emqa*(Ez_emqa+deltaV_emqa/L_emqa+Jez_emqa/sigma_emqa)','Jz_emqa*(Ez_emqa+deltaV_emqa/L_emqa+Jez_emqa/sigma_emqa)', ... 'Jz_emqa*(Ez_emqa+deltaV_emqa/L_emqa+Jez_emqa/sigma_emqa)'}, ... 'W_emqa',{'Wm_emqa','Wm_emqa','Wm_emqa','Wm_emqa'}, ... 'dW_emqa',{'dVol_emqa*W_emqa','dVol_emqa*W_emqa','dVol_emqa*W_emqa', ... 'dVol_emqa*W_emqa'}, ... 'Wm_emqa',{'0.5*(Hx_emqa*Bx_emqa+Hy_emqa*By_emqa)','0.5*(Hx_emqa*Bx_emqa+Hy_emqa*By_emqa)', ... '0.5*(Hx_emqa*Bx_emqa+Hy_emqa*By_emqa)','0.5*(Hx_emqa*Bx_emqa+Hy_emqa*By_emqa)'}, ... 'FLtzx_emqa',{'-Jz_emqa*By_emqa','-Jz_emqa*By_emqa','-Jz_emqa*By_emqa', ... '-Jz_emqa*By_emqa'}, ... 'FLtzy_emqa',{'Jz_emqa*Bx_emqa','Jz_emqa*Bx_emqa','Jz_emqa*Bx_emqa', ... 'Jz_emqa*Bx_emqa'}, ... 'normFLtz_emqa',{'sqrt(abs(FLtzx_emqa)^2+abs(FLtzy_emqa)^2)','sqrt(abs(FLtzx_emqa)^2+abs(FLtzy_emqa)^2)', ... 'sqrt(abs(FLtzx_emqa)^2+abs(FLtzy_emqa)^2)','sqrt(abs(FLtzx_emqa)^2+abs(FLtzy_emqa)^2)'}, ... 'normM_emqa',{'sqrt(abs(Mx_emqa)^2+abs(My_emqa)^2)','sqrt(abs(Mx_emqa)^2+abs(My_emqa)^2)', ... 'sqrt(abs(Mx_emqa)^2+abs(My_emqa)^2)','sqrt(abs(Mx_emqa)^2+abs(My_emqa)^2)'}, ... 'normBr_emqa',{'sqrt(abs(Brx_emqa)^2+abs(Bry_emqa)^2)','sqrt(abs(Brx_emqa)^2+abs(Bry_emqa)^2)', ... 'sqrt(abs(Brx_emqa)^2+abs(Bry_emqa)^2)','sqrt(abs(Brx_emqa)^2+abs(Bry_emqa)^2)'}, ... 'normH_emqa',{'sqrt(abs(Hx_emqa)^2+abs(Hy_emqa)^2)','sqrt(abs(Hx_emqa)^2+abs(Hy_emqa)^2)', ... 'sqrt(abs(Hx_emqa)^2+abs(Hy_emqa)^2)','sqrt(abs(Hx_emqa)^2+abs(Hy_emqa)^2)'}, ... 'normB_emqa',{'sqrt(abs(Bx_emqa)^2+abs(By_emqa)^2)','sqrt(abs(Bx_emqa)^2+abs(By_emqa)^2)', ... 'sqrt(abs(Bx_emqa)^2+abs(By_emqa)^2)','sqrt(abs(Bx_emqa)^2+abs(By_emqa)^2)'}, ... 'normJ_emqa',{'abs(Jz_emqa)','abs(Jz_emqa)','abs(Jz_emqa)','abs(Jz_emqa)'}, ... 'Evz_emqa',{'diff(x,t)*By_emqa-diff(y,t)*Bx_emqa','diff(x,t)*By_emqa-diff(y,t)*Bx_emqa', ... 'diff(x,t)*By_emqa-diff(y,t)*Bx_emqa','diff(x,t)*By_emqa-diff(y,t)*Bx_emqa'}, ... 'normEv_emqa',{'abs(Evz_emqa)','abs(Evz_emqa)','abs(Evz_emqa)','abs(Evz_emqa)'}, ... 'normPo_emqa',{'sqrt(abs(Pox_emqa)^2+abs(Poy_emqa)^2)','sqrt(abs(Pox_emqa)^2+abs(Poy_emqa)^2)', ... 'sqrt(abs(Pox_emqa)^2+abs(Poy_emqa)^2)','sqrt(abs(Pox_emqa)^2+abs(Poy_emqa)^2)'},'Pz_emqa',{'0','0','0','0'}, ... 'Drz_emqa',{'0','0','0','0'}, ... 'normfH_emqa',{'normB_emqa/mu0_emqa','mat3_HB(normB_emqa[1/T])[A/m]', ... 'normB_emqa/mu0_emqa','normB_emqa/mu0_emqa'}, ... 'epsilonr_emqa',{'1','mat3_epsilonr','mat5_epsilonr','mat5_epsilonr'}, ... 'sigma_emqa',{'mat2_sigma','mat3_sigma','mat5_sigma','mat5_sigma'}, ... 'Jez_emqa',{'0','0','(1-flc2hs(-0.2+t,0.1))*R','(-1+flc2hs(-0.2+t,0.1))*R'}, ... 'deltaV_emqa',{'0','0','0','0'}, ... 'L_emqa',{'1','1','1','1'}, ... 'dr_emqa',{'dr_guess_emqa','dr_guess_emqa','dr_guess_emqa','dr_guess_emqa'}, ... 'R0_emqa',{'R0_guess_emqa','R0_guess_emqa','R0_guess_emqa','R0_guess_emqa'}, ... 'ispml_emqa',{'0','0','0','0'}, ... 'srcpntx_emqa',{'0','0','0','0'}, ... 'srcpnty_emqa',{'0','0','0','0'}, ... 'userx_emqa',{'0','0','0','0'}, ... 'usery_emqa',{'0','0','0','0'}, ... 'Sdx_emqa',{'Sdx_guess_emqa','Sdx_guess_emqa','Sdx_guess_emqa','Sdx_guess_emqa'}, ... 'Sdy_emqa',{'Sdy_guess_emqa','Sdy_guess_emqa','Sdy_guess_emqa','Sdy_guess_emqa'}, ... 'S0x_emqa',{'S0x_guess_emqa','S0x_guess_emqa','S0x_guess_emqa','S0x_guess_emqa'}, ... 'S0y_emqa',{'S0y_guess_emqa','S0y_guess_emqa','S0y_guess_emqa','S0y_guess_emqa'}, ... 'SRcoord_emqa',{'','','',''}, ... 'rCylx_emqa',{'','','',''}, ... 'rCyly_emqa',{'','','',''}, ... 'detJ_emqa',{'1','1','1','1'}, ... 'Jxx_emqa',{'1','1','1','1'}, ... 'invJxx_emqa',{'1','1','1','1'}, ... 'Jxy_emqa',{'0','0','0','0'}, ... 'invJxy_emqa',{'0','0','0','0'}, ... 'Jyx_emqa',{'0','0','0','0'}, ... 'invJyx_emqa',{'0','0','0','0'}, ... 'Jyy_emqa',{'1','1','1','1'}, ... 'invJyy_emqa',{'1','1','1','1'}, ... 'depAz_emqa',{'Az','Az','Az','Az'}, ... 'mur_emqa',{'murxx_emqa','murxx_emqa','murxx_emqa','murxx_emqa'}, ... 'Mx_emqa',{'Bx_emqa/mu0_emqa-Hx_emqa','Bx_emqa/mu0_emqa-Hx_emqa', ... 'Bx_emqa/mu0_emqa-Hx_emqa','Bx_emqa/mu0_emqa-Hx_emqa'}, ... 'Brx_emqa',{'0','0','0','0'}, ... 'My_emqa',{'By_emqa/mu0_emqa-Hy_emqa','By_emqa/mu0_emqa-Hy_emqa', ... 'By_emqa/mu0_emqa-Hy_emqa','By_emqa/mu0_emqa-Hy_emqa'}, ... 'Bry_emqa',{'0','0','0','0'}, ... 'murxx_emqa',{'1','mat3_MUR(normB_emqa[1/T])','mat5_mur','mat5_mur'}, ... 'murxy_emqa',{'0','0','0','0'}, ... 'muryx_emqa',{'0','0','0','0'}, ... 'muryy_emqa',{'1','mat3_MUR(normB_emqa[1/T])','mat5_mur','mat5_mur'}, ... 'murinvxx_emqa',{'1/mur_emqa','1/mur_emqa','1/mur_emqa','1/mur_emqa'}, ... 'murinvxy_emqa',{'0','0','0','0'}, ... 'murinvyx_emqa',{'0','0','0','0'}, ... 'murinvyy_emqa',{'1/mur_emqa','1/mur_emqa','1/mur_emqa','1/mur_emqa'}}; equ.expr = {}; equ.bnd.weak = {{'0'}}; equ.bnd.gporder = {{1}}; equ.bnd.ind = [1,1,1,1,1,1,1]; equ.bnd.var = {}; equ.bnd.expr = {}; equ.lock = [0,0,0,0,0,0,0]; equ.mlock = {[0,0,0,0,0,0,0]}; xfem.equ = equ; clear bnd bnd.weak = {{'0'},{'0'}}; bnd.dweak = {{'0'},{'0'}}; bnd.constr = {{'-Az'},{'0'}}; bnd.constrf = {{'test(-Az)'},{'0'}}; bnd.q = {{'0'},{'0'}}; bnd.h = {{'0'},{'0'}}; bnd.g = {{'0'},{'0'}}; bnd.r = {{'0'},{'0'}}; bnd.shape = {[1],[1]}; bnd.sshape = {[1],[1]}; bnd.sshapedim = {{1},{1}}; bnd.gporder = {{1},{1}}; bnd.cporder = {{1},{1}}; bnd.init = {{''},{''}}; bnd.dinit = {{''},{''}}; bnd.ind = [1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1]; bnd.dim = {'Az'}; bnd.var = {'dVolbnd_emqa',{'1','1'}, ... 'murbnd_emqa',{'murbndxx_emqa','murbndxx_emqa'}, ... 'Jsz_emqa',{'unx*(Hy_emqa_down-Hy_emqa_up)-uny*(Hx_emqa_down-Hx_emqa_up)', ... 'unx*(Hy_emqa_down-Hy_emqa_up)-uny*(Hx_emqa_down-Hx_emqa_up)'}, ... 'unTx_emqa',{'-0.5*(Bx_emqa_up*Hx_emqa_up+By_emqa_up*Hy_emqa_up)*dnx+(dnx*Hx_emqa_up+dny*Hy_emqa_up)*Bx_emqa_up', ... '-0.5*(Bx_emqa_up*Hx_emqa_up+By_emqa_up*Hy_emqa_up)*dnx+(dnx*Hx_emqa_up+dny*Hy_emqa_up)*Bx_emqa_up'}, ... 'dnTx_emqa',{'-0.5*(Bx_emqa_down*Hx_emqa_down+By_emqa_down*Hy_emqa_down)*unx+(unx*Hx_emqa_down+uny*Hy_emqa_down)*Bx_emqa_down', ... '-0.5*(Bx_emqa_down*Hx_emqa_down+By_emqa_down*Hy_emqa_down)*unx+(unx*Hx_emqa_down+uny*Hy_emqa_down)*Bx_emqa_down'}, ... 'unTy_emqa',{'-0.5*(Bx_emqa_up*Hx_emqa_up+By_emqa_up*Hy_emqa_up)*dny+(dnx*Hx_emqa_up+dny*Hy_emqa_up)*By_emqa_up', ... '-0.5*(Bx_emqa_up*Hx_emqa_up+By_emqa_up*Hy_emqa_up)*dny+(dnx*Hx_emqa_up+dny*Hy_emqa_up)*By_emqa_up'}, ... 'dnTy_emqa',{'-0.5*(Bx_emqa_down*Hx_emqa_down+By_emqa_down*Hy_emqa_down)*uny+(unx*Hx_emqa_down+uny*Hy_emqa_down)*By_emqa_down', ... '-0.5*(Bx_emqa_down*Hx_emqa_down+By_emqa_down*Hy_emqa_down)*uny+(unx*Hx_emqa_down+uny*Hy_emqa_down)*By_emqa_down'}, ... 'Qs_emqa',{'Jsz_emqa*Ez_emqa','Jsz_emqa*Ez_emqa'}, ... 'nPo_emqa',{'nx_emqa*Pox_emqa+ny_emqa*Poy_emqa','nx_emqa*Pox_emqa+ny_emqa*Poy_emqa'}, ... 'FsLtzx_emqa',{'-Jsz_emqa*By_emqa','-Jsz_emqa*By_emqa'}, ... 'FsLtzy_emqa',{'Jsz_emqa*Bx_emqa','Jsz_emqa*Bx_emqa'}, ... 'normFsLtz_emqa',{'sqrt(abs(FsLtzx_emqa)^2+abs(FsLtzy_emqa)^2)','sqrt(abs(FsLtzx_emqa)^2+abs(FsLtzy_emqa)^2)'},'Js0z_emqa',{'0','0'}, ... 'A0z_emqa',{'0','0'}, ... 'murext_emqa',{'1','1'}, ... 'epsilonrbnd_emqa',{'1','1'}, ... 'sigmabnd_emqa',{'0','0'}, ... 'eta_emqa',{'1','1'}, ... 'Esz_emqa',{'0','0'}, ... 'd_emqa',{'0','0'}, ... 'index_emqa',{'0','0'}, ... 'nsect_emqa',{'2','2'}, ... 'nx_emqa',{'nx','nx'}, ... 'ny_emqa',{'ny','ny'}, ... 'murbndxx_emqa',{'1','1'}, ... 'murbndxy_emqa',{'0','0'}, ... 'murbndyx_emqa',{'0','0'}, ... 'murbndyy_emqa',{'1','1'}, ... 'H0x_emqa',{'0','0'}, ... 'H0y_emqa',{'0','0'}}; bnd.expr = {}; bnd.lock = [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]; bnd.mlock = {[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]}; xfem.bnd = bnd; clear pnt pnt.weak = {{'0'}}; pnt.dweak = {{'0'}}; pnt.constr = {{'0'}}; pnt.constrf = {{'0'}}; pnt.shape = {[1]}; pnt.sshape = {[1]}; pnt.sshapedim = {{1}}; pnt.init = {{''}}; pnt.dinit = {{''}}; pnt.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; pnt.dim = {'Az'}; pnt.var = {'I0_emqa',{'0'}}; pnt.expr = {}; pnt.lock = [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]; pnt.mlock = {[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]}; xfem.pnt = pnt; xfem.var = {'epsilon0_emqa','8.854187817000001e-012','mu0_emqa','4e-007*pi'}; xfem.expr = {}; clear elemmph clear elem elem.elem = 'elcplextr'; elem.g = {'1'}; src = cell(1,1); clear equ equ.expr = {{'dVol_emqa'}}; equ.map = {{'1'}}; equ.ind = {{'1','2','3','4','5','6','7'}}; src{1} = {{},{},equ}; elem.src = src; geomdim = cell(1,1); clear pnt pnt.map = {{'1'}}; pnt.ind = {{'1','2','3','4','5','6','7','8','9','10','11','12','13', ... '14','15','16','17','18','19','20','21','22','23','24','25','26','27', ... '28'}}; geomdim{1} = {pnt,{},{}}; elem.geomdim = geomdim; elem.var = {'dVol_emqa'}; map = cell(1,1); clear submap submap.type = 'local'; submap.expr = {'x','y'}; map{1} = submap; elem.map = map; elemmph{1} = elem; clear elem elem.elem = 'elcplscalar'; elem.g = {'1'}; src = cell(1,1); src{1} = {{},{},{}}; elem.src = src; geomdim = cell(1,1); geomdim{1} = {}; elem.geomdim = geomdim; elem.var = {}; elem.global = {}; elemmph{2} = elem; clear elem elem.elem = 'elcplscalar'; elem.g = {'1'}; src = cell(1,1); src{1} = {{},{},{}}; elem.src = src; geomdim = cell(1,1); geomdim{1} = {}; elem.geomdim = geomdim; elem.var = {}; elem.global = {}; elemmph{3} = elem; clear elem elem.elem = 'elcplscalar'; elem.g = {'1'}; src = cell(1,1); src{1} = {{},{},{}}; elem.src = src; geomdim = cell(1,1); geomdim{1} = {}; elem.geomdim = geomdim; elem.var = {}; elem.global = {}; elemmph{4} = elem; clear elem elem.elem = 'elcplextr'; elem.g = {'1'}; src = cell(1,1); src{1} = {{},{},{}}; elem.src = src; geomdim = cell(1,1); geomdim{1} = {{},{},{}}; elem.geomdim = geomdim; elem.var = {}; map = cell(1,0); elem.map = map; elemmph{5} = elem; xfem.elemmph = elemmph; clear draw draw.p.objs = {}; draw.p.name = {}; draw.c.objs = {}; draw.c.name = {}; draw.s.objs = {flbinary('g21','draw','2 coils, iron core.mph'),flbinary('g7','draw','2 coils, iron core.mph'),flbinary('g16','draw','2 coils, iron core.mph'),flbinary('g17','draw','2 coils, iron core.mph'),flbinary('g12','draw','2 coils, iron core.mph'),flbinary('g14','draw','2 coils, iron core.mph'),flbinary('g15','draw','2 coils, iron core.mph')}; draw.s.name = {'R2','SQ5','SQ4','R1','SQ1','SQ2','SQ3'}; xfem.draw = draw; xfem.const = {'R','1'}; xfem.globalexpr = {}; clear fcns xfem.functions = {}; xfem.sol = flbinary('xfem','solution','2 coils, iron core.mph'); xfem.xmcases = [0]; xfem.mcases = [0]; flbinary clear; xfem.rulingmode = 'emqa'; xfem.solform = 'weak'; clear lib lib.mat{1}.name='Iron'; lib.mat{1}.varname='mat1'; lib.mat{1}.variables.nu='0.29'; lib.mat{1}.variables.E='200e9[Pa]'; lib.mat{1}.variables.mur='4000'; lib.mat{1}.variables.sigma='1.12e7[S/m]'; lib.mat{1}.variables.epsilonr='1'; lib.mat{1}.variables.alpha='12.2e-6[1/K]'; lib.mat{1}.variables.C='440[J/(kg*K)]'; lib.mat{1}.variables.rho='7870[kg/m^3]'; lib.mat{1}.variables.k='76.2[W/(m*K)]'; lib.mat{2}.name='Air'; lib.mat{2}.varname='mat2'; lib.mat{2}.variables.nu0='nu0(T[1/K])[m^2/s]'; lib.mat{2}.variables.eta='eta(T[1/K])[Pa*s]'; lib.mat{2}.variables.gamma='1.4'; lib.mat{2}.variables.sigma='0[S/m]'; lib.mat{2}.variables.C='Cp(T[1/K])[J/(kg*K)]'; lib.mat{2}.variables.rho='rho(p[1/Pa],T[1/K])[kg/m^3]'; lib.mat{2}.variables.k='k(T[1/K])[W/(m*K)]'; lib.mat{2}.variables.cs='cs(T[1/K])[m/s]'; clear fcns fcns{1}.type='inline'; fcns{1}.name='cs(T)'; fcns{1}.expr='sqrt(1.4*287*T)'; fcns{1}.dexpr={'diff(sqrt(1.4*287*T),T)'}; fcns{2}.type='inline'; fcns{2}.name='rho(p,T)'; fcns{2}.expr='p*0.02897/8.314/T'; fcns{2}.dexpr={'diff(p*0.02897/8.314/T,p)','diff(p*0.02897/8.314/T,T)'}; fcns{3}.type='piecewise'; fcns{3}.name='Cp(T)'; fcns{3}.extmethod='const'; fcns{3}.subtype='poly'; fcns{3}.expr={{'0','1.04763657E+03','1','-3.72589265E-01','2', ... '9.45304214E-04','3','-6.02409443E-07','4','1.28589610E-10'}}; fcns{3}.intervals={'200','1600'}; fcns{4}.type='piecewise'; fcns{4}.name='eta(T)'; fcns{4}.extmethod='const'; fcns{4}.subtype='poly'; fcns{4}.expr={{'0','-8.38278000E-07','1','8.35717342E-08','2', ... '-7.69429583E-11','3','4.64372660E-14','4','-1.06585607E-17'}}; fcns{4}.intervals={'200','1600'}; fcns{5}.type='piecewise'; fcns{5}.name='nu0(T)'; fcns{5}.extmethod='const'; fcns{5}.subtype='poly'; fcns{5}.expr={{'0','-5.86912450E-06','1','5.01274491E-08','2', ... '7.50108343E-11','3','1.80336823E-15','4','-2.91688030E-18'}}; fcns{5}.intervals={'200','1600'}; fcns{6}.type='piecewise'; fcns{6}.name='k(T)'; fcns{6}.extmethod='const'; fcns{6}.subtype='poly'; fcns{6}.expr={{'0','-2.27583562E-03','1','1.15480022E-04','2', ... '-7.90252856E-08','3','4.11702505E-11','4','-7.43864331E-15'}}; fcns{6}.intervals={'200','1600'}; lib.mat{2}.functions = fcns; lib.mat{3}.name='Soft Iron (without losses)'; lib.mat{3}.varname='mat3'; lib.mat{3}.variables.normfB='BH(normH[m/A])[T]'; lib.mat{3}.variables.mur='MUR(normB[1/T])'; lib.mat{3}.variables.sigma='0[S/m]'; lib.mat{3}.variables.normfH='HB(normB[1/T])[A/m]'; lib.mat{3}.variables.epsilonr='1'; clear fcns fcns{1}.type='interp'; fcns{1}.name='MUR'; fcns{1}.method='linear'; fcns{1}.extmethod='const'; fcns{1}.x={'1','1.1','1.2','1.3','1.4','1.5','1.6','1.7','1.8','1.9', ... '2.0','2.1','2.2','2.3','2.4'}; fcns{1}.data={'1200','820','560','420','290','220','160','110','70','47', ... '26','15','10','7','6'}; fcns{2}.type='interp'; fcns{2}.name='HB'; fcns{2}.method='linear'; fcns{2}.extmethod='extrap'; fcns{2}.x={'0','1','1.1','1.2','1.3','1.4','1.5','1.6','1.7','1.8', ... '1.9','2.0','2.1','2.2','2.3','2.4'}; fcns{2}.data={'0','663.146','1067.5','1705.23','2463.11','3841.67', ... '5425.74','7957.75','12298.3','20462.8','32169.6','61213.4','111408', ... '175070','261469','318310'}; fcns{3}.type='interp'; fcns{3}.name='BH'; fcns{3}.method='linear'; fcns{3}.extmethod='extrap'; fcns{3}.x={'0','663.146','1067.5','1705.23','2463.11','3841.67', ... '5425.74','7957.75','12298.3','20462.8','32169.6','61213.4','111408', ... '175070','261469','318310'}; fcns{3}.data={'0','1','1.1','1.2','1.3','1.4','1.5','1.6','1.7','1.8', ... '1.9','2.0','2.1','2.2','2.3','2.4'}; lib.mat{3}.functions = fcns; lib.mat{4}.name='Copper'; lib.mat{4}.varname='mat4'; lib.mat{4}.variables.alphares='3.9e-3[1/K]'; lib.mat{4}.variables.mur='1'; lib.mat{4}.variables.sigma='5.998e7[S/m]'; lib.mat{4}.variables.epsilonr='1'; lib.mat{4}.variables.C='385[J/(kg*K)]'; lib.mat{4}.variables.epsilon='0.5'; lib.mat{4}.variables.res0='1.72e-8[ohm*m]'; lib.mat{4}.variables.rho='8700[kg/m^3]'; lib.mat{4}.variables.k='400[W/(m*K)]'; lib.mat{4}.variables.T0='273.15[K]'; lib.mat{5}.name='Silicon Carbide'; lib.mat{5}.varname='mat5'; lib.mat{5}.variables.mur='1'; lib.mat{5}.variables.sigma='1e3[S/m]'; lib.mat{5}.variables.epsilonr='10'; lib.mat{5}.variables.C='1200[J/(kg*K)]'; lib.mat{5}.variables.epsilon='0.5'; lib.mat{5}.variables.rho='3200[kg/m^3]'; lib.mat{5}.variables.k='450[W/(m*K)]*(300[K]/T)^0.75'; lib.matgroups{1}.name='Resistivity'; lib.matgroups{1}.variables={'alphares','T0','res0'}; lib.matgroups{1}.descr={'Temperature coefficient','Reference temperature','Resistivity at reference temperature'}; lib.matgroups{2}.name='Electromagnetic (AC/DC)'; lib.matgroups{2}.variables={'alphares','T0','res0','Br','normfH','fH','normfB','fB'}; lib.matgroups{2}.descr={'Temperature coefficient','Reference temperature','Resistivity at reference temperature','Remanent flux density','Nonlinear magnetic field, norm','Nonlinear magnetic field','Nonlinear magnetic flux density, norm','Nonlinear magnetic flux density'}; xfem.lib = lib; clear ode clear units; units.basesystem = 'SI'; ode.units = units; xfem.ode=ode; uq~ t�Zgui.solvemodel.toutcomp='on'; gui.solvemodel.currsolver='time'; gui.solvemodel.solveroption=''; gui.solvemodel.postsolver='time'; gui.solvemodel.nonlin='auto'; gui.solvemodel.ntol='1.0E-6'; gui.solvemodel.maxiter='25'; gui.solvemodel.segterm='tol'; gui.solvemodel.maxsegiter='100'; gui.solvemodel.segiter='1'; gui.solvemodel.manualdamp='off'; gui.solvemodel.damping='on'; gui.solvemodel.hnlin='off'; gui.solvemodel.initstep='1.0'; gui.solvemodel.minstep='1.0E-4'; gui.solvemodel.rstep='10.0'; gui.solvemodel.useaugsolver='off'; gui.solvemodel.autoaugcomp='on'; gui.solvemodel.augcomp=''; gui.solvemodel.augtol='0.0010'; gui.solvemodel.augmaxiter='25'; gui.solvemodel.augsolver='lumped'; gui.solvemodel.nlsolver='automatic'; gui.solvemodel.timenonlin='auto'; gui.solvemodel.useratelimit='on'; gui.solvemodel.timentolfact='1'; gui.solvemodel.timemaxiter='4'; gui.solvemodel.timesegterm='tol'; gui.solvemodel.timemaxsegiter='10'; gui.solvemodel.timesegiter='1'; gui.solvemodel.timemanualdamp='off'; gui.solvemodel.timedtech='const'; gui.solvemodel.timedamp='1.0'; gui.solvemodel.timejtech='minimal'; gui.solvemodel.timeinitstep='1.0'; gui.solvemodel.timeminstep='1.0E-2'; gui.solvemodel.timerstep='10.0'; gui.solvemodel.atol='0.0010'; gui.solvemodel.rtol='0.01'; gui.solvemodel.tlist='0:0.1:1'; gui.solvemodel.tout='tlist'; gui.solvemodel.tsteps='free'; gui.solvemodel.odesolver='bdf_ida'; gui.solvemodel.timestep='0.01'; gui.solvemodel.incrdelay='off'; gui.solvemodel.incrdelaysteps='15'; gui.solvemodel.manualreassem='off'; gui.solvemodel.emassconst='on'; gui.solvemodel.massconst='on'; gui.solvemodel.loadconst='on'; gui.solvemodel.constrconst='on'; gui.solvemodel.jacobianconst='on'; gui.solvemodel.constrjacobianconst='on'; gui.solvemodel.manualstep='off'; gui.solvemodel.maxstepauto='on'; gui.solvemodel.initialstepauto='on'; gui.solvemodel.initialstep='0.0010'; gui.solvemodel.maxorder='5'; gui.solvemodel.minorder='1'; gui.solvemodel.maxstep='0.1'; gui.solvemodel.rhoinf='0.75'; gui.solvemodel.predictor='linear'; gui.solvemodel.timeusestopcond='off'; gui.solvemodel.paramusestopcond='off'; gui.solvemodel.masssingular='maybe'; gui.solvemodel.consistent='bweuler'; gui.solvemodel.estrat='0'; gui.solvemodel.complex='off'; gui.solvemodel.neigs='6'; gui.solvemodel.shift='0'; gui.solvemodel.maxeigit='300'; gui.solvemodel.etol='0.0'; gui.solvemodel.krylovdim='0'; gui.solvemodel.eigname='lambda'; gui.solvemodel.eigref='0'; gui.solvemodel.pname=''; gui.solvemodel.plist=''; gui.solvemodel.pdistrib='off'; gui.solvemodel.porder='1'; gui.solvemodel.manualparam='off'; gui.solvemodel.pinitstep='0.0'; gui.solvemodel.pminstep='0.0'; gui.solvemodel.pmaxstep='0.0'; gui.solvemodel.autooldcomp='on'; gui.solvemodel.oldcomp=''; gui.solvemodel.outform='auto'; gui.solvemodel.symmetric='auto'; gui.solvemodel.symmhermit='auto'; gui.solvemodel.method='eliminate'; gui.solvemodel.nullfun='auto'; gui.solvemodel.blocksize='1000'; gui.solvemodel.blocksizeauto='on'; gui.solvemodel.uscale='auto'; gui.solvemodel.manscale=''; gui.solvemodel.rowscale='on'; gui.solvemodel.conjugate='off'; gui.solvemodel.complexfun='off'; gui.solvemodel.matherr='on'; gui.solvemodel.solfile='off'; gui.solvemodel.adaptgeom='currgeom'; gui.solvemodel.eefun='l2'; gui.solvemodel.eefunc=''; gui.solvemodel.maxt='10000000'; gui.solvemodel.rmethod='longest'; gui.solvemodel.resmethod='weak'; gui.solvemodel.resorderauto='on'; gui.solvemodel.resorder='0'; gui.solvemodel.l2scale='1'; gui.solvemodel.l2staborder='2'; gui.solvemodel.eigselect='1'; gui.solvemodel.tpfun='fltpft'; gui.solvemodel.ngen='2'; gui.solvemodel.tpmult='1.7'; gui.solvemodel.tpworst='0.5'; gui.solvemodel.tpfract='0.5'; gui.solvemodel.autosolver='on'; gui.solvemodel.varcomp=''; gui.solvemodel.oldvarcomp=''; gui.solvemodel.manualhessupd='off'; gui.solvemodel.manuallimitexpr='off'; gui.solvemodel.designsolver='sensitivity'; gui.solvemodel.sensmethod='adjoint'; gui.solvemodel.sensfunc=''; gui.solvemodel.sensfuncauto='on'; gui.solvemodel.qpsolver='cholesky'; gui.solvemodel.gradient='analytic'; gui.solvemodel.limitexpr=''; gui.solvemodel.nsolvemax='500'; gui.solvemodel.hessupd='10'; gui.solvemodel.opttol='1.0e-6'; gui.solvemodel.feastol='1.0e-6'; gui.solvemodel.majfeastol='1.0e-6'; gui.solvemodel.funcprec='1.0e-6'; gui.solvemodel.callblevel=''; gui.solvemodel.callblevelshow=''; gui.solvemodel.callbfreq=''; gui.solvemodel.callbackrough='0'; gui.solvemodel.callbclose='off'; gui.solvemodel.solcomp='Az'; gui.solvemodel.outcomp='Az'; gui.solvemodel.reacf='on'; gui.solvemodel.inittype='init_expr_currsol_radio'; gui.solvemodel.initsolnum='Automatic'; gui.solvemodel.inittime='0'; gui.solvemodel.utype='u_init_radio'; gui.solvemodel.usolnum='Automatic'; gui.solvemodel.utime='0'; gui.solvemodel.scriptcommands=''; gui.solvemodel.usescript='off'; gui.solvemodel.autoscript='off'; gui.solvemodel.sameaxis='off'; gui.solvemodel.linsolvernode.currlinsolver='umfpack'; gui.solvemodel.linsolvernode.type='linsolver'; gui.solvemodel.linsolvernode.droptol='0.0'; gui.solvemodel.linsolvernode.thresh='0.1'; gui.solvemodel.linsolvernode.umfalloc='0.7'; gui.solvemodel.linsolvernode.preorder='nd'; gui.solvemodel.linsolvernode.preroworder='on'; gui.solvemodel.linsolvernode.pivotstrategy='off'; gui.solvemodel.linsolvernode.pardreorder='nd'; gui.solvemodel.linsolvernode.pardrreorder='on'; gui.solvemodel.linsolvernode.pivotperturb='1.0E-8'; gui.solvemodel.linsolvernode.errorchk='on'; gui.solvemodel.linsolvernode.errorchkd='off'; gui.solvemodel.linsolvernode.termination='tol'; gui.solvemodel.linsolvernode.iter='2'; gui.solvemodel.linsolvernode.itol='1.0E-6'; gui.solvemodel.linsolvernode.rhob='400.0'; gui.solvemodel.linsolvernode.maxlinit='10000'; gui.solvemodel.linsolvernode.prefuntype='left'; gui.solvemodel.linsolvernode.prefuntype2='right'; gui.solvemodel.linsolvernode.iluiter='1'; gui.solvemodel.linsolvernode.itrestart='50'; gui.solvemodel.linsolvernode.seconditer='1'; gui.solvemodel.linsolvernode.relax='1.0'; gui.solvemodel.linsolvernode.amgauto='3'; gui.solvemodel.linsolvernode.mglevels='6'; gui.solvemodel.linsolvernode.mgcycle='v'; gui.solvemodel.linsolvernode.maxcoarsedof='5000'; gui.solvemodel.linsolvernode.oocmemory='512.0'; gui.solvemodel.linsolvernode.oocfilename=''; gui.solvemodel.linsolvernode.modified='off'; gui.solvemodel.linsolvernode.fillratio='2.0'; gui.solvemodel.linsolvernode.respectpattern='on'; gui.solvemodel.linsolvernode.droptype='droptol'; gui.solvemodel.linsolvernode.vankavars=''; gui.solvemodel.linsolvernode.vankasolv='gmres'; gui.solvemodel.linsolvernode.vankatol='0.02'; gui.solvemodel.linsolvernode.vankarestart='100'; gui.solvemodel.linsolvernode.vankarelax='0.8'; gui.solvemodel.linsolvernode.vankablocked='on'; gui.solvemodel.linsolvernode.sorblocked='on'; gui.solvemodel.linsolvernode.sorvecdof=''; gui.solvemodel.linsolvernode.mgauto='shape'; gui.solvemodel.linsolvernode.rmethod='regular'; gui.solvemodel.linsolvernode.coarseassem='on'; gui.solvemodel.linsolvernode.meshscale='2'; gui.solvemodel.linsolvernode.mgautolevels='2'; gui.solvemodel.linsolvernode.mgkeep='off'; gui.solvemodel.linsolvernode.mggeom='Geom1'; gui.solvemodel.linsolvernode.mcase0='on'; gui.solvemodel.linsolvernode.mgassem0='on'; gui.solvemodel.solversegmodel.seggrps{1}.segcomp='Az'; gui.solvemodel.solversegmodel.seggrps{1}.ntol='1e-3'; gui.solvemodel.solversegmodel.seggrps{1}.timentol='1'; gui.solvemodel.solversegmodel.seggrps{1}.linsolvernode.currlinsolver='umfpack'; gui.solvemodel.solversegmodel.seggrps{1}.linsolvernode.type='linsolver'; gui.solvemodel.solversegmodel.seggrps{1}.linsolvernode.droptol='0.0'; gui.solvemodel.solversegmodel.seggrps{1}.linsolvernode.thresh='0.1'; gui.solvemodel.solversegmodel.seggrps{1}.linsolvernode.umfalloc='0.7'; gui.solvemodel.solversegmodel.seggrps{1}.linsolvernode.preorder='nd'; gui.solvemodel.solversegmodel.seggrps{1}.linsolvernode.preroworder='on'; gui.solvemodel.solversegmodel.seggrps{1}.linsolvernode.pivotstrategy='off'; gui.solvemodel.solversegmodel.seggrps{1}.linsolvernode.pardreorder='nd'; gui.solvemodel.solversegmodel.seggrps{1}.linsolvernode.pardrreorder='on'; gui.solvemodel.solversegmodel.seggrps{1}.linsolvernode.pivotperturb='1.0E-8'; gui.solvemodel.solversegmodel.seggrps{1}.linsolvernode.errorchk='on'; gui.solvemodel.solversegmodel.seggrps{1}.linsolvernode.errorchkd='off'; gui.solvemodel.solversegmodel.seggrps{1}.linsolvernode.termination='tol'; gui.solvemodel.solversegmodel.seggrps{1}.linsolvernode.iter='2'; gui.solvemodel.solversegmodel.seggrps{1}.linsolvernode.itol='1.0E-6'; gui.solvemodel.solversegmodel.seggrps{1}.linsolvernode.rhob='400.0'; gui.solvemodel.solversegmodel.seggrps{1}.linsolvernode.maxlinit='10000'; gui.solvemodel.solversegmodel.seggrps{1}.linsolvernode.prefuntype='left'; gui.solvemodel.solversegmodel.seggrps{1}.linsolvernode.prefuntype2='right'; gui.solvemodel.solversegmodel.seggrps{1}.linsolvernode.iluiter='1'; gui.solvemodel.solversegmodel.seggrps{1}.linsolvernode.itrestart='50'; gui.solvemodel.solversegmodel.seggrps{1}.linsolvernode.seconditer='1'; gui.solvemodel.solversegmodel.seggrps{1}.linsolvernode.relax='1.0'; gui.solvemodel.solversegmodel.seggrps{1}.linsolvernode.amgauto='3'; gui.solvemodel.solversegmodel.seggrps{1}.linsolvernode.mglevels='6'; gui.solvemodel.solversegmodel.seggrps{1}.linsolvernode.mgcycle='v'; gui.solvemodel.solversegmodel.seggrps{1}.linsolvernode.maxcoarsedof='5000'; gui.solvemodel.solversegmodel.seggrps{1}.linsolvernode.oocmemory='512.0'; gui.solvemodel.solversegmodel.seggrps{1}.linsolvernode.oocfilename=''; gui.solvemodel.solversegmodel.seggrps{1}.linsolvernode.modified='off'; gui.solvemodel.solversegmodel.seggrps{1}.linsolvernode.fillratio='2.0'; gui.solvemodel.solversegmodel.seggrps{1}.linsolvernode.respectpattern='on'; gui.solvemodel.solversegmodel.seggrps{1}.linsolvernode.droptype='droptol'; gui.solvemodel.solversegmodel.seggrps{1}.linsolvernode.vankavars=''; gui.solvemodel.solversegmodel.seggrps{1}.linsolvernode.vankasolv='gmres'; gui.solvemodel.solversegmodel.seggrps{1}.linsolvernode.vankatol='0.02'; gui.solvemodel.solversegmodel.seggrps{1}.linsolvernode.vankarestart='100'; gui.solvemodel.solversegmodel.seggrps{1}.linsolvernode.vankarelax='0.8'; gui.solvemodel.solversegmodel.seggrps{1}.linsolvernode.vankablocked='on'; gui.solvemodel.solversegmodel.seggrps{1}.linsolvernode.sorblocked='on'; gui.solvemodel.solversegmodel.seggrps{1}.linsolvernode.sorvecdof=''; gui.solvemodel.solversegmodel.seggrps{1}.linsolvernode.mgauto='shape'; gui.solvemodel.solversegmodel.seggrps{1}.linsolvernode.rmethod='regular'; gui.solvemodel.solversegmodel.seggrps{1}.linsolvernode.coarseassem='on'; gui.solvemodel.solversegmodel.seggrps{1}.linsolvernode.meshscale='2'; gui.solvemodel.solversegmodel.seggrps{1}.linsolvernode.mgautolevels='2'; gui.solvemodel.solversegmodel.seggrps{1}.linsolvernode.mgkeep='off'; gui.solvemodel.solversegmodel.seggrps{1}.linsolvernode.mggeom='Geom1'; gui.solvemodel.solversegmodel.seggrps{1}.linsolvernode.mcase0='on'; gui.solvemodel.solversegmodel.seggrps{1}.linsolvernode.mgassem0='on'; gui.solvemodel.solversegmodel.segsteps{1}.segorder='1'; gui.solvemodel.solversegmodel.segsteps{1}.subterm='iter'; gui.solvemodel.solversegmodel.segsteps{1}.subdamp='0.5'; gui.solvemodel.solversegmodel.segsteps{1}.timesubdamp='1'; gui.solvemodel.solversegmodel.segsteps{1}.subiter='1'; gui.solvemodel.solversegmodel.segsteps{1}.maxsubiter='20'; gui.solvemodel.solversegmodel.segsteps{1}.timemaxsubiter='10'; gui.solvemodel.solversegmodel.segsteps{1}.subntol='1.0E-2'; gui.solvemodel.solversegmodel.segsteps{1}.subntolfact='1'; gui.solvemodel.solversegmodel.segsteps{1}.subdtech='const'; gui.solvemodel.solversegmodel.segsteps{1}.submandamp='off'; gui.solvemodel.solversegmodel.segsteps{1}.subinitstep='1.0'; gui.solvemodel.solversegmodel.segsteps{1}.subminstep='1.0E-4'; gui.solvemodel.solversegmodel.segsteps{1}.timesubminstep='1.0E-2'; gui.solvemodel.solversegmodel.segsteps{1}.subrstep='10.0'; gui.solvemodel.solversegmodel.segsteps{1}.timesubjtech='minimal'; gui.solvemodel.solversegmodel.segsteps{1}.subjtech='onevery'; gui.solvemodel.solversegmodel.manualsteps='off'; gui.solvemodel.solversegmodel.llimitdof=''; gui.solvemodel.solversegmodel.llimitval=''; gui.solvemodel.paramsweep.pname=''; gui.solvemodel.paramsweep.plist=''; gui.solvemodel.paramsweep.pdistrib='off'; gui.solvemodel.paramsweep.savefiles='off'; gui.solvemodel.paramsweep.varnames=''; gui.solvemodel.paramsweep.logfile=''; gui.solvemodel.defaults.emqa_toutcomp='on'; gui.solvemodel.defaults.toutcomp='on'; gui.registry.general_currentmodel='Geom1'; gui.registry.general_currmeshcase='0'; gui.registry.general_savedonserver='off'; gui.registry.general_savedchanges='off'; gui.registry.general_rulingmode=''; gui.registry.general_incompletemfilehistory='off'; gui.registry.saved_license='1029930'; gui.registry.saved_version='COMSOL 3.5.0.494'; gui.registry.info_modelname=''; gui.registry.info_author=''; gui.registry.info_company=''; gui.registry.info_department=''; gui.registry.info_reference=''; gui.registry.info_url=''; gui.registry.info_saveddate='1262975065075'; gui.registry.info_creationdate='1262287898528'; gui.registry.info_modelresult=''; gui.registry.spice_netlist=''; gui.registry.spice_forceac='off'; gui.reportregistry.report_contents=''; gui.reportregistry.report_outputformat='html'; gui.reportregistry.report_filename=''; gui.reportregistry.report_autoopen='off'; gui.reportregistry.report_paperformat='a4'; gui.reportregistry.report_includedefaults='off'; gui.reportregistry.report_template='full'; gui.reportregistry.report_showemptysections='off'; gui.flmodel{1}.modelname='Geom1'; gui.flmodel{1}.currmode='post'; gui.flmodel{1}.currappl='0'; gui.flmodel{1}.axis.xmin='-2.1917248854858253'; gui.flmodel{1}.axis.xmax='2.1917248854858244'; gui.flmodel{1}.axis.ymin='-1.295624821604536'; gui.flmodel{1}.axis.ymax='1.2956248216045347'; gui.flmodel{1}.axis.zmin='-1.0'; gui.flmodel{1}.axis.zmax='1.0'; gui.flmodel{1}.axis.xspacing='0.05'; gui.flmodel{1}.axis.yspacing='0.2'; gui.flmodel{1}.axis.zspacing='0.2'; gui.flmodel{1}.axis.extrax=''; gui.flmodel{1}.axis.extray=''; gui.flmodel{1}.axis.extraz=''; gui.flmodel{1}.camera.xmin='-21.91724885485825'; gui.flmodel{1}.camera.xmax='21.91724885485825'; gui.flmodel{1}.camera.ymin='-12.956248216045358'; gui.flmodel{1}.camera.ymax='12.956248216045358'; gui.flmodel{1}.camera.camposx='-5.329070518200751E-15'; gui.flmodel{1}.camera.camposy='-6.217248937900877E-15'; gui.flmodel{1}.camera.camposz='219.17248854858252'; gui.flmodel{1}.camera.camtargetx='-5.329070518200751E-15'; gui.flmodel{1}.camera.camtargety='-6.217248937900877E-15'; gui.flmodel{1}.camera.camtargetz='0.0'; gui.flmodel{1}.camera.camupx='0.0'; gui.flmodel{1}.camera.camupy='1.0'; gui.flmodel{1}.camera.camupz='0.0'; gui.flmodel{1}.lightmodel.headlight.type='point'; gui.flmodel{1}.lightmodel.headlight.name='headlight'; gui.flmodel{1}.lightmodel.headlight.enable='on'; gui.flmodel{1}.lightmodel.headlight.colorr='255'; gui.flmodel{1}.lightmodel.headlight.colorg='255'; gui.flmodel{1}.lightmodel.headlight.colorb='255'; gui.flmodel{1}.lightmodel.headlight.xpos='-5.3290705E-15'; gui.flmodel{1}.lightmodel.headlight.ypos='-6.217249E-15'; gui.flmodel{1}.lightmodel.headlight.zpos='219.17249'; gui.flmodel{1}.lightmodel.scenelight{1}.type='directional'; gui.flmodel{1}.lightmodel.scenelight{1}.name='light 1'; gui.flmodel{1}.lightmodel.scenelight{1}.enable='on'; gui.flmodel{1}.lightmodel.scenelight{1}.colorr='255'; gui.flmodel{1}.lightmodel.scenelight{1}.colorg='255'; gui.flmodel{1}.lightmodel.scenelight{1}.colorb='255'; gui.flmodel{1}.lightmodel.scenelight{1}.xdir='1.0'; gui.flmodel{1}.lightmodel.scenelight{1}.ydir='-1.0'; gui.flmodel{1}.lightmodel.scenelight{1}.zdir='1.0'; gui.flmodel{1}.lightmodel.scenelight{2}.type='directional'; gui.flmodel{1}.lightmodel.scenelight{2}.name='light 2'; gui.flmodel{1}.lightmodel.scenelight{2}.enable='on'; gui.flmodel{1}.lightmodel.scenelight{2}.colorr='255'; gui.flmodel{1}.lightmodel.scenelight{2}.colorg='255'; gui.flmodel{1}.lightmodel.scenelight{2}.colorb='255'; gui.flmodel{1}.lightmodel.scenelight{2}.xdir='-1.0'; gui.flmodel{1}.lightmodel.scenelight{2}.ydir='1.0'; gui.flmodel{1}.lightmodel.scenelight{2}.zdir='-1.0'; gui.flmodel{1}.lightmodel.scenelight{3}.type='directional'; gui.flmodel{1}.lightmodel.scenelight{3}.name='light 3'; gui.flmodel{1}.lightmodel.scenelight{3}.enable='on'; gui.flmodel{1}.lightmodel.scenelight{3}.colorr='255'; gui.flmodel{1}.lightmodel.scenelight{3}.colorg='255'; gui.flmodel{1}.lightmodel.scenelight{3}.colorb='255'; gui.flmodel{1}.lightmodel.scenelight{3}.xdir='-1.0'; gui.flmodel{1}.lightmodel.scenelight{3}.ydir='-1.0'; gui.flmodel{1}.lightmodel.scenelight{3}.zdir='1.0'; gui.flmodel{1}.lightmodel.scenelight{4}.type='directional'; gui.flmodel{1}.lightmodel.scenelight{4}.name='light 4'; gui.flmodel{1}.lightmodel.scenelight{4}.enable='on'; gui.flmodel{1}.lightmodel.scenelight{4}.colorr='255'; gui.flmodel{1}.lightmodel.scenelight{4}.colorg='255'; gui.flmodel{1}.lightmodel.scenelight{4}.colorb='255'; gui.flmodel{1}.lightmodel.scenelight{4}.xdir='1.0'; gui.flmodel{1}.lightmodel.scenelight{4}.ydir='-1.0'; gui.flmodel{1}.lightmodel.scenelight{4}.zdir='-1.0'; gui.flmodel{1}.registry.axis_visible='on'; gui.flmodel{1}.registry.axis_auto='on'; gui.flmodel{1}.registry.axis_autoy='on'; gui.flmodel{1}.registry.axis_autoz='on'; gui.flmodel{1}.registry.axis_box='off'; gui.flmodel{1}.registry.axis_equal='on'; gui.flmodel{1}.registry.axis_csys='on'; gui.flmodel{1}.registry.grid_visible='on'; gui.flmodel{1}.registry.grid_auto='off'; gui.flmodel{1}.registry.grid_autoz='on'; gui.flmodel{1}.registry.grid_labels='on'; gui.flmodel{1}.registry.labels_object='on'; gui.flmodel{1}.registry.labels_vertex='off'; gui.flmodel{1}.registry.labels_edge='off'; gui.flmodel{1}.registry.labels_face='off'; gui.flmodel{1}.registry.labels_subdomain='off'; gui.flmodel{1}.registry.symbols_vertexscale='1.0'; gui.flmodel{1}.registry.symbols_edgescale='1.0'; gui.flmodel{1}.registry.symbols_facescale='1.0'; gui.flmodel{1}.registry.select_draw2d='size'; gui.flmodel{1}.registry.select_adj='cycle'; gui.flmodel{1}.registry.light_headlight='off'; gui.flmodel{1}.registry.light_scenelight='off'; gui.flmodel{1}.registry.light_shininess='0.5'; gui.flmodel{1}.registry.camera_mouse='orbit'; gui.flmodel{1}.registry.camera_camconstr='none'; gui.flmodel{1}.registry.camera_mouseconstr='none'; gui.flmodel{1}.registry.camera_perspective='off'; gui.flmodel{1}.registry.camera_moveasbox='off'; gui.flmodel{1}.registry.draw_assembly='off'; gui.flmodel{1}.registry.draw_dialog='off'; gui.flmodel{1}.registry.draw_keepborders='on'; gui.flmodel{1}.registry.draw_keepedges='off'; gui.flmodel{1}.registry.draw_multi='off'; gui.flmodel{1}.registry.draw_snap2grid='on'; gui.flmodel{1}.registry.draw_snap2vtx='on'; gui.flmodel{1}.registry.draw_solid='on'; gui.flmodel{1}.registry.draw_workplane_coordsys='on'; gui.flmodel{1}.registry.draw_workplane_showgeom='on'; gui.flmodel{1}.registry.draw_repair='on'; gui.flmodel{1}.registry.draw_repairtol='1.0E-6'; gui.flmodel{1}.registry.draw_projection='intersection'; gui.flmodel{1}.registry.transparency_value='1.0'; gui.flmodel{1}.registry.mesh_geomdetail='normal'; gui.flmodel{1}.registry.mesh_showquality='off'; gui.flmodel{1}.registry.post_cameraview='2'; gui.flmodel{1}.registry.graphics_scale='10.0'; gui.flmodel{1}.registry.render_mesh='off'; gui.flmodel{1}.registry.render_bndarrow='on'; gui.flmodel{1}.registry.render_vertex='off'; gui.flmodel{1}.registry.render_edge='on'; gui.flmodel{1}.registry.render_face='off'; gui.flmodel{1}.registry.highlight_vertex='off'; gui.flmodel{1}.registry.highlight_edge='on'; gui.flmodel{1}.registry.highlight_face='on'; gui.flmodel{1}.meshparam.hauto='5'; gui.flmodel{1}.meshparam.usehauto='on'; gui.flmodel{1}.meshparam.hmax=''; gui.flmodel{1}.meshparam.hmaxfact='1'; gui.flmodel{1}.meshparam.hcurve='0.3'; gui.flmodel{1}.meshparam.hgrad='1.3'; gui.flmodel{1}.meshparam.hcutoff='0.001'; gui.flmodel{1}.meshparam.hnarrow='1'; gui.flmodel{1}.meshparam.hpnt='10'; gui.flmodel{1}.meshparam.xscale='1.0'; gui.flmodel{1}.meshparam.yscale='1.0'; gui.flmodel{1}.meshparam.jiggle='on'; gui.flmodel{1}.meshparam.mcase='0'; gui.flmodel{1}.meshparam.rmethod='regular'; gui.flmodel{1}.meshparam.hmaxvtx={'','','','','','','','','','','','','','','','','','','','','','','','','','','',''}; gui.flmodel{1}.meshparam.hgradvtx={'','','','','','','','','','','','','','','','','','','','','','','','','','','',''}; gui.flmodel{1}.meshparam.hmaxedg={'','','','','','','','','','','','','','','','','','','','','','','','','','','',''}; gui.flmodel{1}.meshparam.hcutoffedg={'','','','','','','','','','','','','','','','','','','','','','','','','','','',''}; gui.flmodel{1}.meshparam.hcurveedg={'','','','','','','','','','','','','','','','','','','','','','','','','','','',''}; gui.flmodel{1}.meshparam.hgradedg={'','','','','','','','','','','','','','','','','','','','','','','','','','','',''}; gui.flmodel{1}.meshparam.hgradsub={'','','','','','',''}; gui.flmodel{1}.meshparam.methodsub={'triaf','triaf','triaf','triaf','triaf','triaf','triaf'}; 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gui.flmodel{1}.postmodel.crossplot.selectvia='stored'; gui.flmodel{1}.postmodel.crossplot.autotitle='on'; gui.flmodel{1}.postmodel.crossplot.customtitle=''; gui.flmodel{1}.postmodel.crossplot.autolabelx='on'; gui.flmodel{1}.postmodel.crossplot.customlabelx=''; gui.flmodel{1}.postmodel.crossplot.autolabely='on'; gui.flmodel{1}.postmodel.crossplot.customlabely=''; gui.flmodel{1}.postmodel.crossplot.axistype={'lin','lin'}; gui.flmodel{1}.postmodel.crossplot.smoothinternal='on'; gui.flmodel{1}.postmodel.crossplot.plottypeind='1'; gui.flmodel{1}.postmodel.dataexport.pntdata={'Az'}; gui.flmodel{1}.postmodel.dataexport.pntrecover='off'; gui.flmodel{1}.postmodel.dataexport.pntunit='Wb/m'; gui.flmodel{1}.postmodel.dataexport.pntlocation='element'; gui.flmodel{1}.postmodel.dataexport.pntlagorder='2'; gui.flmodel{1}.postmodel.dataexport.bnddata={'Az'}; gui.flmodel{1}.postmodel.dataexport.bndcont='off'; gui.flmodel{1}.postmodel.dataexport.bndrecover='off'; gui.flmodel{1}.postmodel.dataexport.bndunit='Wb/m'; gui.flmodel{1}.postmodel.dataexport.bndlocation='element'; gui.flmodel{1}.postmodel.dataexport.bndlagorder='2'; gui.flmodel{1}.postmodel.dataexport.subdata={'normB_emqa'}; gui.flmodel{1}.postmodel.dataexport.subcont='off'; gui.flmodel{1}.postmodel.dataexport.subrecover='off'; gui.flmodel{1}.postmodel.dataexport.subunit='T'; gui.flmodel{1}.postmodel.dataexport.subxspacing='10'; gui.flmodel{1}.postmodel.dataexport.subxvectorspacing=''; gui.flmodel{1}.postmodel.dataexport.subxisvector='off'; gui.flmodel{1}.postmodel.dataexport.subyspacing='10'; gui.flmodel{1}.postmodel.dataexport.subyvectorspacing=''; gui.flmodel{1}.postmodel.dataexport.subyisvector='off'; gui.flmodel{1}.postmodel.dataexport.sublocation='element'; gui.flmodel{1}.postmodel.dataexport.sublagorder='2'; gui.flmodel{1}.postmodel.dataexport.phase='0'; gui.flmodel{1}.postmodel.dataexport.solnum='0,1,2,3,4,5,6,7,8,9,10'; gui.flmodel{1}.postmodel.dataexport.selectvia='stored'; gui.flmodel{1}.postmodel.dataexport.smoothinternal='on'; gui.flmodel{1}.postmodel.dataexport.exportformat='ptd'; gui.flmodel{1}.postmodel.dataexport.struct='off'; gui.flmodel{1}.postmodel.dataexport.exportedim='2'; gui.flmodel{1}.postmodel.dataexport.plotexportformat='coorddata'; gui.flmodel{1}.postmodel.dataexport.plotstruct='off'; gui.flmodel{1}.postmodel.datadisplay.fullprecision='off'; gui.flmodel{1}.postmodel.datadisplay.smoothinternal='on'; gui.flmodel{1}.postmodel.datadisplay.phase='0'; gui.flmodel{1}.postmodel.datadisplay.solnum='10'; gui.flmodel{1}.postmodel.datadisplay.selectvia='stored'; gui.flmodel{1}.postmodel.datadisplay.interpdata={'normB_emqa'}; gui.flmodel{1}.postmodel.datadisplay.interprecover='off'; gui.flmodel{1}.postmodel.datadisplay.interpunit='T'; gui.flmodel{1}.postmodel.datadisplay.coord={'0','0'}; gui.flmodel{1}.postmodel.globalplot.globalyaxisexprs={}; gui.flmodel{1}.postmodel.globalplot.globalyaxisexprsdisp={}; gui.flmodel{1}.postmodel.globalplot.linexaxisxaxistype=''; gui.flmodel{1}.postmodel.globalplot.linexaxisuseexpr='off'; gui.flmodel{1}.postmodel.globalplot.globallinestyle='solid'; gui.flmodel{1}.postmodel.globalplot.globallinecolor='cyclecolor'; gui.flmodel{1}.postmodel.globalplot.globallinemarker='none'; gui.flmodel{1}.postmodel.globalplot.globallegend='off'; gui.flmodel{1}.postmodel.globalplot.globallinelabels='off'; gui.flmodel{1}.postmodel.globalplot.globalcolor='255,0,0'; gui.flmodel{1}.postmodel.globalplot.autotitle='on'; gui.flmodel{1}.postmodel.globalplot.customtitle=''; gui.flmodel{1}.postmodel.globalplot.autolabelx='on'; gui.flmodel{1}.postmodel.globalplot.customlabelx=''; gui.flmodel{1}.postmodel.globalplot.autolabely='on'; gui.flmodel{1}.postmodel.globalplot.customlabely=''; gui.flmodel{1}.postmodel.globalplot.axistype={'lin','lin'}; gui.flmodel{1}.postmodel.globalplot.phase='0'; gui.flmodel{1}.postmodel.globalplot.solnum='0,1,2,3,4,5,6,7,8,9,10'; gui.flmodel{1}.postmodel.globalplot.selectvia='stored'; gui.flmodel{1}.geommodel.suppressed{1}=[]; gui.flmodel{1}.geommodel.suppressed{2}=[]; gui.flmodel{1}.geommodel.suppressed{3}=[]; 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Analyzed geometry clear s s.objs={g1}; s.name={'SQ1'}; s.tags={'g1'}; fem.draw=struct('s',s); fem.geom=geomcsg(fem); % Initialize mesh fem.mesh=meshinit(fem, ... 'hauto',5); % (Default values are not included) % Application mode 1 clear appl appl.mode.class = 'PerpendicularCurrents'; appl.module = 'ACDC'; appl.sshape = 2; appl.assignsuffix = '_emqa'; clear prop prop.analysis='transient'; appl.prop = prop; clear bnd bnd.type = 'A0'; bnd.ind = [1,1,1,1]; appl.bnd = bnd; clear equ equ.Jez = 'flsmsign(t-0.5,0.25)'; equ.ind = [1]; appl.equ = equ; fem.appl{1} = appl; fem.frame = {'ref'}; fem.border = 1; clear units; units.basesystem = 'SI'; fem.units = units; % ODE Settings clear ode clear units; units.basesystem = 'SI'; ode.units = units; fem.ode=ode; % Multiphysics fem=multiphysics(fem); % Extend mesh fem.xmesh=meshextend(fem); % Solve problem fem.sol=femtime(fem, ... 'solcomp',{'Az'}, ... 'outcomp',{'Az','Azt'}, ... 'blocksize','auto', ... 'tlist',[0:0.1:1], ... 'tout','tlist'); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'tridata',{'normB_emqa','cont','internal','unit','T'}, ... 'trimap','jet(1024)', ... 'solnum','end', ... 'title','Time=1 Surface: Magnetic flux density, norm [T]', ... 'axis',[-1.6912669126691267,1.6912669126691267,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'Jez_emqa','cont','internal','unit','A/m^2'}, ... 'trimap','jet(1024)', ... 'solnum','end', ... 'title','Time=1 Surface: External current density [A/m^2]', ... 'axis',[-1.6912669126691267,1.6912669126691267,-1.052606679912953,1.052606679912953]); % Plot solution postplot(fem, ... 'tridata',{'Jez_emqa','cont','internal','unit','A/m^2'}, ... 'trimap','jet(1024)', ... 'solnum',2, ... 'title','Time=0.1 Surface: External current density [A/m^2]', ... 'axis',[-1.6912669126691267,1.6912669126691267,-1.0294668164072944,1.0294668164072944]); % Plot solution postplot(fem, ... 'tridata',{'Jez_emqa','cont','internal','unit','A/m^2'}, ... 'trimap','jet(1024)', ... 'solnum',2, ... 'title','Time=0.1 Surface: External current density [A/m^2]', ... 'axis',[-1.6912669126691267,1.6912669126691267,-1.032617441706169,1.032617441706169]); % Geometry g2=square2('0.1','base','center','pos',{'-0.5','0.5'},'rot','0'); g3=square2('0.1','base','center','pos',{'0.5','0.5'},'rot','0'); g4=square2('0.1','base','center','pos',{'0.5','-0.5'},'rot','0'); % Analyzed geometry clear s s.objs={g1,g2,g3,g4}; s.name={'SQ1','SQ2','SQ3','SQ4'}; s.tags={'g1','g2','g3','g4'}; fem.draw=struct('s',s); fem.geom=geomcsg(fem); % Initialize mesh fem.mesh=meshinit(fem, ... 'hauto',5); % (Default values are not included) % Application mode 1 clear appl appl.mode.class = 'PerpendicularCurrents'; appl.module = 'ACDC'; appl.sshape = 2; appl.assignsuffix = '_emqa'; clear prop prop.analysis='transient'; appl.prop = prop; clear bnd bnd.type = 'A0'; bnd.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; appl.bnd = bnd; clear equ equ.Jez = {'flsmsign(t-0.5,0.25)','-flsmsign(t-0.5,0.25)'}; equ.sigma = 'mat1_sigma'; equ.epsilonr = 'mat1_epsilonr'; equ.mur = 'mat1_mur'; equ.ind = [1,2,1,2]; appl.equ = equ; fem.appl{1} = appl; fem.frame = {'ref'}; fem.border = 1; clear units; units.basesystem = 'SI'; fem.units = units; % Library materials clear lib lib.mat{1}.name='Iron'; lib.mat{1}.varname='mat1'; lib.mat{1}.variables.nu='0.29'; lib.mat{1}.variables.E='200e9[Pa]'; lib.mat{1}.variables.mur='4000'; lib.mat{1}.variables.sigma='1.12e7[S/m]'; lib.mat{1}.variables.epsilonr='1'; lib.mat{1}.variables.alpha='12.2e-6[1/K]'; lib.mat{1}.variables.C='440[J/(kg*K)]'; lib.mat{1}.variables.rho='7870[kg/m^3]'; lib.mat{1}.variables.k='76.2[W/(m*K)]'; lib.matgroups{1}.name='Resistivity'; lib.matgroups{1}.variables={'alphares','T0','res0'}; lib.matgroups{1}.descr={'Temperature coefficient','Reference temperature','Resistivity at reference temperature'}; fem.lib = lib; % ODE Settings clear ode clear units; units.basesystem = 'SI'; ode.units = units; fem.ode=ode; % Multiphysics fem=multiphysics(fem); % Extend mesh fem.xmesh=meshextend(fem); % Solve problem fem.sol=femtime(fem, ... 'solcomp',{'Az'}, ... 'outcomp',{'Az','Azt'}, ... 'blocksize','auto', ... 'tlist',[0:0.1:1], ... 'tout','tlist'); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'tridata',{'Jez_emqa','cont','internal','unit','A/m^2'}, ... 'trimap','jet(1024)', ... 'solnum','end', ... 'title','Time=1 Surface: External current density [A/m^2]', ... 'axis',[-1.7230576441102756,1.7230576441102756,-1,1]); % Geometry g5=square2('1','base','center','pos',{'0','0'},'rot','0'); g6=square2('2','base','center','pos',{'0','0'},'rot','0'); g7=square2('4','base','center','pos',{'0','0'},'rot','0'); % Analyzed geometry clear s s.objs={g1,g2,g3,g4,g7}; s.name={'SQ1','SQ2','SQ3','SQ4','SQ5'}; s.tags={'g1','g2','g3','g4','g7'}; fem.draw=struct('s',s); fem.geom=geomcsg(fem); % Initialize mesh fem.mesh=meshinit(fem, ... 'hauto',5); % Refine mesh fem.mesh=meshrefine(fem, ... 'mcase',0, ... 'rmethod','regular'); % (Default values are not included) % Application mode 1 clear appl appl.mode.class = 'PerpendicularCurrents'; appl.module = 'ACDC'; appl.sshape = 2; appl.assignsuffix = '_emqa'; clear prop prop.analysis='transient'; appl.prop = prop; clear bnd bnd.type = 'A0'; bnd.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; appl.bnd = bnd; clear equ equ.Jez = {0,'flsmsign(t-0.5,0.25)','-flsmsign(t-0.5,0.25)'}; equ.sigma = {'mat2_sigma','mat1_sigma','mat1_sigma'}; equ.epsilonr = {1,'mat1_epsilonr','mat1_epsilonr'}; equ.mur = {1,'mat1_mur','mat1_mur'}; equ.ind = [1,2,3,2,3]; appl.equ = equ; fem.appl{1} = appl; fem.frame = {'ref'}; fem.border = 1; clear units; units.basesystem = 'SI'; fem.units = units; % Library materials clear lib lib.mat{1}.name='Iron'; lib.mat{1}.varname='mat1'; lib.mat{1}.variables.nu='0.29'; lib.mat{1}.variables.E='200e9[Pa]'; lib.mat{1}.variables.mur='4000'; lib.mat{1}.variables.sigma='1.12e7[S/m]'; lib.mat{1}.variables.epsilonr='1'; lib.mat{1}.variables.alpha='12.2e-6[1/K]'; lib.mat{1}.variables.C='440[J/(kg*K)]'; lib.mat{1}.variables.rho='7870[kg/m^3]'; lib.mat{1}.variables.k='76.2[W/(m*K)]'; lib.mat{2}.name='Air'; lib.mat{2}.varname='mat2'; lib.mat{2}.variables.nu0='nu0(T[1/K])[m^2/s]'; lib.mat{2}.variables.eta='eta(T[1/K])[Pa*s]'; lib.mat{2}.variables.gamma='1.4'; lib.mat{2}.variables.sigma='0[S/m]'; lib.mat{2}.variables.C='Cp(T[1/K])[J/(kg*K)]'; lib.mat{2}.variables.rho='rho(p[1/Pa],T[1/K])[kg/m^3]'; lib.mat{2}.variables.k='k(T[1/K])[W/(m*K)]'; lib.mat{2}.variables.cs='cs(T[1/K])[m/s]'; clear fcns fcns{1}.type='inline'; fcns{1}.name='cs(T)'; fcns{1}.expr='sqrt(1.4*287*T)'; fcns{1}.dexpr={'diff(sqrt(1.4*287*T),T)'}; fcns{2}.type='inline'; fcns{2}.name='rho(p,T)'; fcns{2}.expr='p*0.02897/8.314/T'; fcns{2}.dexpr={'diff(p*0.02897/8.314/T,p)','diff(p*0.02897/8.314/T,T)'}; fcns{3}.type='piecewise'; fcns{3}.name='Cp(T)'; fcns{3}.extmethod='const'; fcns{3}.subtype='poly'; fcns{3}.expr={{'0','1.04763657E+03','1','-3.72589265E-01','2', ... '9.45304214E-04','3','-6.02409443E-07','4','1.28589610E-10'}}; fcns{3}.intervals={'200','1600'}; fcns{4}.type='piecewise'; fcns{4}.name='eta(T)'; fcns{4}.extmethod='const'; fcns{4}.subtype='poly'; fcns{4}.expr={{'0','-8.38278000E-07','1','8.35717342E-08','2', ... '-7.69429583E-11','3','4.64372660E-14','4','-1.06585607E-17'}}; fcns{4}.intervals={'200','1600'}; fcns{5}.type='piecewise'; fcns{5}.name='nu0(T)'; fcns{5}.extmethod='const'; fcns{5}.subtype='poly'; fcns{5}.expr={{'0','-5.86912450E-06','1','5.01274491E-08','2', ... '7.50108343E-11','3','1.80336823E-15','4','-2.91688030E-18'}}; fcns{5}.intervals={'200','1600'}; fcns{6}.type='piecewise'; fcns{6}.name='k(T)'; fcns{6}.extmethod='const'; fcns{6}.subtype='poly'; fcns{6}.expr={{'0','-2.27583562E-03','1','1.15480022E-04','2', ... '-7.90252856E-08','3','4.11702505E-11','4','-7.43864331E-15'}}; fcns{6}.intervals={'200','1600'}; lib.mat{2}.functions = fcns; lib.matgroups{1}.name='Resistivity'; lib.matgroups{1}.variables={'alphares','T0','res0'}; lib.matgroups{1}.descr={'Temperature coefficient','Reference temperature','Resistivity at reference temperature'}; fem.lib = lib; % ODE Settings clear ode clear units; units.basesystem = 'SI'; ode.units = units; fem.ode=ode; % Multiphysics fem=multiphysics(fem); % Extend mesh fem.xmesh=meshextend(fem); % Solve problem fem.sol=femtime(fem, ... 'solcomp',{'Az'}, ... 'outcomp',{'Az','Azt'}, ... 'blocksize','auto', ... 'tlist',[0:0.1:1], ... 'tout','tlist'); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'tridata',{'Jez_emqa','cont','internal','unit','A/m^2'}, ... 'trimap','jet(1024)', ... 'solnum','end', ... 'title','Time=1 Surface: External current density [A/m^2]', ... 'axis',[-1.6912669126691267,1.6912669126691267,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'Jez_emqa','cont','internal','unit','A/m^2'}, ... 'trimap','jet(1024)', ... 'arrowdata',{'Hx_emqa','Hy_emqa'}, ... 'arrowxspacing',15, ... 'arrowyspacing',15, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[1.0,0.0,0.0], ... 'solnum','end', ... 'title','Time=1 Surface: External current density [A/m^2] Arrow: Magnetic field', ... 'axis',[-1.6912669126691267,1.6912669126691267,-1.0294668164072944,1.0294668164072944]); % Plot solution postplot(fem, ... 'tridata',{'Jez_emqa','cont','internal','unit','A/m^2'}, ... 'trimap','jet(1024)', ... 'arrowdata',{'Hx_emqa','Hy_emqa'}, ... 'arrowxspacing',60, ... 'arrowyspacing',60, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[1.0,0.0,0.0], ... 'solnum','end', ... 'title','Time=1 Surface: External current density [A/m^2] Arrow: Magnetic field', ... 'axis',[-1.6912669126691267,1.6912669126691267,-1.0294668164072944,1.0294668164072944]); % Plot solution postplot(fem, ... 'tridata',{'Jez_emqa','cont','internal','unit','A/m^2'}, ... 'trimap','jet(1024)', ... 'arrowdata',{'Hx_emqa','Hy_emqa'}, ... 'arrowxspacing',60, ... 'arrowyspacing',60, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[1.0,0.0,0.0], ... 'solnum','end', ... 'title','Time=1 Surface: External current density [A/m^2] Arrow: Magnetic field', ... 'axis',[-1.6912669126691267,1.6912669126691267,-1.0294668164072944,1.0294668164072944]); % Geometry g8=rect2('0.2','0.2','base','corner','pos',{'0','0'},'rot','0'); g9=rect2('0.2','0.2','base','center','pos',{'0','0'},'rot','0'); % Analyzed geometry clear s s.objs={g1,g2,g3,g4,g7,g9}; s.name={'SQ1','SQ2','SQ3','SQ4','SQ5','R1'}; s.tags={'g1','g2','g3','g4','g7','g9'}; fem.draw=struct('s',s); fem.geom=geomcsg(fem); % Initialize mesh fem.mesh=meshinit(fem, ... 'hauto',5); % Refine mesh fem.mesh=meshrefine(fem, ... 'mcase',0, ... 'rmethod','regular'); % Refine mesh fem.mesh=meshrefine(fem, ... 'mcase',0, ... 'rmethod','regular'); % (Default values are not included) % Application mode 1 clear appl appl.mode.class = 'PerpendicularCurrents'; appl.module = 'ACDC'; appl.sshape = 2; appl.assignsuffix = '_emqa'; clear prop prop.analysis='transient'; appl.prop = prop; clear bnd bnd.type = {'A0','cont'}; bnd.ind = [1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,1,1,1,1,1,1,1,1,1]; appl.bnd = bnd; clear equ equ.Jez = {0,'flsmsign(t-0.5,0.25)','-flsmsign(t-0.5,0.25)',0}; equ.sigma = {'mat2_sigma','mat1_sigma','mat1_sigma','mat1_sigma'}; equ.epsilonr = {1,'mat1_epsilonr','mat1_epsilonr','mat1_epsilonr'}; equ.mur = {1,'mat1_mur','mat1_mur','mat1_mur'}; equ.ind = [1,2,3,4,2,3]; appl.equ = equ; fem.appl{1} = appl; fem.frame = {'ref'}; fem.border = 1; clear units; units.basesystem = 'SI'; fem.units = units; % Library materials clear lib lib.mat{1}.name='Iron'; lib.mat{1}.varname='mat1'; lib.mat{1}.variables.nu='0.29'; lib.mat{1}.variables.E='200e9[Pa]'; lib.mat{1}.variables.mur='4000'; lib.mat{1}.variables.sigma='1.12e7[S/m]'; lib.mat{1}.variables.epsilonr='1'; lib.mat{1}.variables.alpha='12.2e-6[1/K]'; lib.mat{1}.variables.C='440[J/(kg*K)]'; lib.mat{1}.variables.rho='7870[kg/m^3]'; lib.mat{1}.variables.k='76.2[W/(m*K)]'; lib.mat{2}.name='Air'; lib.mat{2}.varname='mat2'; lib.mat{2}.variables.nu0='nu0(T[1/K])[m^2/s]'; lib.mat{2}.variables.eta='eta(T[1/K])[Pa*s]'; lib.mat{2}.variables.gamma='1.4'; lib.mat{2}.variables.sigma='0[S/m]'; lib.mat{2}.variables.C='Cp(T[1/K])[J/(kg*K)]'; lib.mat{2}.variables.rho='rho(p[1/Pa],T[1/K])[kg/m^3]'; lib.mat{2}.variables.k='k(T[1/K])[W/(m*K)]'; lib.mat{2}.variables.cs='cs(T[1/K])[m/s]'; clear fcns fcns{1}.type='inline'; fcns{1}.name='cs(T)'; fcns{1}.expr='sqrt(1.4*287*T)'; fcns{1}.dexpr={'diff(sqrt(1.4*287*T),T)'}; fcns{2}.type='inline'; fcns{2}.name='rho(p,T)'; fcns{2}.expr='p*0.02897/8.314/T'; fcns{2}.dexpr={'diff(p*0.02897/8.314/T,p)','diff(p*0.02897/8.314/T,T)'}; fcns{3}.type='piecewise'; fcns{3}.name='Cp(T)'; fcns{3}.extmethod='const'; fcns{3}.subtype='poly'; fcns{3}.expr={{'0','1.04763657E+03','1','-3.72589265E-01','2', ... '9.45304214E-04','3','-6.02409443E-07','4','1.28589610E-10'}}; fcns{3}.intervals={'200','1600'}; fcns{4}.type='piecewise'; fcns{4}.name='eta(T)'; fcns{4}.extmethod='const'; fcns{4}.subtype='poly'; fcns{4}.expr={{'0','-8.38278000E-07','1','8.35717342E-08','2', ... '-7.69429583E-11','3','4.64372660E-14','4','-1.06585607E-17'}}; fcns{4}.intervals={'200','1600'}; fcns{5}.type='piecewise'; fcns{5}.name='nu0(T)'; fcns{5}.extmethod='const'; fcns{5}.subtype='poly'; fcns{5}.expr={{'0','-5.86912450E-06','1','5.01274491E-08','2', ... '7.50108343E-11','3','1.80336823E-15','4','-2.91688030E-18'}}; fcns{5}.intervals={'200','1600'}; fcns{6}.type='piecewise'; fcns{6}.name='k(T)'; fcns{6}.extmethod='const'; fcns{6}.subtype='poly'; fcns{6}.expr={{'0','-2.27583562E-03','1','1.15480022E-04','2', ... '-7.90252856E-08','3','4.11702505E-11','4','-7.43864331E-15'}}; fcns{6}.intervals={'200','1600'}; lib.mat{2}.functions = fcns; lib.matgroups{1}.name='Resistivity'; lib.matgroups{1}.variables={'alphares','T0','res0'}; lib.matgroups{1}.descr={'Temperature coefficient','Reference temperature','Resistivity at reference temperature'}; fem.lib = lib; % ODE Settings clear ode clear units; units.basesystem = 'SI'; ode.units = units; fem.ode=ode; % Multiphysics fem=multiphysics(fem); % Extend mesh fem.xmesh=meshextend(fem); % Solve problem fem.sol=femtime(fem, ... 'solcomp',{'Az'}, ... 'outcomp',{'Az','Azt'}, ... 'blocksize','auto', ... 'tlist',[0:0.1:1], ... 'tout','tlist'); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'tridata',{'Jez_emqa','cont','internal','unit','A/m^2'}, ... 'trimap','jet(1024)', ... 'arrowdata',{'Hx_emqa','Hy_emqa'}, ... 'arrowxspacing',60, ... 'arrowyspacing',60, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[1.0,0.0,0.0], ... 'solnum','end', ... 'title','Time=1 Surface: External current density [A/m^2] Arrow: Magnetic field', ... 'axis',[-1.6912669126691267,1.6912669126691267,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'Jez_emqa','cont','internal','unit','A/m^2'}, ... 'trimap','jet(1024)', ... 'arrowdata',{'Mx_emqa','My_emqa'}, ... 'arrowxspacing',60, ... 'arrowyspacing',60, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[1.0,0.0,0.0], ... 'solnum','end', ... 'title','Time=1 Surface: External current density [A/m^2] Arrow: Magnetization', ... 'axis',[-1.6912669126691267,1.6912669126691267,-1.0294668164072944,1.0294668164072944]); % Plot solution postplot(fem, ... 'tridata',{'Jez_emqa','cont','internal','unit','A/m^2'}, ... 'trimap','jet(1024)', ... 'arrowdata',{'Mx_emqa','My_emqa'}, ... 'arrowxspacing',60, ... 'arrowyspacing',60, ... 'arrowtype','arrow', ... 'arrowstyle','normalized', ... 'arrowcolor',[1.0,0.0,0.0], ... 'solnum','end', ... 'title','Time=1 Surface: External current density [A/m^2] Arrow: Magnetization', ... 'axis',[-1.6912669126691267,1.6912669126691267,-1.0294668164072944,1.0294668164072944]); % Plot solution postplot(fem, ... 'tridata',{'Jez_emqa','cont','internal','unit','A/m^2'}, ... 'trimap','jet(1024)', ... 'arrowdata',{'Mx_emqa','My_emqa'}, ... 'arrowxspacing',600, ... 'arrowyspacing',600, ... 'arrowtype','arrow', ... 'arrowstyle','normalized', ... 'arrowcolor',[1.0,0.0,0.0], ... 'solnum','end', ... 'title','Time=1 Surface: External current density [A/m^2] Arrow: Magnetization', ... 'axis',[-1.6912669126691267,1.6912669126691267,-1.0294668164072944,1.0294668164072944]); % Plot solution postplot(fem, ... 'tridata',{'Jez_emqa','cont','internal','unit','A/m^2'}, ... 'trimap','jet(1024)', ... 'arrowdata',{'Mx_emqa','My_emqa'}, ... 'arrowxspacing',120, ... 'arrowyspacing',120, ... 'arrowtype','arrow', ... 'arrowstyle','normalized', ... 'arrowcolor',[1.0,0.0,0.0], ... 'solnum','end', ... 'title','Time=1 Surface: External current density [A/m^2] Arrow: Magnetization', ... 'axis',[-1.6912669126691267,1.6912669126691267,-1.0294668164072944,1.0294668164072944]); % Plot solution postplot(fem, ... 'tridata',{'Jez_emqa','cont','internal','unit','A/m^2'}, ... 'trimap','jet(1024)', ... 'arrowdata',{'Mx_emqa','My_emqa'}, ... 'arrowxspacing',120, ... 'arrowyspacing',120, ... 'arrowtype','arrow', ... 'arrowstyle','normalized', ... 'arrowcolor',[1.0,0.0,0.0], ... 'solnum','end', ... 'title','Time=1 Surface: External current density [A/m^2] Arrow: Magnetization', ... 'axis',[-1.6912669126691267,1.6912669126691267,-1.0294668164072944,1.0294668164072944]); % Geometry g10=rect2(0.8,0.2,'base','center','pos',[0,0]); % Analyzed geometry clear s s.objs={g1,g2,g3,g4,g7,g10}; s.name={'SQ1','SQ2','SQ3','SQ4','SQ5','R1'}; s.tags={'g1','g2','g3','g4','g7','g10'}; fem.draw=struct('s',s); fem.geom=geomcsg(fem); % Initialize mesh fem.mesh=meshinit(fem, ... 'hauto',5); % Refine mesh fem.mesh=meshrefine(fem, ... 'mcase',0, ... 'rmethod','regular'); % (Default values are not included) % Application mode 1 clear appl appl.mode.class = 'PerpendicularCurrents'; appl.module = 'ACDC'; appl.sshape = 2; appl.assignsuffix = '_emqa'; clear prop prop.analysis='transient'; appl.prop = prop; clear bnd bnd.type = {'A0','cont'}; bnd.ind = [1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,1,1,1,1,1,1,1,1,1]; appl.bnd = bnd; clear equ equ.Jez = {0,'flsmsign(t-0.5,0.25)','-flsmsign(t-0.5,0.25)',0}; equ.sigma = {'mat2_sigma','mat1_sigma','mat1_sigma','mat1_sigma'}; equ.epsilonr = {1,'mat1_epsilonr','mat1_epsilonr','mat1_epsilonr'}; equ.mur = {1,'mat1_mur','mat1_mur','mat1_mur'}; equ.ind = [1,2,3,4,2,3]; appl.equ = equ; fem.appl{1} = appl; fem.frame = {'ref'}; fem.border = 1; clear units; units.basesystem = 'SI'; fem.units = units; % Library materials clear lib lib.mat{1}.name='Iron'; lib.mat{1}.varname='mat1'; lib.mat{1}.variables.nu='0.29'; lib.mat{1}.variables.E='200e9[Pa]'; lib.mat{1}.variables.mur='4000'; lib.mat{1}.variables.sigma='1.12e7[S/m]'; lib.mat{1}.variables.epsilonr='1'; lib.mat{1}.variables.alpha='12.2e-6[1/K]'; lib.mat{1}.variables.C='440[J/(kg*K)]'; lib.mat{1}.variables.rho='7870[kg/m^3]'; lib.mat{1}.variables.k='76.2[W/(m*K)]'; lib.mat{2}.name='Air'; lib.mat{2}.varname='mat2'; lib.mat{2}.variables.nu0='nu0(T[1/K])[m^2/s]'; lib.mat{2}.variables.eta='eta(T[1/K])[Pa*s]'; lib.mat{2}.variables.gamma='1.4'; lib.mat{2}.variables.sigma='0[S/m]'; lib.mat{2}.variables.C='Cp(T[1/K])[J/(kg*K)]'; lib.mat{2}.variables.rho='rho(p[1/Pa],T[1/K])[kg/m^3]'; lib.mat{2}.variables.k='k(T[1/K])[W/(m*K)]'; lib.mat{2}.variables.cs='cs(T[1/K])[m/s]'; clear fcns fcns{1}.type='inline'; fcns{1}.name='cs(T)'; fcns{1}.expr='sqrt(1.4*287*T)'; fcns{1}.dexpr={'diff(sqrt(1.4*287*T),T)'}; fcns{2}.type='inline'; fcns{2}.name='rho(p,T)'; fcns{2}.expr='p*0.02897/8.314/T'; fcns{2}.dexpr={'diff(p*0.02897/8.314/T,p)','diff(p*0.02897/8.314/T,T)'}; fcns{3}.type='piecewise'; fcns{3}.name='Cp(T)'; fcns{3}.extmethod='const'; fcns{3}.subtype='poly'; fcns{3}.expr={{'0','1.04763657E+03','1','-3.72589265E-01','2', ... '9.45304214E-04','3','-6.02409443E-07','4','1.28589610E-10'}}; fcns{3}.intervals={'200','1600'}; fcns{4}.type='piecewise'; fcns{4}.name='eta(T)'; fcns{4}.extmethod='const'; fcns{4}.subtype='poly'; fcns{4}.expr={{'0','-8.38278000E-07','1','8.35717342E-08','2', ... '-7.69429583E-11','3','4.64372660E-14','4','-1.06585607E-17'}}; fcns{4}.intervals={'200','1600'}; fcns{5}.type='piecewise'; fcns{5}.name='nu0(T)'; fcns{5}.extmethod='const'; fcns{5}.subtype='poly'; fcns{5}.expr={{'0','-5.86912450E-06','1','5.01274491E-08','2', ... '7.50108343E-11','3','1.80336823E-15','4','-2.91688030E-18'}}; fcns{5}.intervals={'200','1600'}; fcns{6}.type='piecewise'; fcns{6}.name='k(T)'; fcns{6}.extmethod='const'; fcns{6}.subtype='poly'; fcns{6}.expr={{'0','-2.27583562E-03','1','1.15480022E-04','2', ... '-7.90252856E-08','3','4.11702505E-11','4','-7.43864331E-15'}}; fcns{6}.intervals={'200','1600'}; lib.mat{2}.functions = fcns; lib.matgroups{1}.name='Resistivity'; lib.matgroups{1}.variables={'alphares','T0','res0'}; lib.matgroups{1}.descr={'Temperature coefficient','Reference temperature','Resistivity at reference temperature'}; fem.lib = lib; % ODE Settings clear ode clear units; units.basesystem = 'SI'; ode.units = units; fem.ode=ode; % Multiphysics fem=multiphysics(fem); % Extend mesh fem.xmesh=meshextend(fem); % Solve problem fem.sol=femtime(fem, ... 'solcomp',{'Az'}, ... 'outcomp',{'Az','Azt'}, ... 'blocksize','auto', ... 'tlist',[0:0.1:1], ... 'tout','tlist'); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'tridata',{'Jez_emqa','cont','internal','unit','A/m^2'}, ... 'trimap','jet(1024)', ... 'arrowdata',{'Mx_emqa','My_emqa'}, ... 'arrowxspacing',120, ... 'arrowyspacing',120, ... 'arrowtype','arrow', ... 'arrowstyle','normalized', ... 'arrowcolor',[1.0,0.0,0.0], ... 'solnum','end', ... 'title','Time=1 Surface: External current density [A/m^2] Arrow: Magnetization', ... 'axis',[-1.6912669126691267,1.6912669126691267,-1,1]); % Plot solution postplot(fem, ... 'tridata',{'Jez_emqa','cont','internal','unit','A/m^2'}, ... 'trimap','jet(1024)', ... 'contdata',{'normB_emqa','cont','internal','unit','T'}, ... 'contlevels',20, ... 'contlabel','off', ... 'contmap','jet(1024)', ... 'arrowdata',{'Mx_emqa','My_emqa'}, ... 'arrowxspacing',120, ... 'arrowyspacing',120, ... 'arrowtype','arrow', ... 'arrowstyle','normalized', ... 'arrowcolor',[1.0,0.0,0.0], ... 'solnum','end', ... 'title','Time=1 Surface: External current density [A/m^2] Contour: Magnetic flux density, norm [T] Arrow: Magnetization', ... 'axis',[-1.6912669126691267,1.6912669126691267,-1.0294668164072944,1.0294668164072944]); % Plot solution postplot(fem, ... 'tridata',{'Jez_emqa','cont','internal','unit','A/m^2'}, ... 'trimap','jet(1024)', ... 'arrowdata',{'Mx_emqa','My_emqa'}, ... 'arrowxspacing',120, ... 'arrowyspacing',120, ... 'arrowtype','arrow', ... 'arrowstyle','normalized', ... 'arrowcolor',[1.0,0.0,0.0], ... 'solnum','end', ... 'title','Time=1 Surface: External current density [A/m^2] Arrow: Magnetization', ... 'axis',[-1.6912669126691267,1.6912669126691267,-1.1017395888244597,1.1017395888244597]); % Plot solution postplot(fem, ... 'tridata',{'Jez_emqa','cont','internal','unit','A/m^2'}, ... 'trimap','jet(1024)', ... 'arrowdata',{'Mx_emqa','My_emqa'}, ... 'arrowxspacing',120, ... 'arrowyspacing',120, ... 'arrowtype','arrow', ... 'arrowstyle','normalized', ... 'arrowcolor',[1.0,0.0,0.0], ... 'solnum','end', ... 'title','Time=1 Surface: External current density [A/m^2] Arrow: Magnetization', ... 'axis',[-1.6912669126691267,1.6912669126691267,-1.0294668164072944,1.0294668164072944]); % COMSOL Multiphysics Model M-file % Generated by COMSOL 3.5 (COMSOL 3.5.0.494, $Date: 2008/09/19 16:09:48 $) % Plot in cross-section or along domain postcrossplot(fem,1,[-1 1;0 0], ... 'lindata','Mx_emqa', ... 'linxdata','x', ... 'solnum',[2,6,10], ... 'title','Magnetization, x component [A/m]', ... 'axislabel',{'x','Magnetization',' x component [A/m]'}); % Plot in cross-section or along domain postcrossplot(fem,1,[-1 1;0 0], ... 'lindata','Hx_emqa', ... 'linxdata','x', ... 'solnum',[2,6,10], ... 'title','Magnetic field, x component [A/m]', ... 'axislabel',{'x','Magnetic field',' x component [A/m]'}); % Plot in cross-section or along domain postcrossplot(fem,1,[-1 1;0 0], ... 'lindata','Hx_emqa', ... 'linxdata','x', ... 'solnum',[2,6,10], ... 'title','Magnetic field, x component [A/m]', ... 'axislabel',{'x','Magnetic field',' x component [A/m]'}); % Geometry g10=move(g10,[-0.6000000000000001,0]); [g5]=geomcopy({g10}); [g6]=geomcopy({g5}); g6=move(g6,[0.4,0]); g6=move(g6,[0.6000000000000001,0]); g6=move(g6,[0.20000000000000007,0]); % Analyzed geometry clear s s.objs={g10,g7,g2,g1,g4,g3,g6}; s.name={'R1','SQ5','SQ2','SQ1','SQ4','SQ3','R2'}; s.tags={'g10','g7','g2','g1','g4','g3','g6'}; fem.draw=struct('s',s); fem.geom=geomcsg(fem); % Initialize mesh fem.mesh=meshinit(fem, ... 'hauto',5); % Refine mesh fem.mesh=meshrefine(fem, ... 'mcase',0, ... 'rmethod','regular'); % (Default values are not included) % Application mode 1 clear appl appl.mode.class = 'PerpendicularCurrents'; appl.module = 'ACDC'; appl.sshape = 2; appl.assignsuffix = '_emqa'; clear prop prop.analysis='transient'; appl.prop = prop; clear bnd bnd.type = {'A0','cont'}; bnd.ind = [1,1,1,2,2,2,1,1,1,1,1,1,1,1,2,2,2,2,1,1,1,1,1,1,1,1,2,1]; appl.bnd = bnd; clear equ equ.sigma = {'mat2_sigma','mat1_sigma'}; equ.epsilonr = {1,'mat1_epsilonr'}; equ.mur = {1,'mat1_mur'}; equ.ind = [1,2,1,1,2,1,1]; appl.equ = equ; fem.appl{1} = appl; fem.frame = {'ref'}; fem.border = 1; clear units; units.basesystem = 'SI'; fem.units = units; % Library materials clear lib lib.mat{1}.name='Iron'; lib.mat{1}.varname='mat1'; lib.mat{1}.variables.nu='0.29'; lib.mat{1}.variables.E='200e9[Pa]'; lib.mat{1}.variables.mur='4000'; lib.mat{1}.variables.sigma='1.12e7[S/m]'; lib.mat{1}.variables.epsilonr='1'; lib.mat{1}.variables.alpha='12.2e-6[1/K]'; lib.mat{1}.variables.C='440[J/(kg*K)]'; lib.mat{1}.variables.rho='7870[kg/m^3]'; lib.mat{1}.variables.k='76.2[W/(m*K)]'; lib.mat{2}.name='Air'; lib.mat{2}.varname='mat2'; lib.mat{2}.variables.nu0='nu0(T[1/K])[m^2/s]'; lib.mat{2}.variables.eta='eta(T[1/K])[Pa*s]'; lib.mat{2}.variables.gamma='1.4'; lib.mat{2}.variables.sigma='0[S/m]'; lib.mat{2}.variables.C='Cp(T[1/K])[J/(kg*K)]'; lib.mat{2}.variables.rho='rho(p[1/Pa],T[1/K])[kg/m^3]'; lib.mat{2}.variables.k='k(T[1/K])[W/(m*K)]'; lib.mat{2}.variables.cs='cs(T[1/K])[m/s]'; clear fcns fcns{1}.type='inline'; fcns{1}.name='cs(T)'; fcns{1}.expr='sqrt(1.4*287*T)'; fcns{1}.dexpr={'diff(sqrt(1.4*287*T),T)'}; fcns{2}.type='inline'; fcns{2}.name='rho(p,T)'; fcns{2}.expr='p*0.02897/8.314/T'; fcns{2}.dexpr={'diff(p*0.02897/8.314/T,p)','diff(p*0.02897/8.314/T,T)'}; fcns{3}.type='piecewise'; fcns{3}.name='Cp(T)'; fcns{3}.extmethod='const'; fcns{3}.subtype='poly'; fcns{3}.expr={{'0','1.04763657E+03','1','-3.72589265E-01','2', ... '9.45304214E-04','3','-6.02409443E-07','4','1.28589610E-10'}}; fcns{3}.intervals={'200','1600'}; fcns{4}.type='piecewise'; fcns{4}.name='eta(T)'; fcns{4}.extmethod='const'; fcns{4}.subtype='poly'; fcns{4}.expr={{'0','-8.38278000E-07','1','8.35717342E-08','2', ... '-7.69429583E-11','3','4.64372660E-14','4','-1.06585607E-17'}}; fcns{4}.intervals={'200','1600'}; fcns{5}.type='piecewise'; fcns{5}.name='nu0(T)'; fcns{5}.extmethod='const'; fcns{5}.subtype='poly'; fcns{5}.expr={{'0','-5.86912450E-06','1','5.01274491E-08','2', ... '7.50108343E-11','3','1.80336823E-15','4','-2.91688030E-18'}}; fcns{5}.intervals={'200','1600'}; fcns{6}.type='piecewise'; fcns{6}.name='k(T)'; fcns{6}.extmethod='const'; fcns{6}.subtype='poly'; fcns{6}.expr={{'0','-2.27583562E-03','1','1.15480022E-04','2', ... '-7.90252856E-08','3','4.11702505E-11','4','-7.43864331E-15'}}; fcns{6}.intervals={'200','1600'}; lib.mat{2}.functions = fcns; lib.matgroups{1}.name='Resistivity'; lib.matgroups{1}.variables={'alphares','T0','res0'}; lib.matgroups{1}.descr={'Temperature coefficient','Reference temperature','Resistivity at reference temperature'}; fem.lib = lib; % ODE Settings clear ode clear units; units.basesystem = 'SI'; ode.units = units; fem.ode=ode; % Multiphysics fem=multiphysics(fem); % Extend mesh fem.xmesh=meshextend(fem); % Solve problem fem.sol=femtime(fem, ... 'solcomp',{'Az'}, ... 'outcomp',{'Az','Azt'}, ... 'blocksize','auto', ... 'tlist',[0:0.1:1], ... 'tout','tlist'); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'tridata',{'Jez_emqa','cont','internal','unit','A/m^2'}, ... 'trimap','jet(1024)', ... 'arrowdata',{'Mx_emqa','My_emqa'}, ... 'arrowxspacing',120, ... 'arrowyspacing',120, ... 'arrowtype','arrow', ... 'arrowstyle','normalized', ... 'arrowcolor',[1.0,0.0,0.0], ... 'solnum','end', ... 'title','Time=1 Surface: External current density [A/m^2] Arrow: Magnetization', ... 'axis',[-1.7411031642804795,1.7411031642804795,-1.0294668164072944,1.0294668164072944]); % Plot solution postplot(fem, ... 'tridata',{'Jez_emqa','cont','internal','unit','A/m^2'}, ... 'trimap','jet(1024)', ... 'contdata',{'normB_emqa','cont','internal','unit','T'}, ... 'contlevels',20, ... 'contlabel','off', ... 'contmap','jet(1024)', ... 'arrowdata',{'Mx_emqa','My_emqa'}, ... 'arrowxspacing',120, ... 'arrowyspacing',120, ... 'arrowtype','arrow', ... 'arrowstyle','normalized', ... 'arrowcolor',[1.0,0.0,0.0], ... 'solnum','end', ... 'title','Time=1 Surface: External current density [A/m^2] Contour: Magnetic flux density, norm [T] Arrow: Magnetization', ... 'axis',[-1.70287744067372,1.70287744067372,-1.0294668164072944,1.0294668164072944]); % Plot solution postplot(fem, ... 'tridata',{'Jez_emqa','cont','internal','unit','A/m^2'}, ... 'trimap','jet(1024)', ... 'contdata',{'normB_emqa','cont','internal','unit','T'}, ... 'contlevels',20, ... 'contlabel','off', ... 'contmap','jet(1024)', ... 'arrowdata',{'Mx_emqa','My_emqa'}, ... 'arrowxspacing',120, ... 'arrowyspacing',120, ... 'arrowtype','arrow', ... 'arrowstyle','normalized', ... 'arrowcolor',[1.0,0.0,0.0], ... 'solnum','end', ... 'title','Time=1 Surface: External current density [A/m^2] Contour: Magnetic flux density, norm [T] Arrow: Magnetization', ... 'axis',[-1.70287744067372,1.70287744067372,-1.0294668164072944,1.0294668164072944]); % COMSOL Multiphysics Model M-file % Generated by COMSOL 3.5 (COMSOL 3.5.0.494, $Date: 2008/09/19 16:09:48 $) % Plot solution postplot(fem, ... 'tridata',{'Jez_emqa','cont','internal','unit','A/m^2'}, ... 'trimap','jet(1024)', ... 'contdata',{'normB_emqa','cont','internal','unit','T'}, ... 'contlevels',20, ... 'contlabel','off', ... 'contmap','jet(1024)', ... 'arrowdata',{'Hx_emqa','Hy_emqa'}, ... 'arrowxspacing',120, ... 'arrowyspacing',120, ... 'arrowtype','arrow', ... 'arrowstyle','normalized', ... 'arrowcolor',[1.0,0.0,0.0], ... 'solnum','end', ... 'title','Time=1 Surface: External current density [A/m^2] Contour: Magnetic flux density, norm [T] Arrow: Magnetic field', ... 'axis',[-1.79060143004176,1.79060143004176,-1.0294668164072944,1.0294668164072944]); % Plot solution postplot(fem, ... 'tridata',{'Jez_emqa','cont','internal','unit','A/m^2'}, ... 'trimap','jet(1024)', ... 'contdata',{'normB_emqa','cont','internal','unit','T'}, ... 'contlevels',20, ... 'contlabel','off', ... 'contmap','jet(1024)', ... 'arrowdata',{'Hx_emqa','Hy_emqa'}, ... 'arrowxspacing',120, ... 'arrowyspacing',120, ... 'arrowtype','arrow', ... 'arrowstyle','normalized', ... 'arrowcolor',[1.0,0.0,0.0], ... 'solnum',8, ... 'title','Time=0.7 Surface: External current density [A/m^2] Contour: Magnetic flux density, norm [T] Arrow: Magnetic field', ... 'axis',[-1.79060143004176,1.79060143004176,-1.0294668164072944,1.0294668164072944]); % Initialize mesh fem.mesh=meshinit(fem, ... 'hauto',5); % Refine mesh fem.mesh=meshrefine(fem, ... 'mcase',0, ... 'rmethod','regular'); % (Default values are not included) % Application mode 1 clear appl appl.mode.class = 'PerpendicularCurrents'; appl.module = 'ACDC'; appl.sshape = 2; appl.assignsuffix = '_emqa'; clear prop prop.analysis='transient'; appl.prop = prop; clear bnd bnd.type = {'A0','cont'}; bnd.ind = [1,1,1,2,2,2,1,1,1,1,1,1,1,1,2,2,2,2,1,1,1,1,1,1,1,1,2,1]; appl.bnd = bnd; clear equ equ.Jez = {0,0,'flc2hs(t-0.5,0.25)','-flc2hs(t-0.5,0.25)'}; equ.sigma = {'mat2_sigma','mat1_sigma','mat2_sigma','mat2_sigma'}; equ.epsilonr = {1,'mat1_epsilonr',1,1}; equ.mur = {1,'mat1_mur',1,1}; equ.ind = [1,2,3,4,2,3,4]; appl.equ = equ; fem.appl{1} = appl; fem.frame = {'ref'}; fem.border = 1; clear units; units.basesystem = 'SI'; fem.units = units; % Library materials clear lib lib.mat{1}.name='Iron'; lib.mat{1}.varname='mat1'; lib.mat{1}.variables.nu='0.29'; lib.mat{1}.variables.E='200e9[Pa]'; lib.mat{1}.variables.mur='4000'; lib.mat{1}.variables.sigma='1.12e7[S/m]'; lib.mat{1}.variables.epsilonr='1'; lib.mat{1}.variables.alpha='12.2e-6[1/K]'; lib.mat{1}.variables.C='440[J/(kg*K)]'; lib.mat{1}.variables.rho='7870[kg/m^3]'; lib.mat{1}.variables.k='76.2[W/(m*K)]'; lib.mat{2}.name='Air'; lib.mat{2}.varname='mat2'; lib.mat{2}.variables.nu0='nu0(T[1/K])[m^2/s]'; lib.mat{2}.variables.eta='eta(T[1/K])[Pa*s]'; lib.mat{2}.variables.gamma='1.4'; lib.mat{2}.variables.sigma='0[S/m]'; lib.mat{2}.variables.C='Cp(T[1/K])[J/(kg*K)]'; lib.mat{2}.variables.rho='rho(p[1/Pa],T[1/K])[kg/m^3]'; lib.mat{2}.variables.k='k(T[1/K])[W/(m*K)]'; lib.mat{2}.variables.cs='cs(T[1/K])[m/s]'; clear fcns fcns{1}.type='inline'; fcns{1}.name='cs(T)'; fcns{1}.expr='sqrt(1.4*287*T)'; fcns{1}.dexpr={'diff(sqrt(1.4*287*T),T)'}; fcns{2}.type='inline'; fcns{2}.name='rho(p,T)'; fcns{2}.expr='p*0.02897/8.314/T'; fcns{2}.dexpr={'diff(p*0.02897/8.314/T,p)','diff(p*0.02897/8.314/T,T)'}; fcns{3}.type='piecewise'; fcns{3}.name='Cp(T)'; fcns{3}.extmethod='const'; fcns{3}.subtype='poly'; fcns{3}.expr={{'0','1.04763657E+03','1','-3.72589265E-01','2', ... '9.45304214E-04','3','-6.02409443E-07','4','1.28589610E-10'}}; fcns{3}.intervals={'200','1600'}; fcns{4}.type='piecewise'; fcns{4}.name='eta(T)'; fcns{4}.extmethod='const'; fcns{4}.subtype='poly'; fcns{4}.expr={{'0','-8.38278000E-07','1','8.35717342E-08','2', ... '-7.69429583E-11','3','4.64372660E-14','4','-1.06585607E-17'}}; fcns{4}.intervals={'200','1600'}; fcns{5}.type='piecewise'; fcns{5}.name='nu0(T)'; fcns{5}.extmethod='const'; fcns{5}.subtype='poly'; fcns{5}.expr={{'0','-5.86912450E-06','1','5.01274491E-08','2', ... '7.50108343E-11','3','1.80336823E-15','4','-2.91688030E-18'}}; fcns{5}.intervals={'200','1600'}; fcns{6}.type='piecewise'; fcns{6}.name='k(T)'; fcns{6}.extmethod='const'; fcns{6}.subtype='poly'; fcns{6}.expr={{'0','-2.27583562E-03','1','1.15480022E-04','2', ... '-7.90252856E-08','3','4.11702505E-11','4','-7.43864331E-15'}}; fcns{6}.intervals={'200','1600'}; lib.mat{2}.functions = fcns; lib.matgroups{1}.name='Resistivity'; lib.matgroups{1}.variables={'alphares','T0','res0'}; lib.matgroups{1}.descr={'Temperature coefficient','Reference temperature','Resistivity at reference temperature'}; fem.lib = lib; % ODE Settings clear ode clear units; units.basesystem = 'SI'; ode.units = units; fem.ode=ode; % Multiphysics fem=multiphysics(fem); % Extend mesh fem.xmesh=meshextend(fem); % Solve problem fem.sol=femtime(fem, ... 'solcomp',{'Az'}, ... 'outcomp',{'Az','Azt'}, ... 'blocksize','auto', ... 'tlist',[0:0.1:1], ... 'tout','tlist'); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'tridata',{'Jez_emqa','cont','internal','unit','A/m^2'}, ... 'trimap','jet(1024)', ... 'contdata',{'normB_emqa','cont','internal','unit','T'}, ... 'contlevels',20, ... 'contlabel','off', ... 'contmap','jet(1024)', ... 'arrowdata',{'Hx_emqa','Hy_emqa'}, ... 'arrowxspacing',120, ... 'arrowyspacing',120, ... 'arrowtype','arrow', ... 'arrowstyle','normalized', ... 'arrowcolor',[1.0,0.0,0.0], ... 'solnum','end', ... 'title','Time=1 Surface: External current density [A/m^2] Contour: Magnetic flux density, norm [T] Arrow: Magnetic field', ... 'axis',[-1.8272086298594412,1.8272086298594412,-1.0294668164072944,1.0294668164072944]); % Plot solution postplot(fem, ... 'tridata',{'Jez_emqa','cont','internal','unit','A/m^2'}, ... 'trimap','jet(1024)', ... 'arrowdata',{'Hx_emqa','Hy_emqa'}, ... 'arrowxspacing',120, ... 'arrowyspacing',120, ... 'arrowtype','arrow', ... 'arrowstyle','normalized', ... 'arrowcolor',[1.0,0.0,0.0], ... 'solnum','end', ... 'title','Time=1 Surface: External current density [A/m^2] Arrow: Magnetic field', ... 'axis',[-1.70287744067372,1.70287744067372,-1.0509638032928297,1.0509638032928297]); % Plot solution postplot(fem, ... 'tridata',{'Az','cont','internal','unit','Wb/m'}, ... 'trimap','jet(1024)', ... 'arrowdata',{'Hx_emqa','Hy_emqa'}, ... 'arrowxspacing',120, ... 'arrowyspacing',120, ... 'arrowtype','arrow', ... 'arrowstyle','normalized', ... 'arrowcolor',[1.0,0.0,0.0], ... 'solnum','end', ... 'title','Time=1 Surface: Magnetic potential, z component [Wb/m] Arrow: Magnetic field', ... 'axis',[-1.7789909020371666,1.7789909020371666,-1.0294668164072944,1.0294668164072944]); % Plot solution postplot(fem, ... 'tridata',{'Wm_emqa','cont','internal','unit','J/m^3'}, ... 'trimap','jet(1024)', ... 'arrowdata',{'Hx_emqa','Hy_emqa'}, ... 'arrowxspacing',120, ... 'arrowyspacing',120, ... 'arrowtype','arrow', ... 'arrowstyle','normalized', ... 'arrowcolor',[1.0,0.0,0.0], ... 'solnum','end', ... 'title','Time=1 Surface: Magnetic energy density [J/m^3] Arrow: Magnetic field', ... 'axis',[-1.7440530210545548,1.7440530210545548,-1.0294668164072944,1.0294668164072944]); % Plot solution postplot(fem, ... 'tridata',{'Hx_emqa','cont','internal','unit','A/m'}, ... 'trimap','jet(1024)', ... 'arrowdata',{'Hx_emqa','Hy_emqa'}, ... 'arrowxspacing',120, ... 'arrowyspacing',120, ... 'arrowtype','arrow', ... 'arrowstyle','normalized', ... 'arrowcolor',[1.0,0.0,0.0], ... 'solnum','end', ... 'title','Time=1 Surface: Magnetic field, x component [A/m] Arrow: Magnetic field', ... 'axis',[-1.7506096113592713,1.7506096113592713,-1.0294668164072944,1.0294668164072944]); % Plot solution postplot(fem, ... 'tridata',{'normH_emqa','cont','internal','unit','A/m'}, ... 'trimap','jet(1024)', ... 'arrowdata',{'Hx_emqa','Hy_emqa'}, ... 'arrowxspacing',120, ... 'arrowyspacing',120, ... 'arrowtype','arrow', ... 'arrowstyle','normalized', ... 'arrowcolor',[1.0,0.0,0.0], ... 'solnum','end', ... 'title','Time=1 Surface: Magnetic field, norm [A/m] Arrow: Magnetic field', ... 'axis',[-1.7569052909223113,1.7569052909223113,-1.0294668164072944,1.0294668164072944]); % Plot solution postplot(fem, ... 'tridata',{'normH_emqa','cont','internal','unit','A/m'}, ... 'trimap','jet(1024)', ... 'arrowdata',{'Hx_emqa','Hy_emqa'}, ... 'arrowxspacing',120, ... 'arrowyspacing',120, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[1.0,0.0,0.0], ... 'solnum','end', ... 'title','Time=1 Surface: Magnetic field, norm [A/m] Arrow: Magnetic field', ... 'axis',[-1.7491939290016576,1.7491939290016576,-1.0294668164072944,1.0294668164072944]); % Plot solution postplot(fem, ... 'tridata',{'normH_emqa','cont','internal','unit','A/m'}, ... 'trimap','jet(1024)', ... 'arrowdata',{'Hx_emqa','Hy_emqa'}, ... 'arrowxspacing',120, ... 'arrowyspacing',120, ... 'arrowscale',5, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[1.0,0.0,0.0], ... 'solnum','end', ... 'title','Time=1 Surface: Magnetic field, norm [A/m] Arrow: Magnetic field', ... 'axis',[-1.7491939290016576,1.7491939290016576,-1.0294668164072944,1.0294668164072944]); % Plot solution postplot(fem, ... 'tridata',{'normH_emqa','cont','internal','unit','A/m'}, ... 'trimap','jet(1024)', ... 'arrowdata',{'Hx_emqa','Hy_emqa'}, ... 'arrowxspacing',60, ... 'arrowyspacing',60, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[1.0,0.0,0.0], ... 'solnum','end', ... 'title','Time=1 Surface: Magnetic field, norm [A/m] Arrow: Magnetic field', ... 'axis',[-1.7491939290016576,1.7491939290016576,-1.0294668164072944,1.0294668164072944]); % Plot solution postplot(fem, ... 'tridata',{'normH_emqa','cont','internal','unit','A/m'}, ... 'trimap','jet(1024)', ... 'arrowdata',{'Hx_emqa','Hy_emqa'}, ... 'arrowxspacing',60, ... 'arrowyspacing',60, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[1.0,0.0,0.0], ... 'solnum','end', ... 'title','Time=1 Surface: Magnetic field, norm [A/m] Arrow: Magnetic field', ... 'axis',[-1.7491939290016576,1.7491939290016576,-1.0294668164072944,1.0294668164072944]); % COMSOL Multiphysics Model M-file % Generated by COMSOL 3.5 (COMSOL 3.5.0.494, $Date: 2008/09/19 16:09:48 $) % Geometry g5=rect2(1.1,0.2,'base','center','pos',[-0.6,0]); g8=rect2(1.1,0.2,'base','center','pos',[0.6,0]); % Analyzed geometry clear s s.objs={g7,g2,g1,g4,g3,g5,g8}; s.name={'SQ5','SQ2','SQ1','SQ4','SQ3','R1','R2'}; s.tags={'g7','g2','g1','g4','g3','g5','g8'}; fem.draw=struct('s',s); fem.geom=geomcsg(fem); % Initialize mesh fem.mesh=meshinit(fem, ... 'hauto',5); % Refine mesh fem.mesh=meshrefine(fem, ... 'mcase',0, ... 'rmethod','regular'); % Refine mesh fem.mesh=meshrefine(fem, ... 'mcase',0, ... 'rmethod','regular'); % (Default values are not included) % Application mode 1 clear appl appl.mode.class = 'PerpendicularCurrents'; appl.module = 'ACDC'; appl.assignsuffix = '_emqa'; clear prop prop.analysis='transient'; appl.prop = prop; clear bnd bnd.type = {'A0','cont'}; bnd.ind = [1,1,1,2,2,2,1,1,1,1,1,1,1,1,2,2,2,2,1,1,1,1,1,1,1,1,2,1]; appl.bnd = bnd; clear equ equ.Jez = {0,0,'flc2hs(t-0.5,0.25)','-flc2hs(t-0.5,0.25)'}; equ.sigma = {'mat2_sigma','mat1_sigma','mat2_sigma','mat2_sigma'}; equ.epsilonr = {1,'mat1_epsilonr',1,1}; equ.mur = {1,'mat1_mur',1,1}; equ.ind = [1,2,3,4,2,3,4]; appl.equ = equ; fem.appl{1} = appl; fem.frame = {'ref'}; fem.border = 1; clear units; units.basesystem = 'SI'; fem.units = units; % Library materials clear lib lib.mat{1}.name='Iron'; lib.mat{1}.varname='mat1'; lib.mat{1}.variables.nu='0.29'; lib.mat{1}.variables.E='200e9[Pa]'; lib.mat{1}.variables.mur='4000'; lib.mat{1}.variables.sigma='1.12e7[S/m]'; lib.mat{1}.variables.epsilonr='1'; lib.mat{1}.variables.alpha='12.2e-6[1/K]'; lib.mat{1}.variables.C='440[J/(kg*K)]'; lib.mat{1}.variables.rho='7870[kg/m^3]'; lib.mat{1}.variables.k='76.2[W/(m*K)]'; lib.mat{2}.name='Air'; lib.mat{2}.varname='mat2'; lib.mat{2}.variables.nu0='nu0(T[1/K])[m^2/s]'; lib.mat{2}.variables.eta='eta(T[1/K])[Pa*s]'; lib.mat{2}.variables.gamma='1.4'; lib.mat{2}.variables.sigma='0[S/m]'; lib.mat{2}.variables.C='Cp(T[1/K])[J/(kg*K)]'; lib.mat{2}.variables.rho='rho(p[1/Pa],T[1/K])[kg/m^3]'; lib.mat{2}.variables.k='k(T[1/K])[W/(m*K)]'; lib.mat{2}.variables.cs='cs(T[1/K])[m/s]'; clear fcns fcns{1}.type='inline'; fcns{1}.name='cs(T)'; fcns{1}.expr='sqrt(1.4*287*T)'; fcns{1}.dexpr={'diff(sqrt(1.4*287*T),T)'}; fcns{2}.type='inline'; fcns{2}.name='rho(p,T)'; fcns{2}.expr='p*0.02897/8.314/T'; fcns{2}.dexpr={'diff(p*0.02897/8.314/T,p)','diff(p*0.02897/8.314/T,T)'}; fcns{3}.type='piecewise'; fcns{3}.name='Cp(T)'; fcns{3}.extmethod='const'; fcns{3}.subtype='poly'; fcns{3}.expr={{'0','1.04763657E+03','1','-3.72589265E-01','2', ... '9.45304214E-04','3','-6.02409443E-07','4','1.28589610E-10'}}; fcns{3}.intervals={'200','1600'}; fcns{4}.type='piecewise'; fcns{4}.name='eta(T)'; fcns{4}.extmethod='const'; fcns{4}.subtype='poly'; fcns{4}.expr={{'0','-8.38278000E-07','1','8.35717342E-08','2', ... '-7.69429583E-11','3','4.64372660E-14','4','-1.06585607E-17'}}; fcns{4}.intervals={'200','1600'}; fcns{5}.type='piecewise'; fcns{5}.name='nu0(T)'; fcns{5}.extmethod='const'; fcns{5}.subtype='poly'; fcns{5}.expr={{'0','-5.86912450E-06','1','5.01274491E-08','2', ... '7.50108343E-11','3','1.80336823E-15','4','-2.91688030E-18'}}; fcns{5}.intervals={'200','1600'}; fcns{6}.type='piecewise'; fcns{6}.name='k(T)'; fcns{6}.extmethod='const'; fcns{6}.subtype='poly'; fcns{6}.expr={{'0','-2.27583562E-03','1','1.15480022E-04','2', ... '-7.90252856E-08','3','4.11702505E-11','4','-7.43864331E-15'}}; fcns{6}.intervals={'200','1600'}; lib.mat{2}.functions = fcns; lib.matgroups{1}.name='Resistivity'; lib.matgroups{1}.variables={'alphares','T0','res0'}; lib.matgroups{1}.descr={'Temperature coefficient','Reference temperature','Resistivity at reference temperature'}; fem.lib = lib; % ODE Settings clear ode clear units; units.basesystem = 'SI'; ode.units = units; fem.ode=ode; % Multiphysics fem=multiphysics(fem); % Extend mesh fem.xmesh=meshextend(fem); % Solve problem fem.sol=femtime(fem, ... 'solcomp',{'Az'}, ... 'outcomp',{'Az','Azt'}, ... 'blocksize','auto', ... 'tlist',[0:0.1:1], ... 'tout','tlist'); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'tridata',{'normH_emqa','cont','internal','unit','A/m'}, ... 'trimap','jet(1024)', ... 'arrowdata',{'Hx_emqa','Hy_emqa'}, ... 'arrowxspacing',60, ... 'arrowyspacing',60, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[1.0,0.0,0.0], ... 'solnum','end', ... 'title','Time=1 Surface: Magnetic field, norm [A/m] Arrow: Magnetic field', ... 'axis',[-1.827209,1.827209,-1.0294670249480251,1.0294670249480251]); % (Default values are not included) % Application mode 1 clear appl appl.mode.class = 'PerpendicularCurrents'; appl.module = 'ACDC'; appl.sshape = 2; appl.assignsuffix = '_emqa'; clear prop prop.analysis='transient'; appl.prop = prop; clear bnd bnd.type = {'A0','cont'}; bnd.ind = [1,1,1,2,2,2,1,1,1,1,1,1,1,1,2,2,2,2,1,1,1,1,1,1,1,1,2,1]; appl.bnd = bnd; clear equ equ.Jez = {0,0,'1-flc2hs(t-0.5,0.25)','-(1-flc2hs(t-0.5,0.25))'}; equ.sigma = {'mat2_sigma','mat1_sigma','mat2_sigma','mat2_sigma'}; equ.epsilonr = {1,'mat1_epsilonr',1,1}; equ.mur = {1,'mat1_mur',1,1}; equ.ind = [1,2,3,4,2,3,4]; appl.equ = equ; fem.appl{1} = appl; fem.frame = {'ref'}; fem.border = 1; clear units; units.basesystem = 'SI'; fem.units = units; % Library materials clear lib lib.mat{1}.name='Iron'; lib.mat{1}.varname='mat1'; lib.mat{1}.variables.nu='0.29'; lib.mat{1}.variables.E='200e9[Pa]'; lib.mat{1}.variables.mur='4000'; lib.mat{1}.variables.sigma='1.12e7[S/m]'; lib.mat{1}.variables.epsilonr='1'; lib.mat{1}.variables.alpha='12.2e-6[1/K]'; lib.mat{1}.variables.C='440[J/(kg*K)]'; lib.mat{1}.variables.rho='7870[kg/m^3]'; lib.mat{1}.variables.k='76.2[W/(m*K)]'; lib.mat{2}.name='Air'; lib.mat{2}.varname='mat2'; lib.mat{2}.variables.nu0='nu0(T[1/K])[m^2/s]'; lib.mat{2}.variables.eta='eta(T[1/K])[Pa*s]'; lib.mat{2}.variables.gamma='1.4'; lib.mat{2}.variables.sigma='0[S/m]'; lib.mat{2}.variables.C='Cp(T[1/K])[J/(kg*K)]'; lib.mat{2}.variables.rho='rho(p[1/Pa],T[1/K])[kg/m^3]'; lib.mat{2}.variables.k='k(T[1/K])[W/(m*K)]'; lib.mat{2}.variables.cs='cs(T[1/K])[m/s]'; clear fcns fcns{1}.type='inline'; fcns{1}.name='cs(T)'; fcns{1}.expr='sqrt(1.4*287*T)'; fcns{1}.dexpr={'diff(sqrt(1.4*287*T),T)'}; fcns{2}.type='inline'; fcns{2}.name='rho(p,T)'; fcns{2}.expr='p*0.02897/8.314/T'; fcns{2}.dexpr={'diff(p*0.02897/8.314/T,p)','diff(p*0.02897/8.314/T,T)'}; fcns{3}.type='piecewise'; fcns{3}.name='Cp(T)'; fcns{3}.extmethod='const'; fcns{3}.subtype='poly'; fcns{3}.expr={{'0','1.04763657E+03','1','-3.72589265E-01','2', ... '9.45304214E-04','3','-6.02409443E-07','4','1.28589610E-10'}}; fcns{3}.intervals={'200','1600'}; fcns{4}.type='piecewise'; fcns{4}.name='eta(T)'; fcns{4}.extmethod='const'; fcns{4}.subtype='poly'; fcns{4}.expr={{'0','-8.38278000E-07','1','8.35717342E-08','2', ... '-7.69429583E-11','3','4.64372660E-14','4','-1.06585607E-17'}}; fcns{4}.intervals={'200','1600'}; fcns{5}.type='piecewise'; fcns{5}.name='nu0(T)'; fcns{5}.extmethod='const'; fcns{5}.subtype='poly'; fcns{5}.expr={{'0','-5.86912450E-06','1','5.01274491E-08','2', ... '7.50108343E-11','3','1.80336823E-15','4','-2.91688030E-18'}}; fcns{5}.intervals={'200','1600'}; fcns{6}.type='piecewise'; fcns{6}.name='k(T)'; fcns{6}.extmethod='const'; fcns{6}.subtype='poly'; fcns{6}.expr={{'0','-2.27583562E-03','1','1.15480022E-04','2', ... '-7.90252856E-08','3','4.11702505E-11','4','-7.43864331E-15'}}; fcns{6}.intervals={'200','1600'}; lib.mat{2}.functions = fcns; lib.matgroups{1}.name='Resistivity'; lib.matgroups{1}.variables={'alphares','T0','res0'}; lib.matgroups{1}.descr={'Temperature coefficient','Reference temperature','Resistivity at reference temperature'}; fem.lib = lib; % ODE Settings clear ode clear units; units.basesystem = 'SI'; ode.units = units; fem.ode=ode; % Multiphysics fem=multiphysics(fem); % Extend mesh fem.xmesh=meshextend(fem); % Solve problem fem.sol=femtime(fem, ... 'solcomp',{'Az'}, ... 'outcomp',{'Az','Azt'}, ... 'blocksize','auto', ... 'tlist',[0:0.1:1], ... 'tout','tlist'); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'tridata',{'normH_emqa','cont','internal','unit','A/m'}, ... 'trimap','jet(1024)', ... 'arrowdata',{'Hx_emqa','Hy_emqa'}, ... 'arrowxspacing',60, ... 'arrowyspacing',60, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[1.0,0.0,0.0], ... 'solnum','end', ... 'title','Time=1 Surface: Magnetic field, norm [A/m] Arrow: Magnetic field', ... 'axis',[-1.8545828726591755,1.8545828726591755,-1.029467,1.029467]); % Plot solution postplot(fem, ... 'tridata',{'normH_emqa','cont','internal','unit','A/m'}, ... 'trimap','jet(1024)', ... 'arrowdata',{'Hx_emqa','Hy_emqa'}, ... 'arrowxspacing',60, ... 'arrowyspacing',60, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[1.0,0.0,0.0], ... 'solnum',2, ... 'title','Time=0.1 Surface: Magnetic field, norm [A/m] Arrow: Magnetic field', ... 'axis',[-1.827209,1.827209,-1.080143475276753,1.080143475276753]); % Plot solution postplot(fem, ... 'tridata',{'normH_emqa','cont','internal','unit','A/m'}, ... 'trimap','jet(1024)', ... 'arrowdata',{'Hx_emqa','Hy_emqa'}, ... 'arrowxspacing',60, ... 'arrowyspacing',60, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[1.0,0.0,0.0], ... 'solnum',10, ... 'title','Time=0.9 Surface: Magnetic field, norm [A/m] Arrow: Magnetic field', ... 'axis',[-1.827209,1.827209,-1.080143475276753,1.080143475276753]); % Plot solution postplot(fem, ... 'tridata',{'normH_emqa','cont','internal','unit','A/m'}, ... 'trimap','jet(1024)', ... 'arrowdata',{'Hx_emqa','Hy_emqa'}, ... 'arrowxspacing',60, ... 'arrowyspacing',60, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[1.0,0.0,0.0], ... 'solnum',10, ... 'title','Time=0.9 Surface: Magnetic field, norm [A/m] Arrow: Magnetic field', ... 'axis',[-1.827209,1.827209,-1.080143475276753,1.080143475276753]); % Plot in cross-section or along domain postcrossplot(fem,0,[0;0], ... 'pointdata',{'normH_emqa','unit','A/m'}, ... 'title','Magnetic field, norm [A/m]', ... 'axislabel',{'Time','Magnetic field',' norm [A/m]'}); % Plot in cross-section or along domain postcrossplot(fem,0,[0;0], ... 'pointdata',{'normH_emqa','unit','A/m'}, ... 'title','Magnetic field, norm [A/m]', ... 'axislabel',{'Time','Magnetic field',' norm [A/m]'}); % Plot solution postplot(fem, ... 'tridata',{'normH_emqa','cont','internal','unit','A/m'}, ... 'trimap','jet(1024)', ... 'arrowdata',{'Mx_emqa','My_emqa'}, ... 'arrowxspacing',60, ... 'arrowyspacing',60, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[1.0,0.0,0.0], ... 'solnum',10, ... 'title','Time=0.9 Surface: Magnetic field, norm [A/m] Arrow: Magnetization', ... 'axis',[-1.827209,1.827209,-1.080143475276753,1.080143475276753]); % Plot solution postplot(fem, ... 'tridata',{'normH_emqa','cont','internal','unit','A/m'}, ... 'trimap','jet(1024)', ... 'arrowdata',{'Mx_emqa','My_emqa'}, ... 'arrowxspacing',60, ... 'arrowyspacing',60, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[1.0,0.0,0.0], ... 'solnum',10, ... 'title','Time=0.9 Surface: Magnetic field, norm [A/m] Arrow: Magnetization', ... 'axis',[-1.827209,1.827209,-1.080143475276753,1.080143475276753]); % Plot solution postplot(fem, ... 'tridata',{'normH_emqa','cont','internal','unit','A/m'}, ... 'trimap','jet(1024)', ... 'arrowdata',{'Mx_emqa','My_emqa'}, ... 'arrowxspacing',60, ... 'arrowyspacing',60, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[1.0,0.0,0.0], ... 'solnum',10, ... 'title','Time=0.9 Surface: Magnetic field, norm [A/m] Arrow: Magnetization', ... 'axis',[-1.827209,1.827209,-1.080143475276753,1.080143475276753]); % Plot solution postplot(fem, ... 'tridata',{'normH_emqa','cont','internal','unit','A/m'}, ... 'trimap','jet(1024)', ... 'arrowdata',{'Mx_emqa','My_emqa'}, ... 'arrowxspacing',60, ... 'arrowyspacing',60, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[1.0,0.0,0.0], ... 'solnum',10, ... 'title','Time=0.9 Surface: Magnetic field, norm [A/m] Arrow: Magnetization', ... 'sdl',{[2,3,4,5,6,7]}, ... 'axis',[-1.8545828726591755,1.8545828726591755,-1.029467,1.029467]); % Plot solution postplot(fem, ... 'tridata',{'normH_emqa','cont','internal','unit','A/m'}, ... 'trimap','jet(1024)', ... 'arrowdata',{'Mx_emqa','My_emqa'}, ... 'arrowxspacing',60, ... 'arrowyspacing',60, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[1.0,0.0,0.0], ... 'solnum',10, ... 'title','Time=0.9 Surface: Magnetic field, norm [A/m] Arrow: Magnetization', ... 'sdl',{[2,3,4,5,6,7]}, ... 'axis',[-1.8545828726591755,1.8545828726591755,-1.029467,1.029467]); % Plot solution postplot(fem, ... 'tridata',{'normH_emqa','cont','internal','unit','A/m'}, ... 'trimap','jet(1024)', ... 'arrowdata',{'Mx_emqa','My_emqa'}, ... 'arrowxspacing',60, ... 'arrowyspacing',60, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[1.0,0.0,0.0], ... 'solnum',2, ... 'title','Time=0.1 Sut�`rface: Magnetic field, norm [A/m] Arrow: Magnetization', ... 'sdl',{[2,3,4,5,6,7]}, ... 'axis',[-1.827209,1.827209,-1.0785515173176126,1.0785515173176126]); % Plot solution postplot(fem, ... 'tridata',{'normH_emqa','cont','internal','unit','A/m'}, ... 'trimap','jet(1024)', ... 'arrowdata',{'Mx_emqa','My_emqa'}, ... 'arrowxspacing',60, ... 'arrowyspacing',60, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[1.0,0.0,0.0], ... 'solnum',5, ... 'title','Time=0.4 Surface: Magnetic field, norm [A/m] Arrow: Magnetization', ... 'sdl',{[2,3,4,5,6,7]}, ... 'axis',[-1.827209,1.827209,-1.0753816377663485,1.0753816377663485]); % Plot solution postplot(fem, ... 'tridata',{'normH_emqa','cont','internal','unit','A/m'}, ... 'trimap','jet(1024)', ... 'arrowdata',{'Mx_emqa','My_emqa'}, ... 'arrowxspacing',60, ... 'arrowyspacing',60, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[1.0,0.0,0.0], ... 'solnum',6, ... 'title','Time=0.5 Surface: Magnetic field, norm [A/m] Arrow: Magnetization', ... 'sdl',{[2,3,4,5,6,7]}, ... 'axis',[-1.827209,1.827209,-1.080143475276753,1.080143475276753]); % Plot solution postplot(fem, ... 'tridata',{'normH_emqa','cont','internal','unit','A/m'}, ... 'trimap','jet(1024)', ... 'arrowdata',{'Mx_emqa','My_emqa'}, ... 'arrowxspacing',60, ... 'arrowyspacing',60, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[1.0,0.0,0.0], ... 'solnum',10, ... 'title','Time=0.9 Surface: Magnetic field, norm [A/m] Arrow: Magnetization', ... 'sdl',{[2,3,4,5,6,7]}, ... 'axis',[-1.827209,1.827209,-1.0753816377663485,1.0753816377663485]); % COMSOL Multiphysics Model M-file % Generated by COMSOL 3.5 (COMSOL 3.5.0.494, $Date: 2008/09/19 16:09:48 $) % Geometry [g10]=geomcopy({g5}); [g11]=geomcopy({g10}); g11=move(g11,[0.045,0]); [g12]=geomcopy({g8}); [g13]=geomcopy({g12}); g13=move(g13,[-0.045,0]); % Analyzed geometry clear s s.objs={g7,g2,g1,g4,g3,g11,g13}; s.name={'SQ5','SQ2','SQ1','SQ4','SQ3','R1','R2'}; s.tags={'g7','g2','g1','g4','g3','g11','g13'}; fem.draw=struct('s',s); fem.geom=geomcsg(fem); % Initialize mesh fem.mesh=meshinit(fem, ... 'hauto',5); % COMSOL Multiphysics Model M-file % Generated by COMSOL 3.5 (COMSOL 3.5.0.494, $Date: 2008/09/19 16:09:48 $) % (Default values are not included) % Application mode 1 clear appl appl.mode.class = 'PerpendicularCurrents'; appl.module = 'ACDC'; appl.assignsuffix = '_emqa'; clear prop prop.analysis='transient'; appl.prop = prop; clear bnd bnd.type = {'A0','cont'}; bnd.ind = [1,1,1,2,2,2,1,1,1,1,1,1,1,1,2,2,2,2,1,1,1,1,1,1,1,1,2,1]; appl.bnd = bnd; clear equ equ.Jez = {0,0,'1-flc2hs(t-0.5,0.25)','-(1-flc2hs(t-0.5,0.25))'}; equ.sigma = {'mat2_sigma','mat1_sigma','mat2_sigma','mat2_sigma'}; equ.epsilonr = {1,'mat1_epsilonr',1,1}; equ.mur = {1,'mat1_mur',1,1}; equ.ind = [1,2,3,4,2,3,4]; appl.equ = equ; fem.appl{1} = appl; fem.frame = {'ref'}; fem.border = 1; clear units; units.basesystem = 'SI'; fem.units = units; % Library materials clear lib lib.mat{1}.name='Iron'; lib.mat{1}.varname='mat1'; lib.mat{1}.variables.nu='0.29'; lib.mat{1}.variables.E='200e9[Pa]'; lib.mat{1}.variables.mur='4000'; lib.mat{1}.variables.sigma='1.12e7[S/m]'; lib.mat{1}.variables.epsilonr='1'; lib.mat{1}.variables.alpha='12.2e-6[1/K]'; lib.mat{1}.variables.C='440[J/(kg*K)]'; lib.mat{1}.variables.rho='7870[kg/m^3]'; lib.mat{1}.variables.k='76.2[W/(m*K)]'; lib.mat{2}.name='Air'; lib.mat{2}.varname='mat2'; lib.mat{2}.variables.nu0='nu0(T[1/K])[m^2/s]'; lib.mat{2}.variables.eta='eta(T[1/K])[Pa*s]'; lib.mat{2}.variables.gamma='1.4'; lib.mat{2}.variables.sigma='0[S/m]'; lib.mat{2}.variables.C='Cp(T[1/K])[J/(kg*K)]'; lib.mat{2}.variables.rho='rho(p[1/Pa],T[1/K])[kg/m^3]'; lib.mat{2}.variables.k='k(T[1/K])[W/(m*K)]'; lib.mat{2}.variables.cs='cs(T[1/K])[m/s]'; clear fcns fcns{1}.type='inline'; fcns{1}.name='cs(T)'; fcns{1}.expr='sqrt(1.4*287*T)'; fcns{1}.dexpr={'diff(sqrt(1.4*287*T),T)'}; fcns{2}.type='inline'; fcns{2}.name='rho(p,T)'; fcns{2}.expr='p*0.02897/8.314/T'; fcns{2}.dexpr={'diff(p*0.02897/8.314/T,p)','diff(p*0.02897/8.314/T,T)'}; fcns{3}.type='piecewise'; fcns{3}.name='Cp(T)'; fcns{3}.extmethod='const'; fcns{3}.subtype='poly'; fcns{3}.expr={{'0','1.04763657E+03','1','-3.72589265E-01','2', ... '9.45304214E-04','3','-6.02409443E-07','4','1.28589610E-10'}}; fcns{3}.intervals={'200','1600'}; fcns{4}.type='piecewise'; fcns{4}.name='eta(T)'; fcns{4}.extmethod='const'; fcns{4}.subtype='poly'; fcns{4}.expr={{'0','-8.38278000E-07','1','8.35717342E-08','2', ... '-7.69429583E-11','3','4.64372660E-14','4','-1.06585607E-17'}}; fcns{4}.intervals={'200','1600'}; fcns{5}.type='piecewise'; fcns{5}.name='nu0(T)'; fcns{5}.extmethod='const'; fcns{5}.subtype='poly'; fcns{5}.expr={{'0','-5.86912450E-06','1','5.01274491E-08','2', ... '7.50108343E-11','3','1.80336823E-15','4','-2.91688030E-18'}}; fcns{5}.intervals={'200','1600'}; fcns{6}.type='piecewise'; fcns{6}.name='k(T)'; fcns{6}.extmethod='const'; fcns{6}.subtype='poly'; fcns{6}.expr={{'0','-2.27583562E-03','1','1.15480022E-04','2', ... '-7.90252856E-08','3','4.11702505E-11','4','-7.43864331E-15'}}; fcns{6}.intervals={'200','1600'}; lib.mat{2}.functions = fcns; lib.matgroups{1}.name='Resistivity'; lib.matgroups{1}.variables={'alphares','T0','res0'}; lib.matgroups{1}.descr={'Temperature coefficient','Reference temperature','Resistivity at reference temperature'}; fem.lib = lib; % ODE Settings clear ode clear units; units.basesystem = 'SI'; ode.units = units; fem.ode=ode; % Multiphysics fem=multiphysics(fem); % Extend mesh fem.xmesh=meshextend(fem); % Solve problem fem.sol=femtime(fem, ... 'solcomp',{'Az'}, ... 'outcomp',{'Az','Azt'}, ... 'blocksize','auto', ... 'tlist',[0:0.1:1], ... 'tout','tlist'); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'tridata',{'normH_emqa','cont','internal','unit','A/m'}, ... 'trimap','jet(1024)', ... 'arrowdata',{'Mx_emqa','My_emqa'}, ... 'arrowxspacing',60, ... 'arrowyspacing',60, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[1.0,0.0,0.0], ... 'solnum','end', ... 'title','Time=1 Surface: Magnetic field, norm [A/m] Arrow: Magnetization', ... 'axis',[-1.9143294458663163,1.9143294458663163,-1.0785515173176126,1.0785515173176126]); % (Default values are not included) % Application mode 1 clear appl appl.mode.class = 'PerpendicularCurrents'; appl.module = 'ACDC'; appl.sshape = 2; appl.assignsuffix = '_emqa'; clear prop prop.analysis='transient'; appl.prop = prop; clear bnd bnd.type = {'A0','cont'}; bnd.ind = [1,1,1,2,2,2,1,1,1,1,1,1,1,1,2,2,2,2,1,1,1,1,1,1,1,1,2,1]; appl.bnd = bnd; clear equ equ.Jez = {0,0,'1-flc2hs(t-0.5,0.25)','-(1-flc2hs(t-0.5,0.25))'}; equ.sigma = {'mat2_sigma','mat3_sigma','mat2_sigma','mat2_sigma'}; equ.epsilonr = {1,'mat3_epsilonr',1,1}; equ.mur = {1,'mat3_MUR(normB_emqa[1/T])',1,1}; equ.normfH = {'1/mu0_emqa*normB_emqa','mat3_HB(normB_emqa[1/T])[A/m]','1/mu0_emqa*normB_emqa', ... '1/mu0_emqa*normB_emqa'}; equ.ind = [1,2,3,4,2,3,4]; appl.equ = equ; fem.appl{1} = appl; fem.frame = {'ref'}; fem.border = 1; clear units; units.basesystem = 'SI'; fem.units = units; % Library materials clear lib lib.mat{1}.name='Iron'; lib.mat{1}.varname='mat1'; lib.mat{1}.variables.nu='0.29'; lib.mat{1}.variables.E='200e9[Pa]'; lib.mat{1}.variables.mur='4000'; lib.mat{1}.variables.sigma='1.12e7[S/m]'; lib.mat{1}.variables.epsilonr='1'; lib.mat{1}.variables.alpha='12.2e-6[1/K]'; lib.mat{1}.variables.C='440[J/(kg*K)]'; lib.mat{1}.variables.rho='7870[kg/m^3]'; lib.mat{1}.variables.k='76.2[W/(m*K)]'; lib.mat{2}.name='Air'; lib.mat{2}.varname='mat2'; lib.mat{2}.variables.nu0='nu0(T[1/K])[m^2/s]'; lib.mat{2}.variables.eta='eta(T[1/K])[Pa*s]'; lib.mat{2}.variables.gamma='1.4'; lib.mat{2}.variables.sigma='0[S/m]'; lib.mat{2}.variables.C='Cp(T[1/K])[J/(kg*K)]'; lib.mat{2}.variables.rho='rho(p[1/Pa],T[1/K])[kg/m^3]'; lib.mat{2}.variables.k='k(T[1/K])[W/(m*K)]'; lib.mat{2}.variables.cs='cs(T[1/K])[m/s]'; clear fcns fcns{1}.type='inline'; fcns{1}.name='cs(T)'; fcns{1}.expr='sqrt(1.4*287*T)'; fcns{1}.dexpr={'diff(sqrt(1.4*287*T),T)'}; fcns{2}.type='inline'; fcns{2}.name='rho(p,T)'; fcns{2}.expr='p*0.02897/8.314/T'; fcns{2}.dexpr={'diff(p*0.02897/8.314/T,p)','diff(p*0.02897/8.314/T,T)'}; fcns{3}.type='piecewise'; fcns{3}.name='Cp(T)'; fcns{3}.extmethod='const'; fcns{3}.subtype='poly'; fcns{3}.expr={{'0','1.04763657E+03','1','-3.72589265E-01','2', ... '9.45304214E-04','3','-6.02409443E-07','4','1.28589610E-10'}}; fcns{3}.intervals={'200','1600'}; fcns{4}.type='piecewise'; fcns{4}.name='eta(T)'; fcns{4}.extmethod='const'; fcns{4}.subtype='poly'; fcns{4}.expr={{'0','-8.38278000E-07','1','8.35717342E-08','2', ... '-7.69429583E-11','3','4.64372660E-14','4','-1.06585607E-17'}}; fcns{4}.intervals={'200','1600'}; fcns{5}.type='piecewise'; fcns{5}.name='nu0(T)'; fcns{5}.extmethod='const'; fcns{5}.subtype='poly'; fcns{5}.expr={{'0','-5.86912450E-06','1','5.01274491E-08','2', ... '7.50108343E-11','3','1.80336823E-15','4','-2.91688030E-18'}}; fcns{5}.intervals={'200','1600'}; fcns{6}.type='piecewise'; fcns{6}.name='k(T)'; fcns{6}.extmethod='const'; fcns{6}.subtype='poly'; fcns{6}.expr={{'0','-2.27583562E-03','1','1.15480022E-04','2', ... '-7.90252856E-08','3','4.11702505E-11','4','-7.43864331E-15'}}; fcns{6}.intervals={'200','1600'}; lib.mat{2}.functions = fcns; lib.mat{3}.name='Soft Iron (without losses)'; lib.mat{3}.varname='mat3'; lib.mat{3}.variables.normfB='BH(normH[m/A])[T]'; lib.mat{3}.variables.mur='MUR(normB[1/T])'; lib.mat{3}.variables.sigma='0[S/m]'; lib.mat{3}.variables.normfH='HB(normB[1/T])[A/m]'; lib.mat{3}.variables.epsilonr='1'; clear fcns fcns{1}.type='interp'; fcns{1}.name='MUR'; fcns{1}.method='linear'; fcns{1}.extmethod='const'; fcns{1}.x={'1','1.1','1.2','1.3','1.4','1.5','1.6','1.7','1.8','1.9', ... '2.0','2.1','2.2','2.3','2.4'}; fcns{1}.data={'1200','820','560','420','290','220','160','110','70','47', ... '26','15','10','7','6'}; fcns{2}.type='interp'; fcns{2}.name='HB'; fcns{2}.method='linear'; fcns{2}.extmethod='extrap'; fcns{2}.x={'0','1','1.1','1.2','1.3','1.4','1.5','1.6','1.7','1.8', ... '1.9','2.0','2.1','2.2','2.3','2.4'}; fcns{2}.data={'0','663.146','1067.5','1705.23','2463.11','3841.67', ... '5425.74','7957.75','12298.3','20462.8','32169.6','61213.4','111408', ... '175070','261469','318310'}; fcns{3}.type='interp'; fcns{3}.name='BH'; fcns{3}.method='linear'; fcns{3}.extmethod='extrap'; fcns{3}.x={'0','663.146','1067.5','1705.23','2463.11','3841.67', ... '5425.74','7957.75','12298.3','20462.8','32169.6','61213.4','111408', ... '175070','261469','318310'}; fcns{3}.data={'0','1','1.1','1.2','1.3','1.4','1.5','1.6','1.7','1.8', ... '1.9','2.0','2.1','2.2','2.3','2.4'}; lib.mat{3}.functions = fcns; lib.matgroups{1}.name='Resistivity'; lib.matgroups{1}.variables={'alphares','T0','res0'}; lib.matgroups{1}.descr={'Temperature coefficient','Reference temperature','Resistivity at reference temperature'}; lib.matgroups{2}.name='Electromagnetic (AC/DC)'; lib.matgroups{2}.variables={'alphares','T0','res0','Br','normfH','fH','normfB','fB'}; lib.matgroups{2}.descr={'Temperature coefficient','Reference temperature','Resistivity at reference temperature','Remanent flux density','Nonlinear magnetic field, norm','Nonlinear magnetic field','Nonlinear magnetic flux density, norm','Nonlinear magnetic flux density'}; fem.lib = lib; % ODE Settings clear ode clear units; units.basesystem = 'SI'; ode.units = units; fem.ode=ode; % Multiphysics fem=multiphysics(fem); % Extend mesh fem.xmesh=meshextend(fem); % Solve problem fem.sol=femtime(fem, ... 'solcomp',{'Az'}, ... 'outcomp',{'Az','Azt'}, ... 'blocksize','auto', ... 'tlist',[0:0.1:1], ... 'tout','tlist'); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'tridata',{'normH_emqa','cont','internal','unit','A/m'}, ... 'trimap','jet(1024)', ... 'arrowdata',{'Mx_emqa','My_emqa'}, ... 'arrowxspacing',60, ... 'arrowyspacing',60, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[1.0,0.0,0.0], ... 'solnum','end', ... 'title','Time=1 Surface: Magnetic field, norm [A/m] Arrow: Magnetization', ... 'axis',[-1.9430085386882836,1.9430085386882836,-1.0785515173176126,1.0785515173176126]); % Plot solution postplot(fem, ... 'tridata',{'normH_emqa','cont','internal','unit','A/m'}, ... 'trimap','jet(1024)', ... 'arrowdata',{'Mx_emqa','My_emqa'}, ... 'arrowxspacing',60, ... 'arrowyspacing',60, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[1.0,0.0,0.0], ... 'solnum',10, ... 'title','Time=0.9 Surface: Magnetic field, norm [A/m] Arrow: Magnetization', ... 'axis',[-1.9143294458663158,1.9143294458663158,-1.1316441964124861,1.1316441964124861]); % Plot in cross-section or along domain postcrossplot(fem,0,[0;0], ... 'pointdata',{'normH_emqa','unit','A/m'}, ... 'title','Magnetic field, norm [A/m]', ... 'axislabel',{'Time','Magnetic field',' norm [A/m]'}); % (Default values are not included) % Application mode 1 clear appl appl.mode.class = 'PerpendicularCurrents'; appl.module = 'ACDC'; appl.sshape = 2; appl.assignsuffix = '_emqa'; clear prop prop.analysis='transient'; appl.prop = prop; clear bnd bnd.type = {'A0','cont'}; bnd.ind = [1,1,1,2,2,2,1,1,1,1,1,1,1,1,2,2,2,2,1,1,1,1,1,1,1,1,2,1]; appl.bnd = bnd; clear equ equ.magconstrel = {'M','mur','mur','mur'}; equ.Jez = {0,0,'1-flc2hs(t-0.5,0.25)','-(1-flc2hs(t-0.5,0.25))'}; equ.sigma = {'mat2_sigma','mat3_sigma','mat2_sigma','mat2_sigma'}; equ.epsilonr = {1,'mat3_epsilonr',1,1}; equ.mur = {1,'mat3_MUR(normB_emqa[1/T])',1,1}; equ.normfH = {'1/mu0_emqa*normB_emqa','mat3_HB(normB_emqa[1/T])[A/m]','1/mu0_emqa*normB_emqa', ... '1/mu0_emqa*normB_emqa'}; equ.ind = [1,2,3,4,2,3,4]; appl.equ = equ; fem.appl{1} = appl; fem.frame = {'ref'}; fem.border = 1; clear units; units.basesystem = 'SI'; fem.units = units; % Library materials clear lib lib.mat{1}.name='Iron'; lib.mat{1}.varname='mat1'; lib.mat{1}.variables.nu='0.29'; lib.mat{1}.variables.E='200e9[Pa]'; lib.mat{1}.variables.mur='4000'; lib.mat{1}.variables.sigma='1.12e7[S/m]'; lib.mat{1}.variables.epsilonr='1'; lib.mat{1}.variables.alpha='12.2e-6[1/K]'; lib.mat{1}.variables.C='440[J/(kg*K)]'; lib.mat{1}.variables.rho='7870[kg/m^3]'; lib.mat{1}.variables.k='76.2[W/(m*K)]'; lib.mat{2}.name='Air'; lib.mat{2}.varname='mat2'; lib.mat{2}.variables.nu0='nu0(T[1/K])[m^2/s]'; lib.mat{2}.variables.eta='eta(T[1/K])[Pa*s]'; lib.mat{2}.variables.gamma='1.4'; lib.mat{2}.variables.sigma='0[S/m]'; lib.mat{2}.variables.C='Cp(T[1/K])[J/(kg*K)]'; lib.mat{2}.variables.rho='rho(p[1/Pa],T[1/K])[kg/m^3]'; lib.mat{2}.variables.k='k(T[1/K])[W/(m*K)]'; lib.mat{2}.variables.cs='cs(T[1/K])[m/s]'; clear fcns fcns{1}.type='inline'; fcns{1}.name='cs(T)'; fcns{1}.expr='sqrt(1.4*287*T)'; fcns{1}.dexpr={'diff(sqrt(1.4*287*T),T)'}; fcns{2}.type='inline'; fcns{2}.name='rho(p,T)'; fcns{2}.expr='p*0.02897/8.314/T'; fcns{2}.dexpr={'diff(p*0.02897/8.314/T,p)','diff(p*0.02897/8.314/T,T)'}; fcns{3}.type='piecewise'; fcns{3}.name='Cp(T)'; fcns{3}.extmethod='const'; fcns{3}.subtype='poly'; fcns{3}.expr={{'0','1.04763657E+03','1','-3.72589265E-01','2', ... '9.45304214E-04','3','-6.02409443E-07','4','1.28589610E-10'}}; fcns{3}.intervals={'200','1600'}; fcns{4}.type='piecewise'; fcns{4}.name='eta(T)'; fcns{4}.extmethod='const'; fcns{4}.subtype='poly'; fcns{4}.expr={{'0','-8.38278000E-07','1','8.35717342E-08','2', ... '-7.69429583E-11','3','4.64372660E-14','4','-1.06585607E-17'}}; fcns{4}.intervals={'200','1600'}; fcns{5}.type='piecewise'; fcns{5}.name='nu0(T)'; fcns{5}.extmethod='const'; fcns{5}.subtype='poly'; fcns{5}.expr={{'0','-5.86912450E-06','1','5.01274491E-08','2', ... '7.50108343E-11','3','1.80336823E-15','4','-2.91688030E-18'}}; fcns{5}.intervals={'200','1600'}; fcns{6}.type='piecewise'; fcns{6}.name='k(T)'; fcns{6}.extmethod='const'; fcns{6}.subtype='poly'; fcns{6}.expr={{'0','-2.27583562E-03','1','1.15480022E-04','2', ... '-7.90252856E-08','3','4.11702505E-11','4','-7.43864331E-15'}}; fcns{6}.intervals={'200','1600'}; lib.mat{2}.functions = fcns; lib.mat{3}.name='Soft Iron (without losses)'; lib.mat{3}.varname='mat3'; lib.mat{3}.variables.normfB='BH(normH[m/A])[T]'; lib.mat{3}.variables.mur='MUR(normB[1/T])'; lib.mat{3}.variables.sigma='0[S/m]'; lib.mat{3}.variables.normfH='HB(normB[1/T])[A/m]'; lib.mat{3}.variables.epsilonr='1'; clear fcns fcns{1}.type='interp'; fcns{1}.name='MUR'; fcns{1}.method='linear'; fcns{1}.extmethod='const'; fcns{1}.x={'1','1.1','1.2','1.3','1.4','1.5','1.6','1.7','1.8','1.9', ... '2.0','2.1','2.2','2.3','2.4'}; fcns{1}.data={'1200','820','560','420','290','220','160','110','70','47', ... '26','15','10','7','6'}; fcns{2}.type='interp'; fcns{2}.name='HB'; fcns{2}.method='linear'; fcns{2}.extmethod='extrap'; fcns{2}.x={'0','1','1.1','1.2','1.3','1.4','1.5','1.6','1.7','1.8', ... '1.9','2.0','2.1','2.2','2.3','2.4'}; fcns{2}.data={'0','663.146','1067.5','1705.23','2463.11','3841.67', ... '5425.74','7957.75','12298.3','20462.8','32169.6','61213.4','111408', ... '175070','261469','318310'}; fcns{3}.type='interp'; fcns{3}.name='BH'; fcns{3}.method='linear'; fcns{3}.extmethod='extrap'; fcns{3}.x={'0','663.146','1067.5','1705.23','2463.11','3841.67', ... '5425.74','7957.75','12298.3','20462.8','32169.6','61213.4','111408', ... '175070','261469','318310'}; fcns{3}.data={'0','1','1.1','1.2','1.3','1.4','1.5','1.6','1.7','1.8', ... '1.9','2.0','2.1','2.2','2.3','2.4'}; lib.mat{3}.functions = fcns; lib.matgroups{1}.name='Resistivity'; lib.matgroups{1}.variables={'alphares','T0','res0'}; lib.matgroups{1}.descr={'Temperature coefficient','Reference temperature','Resistivity at reference temperature'}; lib.matgroups{2}.name='Electromagnetic (AC/DC)'; lib.matgroups{2}.variables={'alphares','T0','res0','Br','normfH','fH','normfB','fB'}; lib.matgroups{2}.descr={'Temperature coefficient','Reference temperature','Resistivity at reference temperature','Remanent flux density','Nonlinear magnetic field, norm','Nonlinear magnetic field','Nonlinear magnetic flux density, norm','Nonlinear magnetic flux density'}; fem.lib = lib; % ODE Settings clear ode clear units; units.basesystem = 'SI'; ode.units = units; fem.ode=ode; % Multiphysics fem=multiphysics(fem); % Extend mesh fem.xmesh=meshextend(fem); % Solve problem fem.sol=femtime(fem, ... 'solcomp',{'Az'}, ... 'outcomp',{'Az','Azt'}, ... 'blocksize','auto', ... 'tlist',[0:0.1:1], ... 'tout','tlist'); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'tridata',{'normH_emqa','cont','internal','unit','A/m'}, ... 'trimap','jet(1024)', ... 'arrowdata',{'Mx_emqa','My_emqa'}, ... 'arrowxspacing',60, ... 'arrowyspacing',60, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[1.0,0.0,0.0], ... 'solnum','end', ... 'title','Time=1 Surface: Magnetic field, norm [A/m] Arrow: Magnetization', ... 'axis',[-1.9430085386882836,1.9430085386882836,-1.0785515173176126,1.0785515173176126]); % Plot in cross-section or along domain postcrossplot(fem,0,[0;0], ... 'pointdata',{'normH_emqa','unit','A/m'}, ... 'title','Magnetic field, norm [A/m]', ... 'axislabel',{'Time','Magnetic field',' norm [A/m]'}); % (Default values are not included) % Application mode 1 clear appl appl.mode.class = 'PerpendicularCurrents'; appl.module = 'ACDC'; appl.sshape = 2; appl.assignsuffix = '_emqa'; clear prop prop.analysis='transient'; appl.prop = prop; clear bnd bnd.type = {'A0','cont'}; bnd.ind = [1,1,1,2,2,2,1,1,1,1,1,1,1,1,2,2,2,2,1,1,1,1,1,1,1,1,2,1]; appl.bnd = bnd; clear equ equ.magconstrel = {'Br','mur','mur','mur'}; equ.Jez = {0,0,'1-flc2hs(t-0.5,0.25)','-(1-flc2hs(t-0.5,0.25))'}; equ.sigma = {'mat2_sigma','mat3_sigma','mat2_sigma','mat2_sigma'}; equ.epsilonr = {1,'mat3_epsilonr',1,1}; equ.mur = {1,'mat3_MUR(normB_emqa[1/T])',1,1}; equ.normfH = {'1/mu0_emqa*normB_emqa','mat3_HB(normB_emqa[1/T])[A/m]','1/mu0_emqa*normB_emqa', ... '1/mu0_emqa*normB_emqa'}; equ.ind = [1,2,3,4,2,3,4]; appl.equ = equ; fem.appl{1} = appl; fem.frame = {'ref'}; fem.border = 1; clear units; units.basesystem = 'SI'; fem.units = units; % Library materials clear lib lib.mat{1}.name='Iron'; lib.mat{1}.varname='mat1'; lib.mat{1}.variables.nu='0.29'; lib.mat{1}.variables.E='200e9[Pa]'; lib.mat{1}.variables.mur='4000'; lib.mat{1}.variables.sigma='1.12e7[S/m]'; lib.mat{1}.variables.epsilonr='1'; lib.mat{1}.variables.alpha='12.2e-6[1/K]'; lib.mat{1}.variables.C='440[J/(kg*K)]'; lib.mat{1}.variables.rho='7870[kg/m^3]'; lib.mat{1}.variables.k='76.2[W/(m*K)]'; lib.mat{2}.name='Air'; lib.mat{2}.varname='mat2'; lib.mat{2}.variables.nu0='nu0(T[1/K])[m^2/s]'; lib.mat{2}.variables.eta='eta(T[1/K])[Pa*s]'; lib.mat{2}.variables.gamma='1.4'; lib.mat{2}.variables.sigma='0[S/m]'; lib.mat{2}.variables.C='Cp(T[1/K])[J/(kg*K)]'; lib.mat{2}.variables.rho='rho(p[1/Pa],T[1/K])[kg/m^3]'; lib.mat{2}.variables.k='k(T[1/K])[W/(m*K)]'; lib.mat{2}.variables.cs='cs(T[1/K])[m/s]'; clear fcns fcns{1}.type='inline'; fcns{1}.name='cs(T)'; fcns{1}.expr='sqrt(1.4*287*T)'; fcns{1}.dexpr={'diff(sqrt(1.4*287*T),T)'}; fcns{2}.type='inline'; fcns{2}.name='rho(p,T)'; fcns{2}.expr='p*0.02897/8.314/T'; fcns{2}.dexpr={'diff(p*0.02897/8.314/T,p)','diff(p*0.02897/8.314/T,T)'}; fcns{3}.type='piecewise'; fcns{3}.name='Cp(T)'; fcns{3}.extmethod='const'; fcns{3}.subtype='poly'; fcns{3}.expr={{'0','1.04763657E+03','1','-3.72589265E-01','2', ... '9.45304214E-04','3','-6.02409443E-07','4','1.28589610E-10'}}; fcns{3}.intervals={'200','1600'}; fcns{4}.type='piecewise'; fcns{4}.name='eta(T)'; fcns{4}.extmethod='const'; fcns{4}.subtype='poly'; fcns{4}.expr={{'0','-8.38278000E-07','1','8.35717342E-08','2', ... '-7.69429583E-11','3','4.64372660E-14','4','-1.06585607E-17'}}; fcns{4}.intervals={'200','1600'}; fcns{5}.type='piecewise'; fcns{5}.name='nu0(T)'; fcns{5}.extmethod='const'; fcns{5}.subtype='poly'; fcns{5}.expr={{'0','-5.86912450E-06','1','5.01274491E-08','2', ... '7.50108343E-11','3','1.80336823E-15','4','-2.91688030E-18'}}; fcns{5}.intervals={'200','1600'}; fcns{6}.type='piecewise'; fcns{6}.name='k(T)'; fcns{6}.extmethod='const'; fcns{6}.subtype='poly'; fcns{6}.expr={{'0','-2.27583562E-03','1','1.15480022E-04','2', ... '-7.90252856E-08','3','4.11702505E-11','4','-7.43864331E-15'}}; fcns{6}.intervals={'200','1600'}; lib.mat{2}.functions = fcns; lib.mat{3}.name='Soft Iron (without losses)'; lib.mat{3}.varname='mat3'; lib.mat{3}.variables.normfB='BH(normH[m/A])[T]'; lib.mat{3}.variables.mur='MUR(normB[1/T])'; lib.mat{3}.variables.sigma='0[S/m]'; lib.mat{3}.variables.normfH='HB(normB[1/T])[A/m]'; lib.mat{3}.variables.epsilonr='1'; clear fcns fcns{1}.type='interp'; fcns{1}.name='MUR'; fcns{1}.method='linear'; fcns{1}.extmethod='const'; fcns{1}.x={'1','1.1','1.2','1.3','1.4','1.5','1.6','1.7','1.8','1.9', ... '2.0','2.1','2.2','2.3','2.4'}; fcns{1}.data={'1200','820','560','420','290','220','160','110','70','47', ... '26','15','10','7','6'}; fcns{2}.type='interp'; fcns{2}.name='HB'; fcns{2}.method='linear'; fcns{2}.extmethod='extrap'; fcns{2}.x={'0','1','1.1','1.2','1.3','1.4','1.5','1.6','1.7','1.8', ... '1.9','2.0','2.1','2.2','2.3','2.4'}; fcns{2}.data={'0','663.146','1067.5','1705.23','2463.11','3841.67', ... '5425.74','7957.75','12298.3','20462.8','32169.6','61213.4','111408', ... '175070','261469','318310'}; fcns{3}.type='interp'; fcns{3}.name='BH'; fcns{3}.method='linear'; fcns{3}.extmethod='extrap'; fcns{3}.x={'0','663.146','1067.5','1705.23','2463.11','3841.67', ... '5425.74','7957.75','12298.3','20462.8','32169.6','61213.4','111408', ... '175070','261469','318310'}; fcns{3}.data={'0','1','1.1','1.2','1.3','1.4','1.5','1.6','1.7','1.8', ... '1.9','2.0','2.1','2.2','2.3','2.4'}; lib.mat{3}.functions = fcns; lib.matgroups{1}.name='Resistivity'; lib.matgroups{1}.variables={'alphares','T0','res0'}; lib.matgroups{1}.descr={'Temperature coefficient','Reference temperature','Resistivity at reference temperature'}; lib.matgroups{2}.name='Electromagnetic (AC/DC)'; lib.matgroups{2}.variables={'alphares','T0','res0','Br','normfH','fH','normfB','fB'}; lib.matgroups{2}.descr={'Temperature coefficient','Reference temperature','Resistivity at reference temperature','Remanent flux density','Nonlinear magnetic field, norm','Nonlinear magnetic field','Nonlinear magnetic flux density, norm','Nonlinear magnetic flux density'}; fem.lib = lib; % ODE Settings clear ode clear units; units.basesystem = 'SI'; ode.units = units; fem.ode=ode; % Multiphysics fem=multiphysics(fem); % Extend mesh fem.xmesh=meshextend(fem); % Solve problem fem.sol=femtime(fem, ... 'solcomp',{'Az'}, ... 'outcomp',{'Az','Azt'}, ... 'blocksize','auto', ... 'tlist',[0:0.1:1], ... 'tout','tlist'); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'tridata',{'normH_emqa','cont','internal','unit','A/m'}, ... 'trimap','jet(1024)', ... 'arrowdata',{'Mx_emqa','My_emqa'}, ... 'arrowxspacing',60, ... 'arrowyspacing',60, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[1.0,0.0,0.0], ... 'solnum','end', ... 'title','Time=1 Surface: Magnetic field, norm [A/m] Arrow: Magnetization', ... 'axis',[-1.9430085386882836,1.9430085386882836,-1.0785515173176126,1.0785515173176126]); % Plot in cross-section or along domain postcrossplot(fem,0,[0;0], ... 'pointdata',{'normH_emqa','unit','A/m'}, ... 'title','Magnetic field, norm [A/m]', ... 'axislabel',{'Time','Magnetic field',' norm [A/m]'}); % (Default values are not included) % Application mode 1 clear appl appl.mode.class = 'PerpendicularCurrents'; appl.module = 'ACDC'; appl.sshape = 2; appl.assignsuffix = '_emqa'; clear prop prop.analysis='transient'; appl.prop = prop; clear bnd bnd.type = {'A0','cont'}; bnd.ind = [1,1,1,2,2,2,1,1,1,1,1,1,1,1,2,2,2,2,1,1,1,1,1,1,1,1,2,1]; appl.bnd = bnd; clear equ equ.magconstrel = {'fH','mur','mur','mur'}; equ.Jez = {0,0,'1-flc2hs(t-0.5,0.25)','-(1-flc2hs(t-0.5,0.25))'}; equ.sigma = {'mat2_sigma','mat3_sigma','mat2_sigma','mat2_sigma'}; equ.epsilonr = {1,'mat3_epsilonr',1,1}; equ.mur = {1,'mat3_MUR(normB_emqa[1/T])',1,1}; equ.normfH = {'1/mu0_emqa*normB_emqa','mat3_HB(normB_emqa[1/T])[A/m]','1/mu0_emqa*normB_emqa', ... '1/mu0_emqa*normB_emqa'}; equ.ind = [1,2,3,4,2,3,4]; appl.equ = equ; fem.appl{1} = appl; fem.frame = {'ref'}; fem.border = 1; clear units; units.basesystem = 'SI'; fem.units = units; % Library materials clear lib lib.mat{1}.name='Iron'; lib.mat{1}.varname='mat1'; lib.mat{1}.variables.nu='0.29'; lib.mat{1}.variables.E='200e9[Pa]'; lib.mat{1}.variables.mur='4000'; lib.mat{1}.variables.sigma='1.12e7[S/m]'; lib.mat{1}.variables.epsilonr='1'; lib.mat{1}.variables.alpha='12.2e-6[1/K]'; lib.mat{1}.variables.C='440[J/(kg*K)]'; lib.mat{1}.variables.rho='7870[kg/m^3]'; lib.mat{1}.variables.k='76.2[W/(m*K)]'; lib.mat{2}.name='Air'; lib.mat{2}.varname='mat2'; lib.mat{2}.variables.nu0='nu0(T[1/K])[m^2/s]'; lib.mat{2}.variables.eta='eta(T[1/K])[Pa*s]'; lib.mat{2}.variables.gamma='1.4'; lib.mat{2}.variables.sigma='0[S/m]'; lib.mat{2}.variables.C='Cp(T[1/K])[J/(kg*K)]'; lib.mat{2}.variables.rho='rho(p[1/Pa],T[1/K])[kg/m^3]'; lib.mat{2}.variables.k='k(T[1/K])[W/(m*K)]'; lib.mat{2}.variables.cs='cs(T[1/K])[m/s]'; clear fcns fcns{1}.type='inline'; fcns{1}.name='cs(T)'; fcns{1}.expr='sqrt(1.4*287*T)'; fcns{1}.dexpr={'diff(sqrt(1.4*287*T),T)'}; fcns{2}.type='inline'; fcns{2}.name='rho(p,T)'; fcns{2}.expr='p*0.02897/8.314/T'; fcns{2}.dexpr={'diff(p*0.02897/8.314/T,p)','diff(p*0.02897/8.314/T,T)'}; fcns{3}.type='piecewise'; fcns{3}.name='Cp(T)'; fcns{3}.extmethod='const'; fcns{3}.subtype='poly'; fcns{3}.expr={{'0','1.04763657E+03','1','-3.72589265E-01','2', ... '9.45304214E-04','3','-6.02409443E-07','4','1.28589610E-10'}}; fcns{3}.intervals={'200','1600'}; fcns{4}.type='piecewise'; fcns{4}.name='eta(T)'; fcns{4}.extmethod='const'; fcns{4}.subtype='poly'; fcns{4}.expr={{'0','-8.38278000E-07','1','8.35717342E-08','2', ... '-7.69429583E-11','3','4.64372660E-14','4','-1.06585607E-17'}}; fcns{4}.intervals={'200','1600'}; fcns{5}.type='piecewise'; fcns{5}.name='nu0(T)'; fcns{5}.extmethod='const'; fcns{5}.subtype='poly'; fcns{5}.expr={{'0','-5.86912450E-06','1','5.01274491E-08','2', ... '7.50108343E-11','3','1.80336823E-15','4','-2.91688030E-18'}}; fcns{5}.intervals={'200','1600'}; fcns{6}.type='piecewise'; fcns{6}.name='k(T)'; fcns{6}.extmethod='const'; fcns{6}.subtype='poly'; fcns{6}.expr={{'0','-2.27583562E-03','1','1.15480022E-04','2', ... '-7.90252856E-08','3','4.11702505E-11','4','-7.43864331E-15'}}; fcns{6}.intervals={'200','1600'}; lib.mat{2}.functions = fcns; lib.mat{3}.name='Soft Iron (without losses)'; lib.mat{3}.varname='mat3'; lib.mat{3}.variables.normfB='BH(normH[m/A])[T]'; lib.mat{3}.variables.mur='MUR(normB[1/T])'; lib.mat{3}.variables.sigma='0[S/m]'; lib.mat{3}.variables.normfH='HB(normB[1/T])[A/m]'; lib.mat{3}.variables.epsilonr='1'; clear fcns fcns{1}.type='interp'; fcns{1}.name='MUR'; fcns{1}.method='linear'; fcns{1}.extmethod='const'; fcns{1}.x={'1','1.1','1.2','1.3','1.4','1.5','1.6','1.7','1.8','1.9', ... '2.0','2.1','2.2','2.3','2.4'}; fcns{1}.data={'1200','820','560','420','290','220','160','110','70','47', ... '26','15','10','7','6'}; fcns{2}.type='interp'; fcns{2}.name='HB'; fcns{2}.method='linear'; fcns{2}.extmethod='extrap'; fcns{2}.x={'0','1','1.1','1.2','1.3','1.4','1.5','1.6','1.7','1.8', ... '1.9','2.0','2.1','2.2','2.3','2.4'}; fcns{2}.data={'0','663.146','1067.5','1705.23','2463.11','3841.67', ... '5425.74','7957.75','12298.3','20462.8','32169.6','61213.4','111408', ... '175070','261469','318310'}; fcns{3}.type='interp'; fcns{3}.name='BH'; fcns{3}.method='linear'; fcns{3}.extmethod='extrap'; fcns{3}.x={'0','663.146','1067.5','1705.23','2463.11','3841.67', ... '5425.74','7957.75','12298.3','20462.8','32169.6','61213.4','111408', ... '175070','261469','318310'}; fcns{3}.data={'0','1','1.1','1.2','1.3','1.4','1.5','1.6','1.7','1.8', ... '1.9','2.0','2.1','2.2','2.3','2.4'}; lib.mat{3}.functions = fcns; lib.matgroups{1}.name='Resistivity'; lib.matgroups{1}.variables={'alphares','T0','res0'}; lib.matgroups{1}.descr={'Temperature coefficient','Reference temperature','Resistivity at reference temperature'}; lib.matgroups{2}.name='Electromagnetic (AC/DC)'; lib.matgroups{2}.variables={'alphares','T0','res0','Br','normfH','fH','normfB','fB'}; lib.matgroups{2}.descr={'Temperature coefficient','Reference temperature','Resistivity at reference temperature','Remanent flux density','Nonlinear magnetic field, norm','Nonlinear magnetic field','Nonlinear magnetic flux density, norm','Nonlinear magnetic flux density'}; fem.lib = lib; % ODE Settings clear ode clear units; units.basesystem = 'SI'; ode.units = units; fem.ode=ode; % Multiphysics fem=multiphysics(fem); % Extend mesh fem.xmesh=meshextend(fem); % Solve problem fem.sol=femtime(fem, ... 'solcomp',{'Az'}, ... 'outcomp',{'Az','Azt'}, ... 'blocksize','auto', ... 'tlist',[0:0.1:1], ... 'tout','tlist'); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'tridata',{'normH_emqa','cont','internal','unit','A/m'}, ... 'trimap','jet(1024)', ... 'arrowdata',{'Mx_emqa','My_emqa'}, ... 'arrowxspacing',60, ... 'arrowyspacing',60, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[1.0,0.0,0.0], ... 'solnum','end', ... 'title','Time=1 Surface: Magnetic field, norm [A/m] Arrow: Magnetization', ... 'axis',[-1.9430085386882836,1.9430085386882836,-1.0785515173176126,1.0785515173176126]); % Plot in cross-section or along domain postcrossplot(fem,0,[0;0], ... 'pointdata',{'normH_emqa','unit','A/m'}, ... 'title','Magnetic field, norm [A/m]', ... 'axislabel',{'Time','Magnetic field',' norm [A/m]'}); % (Default values are not included) % Application mode 1 clear appl appl.mode.class = 'PerpendicularCurrents'; appl.module = 'ACDC'; appl.sshape = 2; appl.assignsuffix = '_emqa'; clear prop prop.analysis='transient'; appl.prop = prop; clear bnd bnd.type = {'A0','cont'}; bnd.ind = [1,1,1,2,2,2,1,1,1,1,1,1,1,1,2,2,2,2,1,1,1,1,1,1,1,1,2,1]; appl.bnd = bnd; clear equ equ.magconstrel = {'aniso_fH','mur','mur','mur'}; equ.Jez = {0,0,'1-flc2hs(t-0.5,0.25)','-(1-flc2hs(t-0.5,0.25))'}; equ.sigma = {'mat2_sigma','mat3_sigma','mat2_sigma','mat2_sigma'}; equ.epsilonr = {1,'mat3_epsilonr',1,1}; equ.mur = {1,'mat3_MUR(normB_emqa[1/T])',1,1}; equ.normfH = {'1/mu0_emqa*normB_emqa','mat3_HB(normB_emqa[1/T])[A/m]','1/mu0_emqa*normB_emqa', ... '1/mu0_emqa*normB_emqa'}; equ.ind = [1,2,3,4,2,3,4]; appl.equ = equ; fem.appl{1} = appl; fem.frame = {'ref'}; fem.border = 1; clear units; units.basesystem = 'SI'; fem.units = units; % Library materials clear lib lib.mat{1}.name='Iron'; lib.mat{1}.varname='mat1'; lib.mat{1}.variables.nu='0.29'; lib.mat{1}.variables.E='200e9[Pa]'; lib.mat{1}.variables.mur='4000'; lib.mat{1}.variables.sigma='1.12e7[S/m]'; lib.mat{1}.variables.epsilonr='1'; lib.mat{1}.variables.alpha='12.2e-6[1/K]'; lib.mat{1}.variables.C='440[J/(kg*K)]'; lib.mat{1}.variables.rho='7870[kg/m^3]'; lib.mat{1}.variables.k='76.2[W/(m*K)]'; lib.mat{2}.name='Air'; lib.mat{2}.varname='mat2'; lib.mat{2}.variables.nu0='nu0(T[1/K])[m^2/s]'; lib.mat{2}.variables.eta='eta(T[1/K])[Pa*s]'; lib.mat{2}.variables.gamma='1.4'; lib.mat{2}.variables.sigma='0[S/m]'; lib.mat{2}.variables.C='Cp(T[1/K])[J/(kg*K)]'; lib.mat{2}.variables.rho='rho(p[1/Pa],T[1/K])[kg/m^3]'; lib.mat{2}.variables.k='k(T[1/K])[W/(m*K)]'; lib.mat{2}.variables.cs='cs(T[1/K])[m/s]'; clear fcns fcns{1}.type='inline'; fcns{1}.name='cs(T)'; fcns{1}.expr='sqrt(1.4*287*T)'; fcns{1}.dexpr={'diff(sqrt(1.4*287*T),T)'}; fcns{2}.type='inline'; fcns{2}.name='rho(p,T)'; fcns{2}.expr='p*0.02897/8.314/T'; fcns{2}.dexpr={'diff(p*0.02897/8.314/T,p)','diff(p*0.02897/8.314/T,T)'}; fcns{3}.type='piecewise'; fcns{3}.name='Cp(T)'; fcns{3}.extmethod='const'; fcns{3}.subtype='poly'; fcns{3}.expr={{'0','1.04763657E+03','1','-3.72589265E-01','2', ... '9.45304214E-04','3','-6.02409443E-07','4','1.28589610E-10'}}; fcns{3}.intervals={'200','1600'}; fcns{4}.type='piecewise'; fcns{4}.name='eta(T)'; fcns{4}.extmethod='const'; fcns{4}.subtype='poly'; fcns{4}.expr={{'0','-8.38278000E-07','1','8.35717342E-08','2', ... '-7.69429583E-11','3','4.64372660E-14','4','-1.06585607E-17'}}; fcns{4}.intervals={'200','1600'}; fcns{5}.type='piecewise'; fcns{5}.name='nu0(T)'; fcns{5}.extmethod='const'; fcns{5}.subtype='poly'; fcns{5}.expr={{'0','-5.86912450E-06','1','5.01274491E-08','2', ... '7.50108343E-11','3','1.80336823E-15','4','-2.91688030E-18'}}; fcns{5}.intervals={'200','1600'}; fcns{6}.type='piecewise'; fcns{6}.name='k(T)'; fcns{6}.extmethod='const'; fcns{6}.subtype='poly'; fcns{6}.expr={{'0','-2.27583562E-03','1','1.15480022E-04','2', ... '-7.90252856E-08','3','4.11702505E-11','4','-7.43864331E-15'}}; fcns{6}.intervals={'200','1600'}; lib.mat{2}.functions = fcns; lib.mat{3}.name='Soft Iron (without losses)'; lib.mat{3}.varname='mat3'; lib.mat{3}.variables.normfB='BH(normH[m/A])[T]'; lib.mat{3}.variables.mur='MUR(normB[1/T])'; lib.mat{3}.variables.sigma='0[S/m]'; lib.mat{3}.variables.normfH='HB(normB[1/T])[A/m]'; lib.mat{3}.variables.epsilonr='1'; clear fcns fcns{1}.type='interp'; fcns{1}.name='MUR'; fcns{1}.method='linear'; fcns{1}.extmethod='const'; fcns{1}.x={'1','1.1','1.2','1.3','1.4','1.5','1.6','1.7','1.8','1.9', ... '2.0','2.1','2.2','2.3','2.4'}; fcns{1}.data={'1200','820','560','420','290','220','160','110','70','47', ... '26','15','10','7','6'}; fcns{2}.type='interp'; fcns{2}.name='HB'; fcns{2}.method='linear'; fcns{2}.extmethod='extrap'; fcns{2}.x={'0','1','1.1','1.2','1.3','1.4','1.5','1.6','1.7','1.8', ... '1.9','2.0','2.1','2.2','2.3','2.4'}; fcns{2}.data={'0','663.146','1067.5','1705.23','2463.11','3841.67', ... '5425.74','7957.75','12298.3','20462.8','32169.6','61213.4','111408', ... '175070','261469','318310'}; fcns{3}.type='interp'; fcns{3}.name='BH'; fcns{3}.method='linear'; fcns{3}.extmethod='extrap'; fcns{3}.x={'0','663.146','1067.5','1705.23','2463.11','3841.67', ... '5425.74','7957.75','12298.3','20462.8','32169.6','61213.4','111408', ... '175070','261469','318310'}; fcns{3}.data={'0','1','1.1','1.2','1.3','1.4','1.5','1.6','1.7','1.8', ... '1.9','2.0','2.1','2.2','2.3','2.4'}; lib.mat{3}.functions = fcns; lib.matgroups{1}.name='Resistivity'; lib.matgroups{1}.variables={'alphares','T0','res0'}; lib.matgroups{1}.descr={'Temperature coefficient','Reference temperature','Resistivity at reference temperature'}; lib.matgroups{2}.name='Electromagnetic (AC/DC)'; lib.matgroups{2}.variables={'alphares','T0','res0','Br','normfH','fH','normfB','fB'}; lib.matgroups{2}.descr={'Temperature coefficient','Reference temperature','Resistivity at reference temperature','Remanent flux density','Nonlinear magnetic field, norm','Nonlinear magnetic field','Nonlinear magnetic flux density, norm','Nonlinear magnetic flux density'}; fem.lib = lib; % ODE Settings clear ode clear units; units.basesystem = 'SI'; ode.units = units; fem.ode=ode; % Multiphysics fem=multiphysics(fem); % Extend mesh fem.xmesh=meshextend(fem); % Solve problem fem.sol=femtime(fem, ... 'solcomp',{'Az'}, ... 'outcomp',{'Az','Azt'}, ... 'blocksize','auto', ... 'tlist',[0:0.1:1], ... 'tout','tlist'); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'tridata',{'normH_emqa','cont','internal','unit','A/m'}, ... 'trimap','jet(1024)', ... 'arrowdata',{'Mx_emqa','My_emqa'}, ... 'arrowxspacing',60, ... 'arrowyspacing',60, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[1.0,0.0,0.0], ... 'solnum','end', ... 'title','Time=1 Surface: Magnetic field, norm [A/m] Arrow: Magnetization', ... 'axis',[-1.9430085386882836,1.9430085386882836,-1.0785515173176126,1.0785515173176126]); % Plot in cross-section or along domain postcrossplot(fem,0,[0;0], ... 'pointdata',{'normH_emqa','unit','A/m'}, ... 'title','Magnetic field, norm [A/m]', ... 'axislabel',{'Time','Magnetic field',' norm [A/m]'}); % COMSOL Multiphysics Model M-file % Generated by COMSOL 3.5 (COMSOL 3.5.0.494, $Date: 2008/09/19 16:09:48 $) % Constants fem.const = {'R','10000'}; % (Default values are not included) % Application mode 1 clear appl appl.mode.class = 'PerpendicularCurrents'; appl.module = 'ACDC'; appl.sshape = 2; appl.assignsuffix = '_emqa'; clear prop prop.analysis='transient'; appl.prop = prop; clear bnd bnd.type = {'A0','cont'}; bnd.ind = [1,1,1,2,2,2,1,1,1,1,1,1,1,1,2,2,2,2,1,1,1,1,1,1,1,1,2,1]; appl.bnd = bnd; clear equ equ.magconstrel = {'aniso_fH','mur','mur','mur'}; equ.Jez = {0,0,'(1-flc2hs(t-0.5,0.25))*R','(-(1-flc2hs(t-0.5,0.25)))*R'}; equ.sigma = {'mat2_sigma','mat3_sigma','mat2_sigma','mat2_sigma'}; equ.epsilonr = {1,'mat3_epsilonr',1,1}; equ.mur = {1,'mat3_MUR(normB_emqa[1/T])',1,1}; equ.normfH = {'1/mu0_emqa*normB_emqa','mat3_HB(normB_emqa[1/T])[A/m]','1/mu0_emqa*normB_emqa', ... '1/mu0_emqa*normB_emqa'}; equ.ind = [1,2,3,4,2,3,4]; appl.equ = equ; fem.appl{1} = appl; fem.frame = {'ref'}; fem.border = 1; clear units; units.basesystem = 'SI'; fem.units = units; % Library materials clear lib lib.mat{1}.name='Iron'; lib.mat{1}.varname='mat1'; lib.mat{1}.variables.nu='0.29'; lib.mat{1}.variables.E='200e9[Pa]'; lib.mat{1}.variables.mur='4000'; lib.mat{1}.variables.sigma='1.12e7[S/m]'; lib.mat{1}.variables.epsilonr='1'; lib.mat{1}.variables.alpha='12.2e-6[1/K]'; lib.mat{1}.variables.C='440[J/(kg*K)]'; lib.mat{1}.variables.rho='7870[kg/m^3]'; lib.mat{1}.variables.k='76.2[W/(m*K)]'; lib.mat{2}.name='Air'; lib.mat{2}.varname='mat2'; lib.mat{2}.variables.nu0='nu0(T[1/K])[m^2/s]'; lib.mat{2}.variables.eta='eta(T[1/K])[Pa*s]'; lib.mat{2}.variables.gamma='1.4'; lib.mat{2}.variables.sigma='0[S/m]'; lib.mat{2}.variables.C='Cp(T[1/K])[J/(kg*K)]'; lib.mat{2}.variables.rho='rho(p[1/Pa],T[1/K])[kg/m^3]'; lib.mat{2}.variables.k='k(T[1/K])[W/(m*K)]'; lib.mat{2}.variables.cs='cs(T[1/K])[m/s]'; clear fcns fcns{1}.type='inline'; fcns{1}.name='cs(T)'; fcns{1}.expr='sqrt(1.4*287*T)'; fcns{1}.dexpr={'diff(sqrt(1.4*287*T),T)'}; fcns{2}.type='inline'; fcns{2}.name='rho(p,T)'; fcns{2}.expr='p*0.02897/8.314/T'; fcns{2}.dexpr={'diff(p*0.02897/8.314/T,p)','diff(p*0.02897/8.314/T,T)'}; fcns{3}.type='piecewise'; fcns{3}.name='Cp(T)'; fcns{3}.extmethod='const'; fcns{3}.subtype='poly'; fcns{3}.expr={{'0','1.04763657E+03','1','-3.72589265E-01','2', ... '9.45304214E-04','3','-6.02409443E-07','4','1.28589610E-10'}}; fcns{3}.intervals={'200','1600'}; fcns{4}.type='piecewise'; fcns{4}.name='eta(T)'; fcns{4}.extmethod='const'; fcns{4}.subtype='poly'; fcns{4}.expr={{'0','-8.38278000E-07','1','8.35717342E-08','2', ... '-7.69429583E-11','3','4.64372660E-14','4','-1.06585607E-17'}}; fcns{4}.intervals={'200','1600'}; fcns{5}.type='piecewise'; fcns{5}.name='nu0(T)'; fcns{5}.extmethod='const'; fcns{5}.subtype='poly'; fcns{5}.expr={{'0','-5.86912450E-06','1','5.01274491E-08','2', ... '7.50108343E-11','3','1.80336823E-15','4','-2.91688030E-18'}}; fcns{5}.intervals={'200','1600'}; fcns{6}.type='piecewise'; fcns{6}.name='k(T)'; fcns{6}.extmethod='const'; fcns{6}.subtype='poly'; fcns{6}.expr={{'0','-2.27583562E-03','1','1.15480022E-04','2', ... '-7.90252856E-08','3','4.11702505E-11','4','-7.43864331E-15'}}; fcns{6}.intervals={'200','1600'}; lib.mat{2}.functions = fcns; lib.mat{3}.name='Soft Iron (without losses)'; lib.mat{3}.varname='mat3'; lib.mat{3}.variables.normfB='BH(normH[m/A])[T]'; lib.mat{3}.variables.mur='MUR(normB[1/T])'; lib.mat{3}.variables.sigma='0[S/m]'; lib.mat{3}.variables.normfH='HB(normB[1/T])[A/m]'; lib.mat{3}.variables.epsilonr='1'; clear fcns fcns{1}.type='interp'; fcns{1}.name='MUR'; fcns{1}.method='linear'; fcns{1}.extmethod='const'; fcns{1}.x={'1','1.1','1.2','1.3','1.4','1.5','1.6','1.7','1.8','1.9', ... '2.0','2.1','2.2','2.3','2.4'}; fcns{1}.data={'1200','820','560','420','290','220','160','110','70','47', ... '26','15','10','7','6'}; fcns{2}.type='interp'; fcns{2}.name='HB'; fcns{2}.method='linear'; fcns{2}.extmethod='extrap'; fcns{2}.x={'0','1','1.1','1.2','1.3','1.4','1.5','1.6','1.7','1.8', ... '1.9','2.0','2.1','2.2','2.3','2.4'}; fcns{2}.data={'0','663.146','1067.5','1705.23','2463.11','3841.67', ... '5425.74','7957.75','12298.3','20462.8','32169.6','61213.4','111408', ... '175070','261469','318310'}; fcns{3}.type='interp'; fcns{3}.name='BH'; fcns{3}.method='linear'; fcns{3}.extmethod='extrap'; fcns{3}.x={'0','663.146','1067.5','1705.23','2463.11','3841.67', ... '5425.74','7957.75','12298.3','20462.8','32169.6','61213.4','111408', ... '175070','261469','318310'}; fcns{3}.data={'0','1','1.1','1.2','1.3','1.4','1.5','1.6','1.7','1.8', ... '1.9','2.0','2.1','2.2','2.3','2.4'}; lib.mat{3}.functions = fcns; lib.matgroups{1}.name='Resistivity'; lib.matgroups{1}.variables={'alphares','T0','res0'}; lib.matgroups{1}.descr={'Temperature coefficient','Reference temperature','Resistivity at reference temperature'}; fem.lib = lib; % ODE Settings clear ode clear units; units.basesystem = 'SI'; ode.units = units; fem.ode=ode; % Multiphysics fem=multiphysics(fem); % COMSOL Multiphysics Model M-file % Generated by COMSOL 3.5 (COMSOL 3.5.0.494, $Date: 2008/09/19 16:09:48 $) % Initialize mesh fem.mesh=meshinit(fem, ... 'hauto',5); % (Default values are not included) % Application mode 1 clear appl appl.mode.class = 'PerpendicularCurrents'; appl.module = 'ACDC'; appl.sshape = 2; appl.assignsuffix = '_emqa'; clear prop prop.analysis='transient'; appl.prop = prop; clear bnd bnd.type = {'A0','cont'}; bnd.ind = [1,1,1,2,2,2,1,1,1,1,1,1,1,1,2,2,2,2,1,1,1,1,1,1,1,1,2,1]; appl.bnd = bnd; clear equ equ.Jez = {0,0,'(1-flc2hs(t-0.5,0.25))*R','(flc2hs(t-0.5,0.25)-1)*R'}; equ.sigma = {'mat2_sigma','mat3_sigma','mat4_sigma','mat4_sigma'}; equ.epsilonr = {1,'mat3_epsilonr','mat4_epsilonr','mat4_epsilonr'}; equ.mur = {1,'mat3_MUR(normB_emqa[1/T])','mat4_mur','mat4_mur'}; equ.normfH = {'1/mu0_emqa*normB_emqa','mat3_HB(normB_emqa[1/T])[A/m]','1/mu0_emqa*normB_emqa', ... '1/mu0_emqa*normB_emqa'}; equ.ind = [1,2,3,4,2,3,4]; appl.equ = equ; fem.appl{1} = appl; fem.frame = {'ref'}; fem.border = 1; clear units; units.basesystem = 'SI'; fem.units = units; % Library materials clear lib lib.mat{1}.name='Iron'; lib.mat{1}.varname='mat1'; lib.mat{1}.variables.nu='0.29'; lib.mat{1}.variables.E='200e9[Pa]'; lib.mat{1}.variables.mur='4000'; lib.mat{1}.variables.sigma='1.12e7[S/m]'; lib.mat{1}.variables.epsilonr='1'; lib.mat{1}.variables.alpha='12.2e-6[1/K]'; lib.mat{1}.variables.C='440[J/(kg*K)]'; lib.mat{1}.variables.rho='7870[kg/m^3]'; lib.mat{1}.variables.k='76.2[W/(m*K)]'; lib.mat{2}.name='Air'; lib.mat{2}.varname='mat2'; lib.mat{2}.variables.nu0='nu0(T[1/K])[m^2/s]'; lib.mat{2}.variables.eta='eta(T[1/K])[Pa*s]'; lib.mat{2}.variables.gamma='1.4'; lib.mat{2}.variables.sigma='0[S/m]'; lib.mat{2}.variables.C='Cp(T[1/K])[J/(kg*K)]'; lib.mat{2}.variables.rho='rho(p[1/Pa],T[1/K])[kg/m^3]'; lib.mat{2}.variables.k='k(T[1/K])[W/(m*K)]'; lib.mat{2}.variables.cs='cs(T[1/K])[m/s]'; clear fcns fcns{1}.type='inline'; fcns{1}.name='cs(T)'; fcns{1}.expr='sqrt(1.4*287*T)'; fcns{1}.dexpr={'diff(sqrt(1.4*287*T),T)'}; fcns{2}.type='inline'; fcns{2}.name='rho(p,T)'; fcns{2}.expr='p*0.02897/8.314/T'; fcns{2}.dexpr={'diff(p*0.02897/8.314/T,p)','diff(p*0.02897/8.314/T,T)'}; fcns{3}.type='piecewise'; fcns{3}.name='Cp(T)'; fcns{3}.extmethod='const'; fcns{3}.subtype='poly'; fcns{3}.expr={{'0','1.04763657E+03','1','-3.72589265E-01','2', ... '9.45304214E-04','3','-6.02409443E-07','4','1.28589610E-10'}}; fcns{3}.intervals={'200','1600'}; fcns{4}.type='piecewise'; fcns{4}.name='eta(T)'; fcns{4}.extmethod='const'; fcns{4}.subtype='poly'; fcns{4}.expr={{'0','-8.38278000E-07','1','8.35717342E-08','2', ... '-7.69429583E-11','3','4.64372660E-14','4','-1.06585607E-17'}}; fcns{4}.intervals={'200','1600'}; fcns{5}.type='piecewise'; fcns{5}.name='nu0(T)'; fcns{5}.extmethod='const'; fcns{5}.subtype='poly'; fcns{5}.expr={{'0','-5.86912450E-06','1','5.01274491E-08','2', ... '7.50108343E-11','3','1.80336823E-15','4','-2.91688030E-18'}}; fcns{5}.intervals={'200','1600'}; fcns{6}.type='piecewise'; fcns{6}.name='k(T)'; fcns{6}.extmethod='const'; fcns{6}.subtype='poly'; fcns{6}.expr={{'0','-2.27583562E-03','1','1.15480022E-04','2', ... '-7.90252856E-08','3','4.11702505E-11','4','-7.43864331E-15'}}; fcns{6}.intervals={'200','1600'}; lib.mat{2}.functions = fcns; lib.mat{3}.name='Soft Iron (without losses)'; lib.mat{3}.varname='mat3'; lib.mat{3}.variables.normfB='BH(normH[m/A])[T]'; lib.mat{3}.variables.mur='MUR(normB[1/T])'; lib.mat{3}.variables.sigma='0[S/m]'; lib.mat{3}.variables.normfH='HB(normB[1/T])[A/m]'; lib.mat{3}.variables.epsilonr='1'; clear fcns fcns{1}.type='interp'; fcns{1}.name='MUR'; fcns{1}.method='linear'; fcns{1}.extmethod='const'; fcns{1}.x={'1','1.1','1.2','1.3','1.4','1.5','1.6','1.7','1.8','1.9', ... '2.0','2.1','2.2','2.3','2.4'}; fcns{1}.data={'1200','820','560','420','290','220','160','110','70','47', ... '26','15','10','7','6'}; fcns{2}.type='interp'; fcns{2}.name='HB'; fcns{2}.method='linear'; fcns{2}.extmethod='extrap'; fcns{2}.x={'0','1','1.1','1.2','1.3','1.4','1.5','1.6','1.7','1.8', ... '1.9','2.0','2.1','2.2','2.3','2.4'}; fcns{2}.data={'0','663.146','1067.5','1705.23','2463.11','3841.67', ... '5425.74','7957.75','12298.3','20462.8','32169.6','61213.4','111408', ... '175070','261469','318310'}; fcns{3}.type='interp'; fcns{3}.name='BH'; fcns{3}.method='linear'; fcns{3}.extmethod='extrap'; fcns{3}.x={'0','663.146','1067.5','1705.23','2463.11','3841.67', ... '5425.74','7957.75','12298.3','20462.8','32169.6','61213.4','111408', ... '175070','261469','318310'}; fcns{3}.data={'0','1','1.1','1.2','1.3','1.4','1.5','1.6','1.7','1.8', ... '1.9','2.0','2.1','2.2','2.3','2.4'}; lib.mat{3}.functions = fcns; lib.mat{4}.name='Copper'; lib.mat{4}.varname='mat4'; lib.mat{4}.variables.alphares='3.9e-3[1/K]'; lib.mat{4}.variables.mur='1'; lib.mat{4}.variables.sigma='5.998e7[S/m]'; lib.mat{4}.variables.epsilonr='1'; lib.mat{4}.variables.C='385[J/(kg*K)]'; lib.mat{4}.variables.epsilon='0.5'; lib.mat{4}.variables.res0='1.72e-8[ohm*m]'; lib.mat{4}.variables.rho='8700[kg/m^3]'; lib.mat{4}.variables.k='400[W/(m*K)]'; lib.mat{4}.variables.T0='273.15[K]'; lib.matgroups{1}.name='Resistivity'; lib.matgroups{1}.variables={'alphares','T0','res0'}; lib.matgroups{1}.descr={'Temperature coefficient','Reference temperature','Resistivity at reference temperature'}; lib.matgroups{2}.name='Electromagnetic (AC/DC)'; lib.matgroups{2}.variables={'alphares','T0','res0','Br','normfH','fH','normfB','fB'}; lib.matgroups{2}.descr={'Temperature coefficient','Reference temperature','Resistivity at reference temperature','Remanent flux density','Nonlinear magnetic field, norm','Nonlinear magnetic field','Nonlinear magnetic flux density, norm','Nonlinear magnetic flux density'}; fem.lib = lib; % ODE Settings clear ode clear units; units.basesystem = 'SI'; ode.units = units; fem.ode=ode; % Multiphysics fem=multiphysics(fem); % Extend mesh fem.xmesh=meshextend(fem); % Solve problem fem.sol=femtime(fem, ... 'solcomp',{'Az'}, ... 'outcomp',{'Az','Azt'}, ... 'blocksize','auto', ... 'tlist',[0:0.1:1], ... 'tout','tlist'); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'tridata',{'normH_emqa','cont','internal','unit','A/m'}, ... 'trimap','jet(1024)', ... 'arrowdata',{'Mx_emqa','My_emqa'}, ... 'arrowxspacing',60, ... 'arrowyspacing',60, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[1.0,0.0,0.0], ... 'solnum','end', ... 'title','Time=1 Surface: Magnetic field, norm [A/m] Arrow: Magnetization', ... 'axis',[-2.008564053411092,2.008564053411092,-1.1316441964124861,1.1316441964124861]); % Plot solution postplot(fem, ... 'tridata',{'normH_emqa','cont','internal','unit','A/m'}, ... 'trimap','jet(1024)', ... 'arrowdata',{'Mx_emqa','My_emqa'}, ... 'arrowxspacing',10, ... 'arrowyspacing',60, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[1.0,0.0,0.0], ... 'solnum','end', ... 'title','Time=1 Surface: Magnetic field, norm [A/m] Arrow: Magnetization', ... 'axis',[-2.008564053411092,2.008564053411092,-1.1821159491420163,1.1821159491420163]); % Plot solution postplot(fem, ... 'tridata',{'normH_emqa','cont','internal','unit','A/m'}, ... 'trimap','jet(1024)', ... 'arrowdata',{'Mx_emqa','My_emqa'}, ... 'arrowxspacing',10, ... 'arrowyspacing',60, ... 'arrowtype','arrow', ... 'arrowstyle','normalized', ... 'arrowcolor',[1.0,0.0,0.0], ... 'solnum','end', ... 'title','Time=1 Surface: Magnetic field, norm [A/m] Arrow: Magnetization', ... 'axis',[-2.008564053411092,2.008564053411092,-1.1821159491420163,1.1821159491420163]); % Plot solution postplot(fem, ... 'tridata',{'normH_emqa','cont','internal','unit','A/m'}, ... 'trimap','jet(1024)', ... 'arrowdata',{'Mx_emqa','My_emqa'}, ... 'arrowxspacing',10, ... 'arrowyspacing',600, ... 'arrowtype','arrow', ... 'arrowstyle','normalized', ... 'arrowcolor',[1.0,0.0,0.0], ... 'solnum','end', ... 'title','Time=1 Surface: Magnetic field, norm [A/m] Arrow: Magnetization', ... 'axis',[-2.008564053411092,2.008564053411092,-1.1821159491420163,1.1821159491420163]); % Plot solution postplot(fem, ... 'tridata',{'normH_emqa','cont','internal','unit','A/m'}, ... 'trimap','jet(1024)', ... 'arrowdata',{'Mx_emqa','My_emqa'}, ... 'arrowxspacing',100, ... 'arrowyspacing',600, ... 'arrowtype','arrow', ... 'arrowstyle','normalized', ... 'arrowcolor',[1.0,0.0,0.0], ... 'solnum','end', ... 'title','Time=1 Surface: Magnetic field, norm [A/m] Arrow: Magnetization', ... 'axis',[-2.008564053411092,2.008564053411092,-1.1821159491420163,1.1821159491420163]); % Plot solution postplot(fem, ... 'tridata',{'normH_emqa','cont','internal','unit','A/m'}, ... 'trimap','jet(1024)', ... 'arrowdata',{'Mx_emqa','My_emqa'}, ... 'arrowxspacing',100, ... 'arrowyspacing',100, ... 'arrowtype','arrow', ... 'arrowstyle','normalized', ... 'arrowcolor',[1.0,0.0,0.0], ... 'solnum','end', ... 'title','Time=1 Surface: Magnetic field, norm [A/m] Arrow: Magnetization', ... 'axis',[-2.008564053411092,2.008564053411092,-1.1821159491420163,1.1821159491420163]); % Plot solution postplot(fem, ... 'tridata',{'normH_emqa','cont','internal','unit','A/m'}, ... 'trimap','jet(1024)', ... 'arrowdata',{'Mx_emqa','My_emqa'}, ... 'arrowxspacing',100, ... 'arrowyspacing',100, ... 'arrowtype','arrow', ... 'arrowstyle','normalized', ... 'arrowcolor',[1.0,0.0,0.0], ... 'flowdata',{'Hx_emqa','Hy_emqa'}, ... 'flowcolor',[1.0,0.0,0.0], ... 'flowlines',20, ... 'solnum','end', ... 'title','Time=1 Surface: Magnetic field, norm [A/m] Arrow: Magnetization Streamline: Magnetic field', ... 'axis',[-2.008564053411092,2.008564053411092,-1.1821159491420163,1.1821159491420163]); % Plot solution postplot(fem, ... 'tridata',{'normH_emqa','cont','internal','unit','A/m'}, ... 'trimap','jet(1024)', ... 'arrowdata',{'Mx_emqa','My_emqa'}, ... 'arrowxspacing',100, ... 'arrowyspacing',100, ... 'arrowtype','arrow', ... 'arrowstyle','normalized', ... 'arrowcolor',[1.0,0.0,0.0], ... 'solnum','end', ... 'title','Time=1 Surface: Magnetic field, norm [A/m] Arrow: Magnetization', ... 'axis',[-2.0085640534110922,2.0085640534110922,-1.1821159491420175,1.1821159491420166]); % Plot solution postplot(fem, ... 'tridata',{'normH_emqa','cont','internal','unit','A/m'}, ... 'trimap','jet(1024)', ... 'arrowdata',{'Mx_emqa','My_emqa'}, ... 'arrowxspacing',100, ... 'arrowyspacing',100, ... 'arrowtype','arrow', ... 'arrowstyle','normalized', ... 'arrowcolor',[1.0,0.0,0.0], ... 'solnum',4, ... 'title','Time=0.3 Surface: Magnetic field, norm [A/m] Arrow: Magnetization', ... 'axis',[-1.0042820267055468,1.0042820267055468,-0.5910579745710092,0.5910579745710082]); % Plot solution postplot(fem, ... 'tridata',{'normH_emqa','cont','internal','unit','A/m'}, ... 'trimap','jet(1024)', ... 'arrowdata',{'Mx_emqa','My_emqa'}, ... 'arrowxspacing',100, ... 'arrowyspacing',100, ... 'arrowtype','arrow', ... 'arrowstyle','normalized', ... 'arrowcolor',[1.0,0.0,0.0], ... 'solnum',4, ... 'title','Time=0.3 Surface: Magnetic field, norm [A/m] Arrow: Magnetization', ... 'axis',[-1.0042820267055468,1.0042820267055468,-0.5910579745710092,0.5910579745710082]); % Plot in cross-section or along domain postcrossplot(fem,0,[0;0], ... 'pointdata',{'normH_emqa','unit','A/m'}, ... 'title','Magnetic field, norm [A/m]', ... 'axislabel',{'Time','Magnetic field',' norm [A/m]'}); % Plot solution postplot(fem, ... 'tridata',{'normH_emqa','cont','internal','unit','A/m'}, ... 'trimap','jet(1024)', ... 'arrowdata',{'Mx_emqa','My_emqa'}, ... 'arrowxspacing',100, ... 'arrowyspacing',100, ... 'arrowtype','arrow', ... 'arrowstyle','normalized', ... 'arrowcolor',[1.0,0.0,0.0], ... 'solnum',2, ... 'title','Time=0.1 Surface: Magnetic field, norm [A/m] Arrow: Magnetization', ... 'axis',[-1.0042820267055468,1.0042820267055468,-0.5910579745710092,0.5910579745710082]); % Plot solution postplot(fem, ... 'tridata',{'normH_emqa','cont','internal','unit','A/m'}, ... 'trimap','jet(1024)', ... 'arrowdata',{'Mx_emqa','My_emqa'}, ... 'arrowxspacing',100, ... 'arrowyspacing',100, ... 'arrowtype','arrow', ... 'arrowstyle','normalized', ... 'arrowcolor',[1.0,0.0,0.0], ... 'solnum',2, ... 'title','Time=0.1 Surface: Magnetic field, norm [A/m] Arrow: Magnetization', ... 'axis',[-1.0042820267055468,1.0042820267055468,-0.5910579745710092,0.5910579745710082]); % Plot solution postplot(fem, ... 'tridata',{'normH_emqa','cont','internal','unit','A/m'}, ... 'trimap','jet(1024)', ... 'arrowdata',{'Mx_emqa','My_emqa'}, ... 'arrowxspacing',100, ... 'arrowyspacing',100, ... 'arrowtype','arrow', ... 'arrowstyle','normalized', ... 'arrowcolor',[1.0,0.0,0.0], ... 'flowdata',{'Hx_emqa','Hy_emqa'}, ... 'flowcolor',[1.0,0.0,0.0], ... 'flowlines',20, ... 'solnum',2, ... 'title','Time=0.1 Surface: Magnetic field, norm [A/m] Arrow: Magnetization Streamline: Magnetic field', ... 'axis',[-2.008564053411094,2.0085640534110936,-1.182115949142018,1.182115949142017]); % Plot solution postplot(fem, ... 'tridata',{'normH_emqa','cont','internal','unit','A/m'}, ... 'trimap','jet(1024)', ... 'arrowdata',{'Mx_emqa','My_emqa'}, ... 'arrowxspacing',100, ... 'arrowyspacing',100, ... 'arrowtype','arrow', ... 'arrowstyle','normalized', ... 'arrowcolor',[1.0,0.0,0.0], ... 'flowdata',{'Hx_emqa','Hy_emqa'}, ... 'flowcolor',[1.0,0.0,0.0], ... 'flowlines',20, ... 'solnum',3, ... 'title','Time=0.2 Surface: Magnetic field, norm [A/m] Arrow: Magnetization Streamline: Magnetic field', ... 'axis',[-2.00856405t�`3411094,2.0085640534110936,-1.182115949142018,1.182115949142017]); % Plot solution postplot(fem, ... 'tridata',{'normH_emqa','cont','internal','unit','A/m'}, ... 'trimap','jet(1024)', ... 'arrowdata',{'Mx_emqa','My_emqa'}, ... 'arrowxspacing',100, ... 'arrowyspacing',100, ... 'arrowtype','arrow', ... 'arrowstyle','normalized', ... 'arrowcolor',[1.0,0.0,0.0], ... 'flowdata',{'Hx_emqa','Hy_emqa'}, ... 'flowcolor',[1.0,0.0,0.0], ... 'flowlines',20, ... 'solnum',5, ... 'title','Time=0.4 Surface: Magnetic field, norm [A/m] Arrow: Magnetization Streamline: Magnetic field', ... 'axis',[-2.008564053411094,2.0085640534110936,-1.182115949142018,1.182115949142017]); % Plot solution postplot(fem, ... 'tridata',{'normH_emqa','cont','internal','unit','A/m'}, ... 'trimap','jet(1024)', ... 'arrowdata',{'Mx_emqa','My_emqa'}, ... 'arrowxspacing',100, ... 'arrowyspacing',100, ... 'arrowtype','arrow', ... 'arrowstyle','normalized', ... 'arrowcolor',[1.0,0.0,0.0], ... 'flowdata',{'Hx_emqa','Hy_emqa'}, ... 'flowcolor',[1.0,0.0,0.0], ... 'flowlines',20, ... 'solnum',6, ... 'title','Time=0.5 Surface: Magnetic field, norm [A/m] Arrow: Magnetization Streamline: Magnetic field', ... 'axis',[-2.008564053411094,2.0085640534110936,-1.182115949142018,1.182115949142017]); % Plot solution postplot(fem, ... 'tridata',{'normH_emqa','cont','internal','unit','A/m'}, ... 'trimap','jet(1024)', ... 'arrowdata',{'Mx_emqa','My_emqa'}, ... 'arrowxspacing',100, ... 'arrowyspacing',100, ... 'arrowtype','arrow', ... 'arrowstyle','normalized', ... 'arrowcolor',[1.0,0.0,0.0], ... 'flowdata',{'Hx_emqa','Hy_emqa'}, ... 'flowcolor',[1.0,0.0,0.0], ... 'flowlines',20, ... 'solnum',10, ... 'title','Time=0.9 Surface: Magnetic field, norm [A/m] Arrow: Magnetization Streamline: Magnetic field', ... 'axis',[-2.008564053411094,2.0085640534110936,-1.182115949142018,1.182115949142017]); % Plot solution postplot(fem, ... 'tridata',{'normH_emqa','cont','internal','unit','A/m'}, ... 'trimap','jet(1024)', ... 'arrowdata',{'Mx_emqa','My_emqa'}, ... 'arrowxspacing',100, ... 'arrowyspacing',100, ... 'arrowtype','arrow', ... 'arrowstyle','normalized', ... 'arrowcolor',[1.0,0.0,0.0], ... 'flowdata',{'Hx_emqa','Hy_emqa'}, ... 'flowcolor',[1.0,0.0,0.0], ... 'flowlines',200, ... 'solnum',10, ... 'title','Time=0.9 Surface: Magnetic field, norm [A/m] Arrow: Magnetization Streamline: Magnetic field', ... 'axis',[-2.008564053411094,2.0085640534110936,-1.182115949142018,1.182115949142017]); % Plot solution postplot(fem, ... 'tridata',{'normH_emqa','cont','internal','unit','A/m'}, ... 'trimap','jet(1024)', ... 'arrowdata',{'Mx_emqa','My_emqa'}, ... 'arrowxspacing',100, ... 'arrowyspacing',100, ... 'arrowtype','arrow', ... 'arrowstyle','normalized', ... 'arrowcolor',[1.0,0.0,0.0], ... 'flowdata',{'Hx_emqa','Hy_emqa'}, ... 'flowcolor',[1.0,0.0,0.0], ... 'flowlines',100, ... 'solnum',10, ... 'title','Time=0.9 Surface: Magnetic field, norm [A/m] Arrow: Magnetization Streamline: Magnetic field', ... 'axis',[-2.008564053411094,2.0085640534110936,-1.182115949142018,1.182115949142017]); % Plot solution postplot(fem, ... 'tridata',{'normH_emqa','cont','internal','unit','A/m'}, ... 'trimap','jet(1024)', ... 'arrowdata',{'Mx_emqa','My_emqa'}, ... 'arrowxspacing',100, ... 'arrowyspacing',100, ... 'arrowtype','arrow', ... 'arrowstyle','normalized', ... 'arrowcolor',[1.0,0.0,0.0], ... 'flowdata',{'Hx_emqa','Hy_emqa'}, ... 'flowcolor',[1.0,0.0,0.0], ... 'flowlines',100, ... 'solnum',4, ... 'title','Time=0.3 Surface: Magnetic field, norm [A/m] Arrow: Magnetization Streamline: Magnetic field', ... 'axis',[-2.008564053411094,2.0085640534110936,-1.182115949142018,1.182115949142017]); % Animate solution postmovie(fem, ... 'tridata',{'normH_emqa','cont','internal','unit','A/m'}, ... 'trimap','jet(1024)', ... 'arrowdata',{'Mx_emqa','My_emqa'}, ... 'arrowxspacing',100, ... 'arrowyspacing',100, ... 'arrowtype','arrow', ... 'arrowstyle','normalized', ... 'arrowcolor',[1.0,0.0,0.0], ... 'flowdata',{'Hx_emqa','Hy_emqa'}, ... 'flowcolor',[1.0,0.0,0.0], ... 'flowlines',100, ... 'axis',[-2.008564053411094,2.0085640534110936,-1.182115949142018,1.182115949142017], ... 'fps',10); % Plot solution postplot(fem, ... 'tridata',{'normH_emqa','cont','internal','unit','A/m'}, ... 'tridlim',[0 300], ... 'trimap','jet(1024)', ... 'arrowdata',{'Mx_emqa','My_emqa'}, ... 'arrowxspacing',100, ... 'arrowyspacing',100, ... 'arrowtype','arrow', ... 'arrowstyle','normalized', ... 'arrowcolor',[1.0,0.0,0.0], ... 'flowdata',{'Hx_emqa','Hy_emqa'}, ... 'flowcolor',[1.0,0.0,0.0], ... 'flowlines',100, ... 'solnum',4, ... 'title','Time=0.3 Surface: Magnetic field, norm [A/m] Arrow: Magnetization Streamline: Magnetic field', ... 'axis',[-2.008564053411094,2.0085640534110936,-1.182115949142018,1.182115949142017]); % Plot solution postplot(fem, ... 'tridata',{'normH_emqa','cont','internal','unit','A/m'}, ... 'tridlim',[0 300], ... 'trimap','jet(1024)', ... 'arrowdata',{'Mx_emqa','My_emqa'}, ... 'arrowxspacing',100, ... 'arrowyspacing',100, ... 'arrowtype','arrow', ... 'arrowstyle','normalized', ... 'arrowcolor',[1.0,0.0,0.0], ... 'flowdata',{'Hx_emqa','Hy_emqa'}, ... 'flowcolor',[1.0,0.0,0.0], ... 'flowlines',100, ... 'solnum',7, ... 'title','Time=0.6 Surface: Magnetic field, norm [A/m] Arrow: Magnetization Streamline: Magnetic field', ... 'axis',[-2.041031657507379,2.0410316575073786,-1.182115949142018,1.182115949142017]); % Plot solution postplot(fem, ... 'tridata',{'normH_emqa','cont','internal','unit','A/m'}, ... 'tridlim',[0 300], ... 'trimap','jet(1024)', ... 'arrowdata',{'Mx_emqa','My_emqa'}, ... 'arrowxspacing',100, ... 'arrowyspacing',100, ... 'arrowtype','arrow', ... 'arrowstyle','normalized', ... 'arrowcolor',[1.0,0.0,0.0], ... 'solnum',7, ... 'title','Time=0.6 Surface: Magnetic field, norm [A/m] Arrow: Magnetization', ... 'axis',[-2.041031657507379,2.0410316575073786,-1.182115949142018,1.182115949142017]); % Plot solution postplot(fem, ... 'tridata',{'normH_emqa','cont','internal','unit','A/m'}, ... 'tridlim',[0 300], ... 'trimap','jet(1024)', ... 'arrowdata',{'Mx_emqa','My_emqa'}, ... 'arrowxspacing',100, ... 'arrowyspacing',100, ... 'arrowtype','arrow', ... 'arrowstyle','normalized', ... 'arrowcolor',[1.0,0.0,0.0], ... 'solnum',2, ... 'title','Time=0.1 Surface: Magnetic field, norm [A/m] Arrow: Magnetization', ... 'axis',[-2.041031657507379,2.0410316575073786,-1.182115949142018,1.182115949142017]); % Plot solution postplot(fem, ... 'tridata',{'normH_emqa','cont','internal','unit','A/m'}, ... 'tridlim',[0 300], ... 'trimap','jet(1024)', ... 'arrowdata',{'Mx_emqa','My_emqa'}, ... 'arrowxspacing',100, ... 'arrowyspacing',100, ... 'arrowtype','arrow', ... 'arrowstyle','normalized', ... 'arrowcolor',[1.0,0.0,0.0], ... 'solnum',3, ... 'title','Time=0.2 Surface: Magnetic field, norm [A/m] Arrow: Magnetization', ... 'axis',[-2.041031657507379,2.0410316575073786,-1.182115949142018,1.182115949142017]); % Plot solution postplot(fem, ... 'tridata',{'normH_emqa','cont','internal','unit','A/m'}, ... 'tridlim',[0 300], ... 'trimap','jet(1024)', ... 'arrowdata',{'Mx_emqa','My_emqa'}, ... 'arrowxspacing',100, ... 'arrowyspacing',100, ... 'arrowtype','arrow', ... 'arrowstyle','normalized', ... 'arrowcolor',[1.0,0.0,0.0], ... 'solnum',4, ... 'title','Time=0.3 Surface: Magnetic field, norm [A/m] Arrow: Magnetization', ... 'axis',[-2.041031657507379,2.0410316575073786,-1.182115949142018,1.182115949142017]); % Plot solution postplot(fem, ... 'tridata',{'normH_emqa','cont','internal','unit','A/m'}, ... 'tridlim',[0 300], ... 'trimap','jet(1024)', ... 'arrowdata',{'Mx_emqa','My_emqa'}, ... 'arrowxspacing',100, ... 'arrowyspacing',100, ... 'arrowtype','arrow', ... 'arrowstyle','normalized', ... 'arrowcolor',[1.0,0.0,0.0], ... 'solnum',9, ... 'title','Time=0.8 Surface: Magnetic field, norm [A/m] Arrow: Magnetization', ... 'axis',[-2.041031657507379,2.0410316575073786,-1.182115949142018,1.182115949142017]); % Plot solution postplot(fem, ... 'tridata',{'normH_emqa','cont','internal','unit','A/m'}, ... 'tridlim',[0 300], ... 'trimap','jet(1024)', ... 'arrowdata',{'Mx_emqa','My_emqa'}, ... 'arrowxspacing',100, ... 'arrowyspacing',100, ... 'arrowtype','arrow', ... 'arrowstyle','normalized', ... 'arrowcolor',[1.0,0.0,0.0], ... 'solnum',10, ... 'title','Time=0.9 Surface: Magnetic field, norm [A/m] Arrow: Magnetization', ... 'axis',[-2.041031657507379,2.0410316575073786,-1.182115949142018,1.182115949142017]); % Plot in cross-section or along domain postcrossplot(fem,0,[-0.5;-0.5], ... 'pointdata',{'Jez_emqa','unit','A/m^2'}, ... 'title','External current density [A/m^2]', ... 'axislabel',{'Time','External current density [A/m^2]'}); % Constants fem.const = {'R','1'}; % Constants fem.const = {'R','1'}; % (Default values are not included) % Application mode 1 clear appl appl.mode.class = 'PerpendicularCurrents'; appl.module = 'ACDC'; appl.sshape = 2; appl.assignsuffix = '_emqa'; clear prop prop.analysis='transient'; appl.prop = prop; clear bnd bnd.type = {'A0','cont'}; bnd.ind = [1,1,1,2,2,2,1,1,1,1,1,1,1,1,2,2,2,2,1,1,1,1,1,1,1,1,2,1]; appl.bnd = bnd; clear equ equ.Jez = {0,0,'(1-flc2hs(t-0.5,0.25))*R','(flc2hs(t-0.5,0.25)-1)*R'}; equ.sigma = {'mat2_sigma','mat3_sigma','mat4_sigma','mat4_sigma'}; equ.epsilonr = {1,'mat3_epsilonr','mat4_epsilonr','mat4_epsilonr'}; equ.mur = {1,'mat3_MUR(normB_emqa[1/T])','mat4_mur','mat4_mur'}; equ.normfH = {'1/mu0_emqa*normB_emqa','mat3_HB(normB_emqa[1/T])[A/m]','1/mu0_emqa*normB_emqa', ... '1/mu0_emqa*normB_emqa'}; equ.ind = [1,2,3,4,2,3,4]; appl.equ = equ; fem.appl{1} = appl; fem.frame = {'ref'}; fem.border = 1; clear units; units.basesystem = 'SI'; fem.units = units; % Library materials clear lib lib.mat{1}.name='Iron'; lib.mat{1}.varname='mat1'; lib.mat{1}.variables.nu='0.29'; lib.mat{1}.variables.E='200e9[Pa]'; lib.mat{1}.variables.mur='4000'; lib.mat{1}.variables.sigma='1.12e7[S/m]'; lib.mat{1}.variables.epsilonr='1'; lib.mat{1}.variables.alpha='12.2e-6[1/K]'; lib.mat{1}.variables.C='440[J/(kg*K)]'; lib.mat{1}.variables.rho='7870[kg/m^3]'; lib.mat{1}.variables.k='76.2[W/(m*K)]'; lib.mat{2}.name='Air'; lib.mat{2}.varname='mat2'; lib.mat{2}.variables.nu0='nu0(T[1/K])[m^2/s]'; lib.mat{2}.variables.eta='eta(T[1/K])[Pa*s]'; lib.mat{2}.variables.gamma='1.4'; lib.mat{2}.variables.sigma='0[S/m]'; lib.mat{2}.variables.C='Cp(T[1/K])[J/(kg*K)]'; lib.mat{2}.variables.rho='rho(p[1/Pa],T[1/K])[kg/m^3]'; lib.mat{2}.variables.k='k(T[1/K])[W/(m*K)]'; lib.mat{2}.variables.cs='cs(T[1/K])[m/s]'; clear fcns fcns{1}.type='inline'; fcns{1}.name='cs(T)'; fcns{1}.expr='sqrt(1.4*287*T)'; fcns{1}.dexpr={'diff(sqrt(1.4*287*T),T)'}; fcns{2}.type='inline'; fcns{2}.name='rho(p,T)'; fcns{2}.expr='p*0.02897/8.314/T'; fcns{2}.dexpr={'diff(p*0.02897/8.314/T,p)','diff(p*0.02897/8.314/T,T)'}; fcns{3}.type='piecewise'; fcns{3}.name='Cp(T)'; fcns{3}.extmethod='const'; fcns{3}.subtype='poly'; fcns{3}.expr={{'0','1.04763657E+03','1','-3.72589265E-01','2', ... '9.45304214E-04','3','-6.02409443E-07','4','1.28589610E-10'}}; fcns{3}.intervals={'200','1600'}; fcns{4}.type='piecewise'; fcns{4}.name='eta(T)'; fcns{4}.extmethod='const'; fcns{4}.subtype='poly'; fcns{4}.expr={{'0','-8.38278000E-07','1','8.35717342E-08','2', ... '-7.69429583E-11','3','4.64372660E-14','4','-1.06585607E-17'}}; fcns{4}.intervals={'200','1600'}; fcns{5}.type='piecewise'; fcns{5}.name='nu0(T)'; fcns{5}.extmethod='const'; fcns{5}.subtype='poly'; fcns{5}.expr={{'0','-5.86912450E-06','1','5.01274491E-08','2', ... '7.50108343E-11','3','1.80336823E-15','4','-2.91688030E-18'}}; fcns{5}.intervals={'200','1600'}; fcns{6}.type='piecewise'; fcns{6}.name='k(T)'; fcns{6}.extmethod='const'; fcns{6}.subtype='poly'; fcns{6}.expr={{'0','-2.27583562E-03','1','1.15480022E-04','2', ... '-7.90252856E-08','3','4.11702505E-11','4','-7.43864331E-15'}}; fcns{6}.intervals={'200','1600'}; lib.mat{2}.functions = fcns; lib.mat{3}.name='Soft Iron (without losses)'; lib.mat{3}.varname='mat3'; lib.mat{3}.variables.normfB='BH(normH[m/A])[T]'; lib.mat{3}.variables.mur='MUR(normB[1/T])'; lib.mat{3}.variables.sigma='0[S/m]'; lib.mat{3}.variables.normfH='HB(normB[1/T])[A/m]'; lib.mat{3}.variables.epsilonr='1'; clear fcns fcns{1}.type='interp'; fcns{1}.name='MUR'; fcns{1}.method='linear'; fcns{1}.extmethod='const'; fcns{1}.x={'1','1.1','1.2','1.3','1.4','1.5','1.6','1.7','1.8','1.9', ... '2.0','2.1','2.2','2.3','2.4'}; fcns{1}.data={'1200','820','560','420','290','220','160','110','70','47', ... '26','15','10','7','6'}; fcns{2}.type='interp'; fcns{2}.name='HB'; fcns{2}.method='linear'; fcns{2}.extmethod='extrap'; fcns{2}.x={'0','1','1.1','1.2','1.3','1.4','1.5','1.6','1.7','1.8', ... '1.9','2.0','2.1','2.2','2.3','2.4'}; fcns{2}.data={'0','663.146','1067.5','1705.23','2463.11','3841.67', ... '5425.74','7957.75','12298.3','20462.8','32169.6','61213.4','111408', ... '175070','261469','318310'}; fcns{3}.type='interp'; fcns{3}.name='BH'; fcns{3}.method='linear'; fcns{3}.extmethod='extrap'; fcns{3}.x={'0','663.146','1067.5','1705.23','2463.11','3841.67', ... '5425.74','7957.75','12298.3','20462.8','32169.6','61213.4','111408', ... '175070','261469','318310'}; fcns{3}.data={'0','1','1.1','1.2','1.3','1.4','1.5','1.6','1.7','1.8', ... '1.9','2.0','2.1','2.2','2.3','2.4'}; lib.mat{3}.functions = fcns; lib.mat{4}.name='Copper'; lib.mat{4}.varname='mat4'; lib.mat{4}.variables.alphares='3.9e-3[1/K]'; lib.mat{4}.variables.mur='1'; lib.mat{4}.variables.sigma='5.998e7[S/m]'; lib.mat{4}.variables.epsilonr='1'; lib.mat{4}.variables.C='385[J/(kg*K)]'; lib.mat{4}.variables.epsilon='0.5'; lib.mat{4}.variables.res0='1.72e-8[ohm*m]'; lib.mat{4}.variables.rho='8700[kg/m^3]'; lib.mat{4}.variables.k='400[W/(m*K)]'; lib.mat{4}.variables.T0='273.15[K]'; lib.matgroups{1}.name='Resistivity'; lib.matgroups{1}.variables={'alphares','T0','res0'}; lib.matgroups{1}.descr={'Temperature coefficient','Reference temperature','Resistivity at reference temperature'}; lib.matgroups{2}.name='Electromagnetic (AC/DC)'; lib.matgroups{2}.variables={'alphares','T0','res0','Br','normfH','fH','normfB','fB'}; lib.matgroups{2}.descr={'Temperature coefficient','Reference temperature','Resistivity at reference temperature','Remanent flux density','Nonlinear magnetic field, norm','Nonlinear magnetic field','Nonlinear magnetic flux density, norm','Nonlinear magnetic flux density'}; fem.lib = lib; % ODE Settings clear ode clear units; units.basesystem = 'SI'; ode.units = units; fem.ode=ode; % Multiphysics fem=multiphysics(fem); % Extend mesh fem.xmesh=meshextend(fem); % Solve problem fem.sol=femtime(fem, ... 'solcomp',{'Az'}, ... 'outcomp',{'Az','Azt'}, ... 'blocksize','auto', ... 'tlist',[0:0.1:1], ... 'tout','tlist'); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'tridata',{'normH_emqa','cont','internal','unit','A/m'}, ... 'tridlim',[0 300], ... 'trimap','jet(1024)', ... 'arrowdata',{'Mx_emqa','My_emqa'}, ... 'arrowxspacing',100, ... 'arrowyspacing',100, ... 'arrowtype','arrow', ... 'arrowstyle','normalized', ... 'arrowcolor',[1.0,0.0,0.0], ... 'solnum','end', ... 'title','Time=1 Surface: Magnetic field, norm [A/m] Arrow: Magnetization', ... 'axis',[-2.129579668679066,2.1295796686790656,-1.182115949142018,1.182115949142017]); % Plot solution postplot(fem, ... 'tridata',{'normH_emqa','cont','internal','unit','A/m'}, ... 'tridlim',[0 300], ... 'trimap','jet(1024)', ... 'arrowdata',{'Mx_emqa','My_emqa'}, ... 'arrowxspacing',100, ... 'arrowyspacing',100, ... 'arrowtype','arrow', ... 'arrowstyle','normalized', ... 'arrowcolor',[1.0,0.0,0.0], ... 'solnum',2, ... 'title','Time=0.1 Surface: Magnetic field, norm [A/m] Arrow: Magnetization', ... 'axis',[-2.041031657507379,2.0410316575073786,-1.182115949142018,1.182115949142017]); % Plot solution postplot(fem, ... 'tridata',{'normH_emqa','cont','internal','unit','A/m'}, ... 'trimap','jet(1024)', ... 'arrowdata',{'Mx_emqa','My_emqa'}, ... 'arrowxspacing',100, ... 'arrowyspacing',100, ... 'arrowtype','arrow', ... 'arrowstyle','normalized', ... 'arrowcolor',[1.0,0.0,0.0], ... 'solnum',2, ... 'title','Time=0.1 Surface: Magnetic field, norm [A/m] Arrow: Magnetization', ... 'axis',[-2.041031657507379,2.0410316575073786,-1.182115949142018,1.182115949142017]); % Plot solution postplot(fem, ... 'tridata',{'normH_emqa','cont','internal','unit','A/m'}, ... 'tridlim',[0 0.01], ... 'trimap','jet(1024)', ... 'arrowdata',{'Mx_emqa','My_emqa'}, ... 'arrowxspacing',100, ... 'arrowyspacing',100, ... 'arrowtype','arrow', ... 'arrowstyle','normalized', ... 'arrowcolor',[1.0,0.0,0.0], ... 'solnum',2, ... 'title','Time=0.1 Surface: Magnetic field, norm [A/m] Arrow: Magnetization', ... 'axis',[-2.0085640534110936,2.008564053411093,-1.1856004471498054,1.1856004471498045]); % Plot solution postplot(fem, ... 'tridata',{'normH_emqa','cont','internal','unit','A/m'}, ... 'tridlim',[0 0.01], ... 'trimap','jet(1024)', ... 'arrowdata',{'Mx_emqa','My_emqa'}, ... 'arrowxspacing',100, ... 'arrowyspacing',100, ... 'arrowtype','arrow', ... 'arrowstyle','normalized', ... 'arrowcolor',[1.0,0.0,0.0], ... 'solnum',6, ... 'title','Time=0.5 Surface: Magnetic field, norm [A/m] Arrow: Magnetization', ... 'axis',[-2.0174188545282625,2.017418854528262,-1.182115949142018,1.182115949142017]); % Plot solution postplot(fem, ... 'tridata',{'normH_emqa','cont','internal','unit','A/m'}, ... 'trimap','jet(1024)', ... 'arrowdata',{'Mx_emqa','My_emqa'}, ... 'arrowxspacing',100, ... 'arrowyspacing',100, ... 'arrowtype','arrow', ... 'arrowstyle','normalized', ... 'arrowcolor',[1.0,0.0,0.0], ... 'solnum',6, ... 'title','Time=0.5 Surface: Magnetic field, norm [A/m] Arrow: Magnetization', ... 'axis',[-2.0174188545282625,2.017418854528262,-1.182115949142018,1.182115949142017]); % Plot solution postplot(fem, ... 'tridata',{'normH_emqa','cont','internal','unit','A/m'}, ... 'trimap','jet(1024)', ... 'arrowdata',{'Mx_emqa','My_emqa'}, ... 'arrowxspacing',100, ... 'arrowyspacing',100, ... 'arrowtype','arrow', ... 'arrowstyle','normalized', ... 'arrowcolor',[1.0,0.0,0.0], ... 'solnum',10, ... 'title','Time=0.9 Surface: Magnetic field, norm [A/m] Arrow: Magnetization', ... 'axis',[-2.008564053411094,2.0085640534110936,-1.182115949142018,1.182115949142017]); % Plot in cross-section or along domain postcrossplot(fem,0,[-0.5;-0.5], ... 'pointdata',{'Jez_emqa','unit','A/m^2'}, ... 'title','External current density [A/m^2]', ... 'axislabel',{'Time','External current density [A/m^2]'}); % Plot in cross-section or along domain postcrossplot(fem,0,[-0.5;0.5], ... 'pointdata',{'Jez_emqa','unit','A/m^2'}, ... 'title','External current density [A/m^2]', ... 'axislabel',{'Time','External current density [A/m^2]'}); % Plot solution postplot(fem, ... 'tridata',{'normH_emqa','cont','internal','unit','A/m'}, ... 'trimap','jet(1024)', ... 'arrowdata',{'Mx_emqa','My_emqa'}, ... 'arrowxspacing',100, ... 'arrowyspacing',100, ... 'arrowtype','arrow', ... 'arrowstyle','normalized', ... 'arrowcolor',[1.0,0.0,0.0], ... 'solnum',3, ... 'title','Time=0.2 Surface: Magnetic field, norm [A/m] Arrow: Magnetization', ... 'axis',[-2.129579668679066,2.1295796686790656,-1.182115949142018,1.182115949142017]); % Plot solution postplot(fem, ... 'tridata',{'normH_emqa','cont','internal','unit','A/m'}, ... 'tridlim',[0 0.02], ... 'trimap','jet(1024)', ... 'arrowdata',{'Mx_emqa','My_emqa'}, ... 'arrowxspacing',100, ... 'arrowyspacing',100, ... 'arrowtype','arrow', ... 'arrowstyle','normalized', ... 'arrowcolor',[1.0,0.0,0.0], ... 'solnum',3, ... 'title','Time=0.2 Surface: Magnetic field, norm [A/m] Arrow: Magnetization', ... 'axis',[-2.008564053411094,2.0085640534110936,-1.182115949142018,1.182115949142017]); % Plot solution postplot(fem, ... 'tridata',{'normH_emqa','cont','internal','unit','A/m'}, ... 'tridlim',[0 0.02], ... 'trimap','jet(1024)', ... 'arrowdata',{'Mx_emqa','My_emqa'}, ... 'arrowxspacing',100, ... 'arrowyspacing',100, ... 'arrowtype','arrow', ... 'arrowstyle','normalized', ... 'arrowcolor',[1.0,0.0,0.0], ... 'solnum',2, ... 'title','Time=0.1 Surface: Magnetic field, norm [A/m] Arrow: Magnetization', ... 'axis',[-2.0174188545282625,2.017418854528262,-1.182115949142018,1.182115949142017]); % Plot solution postplot(fem, ... 'tridata',{'normH_emqa','cont','internal','unit','A/m'}, ... 'tridlim',[0 0.02], ... 'trimap','jet(1024)', ... 'arrowdata',{'Mx_emqa','My_emqa'}, ... 'arrowxspacing',100, ... 'arrowyspacing',100, ... 'arrowtype','arrow', ... 'arrowstyle','normalized', ... 'arrowcolor',[1.0,0.0,0.0], ... 'solnum',4, ... 'title','Time=0.3 Surface: Magnetic field, norm [A/m] Arrow: Magnetization', ... 'axis',[-2.0174188545282625,2.017418854528262,-1.182115949142018,1.182115949142017]); % Plot solution postplot(fem, ... 'tridata',{'normH_emqa','cont','internal','unit','A/m'}, ... 'tridlim',[0 0.02], ... 'trimap','jet(1024)', ... 'arrowdata',{'Mx_emqa','My_emqa'}, ... 'arrowxspacing',100, ... 'arrowyspacing',100, ... 'arrowtype','arrow', ... 'arrowstyle','normalized', ... 'arrowcolor',[1.0,0.0,0.0], ... 'solnum',5, ... 'title','Time=0.4 Surface: Magnetic field, norm [A/m] Arrow: Magnetization', ... 'axis',[-2.0174188545282625,2.017418854528262,-1.182115949142018,1.182115949142017]); % Plot solution postplot(fem, ... 'tridata',{'normH_emqa','cont','internal','unit','A/m'}, ... 'tridlim',[0 0.02], ... 'trimap','jet(1024)', ... 'arrowdata',{'Mx_emqa','My_emqa'}, ... 'arrowxspacing',100, ... 'arrowyspacing',100, ... 'arrowtype','arrow', ... 'arrowstyle','normalized', ... 'arrowcolor',[1.0,0.0,0.0], ... 'solnum',6, ... 'title','Time=0.5 Surface: Magnetic field, norm [A/m] Arrow: Magnetization', ... 'axis',[-2.0174188545282625,2.017418854528262,-1.182115949142018,1.182115949142017]); % Plot solution postplot(fem, ... 'tridata',{'normH_emqa','cont','internal','unit','A/m'}, ... 'tridlim',[0 0.02], ... 'trimap','jet(1024)', ... 'arrowdata',{'Mx_emqa','My_emqa'}, ... 'arrowxspacing',100, ... 'arrowyspacing',100, ... 'arrowtype','arrow', ... 'arrowstyle','normalized', ... 'arrowcolor',[1.0,0.0,0.0], ... 'solnum',7, ... 'title','Time=0.6 Surface: Magnetic field, norm [A/m] Arrow: Magnetization', ... 'axis',[-2.0174188545282625,2.017418854528262,-1.182115949142018,1.182115949142017]); % Plot solution postplot(fem, ... 'tridata',{'normH_emqa','cont','internal','unit','A/m'}, ... 'tridlim',[0 0.02], ... 'trimap','jet(1024)', ... 'arrowdata',{'Mx_emqa','My_emqa'}, ... 'arrowxspacing',100, ... 'arrowyspacing',100, ... 'arrowtype','arrow', ... 'arrowstyle','normalized', ... 'arrowcolor',[1.0,0.0,0.0], ... 'solnum',8, ... 'title','Time=0.7 Surface: Magnetic field, norm [A/m] Arrow: Magnetization', ... 'axis',[-2.0174188545282625,2.017418854528262,-1.182115949142018,1.182115949142017]); % Plot solution postplot(fem, ... 'tridata',{'normH_emqa','cont','internal','unit','A/m'}, ... 'tridlim',[0 0.02], ... 'trimap','jet(1024)', ... 'arrowdata',{'Mx_emqa','My_emqa'}, ... 'arrowxspacing',100, ... 'arrowyspacing',100, ... 'arrowtype','arrow', ... 'arrowstyle','normalized', ... 'arrowcolor',[1.0,0.0,0.0], ... 'solnum',9, ... 'title','Time=0.8 Surface: Magnetic field, norm [A/m] Arrow: Magnetization', ... 'axis',[-2.0174188545282625,2.017418854528262,-1.182115949142018,1.182115949142017]); % Plot solution postplot(fem, ... 'tridata',{'normH_emqa','cont','internal','unit','A/m'}, ... 'tridlim',[0 0.02], ... 'trimap','jet(1024)', ... 'arrowdata',{'Mx_emqa','My_emqa'}, ... 'arrowxspacing',100, ... 'arrowyspacing',100, ... 'arrowtype','arrow', ... 'arrowstyle','normalized', ... 'arrowcolor',[1.0,0.0,0.0], ... 'solnum',10, ... 'title','Time=0.9 Surface: Magnetic field, norm [A/m] Arrow: Magnetization', ... 'axis',[-2.0174188545282625,2.017418854528262,-1.182115949142018,1.182115949142017]); % Plot solution postplot(fem, ... 'tridata',{'normH_emqa','cont','internal','unit','A/m'}, ... 'tridlim',[0 0.02], ... 'trimap','jet(1024)', ... 'arrowdata',{'Mx_emqa','My_emqa'}, ... 'arrowxspacing',100, ... 'arrowyspacing',100, ... 'arrowtype','arrow', ... 'arrowstyle','normalized', ... 'arrowcolor',[1.0,0.0,0.0], ... 'solnum','end', ... 'title','Time=1 Surface: Magnetic field, norm [A/m] Arrow: Magnetization', ... 'axis',[-2.0174188545282625,2.017418854528262,-1.182115949142018,1.182115949142017]); % Plot in cross-section or along domain postcrossplot(fem,0,[0;0], ... 'pointdata',{'Hx_emqa','unit','A/m'}, ... 'title','Magnetic field, x component [A/m]', ... 'axislabel',{'Time','Magnetic field',' x component [A/m]'}); % (Default values are not included) % Application mode 1 clear appl appl.mode.class = 'PerpendicularCurrents'; appl.module = 'ACDC'; appl.sshape = 2; appl.assignsuffix = '_emqa'; clear prop prop.analysis='transient'; appl.prop = prop; clear bnd bnd.type = {'A0','cont'}; bnd.ind = [1,1,1,2,2,2,1,1,1,1,1,1,1,1,2,2,2,2,1,1,1,1,1,1,1,1,2,1]; appl.bnd = bnd; clear equ equ.Jez = {0,0,'(1-flc2hs(t-0.2,0.1))*R','(flc2hs(t-0.2,0.1)-1)*R'}; equ.sigma = {'mat2_sigma','mat3_sigma','mat4_sigma','mat4_sigma'}; equ.epsilonr = {1,'mat3_epsilonr','mat4_epsilonr','mat4_epsilonr'}; equ.mur = {1,'mat3_MUR(normB_emqa[1/T])','mat4_mur','mat4_mur'}; equ.normfH = {'1/mu0_emqa*normB_emqa','mat3_HB(normB_emqa[1/T])[A/m]','1/mu0_emqa*normB_emqa', ... '1/mu0_emqa*normB_emqa'}; equ.ind = [1,2,3,4,2,3,4]; appl.equ = equ; fem.appl{1} = appl; fem.frame = {'ref'}; fem.border = 1; clear units; units.basesystem = 'SI'; fem.units = units; % Library materials clear lib lib.mat{1}.name='Iron'; lib.mat{1}.varname='mat1'; lib.mat{1}.variables.nu='0.29'; lib.mat{1}.variables.E='200e9[Pa]'; lib.mat{1}.variables.mur='4000'; lib.mat{1}.variables.sigma='1.12e7[S/m]'; lib.mat{1}.variables.epsilonr='1'; lib.mat{1}.variables.alpha='12.2e-6[1/K]'; lib.mat{1}.variables.C='440[J/(kg*K)]'; lib.mat{1}.variables.rho='7870[kg/m^3]'; lib.mat{1}.variables.k='76.2[W/(m*K)]'; lib.mat{2}.name='Air'; lib.mat{2}.varname='mat2'; lib.mat{2}.variables.nu0='nu0(T[1/K])[m^2/s]'; lib.mat{2}.variables.eta='eta(T[1/K])[Pa*s]'; lib.mat{2}.variables.gamma='1.4'; lib.mat{2}.variables.sigma='0[S/m]'; lib.mat{2}.variables.C='Cp(T[1/K])[J/(kg*K)]'; lib.mat{2}.variables.rho='rho(p[1/Pa],T[1/K])[kg/m^3]'; lib.mat{2}.variables.k='k(T[1/K])[W/(m*K)]'; lib.mat{2}.variables.cs='cs(T[1/K])[m/s]'; clear fcns fcns{1}.type='inline'; fcns{1}.name='cs(T)'; fcns{1}.expr='sqrt(1.4*287*T)'; fcns{1}.dexpr={'diff(sqrt(1.4*287*T),T)'}; fcns{2}.type='inline'; fcns{2}.name='rho(p,T)'; fcns{2}.expr='p*0.02897/8.314/T'; fcns{2}.dexpr={'diff(p*0.02897/8.314/T,p)','diff(p*0.02897/8.314/T,T)'}; fcns{3}.type='piecewise'; fcns{3}.name='Cp(T)'; fcns{3}.extmethod='const'; fcns{3}.subtype='poly'; fcns{3}.expr={{'0','1.04763657E+03','1','-3.72589265E-01','2', ... '9.45304214E-04','3','-6.02409443E-07','4','1.28589610E-10'}}; fcns{3}.intervals={'200','1600'}; fcns{4}.type='piecewise'; fcns{4}.name='eta(T)'; fcns{4}.extmethod='const'; fcns{4}.subtype='poly'; fcns{4}.expr={{'0','-8.38278000E-07','1','8.35717342E-08','2', ... '-7.69429583E-11','3','4.64372660E-14','4','-1.06585607E-17'}}; fcns{4}.intervals={'200','1600'}; fcns{5}.type='piecewise'; fcns{5}.name='nu0(T)'; fcns{5}.extmethod='const'; fcns{5}.subtype='poly'; fcns{5}.expr={{'0','-5.86912450E-06','1','5.01274491E-08','2', ... '7.50108343E-11','3','1.80336823E-15','4','-2.91688030E-18'}}; fcns{5}.intervals={'200','1600'}; fcns{6}.type='piecewise'; fcns{6}.name='k(T)'; fcns{6}.extmethod='const'; fcns{6}.subtype='poly'; fcns{6}.expr={{'0','-2.27583562E-03','1','1.15480022E-04','2', ... '-7.90252856E-08','3','4.11702505E-11','4','-7.43864331E-15'}}; fcns{6}.intervals={'200','1600'}; lib.mat{2}.functions = fcns; lib.mat{3}.name='Soft Iron (without losses)'; lib.mat{3}.varname='mat3'; lib.mat{3}.variables.normfB='BH(normH[m/A])[T]'; lib.mat{3}.variables.mur='MUR(normB[1/T])'; lib.mat{3}.variables.sigma='0[S/m]'; lib.mat{3}.variables.normfH='HB(normB[1/T])[A/m]'; lib.mat{3}.variables.epsilonr='1'; clear fcns fcns{1}.type='interp'; fcns{1}.name='MUR'; fcns{1}.method='linear'; fcns{1}.extmethod='const'; fcns{1}.x={'1','1.1','1.2','1.3','1.4','1.5','1.6','1.7','1.8','1.9', ... '2.0','2.1','2.2','2.3','2.4'}; fcns{1}.data={'1200','820','560','420','290','220','160','110','70','47', ... '26','15','10','7','6'}; fcns{2}.type='interp'; fcns{2}.name='HB'; fcns{2}.method='linear'; fcns{2}.extmethod='extrap'; fcns{2}.x={'0','1','1.1','1.2','1.3','1.4','1.5','1.6','1.7','1.8', ... '1.9','2.0','2.1','2.2','2.3','2.4'}; fcns{2}.data={'0','663.146','1067.5','1705.23','2463.11','3841.67', ... '5425.74','7957.75','12298.3','20462.8','32169.6','61213.4','111408', ... '175070','261469','318310'}; fcns{3}.type='interp'; fcns{3}.name='BH'; fcns{3}.method='linear'; fcns{3}.extmethod='extrap'; fcns{3}.x={'0','663.146','1067.5','1705.23','2463.11','3841.67', ... '5425.74','7957.75','12298.3','20462.8','32169.6','61213.4','111408', ... '175070','261469','318310'}; fcns{3}.data={'0','1','1.1','1.2','1.3','1.4','1.5','1.6','1.7','1.8', ... '1.9','2.0','2.1','2.2','2.3','2.4'}; lib.mat{3}.functions = fcns; lib.mat{4}.name='Copper'; lib.mat{4}.varname='mat4'; lib.mat{4}.variables.alphares='3.9e-3[1/K]'; lib.mat{4}.variables.mur='1'; lib.mat{4}.variables.sigma='5.998e7[S/m]'; lib.mat{4}.variables.epsilonr='1'; lib.mat{4}.variables.C='385[J/(kg*K)]'; lib.mat{4}.variables.epsilon='0.5'; lib.mat{4}.variables.res0='1.72e-8[ohm*m]'; lib.mat{4}.variables.rho='8700[kg/m^3]'; lib.mat{4}.variables.k='400[W/(m*K)]'; lib.mat{4}.variables.T0='273.15[K]'; lib.matgroups{1}.name='Resistivity'; lib.matgroups{1}.variables={'alphares','T0','res0'}; lib.matgroups{1}.descr={'Temperature coefficient','Reference temperature','Resistivity at reference temperature'}; lib.matgroups{2}.name='Electromagnetic (AC/DC)'; lib.matgroups{2}.variables={'alphares','T0','res0','Br','normfH','fH','normfB','fB'}; lib.matgroups{2}.descr={'Temperature coefficient','Reference temperature','Resistivity at reference temperature','Remanent flux density','Nonlinear magnetic field, norm','Nonlinear magnetic field','Nonlinear magnetic flux density, norm','Nonlinear magnetic flux density'}; fem.lib = lib; % ODE Settings clear ode clear units; units.basesystem = 'SI'; ode.units = units; fem.ode=ode; % Multiphysics fem=multiphysics(fem); % Extend mesh fem.xmesh=meshextend(fem); % Solve problem fem.sol=femtime(fem, ... 'solcomp',{'Az'}, ... 'outcomp',{'Az','Azt'}, ... 'blocksize','auto', ... 'tlist',[0:0.1:1], ... 'tout','tlist'); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'tridata',{'normH_emqa','cont','internal','unit','A/m'}, ... 'tridlim',[0 0.02], ... 'trimap','jet(1024)', ... 'arrowdata',{'Mx_emqa','My_emqa'}, ... 'arrowxspacing',100, ... 'arrowyspacing',100, ... 'arrowtype','arrow', ... 'arrowstyle','normalized', ... 'arrowcolor',[1.0,0.0,0.0], ... 'solnum','end', ... 'title','Time=1 Surface: Magnetic field, norm [A/m] Arrow: Magnetization', ... 'axis',[-2.129579668679066,2.1295796686790656,-1.182115949142018,1.182115949142017]); % Plot solution postplot(fem, ... 'tridata',{'normH_emqa','cont','internal','unit','A/m'}, ... 'tridlim',[0 0.02], ... 'trimap','jet(1024)', ... 'arrowdata',{'Mx_emqa','My_emqa'}, ... 'arrowxspacing',100, ... 'arrowyspacing',100, ... 'arrowtype','arrow', ... 'arrowstyle','normalized', ... 'arrowcolor',[1.0,0.0,0.0], ... 'solnum',2, ... 'title','Time=0.1 Surface: Magnetic field, norm [A/m] Arrow: Magnetization', ... 'axis',[-2.0174188545282625,2.017418854528262,-1.182115949142018,1.182115949142017]); % Plot solution postplot(fem, ... 'tridata',{'normH_emqa','cont','internal','unit','A/m'}, ... 'trimap','jet(1024)', ... 'arrowdata',{'Mx_emqa','My_emqa'}, ... 'arrowxspacing',100, ... 'arrowyspacing',100, ... 'arrowtype','arrow', ... 'arrowstyle','normalized', ... 'arrowcolor',[1.0,0.0,0.0], ... 'solnum',2, ... 'title','Time=0.1 Surface: Magnetic field, norm [A/m] Arrow: Magnetization', ... 'axis',[-2.0174188545282625,2.017418854528262,-1.182115949142018,1.182115949142017]); % Plot solution postplot(fem, ... 'tridata',{'normH_emqa','cont','internal','unit','A/m'}, ... 'tridlim',[0 0.01], ... 'trimap','jet(1024)', ... 'arrowdata',{'Mx_emqa','My_emqa'}, ... 'arrowxspacing',100, ... 'arrowyspacing',100, ... 'arrowtype','arrow', ... 'arrowstyle','normalized', ... 'arrowcolor',[1.0,0.0,0.0], ... 'solnum',2, ... 'title','Time=0.1 Surface: Magnetic field, norm [A/m] Arrow: Magnetization', ... 'axis',[-2.0085640534110936,2.008564053411093,-1.1856004471498054,1.1856004471498045]); % Plot solution postplot(fem, ... 'tridata',{'normH_emqa','cont','internal','unit','A/m'}, ... 'tridlim',[0 0.01], ... 'trimap','jet(1024)', ... 'arrowdata',{'Mx_emqa','My_emqa'}, ... 'arrowxspacing',100, ... 'arrowyspacing',100, ... 'arrowtype','arrow', ... 'arrowstyle','normalized', ... 'arrowcolor',[1.0,0.0,0.0], ... 'solnum',3, ... 'title','Time=0.2 Surface: Magnetic field, norm [A/m] Arrow: Magnetization', ... 'axis',[-2.0174188545282625,2.017418854528262,-1.182115949142018,1.182115949142017]); % Plot solution postplot(fem, ... 'tridata',{'normH_emqa','cont','internal','unit','A/m'}, ... 'tridlim',[0 0.01], ... 'trimap','jet(1024)', ... 'arrowdata',{'Mx_emqa','My_emqa'}, ... 'arrowxspacing',100, ... 'arrowyspacing',100, ... 'arrowtype','arrow', ... 'arrowstyle','normalized', ... 'arrowcolor',[1.0,0.0,0.0], ... 'solnum',4, ... 'title','Time=0.3 Surface: Magnetic field, norm [A/m] Arrow: Magnetization', ... 'axis',[-2.0174188545282625,2.017418854528262,-1.182115949142018,1.182115949142017]); % Plot solution postplot(fem, ... 'tridata',{'normH_emqa','cont','internal','unit','A/m'}, ... 'tridlim',[0 0.01], ... 'trimap','jet(1024)', ... 'arrowdata',{'Mx_emqa','My_emqa'}, ... 'arrowxspacing',100, ... 'arrowyspacing',100, ... 'arrowtype','arrow', ... 'arrowstyle','normalized', ... 'arrowcolor',[1.0,0.0,0.0], ... 'solnum',5, ... 'title','Time=0.4 Surface: Magnetic field, norm [A/m] Arrow: Magnetization', ... 'axis',[-2.0174188545282625,2.017418854528262,-1.182115949142018,1.182115949142017]); % Plot solution postplot(fem, ... 'tridata',{'normH_emqa','cont','internal','unit','A/m'}, ... 'tridlim',[0 0.01], ... 'trimap','jet(1024)', ... 'arrowdata',{'Mx_emqa','My_emqa'}, ... 'arrowxspacing',100, ... 'arrowyspacing',100, ... 'arrowtype','arrow', ... 'arrowstyle','normalized', ... 'arrowcolor',[1.0,0.0,0.0], ... 'solnum',10, ... 'title','Time=0.9 Surface: Magnetic field, norm [A/m] Arrow: Magnetization', ... 'axis',[-2.0174188545282625,2.017418854528262,-1.182115949142018,1.182115949142017]); % Plot in cross-section or along domain postcrossplot(fem,0,[0;0], ... 'pointdata',{'Hx_emqa','unit','A/m'}, ... 'title','Magnetic field, x component [A/m]', ... 'axislabel',{'Time','Magnetic field',' x component [A/m]'}); % Plot in cross-section or along domain postcrossplot(fem,1,[-1 1;-0.5 -0.5], ... 'lindata','Jez_emqa', ... 'linxdata','x', ... 'title','External current density [A/m^2]', ... 'axislabel',{'x','External current density [A/m^2]'}); % Plot in cross-section or along domain postcrossplot(fem,1,[-0.5 -0.5;-1 1], ... 'lindata','Jez_emqa', ... 'linxdata','y', ... 'title','External current density [A/m^2]', ... 'axislabel',{'y','External current density [A/m^2]'}); % Plot in cross-section or along domain postcrossplot(fem,1,[-0.5 -0.5;-1 1], ... 'lindata','Jez_emqa', ... 'linxdata','y', ... 'solnum',[2], ... 'title','External current density [A/m^2]', ... 'axislabel',{'y','External current density [A/m^2]'}); % Plot in cross-section or along domain postcrossplot(fem,1,[-0.5 -0.5;-1 1], ... 'lindata','Jez_emqa', ... 'linxdata','y', ... 'solnum',[2,7], ... 'title','External current density [A/m^2]', ... 'axislabel',{'y','External current density [A/m^2]'}); % COMSOL Multiphysics Model M-file % Generated by COMSOL 3.5 (COMSOL 3.5.0.494, $Date: 2008/09/19 16:09:48 $) % Plot in cross-section or along domain postcrossplot(fem,1,[-0.5 -0.5;-1 1], ... 'lindata','Jez_emqa', ... 'linxdata','y', ... 'solnum',[2,7], ... 'title','External current density [A/m^2]', ... 'axislabel',{'y','External current density [A/m^2]'}); % Plot solution postplot(fem, ... 'tridata',{'normH_emqa','cont','internal','unit','A/m'}, ... 'tridlim',[0 0.01], ... 'trimap','jet(1024)', ... 'arrowdata',{'Mx_emqa','My_emqa'}, ... 'arrowxspacing',100, ... 'arrowyspacing',100, ... 'arrowtype','arrow', ... 'arrowstyle','normalized', ... 'arrowcolor',[1.0,0.0,0.0], ... 'solnum',10, ... 'title','Time=0.9 Surface: Magnetic field, norm [A/m] Arrow: Magnetization', ... 'axis',[-4.25915933735813,4.25915933735813,-2.3642318982840353,2.3642318982840345]); % Plot solution postplot(fem, ... 'tridata',{'normH_emqa','cont','internal','unit','A/m'}, ... 'tridlim',[0 0.01], ... 'trimap','jet(1024)', ... 'arrowdata',{'Mx_emqa','My_emqa'}, ... 'arrowxspacing',100, ... 'arrowyspacing',100, ... 'arrowtype','arrow', ... 'arrowstyle','normalized', ... 'arrowcolor',[1.0,0.0,0.0], ... 'solnum',10, ... 'title','Time=0.9 Surface: Magnetic field, norm [A/m] Arrow: Magnetization', ... 'axis',[-4.1962935168805195,4.1962935168805195,-2.458837678874394,2.458837678874393]); % Plot solution postplot(fem, ... 'tridata',{'normH_emqa','cont','internal','unit','A/m'}, ... 'tridlim',[0 0.01], ... 'trimap','jet(1024)', ... 'contdata',{'normB_emqa','cont','internal','unit','T'}, ... 'contlevels',20, ... 'contlabel','off', ... 'contmap','jet(1024)', ... 'arrowdata',{'Mx_emqa','My_emqa'}, ... 'arrowxspacing',100, ... 'arrowyspacing',100, ... 'arrowtype','arrow', ... 'arrowstyle','normalized', ... 'arrowcolor',[1.0,0.0,0.0], ... 'solnum',10, ... 'title','Time=0.9 Surface: Magnetic field, norm [A/m] Contour: Magnetic flux density, norm [T] Arrow: Magnetization', ... 'axis',[-4.1962935168805195,4.1962935168805195,-2.458837678874394,2.458837678874393]); % Plot solution postplot(fem, ... 'tridata',{'normH_emqa','cont','internal','unit','A/m'}, ... 'tridlim',[0 0.01], ... 'trimap','jet(1024)', ... 'arrowdata',{'Mx_emqa','My_emqa'}, ... 'arrowxspacing',100, ... 'arrowyspacing',100, ... 'arrowtype','arrow', ... 'arrowstyle','normalized', ... 'arrowcolor',[1.0,0.0,0.0], ... 'solnum',10, ... 'title','Time=0.9 Surface: Magnetic field, norm [A/m] Arrow: Magnetization', ... 'axis',[-4.1962935168805195,4.1962935168805195,-2.628014939031506,2.6280149390315053]); % Plot solution postplot(fem, ... 'tridata',{'normH_emqa','cont','internal','unit','A/m'}, ... 'tridlim',[0 0.01], ... 'trimap','jet(1024)', ... 'arrowdata',{'Mx_emqa','My_emqa'}, ... 'arrowxspacing',100, ... 'arrowyspacing',100, ... 'arrowtype','arrow', ... 'arrowstyle','normalized', ... 'arrowcolor',[1.0,0.0,0.0], ... 'solnum',2, ... 'title','Time=0.1 Surface: Magnetic field, norm [A/m] Arrow: Magnetization', ... 'axis',[-4.1962935168805195,4.1962935168805195,-2.458837678874394,2.458837678874393]); % Plot solution postplot(fem, ... 'tridata',{'normH_emqa','cont','internal','unit','A/m'}, ... 'tridlim',[0 0.01], ... 'trimap','jet(1024)', ... 'arrowdata',{'Mx_emqa','My_emqa'}, ... 'arrowxspacing',100, ... 'arrowyspacing',100, ... 'arrowtype','arrow', ... 'arrowstyle','normalized', ... 'arrowcolor',[1.0,0.0,0.0], ... 'solnum',3, ... 'title','Time=0.2 Surface: Magnetic field, norm [A/m] Arrow: Magnetization', ... 'axis',[-4.1962935168805195,4.1962935168805195,-2.458837678874394,2.458837678874393]); % Plot solution postplot(fem, ... 'tridata',{'normH_emqa','cont','internal','unit','A/m'}, ... 'tridlim',[0 0.01], ... 'trimap','jet(1024)', ... 'arrowdata',{'Mx_emqa','My_emqa'}, ... 'arrowxspacing',100, ... 'arrowyspacing',100, ... 'arrowtype','arrow', ... 'arrowstyle','normalized', ... 'arrowcolor',[1.0,0.0,0.0], ... 'solnum',3, ... 'title','Time=0.2 Surface: Magnetic field, norm [A/m] Arrow: Magnetization', ... 'geom','off', ... 'axis',[-4.1962935168805195,4.1962935168805195,-2.458837678874394,2.458837678874393]); % Plot solution postplot(fem, ... 'tridata',{'normH_emqa','cont','internal','unit','A/m'}, ... 'tridlim',[0 0.01], ... 'trimap','jet(1024)', ... 'arrowdata',{'Mx_emqa','My_emqa'}, ... 'arrowxspacing',100, ... 'arrowyspacing',100, ... 'arrowtype','arrow', ... 'arrowstyle','normalized', ... 'arrowcolor',[1.0,0.0,0.0], ... 'solnum',3, ... 'title','Time=0.2 Surface: Magnetic field, norm [A/m] Arrow: Magnetization', ... 'axis',[-4.1962935168805195,4.1962935168805195,-2.458837678874394,2.458837678874393]); % Plot solution postplot(fem, ... 'tridata',{'normH_emqa','cont','internal','unit','A/m'}, ... 'tridlim',[0 0.01], ... 'trimap','jet(1024)', ... 'arrowdata',{{'Mx_emqa','My_emqa'},'recover','pprint'}, ... 'arrowxspacing',100, ... 'arrowyspacing',100, ... 'arrowtype','arrow', ... 'arrowstyle','normalized', ... 'arrowcolor',[1.0,0.0,0.0], ... 'solnum',3, ... 'title','Time=0.2 Surface: Magnetic field, norm [A/m] Arrow: Magnetization', ... 'axis',[-4.1962935168805195,4.1962935168805195,-2.458837678874394,2.458837678874393]); % Plot solution postplot(fem, ... 'tridata',{'normH_emqa','cont','internal','unit','A/m'}, ... 'tridlim',[0 0.01], ... 'trimap','jet(1024)', ... 'arrowdata',{'Mx_emqa','My_emqa'}, ... 'arrowxspacing',100, ... 'arrowyspacing',100, ... 'arrowtype','arrow', ... 'arrowstyle','normalized', ... 'arrowcolor',[1.0,0.0,0.0], ... 'arrowz',{'normB_emqa','unit','T'}, ... 'solnum',3, ... 'title','Time=0.2 Surface: Magnetic field, norm [A/m] Arrow: Magnetization Height: Magnetic flux density, norm [T]', ... 'grid','on'); % Plot solution postplot(fem, ... 'tridata',{'normH_emqa','cont','internal','unit','A/m'}, ... 'tridlim',[0 0.01], ... 'trimap','jet(1024)', ... 'arrowdata',{'Mx_emqa','My_emqa'}, ... 'arrowxspacing',100, ... 'arrowyspacing',100, ... 'arrowtype','arrow', ... 'arrowstyle','normalized', ... 'arrowcolor',[1.0,0.0,0.0], ... 'solnum',3, ... 'title','Time=0.2 Surface: Magnetic field, norm [A/m] Arrow: Magnetization', ... 'axis',[-2,2,-2,2]); % Plot solution postplot(fem, ... 'tridata',{'normH_emqa','cont','internal','unit','A/m'}, ... 'tridlim',[0 0.01], ... 'trimap','jet(1024)', ... 'arrowdata',{'Mx_emqa','My_emqa'}, ... 'arrowxspacing',100, ... 'arrowyspacing',100, ... 'arrowtype','arrow', ... 'arrowstyle','normalized', ... 'arrowcolor',[1.0,0.0,0.0], ... 'solnum',3, ... 'title','Time=0.2 Surface: Magnetic field, norm [A/m] Arrow: Magnetization', ... 'axis',[-4.1962935168805195,4.1962935168805195,-2.458837678874394,2.458837678874393]); % COMSOL Multiphysics Model M-file % Generated by COMSOL 3.5 (COMSOL 3.5.0.494, $Date: 2008/09/19 16:09:48 $) % (Default values are not included) % Application mode 1 clear appl appl.mode.class = 'PerpendicularCurrents'; appl.module = 'ACDC'; appl.assignsuffix = '_emqa'; clear prop prop.analysis='transient'; appl.prop = prop; clear bnd bnd.type = {'A0','cont'}; bnd.ind = [1,1,1,2,2,2,1,1,1,1,1,1,1,1,2,2,2,2,1,1,1,1,1,1,1,1,2,1]; appl.bnd = bnd; clear equ equ.Jez = {0,0,'(1-flc2hs(t-0.2,0.1))*R','(flc2hs(t-0.2,0.1)-1)*R'}; equ.sigma = {'mat2_sigma','mat3_sigma','mat4_sigma','mat4_sigma'}; equ.epsilonr = {1,'mat3_epsilonr','mat4_epsilonr','mat4_epsilonr'}; equ.mur = {1,'mat3_MUR(normB_emqa[1/T])','mat4_mur','mat4_mur'}; equ.normfH = {'1/mu0_emqa*normB_emqa','mat3_HB(normB_emqa[1/T])[A/m]','1/mu0_emqa*normB_emqa', ... '1/mu0_emqa*normB_emqa'}; equ.ind = [1,2,3,4,2,3,4]; appl.equ = equ; fem.appl{1} = appl; fem.frame = {'ref'}; fem.border = 1; clear units; units.basesystem = 'SI'; fem.units = units; % Library materials clear lib lib.mat{1}.name='Iron'; lib.mat{1}.varname='mat1'; lib.mat{1}.variables.nu='0.29'; lib.mat{1}.variables.E='200e9[Pa]'; lib.mat{1}.variables.mur='4000'; lib.mat{1}.variables.sigma='1.12e7[S/m]'; lib.mat{1}.variables.epsilonr='1'; lib.mat{1}.variables.alpha='12.2e-6[1/K]'; lib.mat{1}.variables.C='440[J/(kg*K)]'; lib.mat{1}.variables.rho='7870[kg/m^3]'; lib.mat{1}.variables.k='76.2[W/(m*K)]'; lib.mat{2}.name='Air'; lib.mat{2}.varname='mat2'; lib.mat{2}.variables.nu0='nu0(T[1/K])[m^2/s]'; lib.mat{2}.variables.eta='eta(T[1/K])[Pa*s]'; lib.mat{2}.variables.gamma='1.4'; lib.mat{2}.variables.sigma='0[S/m]'; lib.mat{2}.variables.C='Cp(T[1/K])[J/(kg*K)]'; lib.mat{2}.variables.rho='rho(p[1/Pa],T[1/K])[kg/m^3]'; lib.mat{2}.variables.k='k(T[1/K])[W/(m*K)]'; lib.mat{2}.variables.cs='cs(T[1/K])[m/s]'; clear fcns fcns{1}.type='inline'; fcns{1}.name='cs(T)'; fcns{1}.expr='sqrt(1.4*287*T)'; fcns{1}.dexpr={'diff(sqrt(1.4*287*T),T)'}; fcns{2}.type='inline'; fcns{2}.name='rho(p,T)'; fcns{2}.expr='p*0.02897/8.314/T'; fcns{2}.dexpr={'diff(p*0.02897/8.314/T,p)','diff(p*0.02897/8.314/T,T)'}; fcns{3}.type='piecewise'; fcns{3}.name='Cp(T)'; fcns{3}.extmethod='const'; fcns{3}.subtype='poly'; fcns{3}.expr={{'0','1.04763657E+03','1','-3.72589265E-01','2', ... '9.45304214E-04','3','-6.02409443E-07','4','1.28589610E-10'}}; fcns{3}.intervals={'200','1600'}; fcns{4}.type='piecewise'; fcns{4}.name='eta(T)'; fcns{4}.extmethod='const'; fcns{4}.subtype='poly'; fcns{4}.expr={{'0','-8.38278000E-07','1','8.35717342E-08','2', ... '-7.69429583E-11','3','4.64372660E-14','4','-1.06585607E-17'}}; fcns{4}.intervals={'200','1600'}; fcns{5}.type='piecewise'; fcns{5}.name='nu0(T)'; fcns{5}.extmethod='const'; fcns{5}.subtype='poly'; fcns{5}.expr={{'0','-5.86912450E-06','1','5.01274491E-08','2', ... '7.50108343E-11','3','1.80336823E-15','4','-2.91688030E-18'}}; fcns{5}.intervals={'200','1600'}; fcns{6}.type='piecewise'; fcns{6}.name='k(T)'; fcns{6}.extmethod='const'; fcns{6}.subtype='poly'; fcns{6}.expr={{'0','-2.27583562E-03','1','1.15480022E-04','2', ... '-7.90252856E-08','3','4.11702505E-11','4','-7.43864331E-15'}}; fcns{6}.intervals={'200','1600'}; lib.mat{2}.functions = fcns; lib.mat{3}.name='Soft Iron (without losses)'; lib.mat{3}.varname='mat3'; lib.mat{3}.variables.normfB='BH(normH[m/A])[T]'; lib.mat{3}.variables.mur='MUR(normB[1/T])'; lib.mat{3}.variables.sigma='0[S/m]'; lib.mat{3}.variables.normfH='HB(normB[1/T])[A/m]'; lib.mat{3}.variables.epsilonr='1'; clear fcns fcns{1}.type='interp'; fcns{1}.name='MUR'; fcns{1}.method='linear'; fcns{1}.extmethod='const'; fcns{1}.x={'1','1.1','1.2','1.3','1.4','1.5','1.6','1.7','1.8','1.9', ... '2.0','2.1','2.2','2.3','2.4'}; fcns{1}.data={'1200','820','560','420','290','220','160','110','70','47', ... '26','15','10','7','6'}; fcns{2}.type='interp'; fcns{2}.name='HB'; fcns{2}.method='linear'; fcns{2}.extmethod='extrap'; fcns{2}.x={'0','1','1.1','1.2','1.3','1.4','1.5','1.6','1.7','1.8', ... '1.9','2.0','2.1','2.2','2.3','2.4'}; fcns{2}.data={'0','663.146','1067.5','1705.23','2463.11','3841.67', ... '5425.74','7957.75','12298.3','20462.8','32169.6','61213.4','111408', ... '175070','261469','318310'}; fcns{3}.type='interp'; fcns{3}.name='BH'; fcns{3}.method='linear'; fcns{3}.extmethod='extrap'; fcns{3}.x={'0','663.146','1067.5','1705.23','2463.11','3841.67', ... '5425.74','7957.75','12298.3','20462.8','32169.6','61213.4','111408', ... '175070','261469','318310'}; fcns{3}.data={'0','1','1.1','1.2','1.3','1.4','1.5','1.6','1.7','1.8', ... '1.9','2.0','2.1','2.2','2.3','2.4'}; lib.mat{3}.functions = fcns; lib.mat{4}.name='Copper'; lib.mat{4}.varname='mat4'; lib.mat{4}.variables.alphares='3.9e-3[1/K]'; lib.mat{4}.variables.mur='1'; lib.mat{4}.variables.sigma='5.998e7[S/m]'; lib.mat{4}.variables.epsilonr='1'; lib.mat{4}.variables.C='385[J/(kg*K)]'; lib.mat{4}.variables.epsilon='0.5'; lib.mat{4}.variables.res0='1.72e-8[ohm*m]'; lib.mat{4}.variables.rho='8700[kg/m^3]'; lib.mat{4}.variables.k='400[W/(m*K)]'; lib.mat{4}.variables.T0='273.15[K]'; lib.matgroups{1}.name='Resistivity'; lib.matgroups{1}.variables={'alphares','T0','res0'}; lib.matgroups{1}.descr={'Temperature coefficient','Reference temperature','Resistivity at reference temperature'}; fem.lib = lib; % ODE Settings clear ode clear units; units.basesystem = 'SI'; ode.units = units; fem.ode=ode; % Multiphysics fem=multiphysics(fem); % Extend mesh fem.xmesh=meshextend(fem); % Solve problem fem.sol=femtime(fem, ... 'solcomp',{'Az'}, ... 'outcomp',{'Az','Azt'}, ... 'blocksize','auto', ... 'tlist',[0:0.1:1], ... 'tout','tlist'); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'tridata',{'normH_emqa','cont','internal','unit','A/m'}, ... 'tridlim',[0 0.01], ... 'trimap','jet(1024)', ... 'arrowdata',{'Mx_emqa','My_emqa'}, ... 'arrowxspacing',100, ... 'arrowyspacing',100, ... 'arrowtype','arrow', ... 'arrowstyle','normalized', ... 'arrowcolor',[1.0,0.0,0.0], ... 'solnum','end', ... 'title','Time=1 Surface: Magnetic field, norm [A/m] Arrow: Magnetization', ... 'axis',[-1.10739786848182,1.10739786848182,-0.6147094197185987,0.6147094197185983]); % Plot solution postplot(fem, ... 'tridata',{'normH_emqa','cont','internal','unit','A/m'}, ... 'trimap','jet(1024)', ... 'arrowdata',{'Mx_emqa','My_emqa'}, ... 'arrowxspacing',100, ... 'arrowyspacing',100, ... 'arrowtype','arrow', ... 'arrowstyle','normalized', ... 'arrowcolor',[1.0,0.0,0.0], ... 'solnum','end', ... 'title','Time=1 Surface: Magnetic field, norm [A/m] Arrow: Magnetization', ... 'axis',[-1.04907337922013,1.04907337922013,-0.6147094197185987,0.6147094197185983]); % Plot solution postplot(fem, ... 'tridata',{'normH_emqa','cont','internal','unit','A/m'}, ... 'trimap','jet(1024)', ... 'arrowdata',{'Mx_emqa','My_emqa'}, ... 'arrowxspacing',100, ... 'arrowyspacing',100, ... 'arrowtype','arrow', ... 'arrowstyle','normalized', ... 'arrowcolor',[1.0,0.0,0.0], ... 'solnum',5, ... 'title','Time=0.4 Surface: Magnetic field, norm [A/m] Arrow: Magnetization', ... 'axis',[-1.04907337922013,1.04907337922013,-0.6192393343812266,0.6192393343812261]); % Plot solution postplot(fem, ... 'tridata',{'normH_emqa','cont','internal','unit','A/m'}, ... 'trimap','jet(1024)', ... 'arrowdata',{'Mx_emqa','My_emqa'}, ... 'arrowxspacing',100, ... 'arrowyspacing',100, ... 'arrowtype','arrow', ... 'arrowstyle','normalized', ... 'arrowcolor',[1.0,0.0,0.0], ... 'solnum',2, ... 'title','Time=0.1 Surface: Magnetic field, norm [A/m] Arrow: Magnetization', ... 'axis',[-1.04907337922013,1.04907337922013,-0.6174193804227219,0.6174193804227215]); % Plot in cross-section or along domain postcrossplot(fem,0,[0;0], ... 'pointdata',{'Hx_emqa','unit','A/m'}, ... 'title','Magnetic field, x component [A/m]', ... 'axislabel',{'Time','Magnetic field',' x component [A/m]'}); % Plot in cross-section or along domain postcrossplot(fem,0,[-0.2;0], ... 'pointdata',{'normM_emqa','unit','A/m'}, ... 'title','Magnetization, norm [A/m]', ... 'axislabel',{'Time','Magnetization',' norm [A/m]'}); % Plot in cross-section or along domain postcrossplot(fem,0,[-0.5;-0.5], ... 'pointdata',{'normJ_emqa','unit','A/m^2'}, ... 'title','Total current density, norm [A/m^2]', ... 'axislabel',{'Time','Total current density',' norm [A/m^2]'}); % Plot solution postplot(fem, ... 'tridata',{'normH_emqa','cont','internal','unit','A/m'}, ... 'trimap','jet(1024)', ... 'arrowdata',{'Mx_emqa','My_emqa'}, ... 'arrowxspacing',100, ... 'arrowyspacing',100, ... 'arrowtype','arrow', ... 'arrowstyle','normalized', ... 'arrowcolor',[1.0,0.0,0.0], ... 'solnum',2, ... 'title','Time=0.1 Surface: Magnetic field, norm [A/m] Arrow: Magnetization', ... 'axis',[-1.10739786848182,1.10739786848182,-0.6147094197185987,0.6147094197185983]); % Plot solution postplot(fem, ... 'tridata',{'normH_emqa','cont','internal','unit','A/m'}, ... 'trimap','jet(1024)', ... 'arrowdata',{'Mx_emqa','My_emqa'}, ... 'arrowxspacing',100, ... 'arrowyspacing',100, ... 'arrowtype','arrow', ... 'arrowstyle','normalized', ... 'arrowcolor',[1.0,0.0,0.0], ... 'solnum',9, ... 'title','Time=0.8 Surface: Magnetic field, norm [A/m] Arrow: Magnetization', ... 'axis',[-1.04907337922013,1.04907337922013,-0.6192393343812266,0.6192393343812261]); % Plot solution postplot(fem, ... 'tridata',{'normH_emqa','cont','internal','unit','A/m'}, ... 'trimap','jet(1024)', ... 'arrowdata',{'Mx_emqa','My_emqa'}, ... 'arrowxspacing',1000, ... 'arrowyspacing',100, ... 'arrowtype','arrow', ... 'arrowstyle','normalized', ... 'arrowcolor',[1.0,0.0,0.0], ... 'solnum',9, ... 'title','Time=0.8 Surface: Magnetic field, norm [A/m] Arrow: Magnetization', ... 'axis',[-2.098146758440261,2.098146758440261,-1.2348387608454443,1.2348387608454432]); % Plot solution postplot(fem, ... 'tridata',{'normH_emqa','cont','internal','unit','A/m'}, ... 'trimap','jet(1024)', ... t�` 'arrowdata',{'Mx_emqa','My_emqa'}, ... 'arrowxspacing',1000, ... 'arrowyspacing',100, ... 'arrowtype','arrow', ... 'arrowstyle','proportional', ... 'arrowcolor',[1.0,0.0,0.0], ... 'solnum',9, ... 'title','Time=0.8 Surface: Magnetic field, norm [A/m] Arrow: Magnetization', ... 'axis',[-2.098146758440261,2.098146758440261,-1.2348387608454443,1.2348387608454432]); % Plot solution postplot(fem, ... 'tridata',{'normH_emqa','cont','internal','unit','A/m'}, ... 'trimap','jet(1024)', ... 'arrowdata',{'Mx_emqa','My_emqa'}, ... 'arrowxspacing',1000, ... 'arrowyspacing',100, ... 'arrowscale',5, ... 'arrowtype','arrow', ... 'arrowstyle','normalized', ... 'arrowcolor',[1.0,0.0,0.0], ... 'solnum',9, ... 'title','Time=0.8 Surface: Magnetic field, norm [A/m] Arrow: Magnetization', ... 'axis',[-2.098146758440261,2.098146758440261,-1.2348387608454443,1.2348387608454432]); % Plot solution postplot(fem, ... 'tridata',{'normH_emqa','cont','internal','unit','A/m'}, ... 'trimap','jet(1024)', ... 'arrowdata',{'Mx_emqa','My_emqa'}, ... 'arrowxspacing',1000, ... 'arrowyspacing',1000, ... 'arrowscale',5, ... 'arrowtype','arrow', ... 'arrowstyle','normalized', ... 'arrowcolor',[1.0,0.0,0.0], ... 'solnum',9, ... 'title','Time=0.8 Surface: Magnetic field, norm [A/m] Arrow: Magnetization', ... 'axis',[-2.098146758440261,2.098146758440261,-1.2348387608454443,1.2348387608454432]); % Plot solution postplot(fem, ... 'tridata',{'normH_emqa','cont','internal','unit','A/m'}, ... 'trimap','jet(1024)', ... 'arrowdata',{{'Mx_emqa','My_emqa'},'recover','pprint'}, ... 'arrowxspacing',1000, ... 'arrowyspacing',1000, ... 'arrowscale',5, ... 'arrowtype','arrow', ... 'arrowstyle','normalized', ... 'arrowcolor',[1.0,0.0,0.0], ... 'solnum',9, ... 'title','Time=0.8 Surface: Magnetic field, norm [A/m] Arrow: Magnetization', ... 'axis',[-1.0490733792201308,1.0490733792201306,-0.6174193804227226,0.6174193804227213]); % Plot solution postplot(fem, ... 'tridata',{'normH_emqa','cont','internal','unit','A/m'}, ... 'trimap','jet(1024)', ... 'arrowdata',{'Mx_emqa','My_emqa'}, ... 'arrowxspacing',100, ... 'arrowyspacing',100, ... 'arrowscale',5, ... 'arrowtype','arrow', ... 'arrowstyle','normalized', ... 'arrowcolor',[1.0,0.0,0.0], ... 'solnum',9, ... 'title','Time=0.8 Surface: Magnetic field, norm [A/m] Arrow: Magnetization', ... 'axis',[-1.0490733792201308,1.0490733792201306,-0.6174193804227226,0.6174193804227213]); % Plot solution postplot(fem, ... 'arrowdata',{'Mx_emqa','My_emqa'}, ... 'arrowxspacing',100, ... 'arrowyspacing',100, ... 'arrowscale',5, ... 'arrowtype','arrow', ... 'arrowstyle','normalized', ... 'arrowcolor',[1.0,0.0,0.0], ... 'solnum',9, ... 'title','Time=0.8 Arrow: Magnetization', ... 'axis',[-1.0490733792201308,1.0490733792201306,-0.6174193804227226,0.6174193804227213]); % Plot solution postplot(fem, ... 'arrowdata',{'Mx_emqa','My_emqa'}, ... 'arrowxspacing',10, ... 'arrowyspacing',100, ... 'arrowscale',5, ... 'arrowtype','arrow', ... 'arrowstyle','normalized', ... 'arrowcolor',[1.0,0.0,0.0], ... 'solnum',9, ... 'title','Time=0.8 Arrow: Magnetization', ... 'axis',[-1.1122798576154658,1.1122798576154656,-0.6174193804227226,0.6174193804227213]); % Plot solution postplot(fem, ... 'arrowdata',{'Mx_emqa','My_emqa'}, ... 'arrowxspacing',10, ... 'arrowyspacing',100, ... 'arrowtype','arrow', ... 'arrowstyle','normalized', ... 'arrowcolor',[1.0,0.0,0.0], ... 'solnum',9, ... 'title','Time=0.8 Arrow: Magnetization', ... 'axis',[-1.1122798576154658,1.1122798576154656,-0.6174193804227226,0.6174193804227213]); % Plot solution postplot(fem, ... 'tridata',{'normH_emqa','cont','internal','unit','A/m'}, ... 'trimap','jet(1024)', ... 'arrowdata',{'Mx_emqa','My_emqa'}, ... 'arrowxspacing',10, ... 'arrowyspacing',100, ... 'arrowtype','arrow', ... 'arrowstyle','normalized', ... 'arrowcolor',[1.0,0.0,0.0], ... 'solnum',9, ... 'title','Time=0.8 Surface: Magnetic field, norm [A/m] Arrow: Magnetization', ... 'axis',[-1.1122798576154658,1.1122798576154656,-0.6174193804227226,0.6174193804227213]); % Plot solution postplot(fem, ... 'tridata',{'normH_emqa','cont','internal','unit','A/m'}, ... 'trimap','jet(1024)', ... 'arrowdata',{'Mx_emqa','My_emqa'}, ... 'arrowxspacing',10, ... 'arrowyspacing',100, ... 'arrowtype','arrow', ... 'arrowstyle','normalized', ... 'arrowcolor',[1.0,0.0,0.0], ... 'solnum',9, ... 'title','Time=0.8 Surface: Magnetic field, norm [A/m] Arrow: Magnetization', ... 'axis',[-1.0490733792201308,1.0490733792201306,-0.6174193804227226,0.6174193804227213]); % COMSOL Multiphysics Model M-file % Generated by COMSOL 3.5 (COMSOL 3.5.0.494, $Date: 2008/09/19 16:09:48 $) % Geometry g7=move(g7,[0,0.10000000000000009]); g11=move(g11,[0,0.10000000000000009]); g2=move(g2,[0,0.10000000000000009]); g1=move(g1,[0,0.10000000000000009]); g13=move(g13,[0,0.10000000000000009]); g4=move(g4,[0,0.10000000000000009]); g3=move(g3,[0,0.10000000000000009]); % Analyzed geometry clear s s.objs={g7,g11,g2,g1,g13,g4,g3}; s.name={'SQ5','R1','SQ2','SQ1','R2','SQ4','SQ3'}; s.tags={'g7','g11','g2','g1','g13','g4','g3'}; fem.draw=struct('s',s); fem.geom=geomcsg(fem); % Analyzed geometry clear s s.objs={g7,g2,g1,g4,g3}; s.name={'SQ5','SQ2','SQ1','SQ4','SQ3'}; s.tags={'g7','g2','g1','g4','g3'}; fem.draw=struct('s',s); fem.geom=geomcsg(fem); % Initialize mesh fem.mesh=meshinit(fem, ... 'hauto',5); % (Default values are not included) % Application mode 1 clear appl appl.mode.class = 'PerpendicularCurrents'; appl.module = 'ACDC'; appl.assignsuffix = '_emqa'; clear prop prop.analysis='transient'; appl.prop = prop; clear bnd bnd.type = 'A0'; bnd.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; appl.bnd = bnd; clear equ equ.Jez = {0,'(1-flc2hs(t-0.2,0.1))*R','(flc2hs(t-0.2,0.1)-1)*R'}; equ.sigma = {'mat2_sigma','mat4_sigma','mat4_sigma'}; equ.epsilonr = {1,'mat4_epsilonr','mat4_epsilonr'}; equ.mur = {1,'mat4_mur','mat4_mur'}; equ.ind = [1,2,3,2,3]; appl.equ = equ; fem.appl{1} = appl; fem.frame = {'ref'}; fem.border = 1; clear units; units.basesystem = 'SI'; fem.units = units; % Library materials clear lib lib.mat{1}.name='Iron'; lib.mat{1}.varname='mat1'; lib.mat{1}.variables.nu='0.29'; lib.mat{1}.variables.E='200e9[Pa]'; lib.mat{1}.variables.mur='4000'; lib.mat{1}.variables.sigma='1.12e7[S/m]'; lib.mat{1}.variables.epsilonr='1'; lib.mat{1}.variables.alpha='12.2e-6[1/K]'; lib.mat{1}.variables.C='440[J/(kg*K)]'; lib.mat{1}.variables.rho='7870[kg/m^3]'; lib.mat{1}.variables.k='76.2[W/(m*K)]'; lib.mat{2}.name='Air'; lib.mat{2}.varname='mat2'; lib.mat{2}.variables.nu0='nu0(T[1/K])[m^2/s]'; lib.mat{2}.variables.eta='eta(T[1/K])[Pa*s]'; lib.mat{2}.variables.gamma='1.4'; lib.mat{2}.variables.sigma='0[S/m]'; lib.mat{2}.variables.C='Cp(T[1/K])[J/(kg*K)]'; lib.mat{2}.variables.rho='rho(p[1/Pa],T[1/K])[kg/m^3]'; lib.mat{2}.variables.k='k(T[1/K])[W/(m*K)]'; lib.mat{2}.variables.cs='cs(T[1/K])[m/s]'; clear fcns fcns{1}.type='inline'; fcns{1}.name='cs(T)'; fcns{1}.expr='sqrt(1.4*287*T)'; fcns{1}.dexpr={'diff(sqrt(1.4*287*T),T)'}; fcns{2}.type='inline'; fcns{2}.name='rho(p,T)'; fcns{2}.expr='p*0.02897/8.314/T'; fcns{2}.dexpr={'diff(p*0.02897/8.314/T,p)','diff(p*0.02897/8.314/T,T)'}; fcns{3}.type='piecewise'; fcns{3}.name='Cp(T)'; fcns{3}.extmethod='const'; fcns{3}.subtype='poly'; fcns{3}.expr={{'0','1.04763657E+03','1','-3.72589265E-01','2', ... '9.45304214E-04','3','-6.02409443E-07','4','1.28589610E-10'}}; fcns{3}.intervals={'200','1600'}; fcns{4}.type='piecewise'; fcns{4}.name='eta(T)'; fcns{4}.extmethod='const'; fcns{4}.subtype='poly'; fcns{4}.expr={{'0','-8.38278000E-07','1','8.35717342E-08','2', ... '-7.69429583E-11','3','4.64372660E-14','4','-1.06585607E-17'}}; fcns{4}.intervals={'200','1600'}; fcns{5}.type='piecewise'; fcns{5}.name='nu0(T)'; fcns{5}.extmethod='const'; fcns{5}.subtype='poly'; fcns{5}.expr={{'0','-5.86912450E-06','1','5.01274491E-08','2', ... '7.50108343E-11','3','1.80336823E-15','4','-2.91688030E-18'}}; fcns{5}.intervals={'200','1600'}; fcns{6}.type='piecewise'; fcns{6}.name='k(T)'; fcns{6}.extmethod='const'; fcns{6}.subtype='poly'; fcns{6}.expr={{'0','-2.27583562E-03','1','1.15480022E-04','2', ... '-7.90252856E-08','3','4.11702505E-11','4','-7.43864331E-15'}}; fcns{6}.intervals={'200','1600'}; lib.mat{2}.functions = fcns; lib.mat{3}.name='Soft Iron (without losses)'; lib.mat{3}.varname='mat3'; lib.mat{3}.variables.normfB='BH(normH[m/A])[T]'; lib.mat{3}.variables.mur='MUR(normB[1/T])'; lib.mat{3}.variables.sigma='0[S/m]'; lib.mat{3}.variables.normfH='HB(normB[1/T])[A/m]'; lib.mat{3}.variables.epsilonr='1'; clear fcns fcns{1}.type='interp'; fcns{1}.name='MUR'; fcns{1}.method='linear'; fcns{1}.extmethod='const'; fcns{1}.x={'1','1.1','1.2','1.3','1.4','1.5','1.6','1.7','1.8','1.9', ... '2.0','2.1','2.2','2.3','2.4'}; fcns{1}.data={'1200','820','560','420','290','220','160','110','70','47', ... '26','15','10','7','6'}; fcns{2}.type='interp'; fcns{2}.name='HB'; fcns{2}.method='linear'; fcns{2}.extmethod='extrap'; fcns{2}.x={'0','1','1.1','1.2','1.3','1.4','1.5','1.6','1.7','1.8', ... '1.9','2.0','2.1','2.2','2.3','2.4'}; fcns{2}.data={'0','663.146','1067.5','1705.23','2463.11','3841.67', ... '5425.74','7957.75','12298.3','20462.8','32169.6','61213.4','111408', ... '175070','261469','318310'}; fcns{3}.type='interp'; fcns{3}.name='BH'; fcns{3}.method='linear'; fcns{3}.extmethod='extrap'; fcns{3}.x={'0','663.146','1067.5','1705.23','2463.11','3841.67', ... '5425.74','7957.75','12298.3','20462.8','32169.6','61213.4','111408', ... '175070','261469','318310'}; fcns{3}.data={'0','1','1.1','1.2','1.3','1.4','1.5','1.6','1.7','1.8', ... '1.9','2.0','2.1','2.2','2.3','2.4'}; lib.mat{3}.functions = fcns; lib.mat{4}.name='Copper'; lib.mat{4}.varname='mat4'; lib.mat{4}.variables.alphares='3.9e-3[1/K]'; lib.mat{4}.variables.mur='1'; lib.mat{4}.variables.sigma='5.998e7[S/m]'; lib.mat{4}.variables.epsilonr='1'; lib.mat{4}.variables.C='385[J/(kg*K)]'; lib.mat{4}.variables.epsilon='0.5'; lib.mat{4}.variables.res0='1.72e-8[ohm*m]'; lib.mat{4}.variables.rho='8700[kg/m^3]'; lib.mat{4}.variables.k='400[W/(m*K)]'; lib.mat{4}.variables.T0='273.15[K]'; lib.matgroups{1}.name='Resistivity'; lib.matgroups{1}.variables={'alphares','T0','res0'}; lib.matgroups{1}.descr={'Temperature coefficient','Reference temperature','Resistivity at reference temperature'}; fem.lib = lib; % ODE Settings clear ode clear units; units.basesystem = 'SI'; ode.units = units; fem.ode=ode; % Multiphysics fem=multiphysics(fem); % Extend mesh fem.xmesh=meshextend(fem); % Solve problem fem.sol=femtime(fem, ... 'solcomp',{'Az'}, ... 'outcomp',{'Az','Azt'}, ... 'blocksize','auto', ... 'tlist',[0:0.1:1], ... 'tout','tlist'); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'tridata',{'normH_emqa','cont','internal','unit','A/m'}, ... 'trimap','jet(1024)', ... 'arrowdata',{'Mx_emqa','My_emqa'}, ... 'arrowxspacing',10, ... 'arrowyspacing',100, ... 'arrowtype','arrow', ... 'arrowstyle','normalized', ... 'arrowcolor',[1.0,0.0,0.0], ... 'solnum','end', ... 'title','Time=1 Surface: Magnetic field, norm [A/m] Arrow: Magnetization', ... 'axis',[-2.1917248854858253,2.1917248854858244,-1.2348387608454447,1.2348387608454434]); % Plot solution postplot(fem, ... 'tridata',{'normH_emqa','cont','internal','unit','A/m'}, ... 'trimap','jet(1024)', ... 'arrowdata',{'Hx_emqa','Hy_emqa'}, ... 'arrowxspacing',10, ... 'arrowyspacing',100, ... 'arrowtype','arrow', ... 'arrowstyle','normalized', ... 'arrowcolor',[1.0,0.0,0.0], ... 'solnum','end', ... 'title','Time=1 Surface: Magnetic field, norm [A/m] Arrow: Magnetic field', ... 'axis',[-2.1917248854858253,2.1917248854858244,-1.2937152787576616,1.2937152787576602]); % Plot solution postplot(fem, ... 'tridata',{'normH_emqa','cont','internal','unit','A/m'}, ... 'trimap','jet(1024)', ... 'arrowdata',{'Hx_emqa','Hy_emqa'}, ... 'arrowxspacing',25, ... 'arrowyspacing',25, ... 'arrowtype','arrow', ... 'arrowstyle','normalized', ... 'arrowcolor',[1.0,0.0,0.0], ... 'solnum','end', ... 'title','Time=1 Surface: Magnetic field, norm [A/m] Arrow: Magnetic field', ... 'axis',[-2.1917248854858253,2.1917248854858244,-1.2937152787576616,1.2937152787576602]); % Plot solution postplot(fem, ... 'tridata',{'normH_emqa','cont','internal','unit','A/m'}, ... 'trimap','jet(1024)', ... 'arrowdata',{'Hx_emqa','Hy_emqa'}, ... 'arrowxspacing',25, ... 'arrowyspacing',25, ... 'arrowtype','arrow', ... 'arrowstyle','normalized', ... 'arrowcolor',[1.0,0.0,0.0], ... 'solnum',2, ... 'title','Time=0.1 Surface: Magnetic field, norm [A/m] Arrow: Magnetic field', ... 'axis',[-2.1917248854858253,2.1917248854858244,-1.2937152787576616,1.2937152787576602]); % Plot in cross-section or along domain postcrossplot(fem,0,[0;0], ... 'pointdata',{'normH_emqa','unit','A/m'}, ... 'title','Magnetic field, norm [A/m]', ... 'axislabel',{'Time','Magnetic field',' norm [A/m]'}); % (Default values are not included) % Application mode 1 clear appl appl.mode.class = 'PerpendicularCurrents'; appl.module = 'ACDC'; appl.sshape = 2; appl.assignsuffix = '_emqa'; clear prop prop.analysis='transient'; appl.prop = prop; clear bnd bnd.type = 'A0'; bnd.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; appl.bnd = bnd; clear equ equ.Jez = {0,'(1-flc2hs(t-0.2,0.1))*R','(flc2hs(t-0.2,0.1)-1)*R','(1-flc2hs(t-0.2,0.1))*R', ... '(flc2hs(t-0.2,0.1)-1)*R'}; equ.sigma = {'mat2_sigma','mat5_sigma','mat5_sigma','mat4_sigma','mat4_sigma'}; equ.epsilonr = {1,'mat5_epsilonr','mat5_epsilonr','mat4_epsilonr','mat4_epsilonr'}; equ.mur = {1,'mat5_mur','mat5_mur','mat4_mur','mat4_mur'}; equ.ind = [1,2,3,4,5]; appl.equ = equ; fem.appl{1} = appl; fem.frame = {'ref'}; fem.border = 1; clear units; units.basesystem = 'SI'; fem.units = units; % Library materials clear lib lib.mat{1}.name='Iron'; lib.mat{1}.varname='mat1'; lib.mat{1}.variables.nu='0.29'; lib.mat{1}.variables.E='200e9[Pa]'; lib.mat{1}.variables.mur='4000'; lib.mat{1}.variables.sigma='1.12e7[S/m]'; lib.mat{1}.variables.epsilonr='1'; lib.mat{1}.variables.alpha='12.2e-6[1/K]'; lib.mat{1}.variables.C='440[J/(kg*K)]'; lib.mat{1}.variables.rho='7870[kg/m^3]'; lib.mat{1}.variables.k='76.2[W/(m*K)]'; lib.mat{2}.name='Air'; lib.mat{2}.varname='mat2'; lib.mat{2}.variables.nu0='nu0(T[1/K])[m^2/s]'; lib.mat{2}.variables.eta='eta(T[1/K])[Pa*s]'; lib.mat{2}.variables.gamma='1.4'; lib.mat{2}.variables.sigma='0[S/m]'; lib.mat{2}.variables.C='Cp(T[1/K])[J/(kg*K)]'; lib.mat{2}.variables.rho='rho(p[1/Pa],T[1/K])[kg/m^3]'; lib.mat{2}.variables.k='k(T[1/K])[W/(m*K)]'; lib.mat{2}.variables.cs='cs(T[1/K])[m/s]'; clear fcns fcns{1}.type='inline'; fcns{1}.name='cs(T)'; fcns{1}.expr='sqrt(1.4*287*T)'; fcns{1}.dexpr={'diff(sqrt(1.4*287*T),T)'}; fcns{2}.type='inline'; fcns{2}.name='rho(p,T)'; fcns{2}.expr='p*0.02897/8.314/T'; fcns{2}.dexpr={'diff(p*0.02897/8.314/T,p)','diff(p*0.02897/8.314/T,T)'}; fcns{3}.type='piecewise'; fcns{3}.name='Cp(T)'; fcns{3}.extmethod='const'; fcns{3}.subtype='poly'; fcns{3}.expr={{'0','1.04763657E+03','1','-3.72589265E-01','2', ... '9.45304214E-04','3','-6.02409443E-07','4','1.28589610E-10'}}; fcns{3}.intervals={'200','1600'}; fcns{4}.type='piecewise'; fcns{4}.name='eta(T)'; fcns{4}.extmethod='const'; fcns{4}.subtype='poly'; fcns{4}.expr={{'0','-8.38278000E-07','1','8.35717342E-08','2', ... '-7.69429583E-11','3','4.64372660E-14','4','-1.06585607E-17'}}; fcns{4}.intervals={'200','1600'}; fcns{5}.type='piecewise'; fcns{5}.name='nu0(T)'; fcns{5}.extmethod='const'; fcns{5}.subtype='poly'; fcns{5}.expr={{'0','-5.86912450E-06','1','5.01274491E-08','2', ... '7.50108343E-11','3','1.80336823E-15','4','-2.91688030E-18'}}; fcns{5}.intervals={'200','1600'}; fcns{6}.type='piecewise'; fcns{6}.name='k(T)'; fcns{6}.extmethod='const'; fcns{6}.subtype='poly'; fcns{6}.expr={{'0','-2.27583562E-03','1','1.15480022E-04','2', ... '-7.90252856E-08','3','4.11702505E-11','4','-7.43864331E-15'}}; fcns{6}.intervals={'200','1600'}; lib.mat{2}.functions = fcns; lib.mat{3}.name='Soft Iron (without losses)'; lib.mat{3}.varname='mat3'; lib.mat{3}.variables.normfB='BH(normH[m/A])[T]'; lib.mat{3}.variables.mur='MUR(normB[1/T])'; lib.mat{3}.variables.sigma='0[S/m]'; lib.mat{3}.variables.normfH='HB(normB[1/T])[A/m]'; lib.mat{3}.variables.epsilonr='1'; clear fcns fcns{1}.type='interp'; fcns{1}.name='MUR'; fcns{1}.method='linear'; fcns{1}.extmethod='const'; fcns{1}.x={'1','1.1','1.2','1.3','1.4','1.5','1.6','1.7','1.8','1.9', ... '2.0','2.1','2.2','2.3','2.4'}; fcns{1}.data={'1200','820','560','420','290','220','160','110','70','47', ... '26','15','10','7','6'}; fcns{2}.type='interp'; fcns{2}.name='HB'; fcns{2}.method='linear'; fcns{2}.extmethod='extrap'; fcns{2}.x={'0','1','1.1','1.2','1.3','1.4','1.5','1.6','1.7','1.8', ... '1.9','2.0','2.1','2.2','2.3','2.4'}; fcns{2}.data={'0','663.146','1067.5','1705.23','2463.11','3841.67', ... '5425.74','7957.75','12298.3','20462.8','32169.6','61213.4','111408', ... '175070','261469','318310'}; fcns{3}.type='interp'; fcns{3}.name='BH'; fcns{3}.method='linear'; fcns{3}.extmethod='extrap'; fcns{3}.x={'0','663.146','1067.5','1705.23','2463.11','3841.67', ... '5425.74','7957.75','12298.3','20462.8','32169.6','61213.4','111408', ... '175070','261469','318310'}; fcns{3}.data={'0','1','1.1','1.2','1.3','1.4','1.5','1.6','1.7','1.8', ... '1.9','2.0','2.1','2.2','2.3','2.4'}; lib.mat{3}.functions = fcns; lib.mat{4}.name='Copper'; lib.mat{4}.varname='mat4'; lib.mat{4}.variables.alphares='3.9e-3[1/K]'; lib.mat{4}.variables.mur='1'; lib.mat{4}.variables.sigma='5.998e7[S/m]'; lib.mat{4}.variables.epsilonr='1'; lib.mat{4}.variables.C='385[J/(kg*K)]'; lib.mat{4}.variables.epsilon='0.5'; lib.mat{4}.variables.res0='1.72e-8[ohm*m]'; lib.mat{4}.variables.rho='8700[kg/m^3]'; lib.mat{4}.variables.k='400[W/(m*K)]'; lib.mat{4}.variables.T0='273.15[K]'; lib.mat{5}.name='Silicon Carbide'; lib.mat{5}.varname='mat5'; lib.mat{5}.variables.mur='1'; lib.mat{5}.variables.sigma='1e3[S/m]'; lib.mat{5}.variables.epsilonr='10'; lib.mat{5}.variables.C='1200[J/(kg*K)]'; lib.mat{5}.variables.epsilon='0.5'; lib.mat{5}.variables.rho='3200[kg/m^3]'; lib.mat{5}.variables.k='450[W/(m*K)]*(300[K]/T)^0.75'; lib.matgroups{1}.name='Resistivity'; lib.matgroups{1}.variables={'alphares','T0','res0'}; lib.matgroups{1}.descr={'Temperature coefficient','Reference temperature','Resistivity at reference temperature'}; lib.matgroups{2}.name='Electromagnetic (AC/DC)'; lib.matgroups{2}.variables={'alphares','T0','res0','Br','normfH','fH','normfB','fB'}; lib.matgroups{2}.descr={'Temperature coefficient','Reference temperature','Resistivity at reference temperature','Remanent flux density','Nonlinear magnetic field, norm','Nonlinear magnetic field','Nonlinear magnetic flux density, norm','Nonlinear magnetic flux density'}; fem.lib = lib; % ODE Settings clear ode clear units; units.basesystem = 'SI'; ode.units = units; fem.ode=ode; % Multiphysics fem=multiphysics(fem); % Extend mesh fem.xmesh=meshextend(fem); % Solve problem fem.sol=femtime(fem, ... 'solcomp',{'Az'}, ... 'outcomp',{'Az','Azt'}, ... 'blocksize','auto', ... 'tlist',[0:0.1:1], ... 'tout','tlist'); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'tridata',{'normH_emqa','cont','internal','unit','A/m'}, ... 'trimap','jet(1024)', ... 'arrowdata',{'Hx_emqa','Hy_emqa'}, ... 'arrowxspacing',25, ... 'arrowyspacing',25, ... 'arrowtype','arrow', ... 'arrowstyle','normalized', ... 'arrowcolor',[1.0,0.0,0.0], ... 'solnum','end', ... 'title','Time=1 Surface: Magnetic field, norm [A/m] Arrow: Magnetic field', ... 'axis',[-2.2245597152309315,2.2245597152309307,-1.2348387608454447,1.2348387608454434]); % Plot in cross-section or along domain postcrossplot(fem,0,[0;0], ... 'pointdata',{'normH_emqa','unit','A/m'}, ... 'title','Magnetic field, norm [A/m]', ... 'axislabel',{'Time','Magnetic field',' norm [A/m]'}); % Plot solution postplot(fem, ... 'tridata',{'normH_emqa','cont','internal','unit','A/m'}, ... 'trimap','jet(1024)', ... 'arrowdata',{'Hx_emqa','Hy_emqa'}, ... 'arrowxspacing',25, ... 'arrowyspacing',25, ... 'arrowtype','arrow', ... 'arrowstyle','normalized', ... 'arrowcolor',[1.0,0.0,0.0], ... 'solnum',3, ... 'title','Time=0.2 Surface: Magnetic field, norm [A/m] Arrow: Magnetic field', ... 'axis',[-2.1917248854858253,2.1917248854858244,-1.295624821604536,1.2956248216045347]); % (Default values are not included) % Application mode 1 clear appl appl.mode.class = 'PerpendicularCurrents'; appl.module = 'ACDC'; appl.sshape = 2; appl.assignsuffix = '_emqa'; clear prop prop.analysis='transient'; appl.prop = prop; clear bnd bnd.type = 'A0'; bnd.ind = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; appl.bnd = bnd; clear equ equ.Jez = {0,'(1-flc2hs(t-0.2,0.1))*R','(flc2hs(t-0.2,0.1)-1)*R'}; equ.sigma = {'mat2_sigma','mat5_sigma','mat5_sigma'}; equ.epsilonr = {1,'mat5_epsilonr','mat5_epsilonr'}; equ.mur = {1,'mat5_mur','mat5_mur'}; equ.ind = [1,2,3,2,3]; appl.equ = equ; fem.appl{1} = appl; fem.frame = {'ref'}; fem.border = 1; clear units; units.basesystem = 'SI'; fem.units = units; % Library materials clear lib lib.mat{1}.name='Iron'; lib.mat{1}.varname='mat1'; lib.mat{1}.variables.nu='0.29'; lib.mat{1}.variables.E='200e9[Pa]'; lib.mat{1}.variables.mur='4000'; lib.mat{1}.variables.sigma='1.12e7[S/m]'; lib.mat{1}.variables.epsilonr='1'; lib.mat{1}.variables.alpha='12.2e-6[1/K]'; lib.mat{1}.variables.C='440[J/(kg*K)]'; lib.mat{1}.variables.rho='7870[kg/m^3]'; lib.mat{1}.variables.k='76.2[W/(m*K)]'; lib.mat{2}.name='Air'; lib.mat{2}.varname='mat2'; lib.mat{2}.variables.nu0='nu0(T[1/K])[m^2/s]'; lib.mat{2}.variables.eta='eta(T[1/K])[Pa*s]'; lib.mat{2}.variables.gamma='1.4'; lib.mat{2}.variables.sigma='0[S/m]'; lib.mat{2}.variables.C='Cp(T[1/K])[J/(kg*K)]'; lib.mat{2}.variables.rho='rho(p[1/Pa],T[1/K])[kg/m^3]'; lib.mat{2}.variables.k='k(T[1/K])[W/(m*K)]'; lib.mat{2}.variables.cs='cs(T[1/K])[m/s]'; clear fcns fcns{1}.type='inline'; fcns{1}.name='cs(T)'; fcns{1}.expr='sqrt(1.4*287*T)'; fcns{1}.dexpr={'diff(sqrt(1.4*287*T),T)'}; fcns{2}.type='inline'; fcns{2}.name='rho(p,T)'; fcns{2}.expr='p*0.02897/8.314/T'; fcns{2}.dexpr={'diff(p*0.02897/8.314/T,p)','diff(p*0.02897/8.314/T,T)'}; fcns{3}.type='piecewise'; fcns{3}.name='Cp(T)'; fcns{3}.extmethod='const'; fcns{3}.subtype='poly'; fcns{3}.expr={{'0','1.04763657E+03','1','-3.72589265E-01','2', ... '9.45304214E-04','3','-6.02409443E-07','4','1.28589610E-10'}}; fcns{3}.intervals={'200','1600'}; fcns{4}.type='piecewise'; fcns{4}.name='eta(T)'; fcns{4}.extmethod='const'; fcns{4}.subtype='poly'; fcns{4}.expr={{'0','-8.38278000E-07','1','8.35717342E-08','2', ... '-7.69429583E-11','3','4.64372660E-14','4','-1.06585607E-17'}}; fcns{4}.intervals={'200','1600'}; fcns{5}.type='piecewise'; fcns{5}.name='nu0(T)'; fcns{5}.extmethod='const'; fcns{5}.subtype='poly'; fcns{5}.expr={{'0','-5.86912450E-06','1','5.01274491E-08','2', ... '7.50108343E-11','3','1.80336823E-15','4','-2.91688030E-18'}}; fcns{5}.intervals={'200','1600'}; fcns{6}.type='piecewise'; fcns{6}.name='k(T)'; fcns{6}.extmethod='const'; fcns{6}.subtype='poly'; fcns{6}.expr={{'0','-2.27583562E-03','1','1.15480022E-04','2', ... '-7.90252856E-08','3','4.11702505E-11','4','-7.43864331E-15'}}; fcns{6}.intervals={'200','1600'}; lib.mat{2}.functions = fcns; lib.mat{3}.name='Soft Iron (without losses)'; lib.mat{3}.varname='mat3'; lib.mat{3}.variables.normfB='BH(normH[m/A])[T]'; lib.mat{3}.variables.mur='MUR(normB[1/T])'; lib.mat{3}.variables.sigma='0[S/m]'; lib.mat{3}.variables.normfH='HB(normB[1/T])[A/m]'; lib.mat{3}.variables.epsilonr='1'; clear fcns fcns{1}.type='interp'; fcns{1}.name='MUR'; fcns{1}.method='linear'; fcns{1}.extmethod='const'; fcns{1}.x={'1','1.1','1.2','1.3','1.4','1.5','1.6','1.7','1.8','1.9', ... '2.0','2.1','2.2','2.3','2.4'}; fcns{1}.data={'1200','820','560','420','290','220','160','110','70','47', ... '26','15','10','7','6'}; fcns{2}.type='interp'; fcns{2}.name='HB'; fcns{2}.method='linear'; fcns{2}.extmethod='extrap'; fcns{2}.x={'0','1','1.1','1.2','1.3','1.4','1.5','1.6','1.7','1.8', ... '1.9','2.0','2.1','2.2','2.3','2.4'}; fcns{2}.data={'0','663.146','1067.5','1705.23','2463.11','3841.67', ... '5425.74','7957.75','12298.3','20462.8','32169.6','61213.4','111408', ... '175070','261469','318310'}; fcns{3}.type='interp'; fcns{3}.name='BH'; fcns{3}.method='linear'; fcns{3}.extmethod='extrap'; fcns{3}.x={'0','663.146','1067.5','1705.23','2463.11','3841.67', ... '5425.74','7957.75','12298.3','20462.8','32169.6','61213.4','111408', ... '175070','261469','318310'}; fcns{3}.data={'0','1','1.1','1.2','1.3','1.4','1.5','1.6','1.7','1.8', ... '1.9','2.0','2.1','2.2','2.3','2.4'}; lib.mat{3}.functions = fcns; lib.mat{4}.name='Copper'; lib.mat{4}.varname='mat4'; lib.mat{4}.variables.alphares='3.9e-3[1/K]'; lib.mat{4}.variables.mur='1'; lib.mat{4}.variables.sigma='5.998e7[S/m]'; lib.mat{4}.variables.epsilonr='1'; lib.mat{4}.variables.C='385[J/(kg*K)]'; lib.mat{4}.variables.epsilon='0.5'; lib.mat{4}.variables.res0='1.72e-8[ohm*m]'; lib.mat{4}.variables.rho='8700[kg/m^3]'; lib.mat{4}.variables.k='400[W/(m*K)]'; lib.mat{4}.variables.T0='273.15[K]'; lib.mat{5}.name='Silicon Carbide'; lib.mat{5}.varname='mat5'; lib.mat{5}.variables.mur='1'; lib.mat{5}.variables.sigma='1e3[S/m]'; lib.mat{5}.variables.epsilonr='10'; lib.mat{5}.variables.C='1200[J/(kg*K)]'; lib.mat{5}.variables.epsilon='0.5'; lib.mat{5}.variables.rho='3200[kg/m^3]'; lib.mat{5}.variables.k='450[W/(m*K)]*(300[K]/T)^0.75'; lib.matgroups{1}.name='Resistivity'; lib.matgroups{1}.variables={'alphares','T0','res0'}; lib.matgroups{1}.descr={'Temperature coefficient','Reference temperature','Resistivity at reference temperature'}; lib.matgroups{2}.name='Electromagnetic (AC/DC)'; lib.matgroups{2}.variables={'alphares','T0','res0','Br','normfH','fH','normfB','fB'}; lib.matgroups{2}.descr={'Temperature coefficient','Reference temperature','Resistivity at reference temperature','Remanent flux density','Nonlinear magnetic field, norm','Nonlinear magnetic field','Nonlinear magnetic flux density, norm','Nonlinear magnetic flux density'}; fem.lib = lib; % ODE Settings clear ode clear units; units.basesystem = 'SI'; ode.units = units; fem.ode=ode; % Multiphysics fem=multiphysics(fem); % Extend mesh fem.xmesh=meshextend(fem); % Solve problem fem.sol=femtime(fem, ... 'solcomp',{'Az'}, ... 'outcomp',{'Az','Azt'}, ... 'blocksize','auto', ... 'tlist',[0:0.1:1], ... 'tout','tlist'); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'tridata',{'normH_emqa','cont','internal','unit','A/m'}, ... 'trimap','jet(1024)', ... 'arrowdata',{'Hx_emqa','Hy_emqa'}, ... 'arrowxspacing',25, ... 'arrowyspacing',25, ... 'arrowtype','arrow', ... 'arrowstyle','normalized', ... 'arrowcolor',[1.0,0.0,0.0], ... 'solnum','end', ... 'title','Time=1 Surface: Magnetic field, norm [A/m] Arrow: Magnetic field', ... 'axis',[-2.2245597152309315,2.2245597152309307,-1.2348387608454447,1.2348387608454434]); % Plot in cross-section or along domain postcrossplot(fem,0,[0;0], ... 'pointdata',{'normH_emqa','unit','A/m'}, ... 'title','Magnetic field, norm [A/m]', ... 'axislabel',{'Time','Magnetic field',' norm [A/m]'}); % Plot in cross-section or along domain postcrossplot(fem,0,[-0.5;-0.5], ... 'pointdata',{'Jz_emqa','unit','A/m^2'}, ... 'title','Total current density, z component [A/m^2]', ... 'axislabel',{'Time','Total current density',' z component [A/m^2]'}); % Plot in cross-section or along domain postcrossplot(fem,0,[-0.5;-0.4], ... 'pointdata',{'Jz_emqa','unit','A/m^2'}, ... 'title','Total current density, z component [A/m^2]', ... 'axislabel',{'Time','Total current density',' z component [A/m^2]'}); % Plot solution postplot(fem, ... 'tridata',{'normH_emqa','cont','internal','unit','A/m'}, ... 'trimap','jet(1024)', ... 'arrowdata',{'Hx_emqa','Hy_emqa'}, ... 'arrowxspacing',25, ... 'arrowyspacing',25, ... 'arrowtype','arrow', ... 'arrowstyle','normalized', ... 'arrowcolor',[1.0,0.0,0.0], ... 'solnum',2, ... 'title','Time=0.1 Surface: Magnetic field, norm [A/m] Arrow: Magnetic field', ... 'axis',[-2.1917248854858253,2.1917248854858244,-1.295624821604536,1.2956248216045347]); % Geometry g5=rect2('0.4','0.1','base','center','pos',{'-0.25','0'},'rot','0'); [g6,g8,g9,g10]=geomcopy({g2,g1,g4,g3}); [g12,g14,g15,g16]=geomcopy({g6,g8,g9,g10}); g12=move(g12,[0,-0.1]); g14=move(g14,[0,-0.1]); g15=move(g15,[0,-0.1]); g16=move(g16,[0,-0.1]); % Analyzed geometry clear s s.objs={g7,g12,g14,g15,g16}; s.name={'SQ5','SQ1','SQ2','SQ3','SQ4'}; s.tags={'g7','g12','g14','g15','g16'}; fem.draw=struct('s',s); fem.geom=geomcsg(fem); % Initialize mesh fem.mesh=meshinit(fem, ... 'hauto',5); % (Default values are not included) % Application mode 1 clear appl appl.mode.class = 'PerpendicularCurrents'; appl.module = 'ACDC'; appl.assignsuffix = '_emqa'; clear prop prop.analysis='transient'; appl.prop = prop; clear bnd bnd.type = {'A0','cont'}; bnd.ind = [1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1]; appl.bnd = bnd; clear equ equ.Jez = {0,'(1-flc2hs(t-0.2,0.1))*R','(flc2hs(t-0.2,0.1)-1)*R'}; equ.sigma = {'mat2_sigma','mat5_sigma','mat5_sigma'}; equ.epsilonr = {1,'mat5_epsilonr','mat5_epsilonr'}; equ.mur = {1,'mat5_mur','mat5_mur'}; equ.ind = [1,2,3,2,3]; appl.equ = equ; fem.appl{1} = appl; fem.frame = {'ref'}; fem.border = 1; clear units; units.basesystem = 'SI'; fem.units = units; % Library materials clear lib lib.mat{1}.name='Iron'; lib.mat{1}.varname='mat1'; lib.mat{1}.variables.nu='0.29'; lib.mat{1}.variables.E='200e9[Pa]'; lib.mat{1}.variables.mur='4000'; lib.mat{1}.variables.sigma='1.12e7[S/m]'; lib.mat{1}.variables.epsilonr='1'; lib.mat{1}.variables.alpha='12.2e-6[1/K]'; lib.mat{1}.variables.C='440[J/(kg*K)]'; lib.mat{1}.variables.rho='7870[kg/m^3]'; lib.mat{1}.variables.k='76.2[W/(m*K)]'; lib.mat{2}.name='Air'; lib.mat{2}.varname='mat2'; lib.mat{2}.variables.nu0='nu0(T[1/K])[m^2/s]'; lib.mat{2}.variables.eta='eta(T[1/K])[Pa*s]'; lib.mat{2}.variables.gamma='1.4'; lib.mat{2}.variables.sigma='0[S/m]'; lib.mat{2}.variables.C='Cp(T[1/K])[J/(kg*K)]'; lib.mat{2}.variables.rho='rho(p[1/Pa],T[1/K])[kg/m^3]'; lib.mat{2}.variables.k='k(T[1/K])[W/(m*K)]'; lib.mat{2}.variables.cs='cs(T[1/K])[m/s]'; clear fcns fcns{1}.type='inline'; fcns{1}.name='cs(T)'; fcns{1}.expr='sqrt(1.4*287*T)'; fcns{1}.dexpr={'diff(sqrt(1.4*287*T),T)'}; fcns{2}.type='inline'; fcns{2}.name='rho(p,T)'; fcns{2}.expr='p*0.02897/8.314/T'; fcns{2}.dexpr={'diff(p*0.02897/8.314/T,p)','diff(p*0.02897/8.314/T,T)'}; fcns{3}.type='piecewise'; fcns{3}.name='Cp(T)'; fcns{3}.extmethod='const'; fcns{3}.subtype='poly'; fcns{3}.expr={{'0','1.04763657E+03','1','-3.72589265E-01','2', ... '9.45304214E-04','3','-6.02409443E-07','4','1.28589610E-10'}}; fcns{3}.intervals={'200','1600'}; fcns{4}.type='piecewise'; fcns{4}.name='eta(T)'; fcns{4}.extmethod='const'; fcns{4}.subtype='poly'; fcns{4}.expr={{'0','-8.38278000E-07','1','8.35717342E-08','2', ... '-7.69429583E-11','3','4.64372660E-14','4','-1.06585607E-17'}}; fcns{4}.intervals={'200','1600'}; fcns{5}.type='piecewise'; fcns{5}.name='nu0(T)'; fcns{5}.extmethod='const'; fcns{5}.subtype='poly'; fcns{5}.expr={{'0','-5.86912450E-06','1','5.01274491E-08','2', ... '7.50108343E-11','3','1.80336823E-15','4','-2.91688030E-18'}}; fcns{5}.intervals={'200','1600'}; fcns{6}.type='piecewise'; fcns{6}.name='k(T)'; fcns{6}.extmethod='const'; fcns{6}.subtype='poly'; fcns{6}.expr={{'0','-2.27583562E-03','1','1.15480022E-04','2', ... '-7.90252856E-08','3','4.11702505E-11','4','-7.43864331E-15'}}; fcns{6}.intervals={'200','1600'}; lib.mat{2}.functions = fcns; lib.mat{3}.name='Soft Iron (without losses)'; lib.mat{3}.varname='mat3'; lib.mat{3}.variables.normfB='BH(normH[m/A])[T]'; lib.mat{3}.variables.mur='MUR(normB[1/T])'; lib.mat{3}.variables.sigma='0[S/m]'; lib.mat{3}.variables.normfH='HB(normB[1/T])[A/m]'; lib.mat{3}.variables.epsilonr='1'; clear fcns fcns{1}.type='interp'; fcns{1}.name='MUR'; fcns{1}.method='linear'; fcns{1}.extmethod='const'; fcns{1}.x={'1','1.1','1.2','1.3','1.4','1.5','1.6','1.7','1.8','1.9', ... '2.0','2.1','2.2','2.3','2.4'}; fcns{1}.data={'1200','820','560','420','290','220','160','110','70','47', ... '26','15','10','7','6'}; fcns{2}.type='interp'; fcns{2}.name='HB'; fcns{2}.method='linear'; fcns{2}.extmethod='extrap'; fcns{2}.x={'0','1','1.1','1.2','1.3','1.4','1.5','1.6','1.7','1.8', ... '1.9','2.0','2.1','2.2','2.3','2.4'}; fcns{2}.data={'0','663.146','1067.5','1705.23','2463.11','3841.67', ... '5425.74','7957.75','12298.3','20462.8','32169.6','61213.4','111408', ... '175070','261469','318310'}; fcns{3}.type='interp'; fcns{3}.name='BH'; fcns{3}.method='linear'; fcns{3}.extmethod='extrap'; fcns{3}.x={'0','663.146','1067.5','1705.23','2463.11','3841.67', ... '5425.74','7957.75','12298.3','20462.8','32169.6','61213.4','111408', ... '175070','261469','318310'}; fcns{3}.data={'0','1','1.1','1.2','1.3','1.4','1.5','1.6','1.7','1.8', ... '1.9','2.0','2.1','2.2','2.3','2.4'}; lib.mat{3}.functions = fcns; lib.mat{4}.name='Copper'; lib.mat{4}.varname='mat4'; lib.mat{4}.variables.alphares='3.9e-3[1/K]'; lib.mat{4}.variables.mur='1'; lib.mat{4}.variables.sigma='5.998e7[S/m]'; lib.mat{4}.variables.epsilonr='1'; lib.mat{4}.variables.C='385[J/(kg*K)]'; lib.mat{4}.variables.epsilon='0.5'; lib.mat{4}.variables.res0='1.72e-8[ohm*m]'; lib.mat{4}.variables.rho='8700[kg/m^3]'; lib.mat{4}.variables.k='400[W/(m*K)]'; lib.mat{4}.variables.T0='273.15[K]'; lib.mat{5}.name='Silicon Carbide'; lib.mat{5}.varname='mat5'; lib.mat{5}.variables.mur='1'; lib.mat{5}.variables.sigma='1e3[S/m]'; lib.mat{5}.variables.epsilonr='10'; lib.mat{5}.variables.C='1200[J/(kg*K)]'; lib.mat{5}.variables.epsilon='0.5'; lib.mat{5}.variables.rho='3200[kg/m^3]'; lib.mat{5}.variables.k='450[W/(m*K)]*(300[K]/T)^0.75'; lib.matgroups{1}.name='Resistivity'; lib.matgroups{1}.variables={'alphares','T0','res0'}; lib.matgroups{1}.descr={'Temperature coefficient','Reference temperature','Resistivity at reference temperature'}; lib.matgroups{2}.name='Electromagnetic (AC/DC)'; lib.matgroups{2}.variables={'alphares','T0','res0','Br','normfH','fH','normfB','fB'}; lib.matgroups{2}.descr={'Temperature coefficient','Reference temperature','Resistivity at reference temperature','Remanent flux density','Nonlinear magnetic field, norm','Nonlinear magnetic field','Nonlinear magnetic flux density, norm','Nonlinear magnetic flux density'}; fem.lib = lib; % ODE Settings clear ode clear units; units.basesystem = 'SI'; ode.units = units; fem.ode=ode; % Multiphysics fem=multiphysics(fem); % Extend mesh fem.xmesh=meshextend(fem); % Solve problem fem.sol=femtime(fem, ... 'solcomp',{'Az'}, ... 'outcomp',{'Az','Azt'}, ... 'blocksize','auto', ... 'tlist',[0:0.1:1], ... 'tout','tlist'); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'tridata',{'normH_emqa','cont','internal','unit','A/m'}, ... 'trimap','jet(1024)', ... 'arrowdata',{'Hx_emqa','Hy_emqa'}, ... 'arrowxspacing',25, ... 'arrowyspacing',25, ... 'arrowtype','arrow', ... 'arrowstyle','normalized', ... 'arrowcolor',[1.0,0.0,0.0], ... 'solnum','end', ... 'title','Time=1 Surface: Magnetic field, norm [A/m] Arrow: Magnetic field', ... 'axis',[-2.1917248854858253,2.1917248854858244,-1.2348387608454447,1.2348387608454434]); % Plot in cross-section or along domain postcrossplot(fem,0,[-0.5;-0.5], ... 'pointdata',{'Jz_emqa','unit','A/m^2'}, ... 'title','Total current density, z component [A/m^2]', ... 'axislabel',{'Time','Total current density',' z component [A/m^2]'}); % Geometry g17=rect2('1','0.1','base','center','pos',{'-0.55','0'},'rot','0'); [g18]=geomcopy({g17}); [g19]=geomcopy({g18}); g19=move(g19,[1,0]); [g20]=geomcopy({g19}); [g21]=geomcopy({g20}); g21=move(g21,[0.1,0]); % Analyzed geometry clear s s.objs={g7,g12,g14,g15,g16,g17,g21}; s.name={'SQ5','SQ1','SQ2','SQ3','SQ4','R1','R2'}; s.tags={'g7','g12','g14','g15','g16','g17','g21'}; fem.draw=struct('s',s); fem.geom=geomcsg(fem); % Initialize mesh fem.mesh=meshinit(fem, ... 'hauto',5); % (Default values are not included) % Application mode 1 clear appl appl.mode.class = 'PerpendicularCurrents'; appl.module = 'ACDC'; appl.sshape = 2; appl.assignsuffix = '_emqa'; clear prop prop.analysis='transient'; appl.prop = prop; clear bnd bnd.type = {'A0','cont'}; bnd.ind = [1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1]; appl.bnd = bnd; clear equ equ.Jez = {0,0,'(1-flc2hs(t-0.2,0.1))*R','(flc2hs(t-0.2,0.1)-1)*R'}; equ.sigma = {'mat2_sigma','mat3_sigma','mat5_sigma','mat5_sigma'}; equ.epsilonr = {1,'mat3_epsilonr','mat5_epsilonr','mat5_epsilonr'}; equ.mur = {1,'mat3_MUR(normB_emqa[1/T])','mat5_mur','mat5_mur'}; equ.normfH = {'1/mu0_emqa*normB_emqa','mat3_HB(normB_emqa[1/T])[A/m]','1/mu0_emqa*normB_emqa', ... '1/mu0_emqa*normB_emqa'}; equ.ind = [1,2,3,4,2,3,4]; appl.equ = equ; fem.appl{1} = appl; fem.frame = {'ref'}; fem.border = 1; clear units; units.basesystem = 'SI'; fem.units = units; % Library materials clear lib lib.mat{1}.name='Iron'; lib.mat{1}.varname='mat1'; lib.mat{1}.variables.nu='0.29'; lib.mat{1}.variables.E='200e9[Pa]'; lib.mat{1}.variables.mur='4000'; lib.mat{1}.variables.sigma='1.12e7[S/m]'; lib.mat{1}.variables.epsilonr='1'; lib.mat{1}.variables.alpha='12.2e-6[1/K]'; lib.mat{1}.variables.C='440[J/(kg*K)]'; lib.mat{1}.variables.rho='7870[kg/m^3]'; lib.mat{1}.variables.k='76.2[W/(m*K)]'; lib.mat{2}.name='Air'; lib.mat{2}.varname='mat2'; lib.mat{2}.variables.nu0='nu0(T[1/K])[m^2/s]'; lib.mat{2}.variables.eta='eta(T[1/K])[Pa*s]'; lib.mat{2}.variables.gamma='1.4'; lib.mat{2}.variables.sigma='0[S/m]'; lib.mat{2}.variables.C='Cp(T[1/K])[J/(kg*K)]'; lib.mat{2}.variables.rho='rho(p[1/Pa],T[1/K])[kg/m^3]'; lib.mat{2}.variables.k='k(T[1/K])[W/(m*K)]'; lib.mat{2}.variables.cs='cs(T[1/K])[m/s]'; clear fcns fcns{1}.type='inline'; fcns{1}.name='cs(T)'; fcns{1}.expr='sqrt(1.4*287*T)'; fcns{1}.dexpr={'diff(sqrt(1.4*287*T),T)'}; fcns{2}.type='inline'; fcns{2}.name='rho(p,T)'; fcns{2}.expr='p*0.02897/8.314/T'; fcns{2}.dexpr={'diff(p*0.02897/8.314/T,p)','diff(p*0.02897/8.314/T,T)'}; fcns{3}.type='piecewise'; fcns{3}.name='Cp(T)'; fcns{3}.extmethod='const'; fcns{3}.subtype='poly'; fcns{3}.expr={{'0','1.04763657E+03','1','-3.72589265E-01','2', ... '9.45304214E-04','3','-6.02409443E-07','4','1.28589610E-10'}}; fcns{3}.intervals={'200','1600'}; fcns{4}.type='piecewise'; fcns{4}.name='eta(T)'; fcns{4}.extmethod='const'; fcns{4}.subtype='poly'; fcns{4}.expr={{'0','-8.38278000E-07','1','8.35717342E-08','2', ... '-7.69429583E-11','3','4.64372660E-14','4','-1.06585607E-17'}}; fcns{4}.intervals={'200','1600'}; fcns{5}.type='piecewise'; fcns{5}.name='nu0(T)'; fcns{5}.extmethod='const'; fcns{5}.subtype='poly'; fcns{5}.expr={{'0','-5.86912450E-06','1','5.01274491E-08','2', ... '7.50108343E-11','3','1.80336823E-15','4','-2.91688030E-18'}}; fcns{5}.intervals={'200','1600'}; fcns{6}.type='piecewise'; fcns{6}.name='k(T)'; fcns{6}.extmethod='const'; fcns{6}.subtype='poly'; fcns{6}.expr={{'0','-2.27583562E-03','1','1.15480022E-04','2', ... '-7.90252856E-08','3','4.11702505E-11','4','-7.43864331E-15'}}; fcns{6}.intervals={'200','1600'}; lib.mat{2}.functions = fcns; lib.mat{3}.name='Soft Iron (without losses)'; lib.mat{3}.varname='mat3'; lib.mat{3}.variables.normfB='BH(normH[m/A])[T]'; lib.mat{3}.variables.mur='MUR(normB[1/T])'; lib.mat{3}.variables.sigma='0[S/m]'; lib.mat{3}.variables.normfH='HB(normB[1/T])[A/m]'; lib.mat{3}.variables.epsilonr='1'; clear fcns fcns{1}.type='interp'; fcns{1}.name='MUR'; fcns{1}.method='linear'; fcns{1}.extmethod='const'; fcns{1}.x={'1','1.1','1.2','1.3','1.4','1.5','1.6','1.7','1.8','1.9', ... '2.0','2.1','2.2','2.3','2.4'}; fcns{1}.data={'1200','820','560','420','290','220','160','110','70','47', ... '26','15','10','7','6'}; fcns{2}.type='interp'; fcns{2}.name='HB'; fcns{2}.method='linear'; fcns{2}.extmethod='extrap'; fcns{2}.x={'0','1','1.1','1.2','1.3','1.4','1.5','1.6','1.7','1.8', ... '1.9','2.0','2.1','2.2','2.3','2.4'}; fcns{2}.data={'0','663.146','1067.5','1705.23','2463.11','3841.67', ... '5425.74','7957.75','12298.3','20462.8','32169.6','61213.4','111408', ... '175070','261469','318310'}; fcns{3}.type='interp'; fcns{3}.name='BH'; fcns{3}.method='linear'; fcns{3}.extmethod='extrap'; fcns{3}.x={'0','663.146','1067.5','1705.23','2463.11','3841.67', ... '5425.74','7957.75','12298.3','20462.8','32169.6','61213.4','111408', ... '175070','261469','318310'}; fcns{3}.data={'0','1','1.1','1.2','1.3','1.4','1.5','1.6','1.7','1.8', ... '1.9','2.0','2.1','2.2','2.3','2.4'}; lib.mat{3}.functions = fcns; lib.mat{4}.name='Copper'; lib.mat{4}.varname='mat4'; lib.mat{4}.variables.alphares='3.9e-3[1/K]'; lib.mat{4}.variables.mur='1'; lib.mat{4}.variables.sigma='5.998e7[S/m]'; lib.mat{4}.variables.epsilonr='1'; lib.mat{4}.variables.C='385[J/(kg*K)]'; lib.mat{4}.variables.epsilon='0.5'; lib.mat{4}.variables.res0='1.72e-8[ohm*m]'; lib.mat{4}.variables.rho='8700[kg/m^3]'; lib.mat{4}.variables.k='400[W/(m*K)]'; lib.mat{4}.variables.T0='273.15[K]'; lib.mat{5}.name='Silicon Carbide'; lib.mat{5}.varname='mat5'; lib.mat{5}.variables.mur='1'; lib.mat{5}.variables.sigma='1e3[S/m]'; lib.mat{5}.variables.epsilonr='10'; lib.mat{5}.variables.C='1200[J/(kg*K)]'; lib.mat{5}.variables.epsilon='0.5'; lib.mat{5}.variables.rho='3200[kg/m^3]'; lib.mat{5}.variables.k='450[W/(m*K)]*(300[K]/T)^0.75'; lib.matgroups{1}.name='Resistivity'; lib.matgroups{1}.variables={'alphares','T0','res0'}; lib.matgroups{1}.descr={'Temperature coefficient','Reference temperature','Resistivity at reference temperature'}; lib.matgroups{2}.name='Electromagnetic (AC/DC)'; lib.matgroups{2}.variables={'alphares','T0','res0','Br','normfH','fH','normfB','fB'}; lib.matgroups{2}.descr={'Temperature coefficient','Reference temperature','Resistivity at reference temperature','Remanent flux density','Nonlinear magnetic field, norm','Nonlinear magnetic field','Nonlinear magnetic flux density, norm','Nonlinear magnetic flux density'}; fem.lib = lib; % ODE Settings clear ode clear units; units.basesystem = 'SI'; ode.units = units; fem.ode=ode; % Multiphysics fem=multiphysics(fem); % Extend mesh fem.xmesh=meshextend(fem); % Solve problem fem.sol=femtime(fem, ... 'solcomp',{'Az'}, ... 'outcomp',{'Az','Azt'}, ... 'blocksize','auto', ... 'tlist',[0:0.1:1], ... 'tout','tlist'); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'tridata',{'normH_emqa','cont','internal','unit','A/m'}, ... 'trimap','jet(1024)', ... 'arrowdata',{'Hx_emqa','Hy_emqa'}, ... 'arrowxspacing',25, ... 'arrowyspacing',25, ... 'arrowtype','arrow', ... 'arrowstyle','normalized', ... 'arrowcolor',[1.0,0.0,0.0], ... 'solnum','end', ... 'title','Time=1 Surface: Magnetic field, norm [A/m] Arrow: Magnetic field', ... 'axis',[-2.1917248854858253,2.1917248854858244,-1.2348387608454447,1.2348387608454434]); % Plot solution postplot(fem, ... 'tridata',{'normH_emqa','cont','internal','unit','A/m'}, ... 'trimap','jet(1024)', ... 'arrowdata',{'Mx_emqa','My_emqa'}, ... 'arrowxspacing',25, ... 'arrowyspacing',25, ... 'arrowtype','arrow', ... 'arrowstyle','normalized', ... 'arrowcolor',[1.0,0.0,0.0], ... 'solnum','end', ... 'title','Time=1 Surface: Magnetic field, norm [A/m] Arrow: Magnetization', ... 'axis',[-2.1917248854858253,2.1917248854858244,-1.295624821604536,1.2956248216045347]); % Plot solution postplot(fem, ... 'tridata',{'normH_emqa','cont','internal','unit','A/m'}, ... 'trimap','jet(1024)', ... 'arrowdata',{'Mx_emqa','My_emqa'}, ... 'arrowxspacing',25, ... 'arrowyspacing',100, ... 'arrowtype','arrow', ... 'arrowstyle','normalized', ... 'arrowcolor',[1.0,0.0,0.0], ... 'solnum','end', ... 'title','Time=1 Surface: Magnetic field, norm [A/m] Arrow: Magnetization', ... 'axis',[-2.1917248854858253,2.1917248854858244,-1.295624821604536,1.2956248216045347]); % Plot solution postplot(fem, ... 'tridata',{'normH_emqa','cont','internal','unit','A/m'}, ... 'trimap','jet(1024)', ... 'arrowdata',{'Mx_emqa','My_emqa'}, ... 'arrowxspacing',25, ... 'arrowyspacing',100, ... 'arrowtype','arrow', ... 'arrowstyle','normalized', ... 'arrowcolor',[1.0,0.0,0.0], ... 'solnum','end', ... 'title','Time=1 Surface: Magnetic field, norm [A/m] Arrow: Magnetization', ... 'axis',[-2.1917248854858253,2.1917248854858244,-1.295624821604536,1.2956248216045347]); % Plot solution postplot(fem, ... 'tridata',{'normH_emqa','cont','internal','unit','A/m'}, ... 'trimap','jet(1024)', ... 'arrowdata',{'Mx_emqa','My_emqa'}, ... 'arrowxspacing',25, ... 'arrowyspacing',100, ... 'arrowtype','arrow', ... 'arrowstyle','normalized', ... 'arrowcolor',[1.0,0.0,0.0], ... 'solnum','end', ... 'title','Time=1 Surface: Magnetic field, norm [A/m] Arrow: Magnetization', ... 'axis',[-2.1917248854858253,2.1917248854858244,-1.295624821604536,1.2956248216045347]); % Plot solution postplot(fem, ... 'tridata',{'normH_emqa','cont','internal','unit','A/m'}, ... 'trimap','jet(1024)', ... 'arrowdata',{'Mx_emqa','My_emqa'}, ... 'arrowxspacing',25, ... 'arrowyspacing',100, ... 'arrowtype','arrow', ... 'arrowstyle','normalized', ... 'arrowcolor',[1.0,0.0,0.0], ... 'solnum',2, ... 'title','Time=0.1 Surface: Magnetic field, norm [A/m] Arrow: Magnetization', ... 'axis',[-2.1917248854858253,2.1917248854858244,-1.295624821604536,1.2956248216045347]); % Plot in cross-section or along domain postcrossplot(fem,0,[0.5;0.5], ... 'pointdata',{'normJ_emqa','unit','A/m^2'}, ... 'title','Total current density, norm [A/m^2]', ... 'axislabel',{'Time','Total current density',' norm [A/m^2]'}); % Plot in cross-section or along domain postcrossplot(fem,0,[0;0], ... 'pointdata',{'normH_emqa','unit','A/m'}, ... 'title','Magnetic field, norm [A/m]', ... 'axislabel',{'Time','Magnetic field',' norm [A/m]'}); % Plot in cross-section or along domain postcrossplot(fem,0,[-.5;0], ... 'pointdata',{'normM_emqa','unit','A/m'}, ... 'title','Magnetization, norm [A/m]', ... 'axislabel',{'Time','Magnetization',' norm [A/m]'}); % Initialize mesh fem.mesh=meshinit(fem, ... 'hauto',5); % (Default values are not included) % Application mode 1 clear appl appl.mode.class = 'PerpendicularCurrents'; appl.module = 'ACDC'; appl.sshape = 2; appl.assignsuffix = '_emqa'; clear prop prop.analysis='transient'; appl.prop = prop; clear bnd bnd.type = {'A0','cont'}; bnd.ind = [1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1]; appl.bnd = bnd; clear equ equ.magconstrel = {'mur','M','mur','mur'}; equ.Jez = {0,0,'(1-flc2hs(t-0.2,0.1))*R','(flc2hs(t-0.2,0.1)-1)*R'}; equ.sigma = {'mat2_sigma','mat3_sigma','mat5_sigma','mat5_sigma'}; equ.epsilonr = {1,'mat3_epsilonr','mat5_epsilonr','mat5_epsilonr'}; equ.mur = {1,'mat3_MUR(normB_emqa[1/T])','mat5_mur','mat5_mur'}; equ.normfH = {'1/mu0_emqa*normB_emqa','mat3_HB(normB_emqa[1/T])[A/m]','1/mu0_emqa*normB_emqa', ... '1/mu0_emqa*normB_emqa'}; equ.ind = [1,2,3,4,2,3,4]; appl.equ = equ; fem.appl{1} = appl; fem.frame = {'ref'}; fem.border = 1; clear units; units.basesystem = 'SI'; fem.units = units; % Library materials clear lib lib.mat{1}.name='Iron'; lib.mat{1}.varname='mat1'; lib.mat{1}.variables.nu='0.29'; lib.mat{1}.variables.E='200e9[Pa]'; lib.mat{1}.variables.mur='4000'; lib.mat{1}.variables.sigma='1.12e7[S/m]'; lib.mat{1}.variables.epsilonr='1'; lib.mat{1}.variables.alpha='12.2e-6[1/K]'; lib.mat{1}.variables.C='440[J/(kg*K)]'; lib.mat{1}.variables.rho='7870[kg/m^3]'; lib.mat{1}.variables.k='76.2[W/(m*K)]'; lib.mat{2}.name='Air'; lib.mat{2}.varname='mat2'; lib.mat{2}.variables.nu0='nu0(T[1/K])[m^2/s]'; lib.mat{2}.variables.eta='eta(T[1/K])[Pa*s]'; lib.mat{2}.variables.gamma='1.4'; lib.mat{2}.variables.sigma='0[S/m]'; lib.mat{2}.variables.C='Cp(T[1/K])[J/(kg*K)]'; lib.mat{2}.variables.rho='rho(p[1/Pa],T[1/K])[kg/m^3]'; lib.mat{2}.variables.k='k(T[1/K])[W/(m*K)]'; lib.mat{2}.variables.cs='cs(T[1/K])[m/s]'; clear fcns fcns{1}.type='inline'; fcns{1}.name='cs(T)'; fcns{1}.expr='sqrt(1.4*287*T)'; fcns{1}.dexpr={'diff(sqrt(1.4*287*T),T)'}; fcns{2}.type='inline'; fcns{2}.name='rho(p,T)'; fcns{2}.expr='p*0.02897/8.314/T'; fcns{2}.dexpr={'diff(p*0.02897/8.314/T,p)','diff(p*0.02897/8.314/T,T)'}; fcns{3}.type='piecewise'; fcns{3}.name='Cp(T)'; fcns{3}.extmethod='const'; fcns{3}.subtype='poly'; fcns{3}.expr={{'0','1.04763657E+03','1','-3.72589265E-01','2', ... '9.45304214E-04','3','-6.02409443E-07','4','1.28589610E-10'}}; fcns{3}.intervals={'200','1600'}; fcns{4}.type='piecewise'; fcns{4}.name='eta(T)'; fcns{4}.extmethod='const'; fcns{4}.subtype='poly'; fcns{4}.expr={{'0','-8.38278000E-07','1','8.35717342E-08','2', ... '-7.69429583E-11','3','4.64372660E-14','4','-1.06585607E-17'}}; fcns{4}.intervals={'200','1600'}; fcns{5}.type='piecewise'; fcns{5}.name='nu0(T)'; fcns{5}.extmethod='const'; fcns{5}.subtype='poly'; fcns{5}.expr={{'0','-5.86912450E-06','1','5.01274491E-08','2', ... '7.50108343E-11','3','1.80336823E-15','4','-2.91688030E-18'}}; fcns{5}.intervals={'200','1600'}; fcns{6}.type='piecewise'; fcns{6}.name='k(T)'; fcns{6}.extmethod='const'; fcns{6}.subtype='poly'; fcns{6}.expr={{'0','-2.27583562E-03','1','1.15480022E-04','2', ... '-7.90252856E-08','3','4.11702505E-11','4','-7.43864331E-15'}}; fcns{6}.intervals={'200','1600'}; lib.mat{2}.functions = fcns; lib.mat{3}.name='Soft Iron (without losses)'; lib.mat{3}.varname='mat3'; lib.mat{3}.variables.normfB='BH(normH[m/A])[T]'; lib.mat{3}.variables.mur='MUR(normB[1/T])'; lib.mat{3}.variables.sigma='0[S/m]'; lib.mat{3}.variables.normfH='HB(normB[1/T])[A/m]'; lib.mat{3}.variables.epsilonr='1'; clear fcns fcns{1}.type='interp'; fcns{1}.name='MUR'; fcns{1}.method='linear'; fcns{1}.extmethod='const'; fcns{1}.x={'1','1.1','1.2','1.3','1.4','1.5','1.6','1.7','1.8','1.9', ... '2.0','2.1','2.2','2.3','2.4'}; fcns{1}.data={'1200','820','560','420','290','220','160','110','70','47', ... '26','15','10','7','6'}; fcns{2}.type='interp'; fcns{2}.name='HB'; fcns{2}.method='linear'; fcns{2}.extmethod='extrap'; fcns{2}.x={'0','1','1.1','1.2','1.3','1.4','1.5','1.6','1.7','1.8', ... '1.9','2.0','2.1','2.2','2.3','2.4'}; fcns{2}.data={'0','663.146','1067.5','1705.23','2463.11','3841.67', ... '5425.74','7957.75','12298.3','20462.8','32169.6','61213.4','111408', ... '175070','261469','318310'}; fcns{3}.type='interp'; fcns{3}.name='BH'; fcns{3}.method='linear'; fcns{3}.extmethod='extrap'; fcns{3}.x={'0','663.146','1067.5','1705.23','2463.11','3841.67', ... '5425.74','7957.75','12298.3','20462.8','32169.6','61213.4','111408', ... '175070','261469','318310'}; fcns{3}.data={'0','1','1.1','1.2','1.3','1.4','1.5','1.6','1.7','1.8', ... '1.9','2.0','2.1','2.2','2.3','2.4'}; lib.mat{3}.functions = fcns; lib.mat{4}.name='Copper'; lib.mat{4}.varname='mat4'; lib.mat{4}.variables.alphares='3.9e-3[1/K]'; lib.mat{4}.variables.mur='1'; lib.mat{4}.variables.sigma='5.998e7[S/m]'; lib.mat{4}.variables.epsilonr='1'; lib.mat{4}.variables.C='385[J/(kg*K)]'; lib.mat{4}.variables.epsilon='0.5'; lib.mat{4}.variables.res0='1.72e-8[ohm*m]'; lib.mat{4}.variables.rho='8700[kg/m^3]'; lib.mat{4}.variables.k='400[W/(m*K)]'; lib.mat{4}.variables.T0='273.15[K]'; lib.mat{5}.name='Silicon Carbide'; lib.mat{5}.varname='mat5'; lib.mat{5}.variables.mur='1'; lib.mat{5}.variables.sigma='1e3[S/m]'; lib.mat{5}.variables.epsilonr='10'; lib.mat{5}.variables.C='1200[J/(kg*K)]'; lib.mat{5}.variables.epsilon='0.5'; lib.mat{5}.variables.rho='3200[kg/m^3]'; lib.mat{5}.variables.k='450[W/(m*K)]*(300[K]/T)^0.75'; lib.matgroups{1}.name='Resistivity'; lib.matgroups{1}.variables={'alphares','T0','res0'}; lib.matgroups{1}.descr={'Temperature coefficient','Reference temperature','Resistivity at reference temperature'}; lib.matgroups{2}.name='Electromagnetic (AC/DC)'; lib.matgroups{2}.variables={'alphares','T0','res0','Br','normfH','fH','normfB','fB'}; lib.matgroups{2}.descr={'Temperature coefficient','Reference temperature','Resistivity at reference temperature','Remanent flux density','Nonlinear magnetic field, norm','Nonlinear magnetic field','Nonlinear magnetic flux density, norm','Nonlinear magnetic flux density'}; fem.lib = lib; % ODE Settings clear ode clear units; units.basesystem = 'SI'; ode.units = units; fem.ode=ode; % Multiphysics fem=multiphysics(fem); % Extend mesh fem.xmesh=meshextend(fem); % Solve problem fem.sol=femtime(fem, ... 'solcomp',{'Az'}, ... 'outcomp',{'Az','Azt'}, ... 'blocksize','auto', ... 'tlist',[0:0.1:1], ... 'tout','tlist'); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'tridata',{'normH_emqa','cont','internal','unit','A/m'}, ... 'trimap','jet(1024)', ... 'arrowdata',{'Mx_emqa','My_emqa'}, ... 'arrowxspacing',25, ... 'arrowyspacing',100, ... 'arrowtype','arrow', ... 'arrowstyle','normalized', ... 'arrowcolor',[1.0,0.0,0.0], ... 'solnum','end', ... 'title','Time=1 Surface: Magnetic field, norm [A/m] Arrow: Magnetization', ... 'axis',[-2.1917248854858253,2.1917248854858244,-1.2348387608454447,1.2348387608454434]); % Plot in cross-section or along domain postcrossplot(fem,0,[-.5;0], ... 'pointdata',{'normM_emqa','unit','A/m'}, ... 'title','Magnetization, norm [A/m]', ... 'axislabel',{'Time','Magnetization',' norm [A/m]'}); % Plot solution postplot(fem, ... 'tridata',{'normH_emqa','cont','internal','unit','A/m'}, ... 'trimap','jet(1024)', ... 'arrowdata',{'Mx_emqa','My_emqa'}, ... 'arrowxspacing',25, ... 'arrowyspacing',100, ... 'arrowtype','arrow', ... 'arrowstyle','normalized', ... 'arrowcolor',[1.0,0.0,0.0], ... 'solnum',2, ... 'title','Time=0.1 Surface: Magnetic field, norm [A/m] Arrow: Magnetization', ... 'axis',[-2.1917248854858253,2.1917248854858244,-1.295624821604536,1.2956248216045347]); % Plot solution postplot(fem, ... 'tridata',{'normH_emqa','cont','internal','unit','A/m'}, ... 'trimap','jet(1024)', ... 'arrowdata',{'Mx_emqa','My_emqa'}, ... 'arrowxspacing',25, ... 'arrowyspacing',100, ... 'arrowtype','arrow', ... 'arrowstyle','normalized', ... 'arrowcolor',[1.0,0.0,0.0], ... 'solnum',2, ... 'title','Time=0.1 Surface: Magnetic field, norm [A/m] Arrow: Magnetization', ... 'axis',[-2.1917248854858253,2.1917248854858244,-1.2899130295915846,1.2899130295915833]); % Initialize mesh fem.mesh=meshinit(fem, ... 'hauto',5); % (Default values are not included) % Application mode 1 clear appl appl.mode.class = 'PerpendicularCurrents'; appl.module = 'ACDC'; appl.sshape = 2; appl.assignsuffix = '_emqa'; clear prop prop.analysis='transient'; appl.prop = prop; clear bnd bnd.type = {'A0','cont'}; bnd.ind = [1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1]; appl.bnd = bnd; clear equ equ.Jez = {0,0,'(1-flc2hs(t-0.2,0.1))*R','(flc2hs(t-0.2,0.1)-1)*R'}; equ.sigma = {'mat2_sigma','mat3_sigma','mat5_sigma','mat5_sigma'}; equ.epsilonr = {1,'mat3_epsilonr','mat5_epsilonr','mat5_epsilonr'}; equ.mur = {1,'mat3_MUR(normB_emqa[1/T])','mat5_mur','mat5_mur'}; equ.normfH = {'1/mu0_emqa*normB_emqa','mat3_HB(normB_emqa[1/T])[A/m]','1/mu0_emqa*normB_emqa', ... '1/mu0_emqa*normB_emqa'}; equ.ind = [1,2,3,4,2,3,4]; appl.equ = equ; fem.appl{1} = appl; fem.frame = {'ref'}; fem.border = 1; clear units; units.basesystem = 'SI'; fem.units = units; % Library materials clear lib lib.mat{1}.name='Iron'; lib.mat{1}.varname='mat1'; lib.mat{1}.variables.nu='0.29'; lib.mat{1}.variables.E='200e9[Pa]'; lib.mat{1}.variables.mur='4000'; lib.mat{1}.variables.sigma='1.12e7[S/m]'; lib.mat{1}.variables.epsilonr='1'; lib.mat{1}.variables.alpha='12.2e-6[1/K]'; lib.mat{1}.variables.C='440[J/(kg*K)]'; lib.mat{1}.variables.rho='7870[kg/m^3]'; lib.mat{1}.variables.k='76.2[W/(m*K)]'; lib.mat{2}.name='Air'; lib.mat{2}.varname='mat2'; lib.mat{2}.variables.nu0='nu0(T[1/K])[m^2/s]'; lib.mat{2}.variables.eta='eta(T[1/K])[Pa*s]'; lib.mat{2}.variables.gamma='1.4'; lib.mat{2}.variables.sigma='0[S/m]'; lib.mat{2}.variables.C='Cp(T[1/K])[J/(kg*K)]'; lib.mat{2}.variables.rho='rho(p[1/Pa],T[1/K])[kg/m^3]'; lib.mat{2}.variables.k='k(T[1/K])[W/(m*K)]'; lib.mat{2}.variables.cs='cs(T[1/K])[m/s]'; clear fcns fcns{1}.type='inline'; fcns{1}.name='cs(T)'; fcns{1}.expr='sqrt(1.4*287*T)'; fcns{1}.dexpr={'diff(sqrt(1.4*287*T),T)'}; fcns{2}.type='inline'; fcns{2}.name='rho(p,T)'; fcns{2}.expr='p*0.02897/8.314/T'; fcns{2}.dexpr={'diff(p*0.02897/8.314/T,p)','diff(p*0.02897/8.314/T,T)'}; fcns{3}.type='piecewise'; fcns{3}.name='Cp(T)'; fcntLs{3}.extmethod='const'; fcns{3}.subtype='poly'; fcns{3}.expr={{'0','1.04763657E+03','1','-3.72589265E-01','2', ... '9.45304214E-04','3','-6.02409443E-07','4','1.28589610E-10'}}; fcns{3}.intervals={'200','1600'}; fcns{4}.type='piecewise'; fcns{4}.name='eta(T)'; fcns{4}.extmethod='const'; fcns{4}.subtype='poly'; fcns{4}.expr={{'0','-8.38278000E-07','1','8.35717342E-08','2', ... '-7.69429583E-11','3','4.64372660E-14','4','-1.06585607E-17'}}; fcns{4}.intervals={'200','1600'}; fcns{5}.type='piecewise'; fcns{5}.name='nu0(T)'; fcns{5}.extmethod='const'; fcns{5}.subtype='poly'; fcns{5}.expr={{'0','-5.86912450E-06','1','5.01274491E-08','2', ... '7.50108343E-11','3','1.80336823E-15','4','-2.91688030E-18'}}; fcns{5}.intervals={'200','1600'}; fcns{6}.type='piecewise'; fcns{6}.name='k(T)'; fcns{6}.extmethod='const'; fcns{6}.subtype='poly'; fcns{6}.expr={{'0','-2.27583562E-03','1','1.15480022E-04','2', ... '-7.90252856E-08','3','4.11702505E-11','4','-7.43864331E-15'}}; fcns{6}.intervals={'200','1600'}; lib.mat{2}.functions = fcns; lib.mat{3}.name='Soft Iron (without losses)'; lib.mat{3}.varname='mat3'; lib.mat{3}.variables.normfB='BH(normH[m/A])[T]'; lib.mat{3}.variables.mur='MUR(normB[1/T])'; lib.mat{3}.variables.sigma='0[S/m]'; lib.mat{3}.variables.normfH='HB(normB[1/T])[A/m]'; lib.mat{3}.variables.epsilonr='1'; clear fcns fcns{1}.type='interp'; fcns{1}.name='MUR'; fcns{1}.method='linear'; fcns{1}.extmethod='const'; fcns{1}.x={'1','1.1','1.2','1.3','1.4','1.5','1.6','1.7','1.8','1.9', ... '2.0','2.1','2.2','2.3','2.4'}; fcns{1}.data={'1200','820','560','420','290','220','160','110','70','47', ... '26','15','10','7','6'}; fcns{2}.type='interp'; fcns{2}.name='HB'; fcns{2}.method='linear'; fcns{2}.extmethod='extrap'; fcns{2}.x={'0','1','1.1','1.2','1.3','1.4','1.5','1.6','1.7','1.8', ... '1.9','2.0','2.1','2.2','2.3','2.4'}; fcns{2}.data={'0','663.146','1067.5','1705.23','2463.11','3841.67', ... '5425.74','7957.75','12298.3','20462.8','32169.6','61213.4','111408', ... '175070','261469','318310'}; fcns{3}.type='interp'; fcns{3}.name='BH'; fcns{3}.method='linear'; fcns{3}.extmethod='extrap'; fcns{3}.x={'0','663.146','1067.5','1705.23','2463.11','3841.67', ... '5425.74','7957.75','12298.3','20462.8','32169.6','61213.4','111408', ... '175070','261469','318310'}; fcns{3}.data={'0','1','1.1','1.2','1.3','1.4','1.5','1.6','1.7','1.8', ... '1.9','2.0','2.1','2.2','2.3','2.4'}; lib.mat{3}.functions = fcns; lib.mat{4}.name='Copper'; lib.mat{4}.varname='mat4'; lib.mat{4}.variables.alphares='3.9e-3[1/K]'; lib.mat{4}.variables.mur='1'; lib.mat{4}.variables.sigma='5.998e7[S/m]'; lib.mat{4}.variables.epsilonr='1'; lib.mat{4}.variables.C='385[J/(kg*K)]'; lib.mat{4}.variables.epsilon='0.5'; lib.mat{4}.variables.res0='1.72e-8[ohm*m]'; lib.mat{4}.variables.rho='8700[kg/m^3]'; lib.mat{4}.variables.k='400[W/(m*K)]'; lib.mat{4}.variables.T0='273.15[K]'; lib.mat{5}.name='Silicon Carbide'; lib.mat{5}.varname='mat5'; lib.mat{5}.variables.mur='1'; lib.mat{5}.variables.sigma='1e3[S/m]'; lib.mat{5}.variables.epsilonr='10'; lib.mat{5}.variables.C='1200[J/(kg*K)]'; lib.mat{5}.variables.epsilon='0.5'; lib.mat{5}.variables.rho='3200[kg/m^3]'; lib.mat{5}.variables.k='450[W/(m*K)]*(300[K]/T)^0.75'; lib.matgroups{1}.name='Resistivity'; lib.matgroups{1}.variables={'alphares','T0','res0'}; lib.matgroups{1}.descr={'Temperature coefficient','Reference temperature','Resistivity at reference temperature'}; lib.matgroups{2}.name='Electromagnetic (AC/DC)'; lib.matgroups{2}.variables={'alphares','T0','res0','Br','normfH','fH','normfB','fB'}; lib.matgroups{2}.descr={'Temperature coefficient','Reference temperature','Resistivity at reference temperature','Remanent flux density','Nonlinear magnetic field, norm','Nonlinear magnetic field','Nonlinear magnetic flux density, norm','Nonlinear magnetic flux density'}; fem.lib = lib; % ODE Settings clear ode clear units; units.basesystem = 'SI'; ode.units = units; fem.ode=ode; % Multiphysics fem=multiphysics(fem); % Extend mesh fem.xmesh=meshextend(fem); % Solve problem fem.sol=femtime(fem, ... 'solcomp',{'Az'}, ... 'outcomp',{'Az','Azt'}, ... 'blocksize','auto', ... 'tlist',[0:0.1:1], ... 'tout','tlist'); % Save current fem structure for restart purposes fem0=fem; % Plot solution postplot(fem, ... 'tridata',{'normH_emqa','cont','internal','unit','A/m'}, ... 'trimap','jet(1024)', ... 'arrowdata',{'Mx_emqa','My_emqa'}, ... 'arrowxspacing',25, ... 'arrowyspacing',100, ... 'arrowtype','arrow', ... 'arrowstyle','normalized', ... 'arrowcolor',[1.0,0.0,0.0], ... 'solnum','end', ... 'title','Time=1 Surface: Magnetic field, norm [A/m] Arrow: Magnetization', ... 'axis',[-2.1917248854858253,2.1917248854858244,-1.2348387608454447,1.2348387608454434]); % Plot in cross-section or along domain postcrossplot(fem,0,[-.5;0], ... 'pointdata',{'normM_emqa','unit','A/m'}, ... 'title','Magnetization, norm [A/m]', ... 'axislabel',{'Time','Magnetization',' norm [A/m]'}); % Plot in cross-section or along domain postcrossplot(fem,0,[-.5;0], ... 'pointdata',{'normM_emqa','unit','A/m'}, ... 'title','Magnetization, norm [A/m]', ... 'axislabel',{'Time','Magnetization',' norm [A/m]'}); % Plot in cross-section or along domain postcrossplot(fem,1,[-1 1;0 0], ... 'lindata','normM_emqa', ... 'linxdata','x', ... 'title','Magnetization, norm [A/m]', ... 'axislabel',{'x','Magnetization',' norm [A/m]'}); % Plot in cross-section or along domain postcrossplot(fem,0,[0;0], ... 'pointdata',{'normH_emqa','unit','A/m'}, ... 'title','Magnetic field, norm [A/m]', ... 'axislabel',{'Time','Magnetic field',' norm [A/m]'}); uq~ t�% COMSOL Multiphysics Model M-file % Generated by COMSOL 3.5 (COMSOL 3.5.0.494, $Date: 2008/09/19 16:09:48 $) flclear fem % COMSOL version clear vrsn vrsn.name = 'COMSOL 3.5'; vrsn.ext = ''; vrsn.major = 0; vrsn.build = 494; vrsn.rcs = '$Name: $'; vrsn.date = '$Date: 2008/09/19 16:09:48 $'; fem.version = vrsn; % Geometry g1=square2('0.1','base','center','pos',{'-0.5','-0.5'},'rot','0'); % Analyzed geometry clear s s.objs={g1}; s.name={'SQ1'}; s.tags={'g1'}; fem.draw=struct('s',s); fem.geom=geomcsg(fem); g2=square2('0.1','base','center','pos',{'-0.5','0.5'},'rot','0'); g3=square2('0.1','base','center','pos',{'0.5','0.5'},'rot','0'); g4=square2('0.1','base','center','pos',{'0.5','-0.5'},'rot','0'); % Analyzed geometry clear s s.objs={g1,g2,g3,g4}; s.name={'SQ1','SQ2','SQ3','SQ4'}; s.tags={'g1','g2','g3','g4'}; fem.draw=struct('s',s); fem.geom=geomcsg(fem); g5=square2('1','base','center','pos',{'0','0'},'rot','0'); g6=square2('2','base','center','pos',{'0','0'},'rot','0'); g7=square2('4','base','center','pos',{'0','0'},'rot','0'); % Analyzed geometry clear s s.objs={g1,g2,g3,g4,g7}; s.name={'SQ1','SQ2','SQ3','SQ4','SQ5'}; s.tags={'g1','g2','g3','g4','g7'}; fem.draw=struct('s',s); fem.geom=geomcsg(fem); g8=rect2('0.2','0.2','base','corner','pos',{'0','0'},'rot','0'); g9=rect2('0.2','0.2','base','center','pos',{'0','0'},'rot','0'); % Analyzed geometry clear s s.objs={g1,g2,g3,g4,g7,g9}; s.name={'SQ1','SQ2','SQ3','SQ4','SQ5','R1'}; s.tags={'g1','g2','g3','g4','g7','g9'}; fem.draw=struct('s',s); fem.geom=geomcsg(fem); g10=rect2(0.8,0.2,'base','center','pos',[0,0]); % Analyzed geometry clear s s.objs={g1,g2,g3,g4,g7,g10}; s.name={'SQ1','SQ2','SQ3','SQ4','SQ5','R1'}; s.tags={'g1','g2','g3','g4','g7','g10'}; fem.draw=struct('s',s); fem.geom=geomcsg(fem); % COMSOL Multiphysics Model M-file % Generated by COMSOL 3.5 (COMSOL 3.5.0.494, $Date: 2008/09/19 16:09:48 $) % Geometry g10=move(g10,[-0.6000000000000001,0]); [g5]=geomcopy({g10}); [g6]=geomcopy({g5}); g6=move(g6,[0.4,0]); g6=move(g6,[0.6000000000000001,0]); g6=move(g6,[0.20000000000000007,0]); % Analyzed geometry clear s s.objs={g10,g7,g2,g1,g4,g3,g6}; s.name={'R1','SQ5','SQ2','SQ1','SQ4','SQ3','R2'}; s.tags={'g10','g7','g2','g1','g4','g3','g6'}; fem.draw=struct('s',s); fem.geom=geomcsg(fem); % COMSOL Multiphysics Model M-file % Generated by COMSOL 3.5 (COMSOL 3.5.0.494, $Date: 2008/09/19 16:09:48 $) % Geometry g5=rect2(1.1,0.2,'base','center','pos',[-0.6,0]); g8=rect2(1.1,0.2,'base','center','pos',[0.6,0]); % Analyzed geometry clear s s.objs={g7,g2,g1,g4,g3,g5,g8}; s.name={'SQ5','SQ2','SQ1','SQ4','SQ3','R1','R2'}; s.tags={'g7','g2','g1','g4','g3','g5','g8'}; fem.draw=struct('s',s); fem.geom=geomcsg(fem); % COMSOL Multiphysics Model M-file % Generated by COMSOL 3.5 (COMSOL 3.5.0.494, $Date: 2008/09/19 16:09:48 $) % Geometry [g10]=geomcopy({g5}); [g11]=geomcopy({g10}); g11=move(g11,[0.045,0]); [g12]=geomcopy({g8}); [g13]=geomcopy({g12}); g13=move(g13,[-0.045,0]); % Analyzed geometry clear s s.objs={g7,g2,g1,g4,g3,g11,g13}; s.name={'SQ5','SQ2','SQ1','SQ4','SQ3','R1','R2'}; s.tags={'g7','g2','g1','g4','g3','g11','g13'}; fem.draw=struct('s',s); fem.geom=geomcsg(fem); % COMSOL Multiphysics Model M-file % Generated by COMSOL 3.5 (COMSOL 3.5.0.494, $Date: 2008/09/19 16:09:48 $) % Constants fem.const = {'R','10000'}; % COMSOL Multiphysics Model M-file % Generated by COMSOL 3.5 (COMSOL 3.5.0.494, $Date: 2008/09/19 16:09:48 $) % Constants fem.const = {'R','1'}; % COMSOL Multiphysics Model M-file % Generated by COMSOL 3.5 (COMSOL 3.5.0.494, $Date: 2008/09/19 16:09:48 $) % Geometry g7=move(g7,[0,0.10000000000000009]); g11=move(g11,[0,0.10000000000000009]); g2=move(g2,[0,0.10000000000000009]); g1=move(g1,[0,0.10000000000000009]); g13=move(g13,[0,0.10000000000000009]); g4=move(g4,[0,0.10000000000000009]); g3=move(g3,[0,0.10000000000000009]); % Analyzed geometry clear s s.objs={g7,g11,g2,g1,g13,g4,g3}; s.name={'SQ5','R1','SQ2','SQ1','R2','SQ4','SQ3'}; s.tags={'g7','g11','g2','g1','g13','g4','g3'}; fem.draw=struct('s',s); fem.geom=geomcsg(fem); % Analyzed geometry clear s s.objs={g7,g2,g1,g4,g3}; s.name={'SQ5','SQ2','SQ1','SQ4','SQ3'}; s.tags={'g7','g2','g1','g4','g3'}; fem.draw=struct('s',s); fem.geom=geomcsg(fem); g5=rect2('0.4','0.1','base','center','pos',{'-0.25','0'},'rot','0'); [g6,g8,g9,g10]=geomcopy({g2,g1,g4,g3}); [g12,g14,g15,g16]=geomcopy({g6,g8,g9,g10}); g12=move(g12,[0,-0.1]); g14=move(g14,[0,-0.1]); g15=move(g15,[0,-0.1]); g16=move(g16,[0,-0.1]); % Analyzed geometry clear s s.objs={g7,g12,g14,g15,g16}; s.name={'SQ5','SQ1','SQ2','SQ3','SQ4'}; s.tags={'g7','g12','g14','g15','g16'}; fem.draw=struct('s',s); fem.geom=geomcsg(fem); g17=rect2('1','0.1','base','center','pos',{'-0.55','0'},'rot','0'); [g18]=geomcopy({g17}); [g19]=geomcopy({g18}); g19=move(g19,[1,0]); [g20]=geomcopy({g19}); [g21]=geomcopy({g20}); g21=move(g21,[0.1,0]); % Analyzed geometry clear s s.objs={g7,g12,g14,g15,g16,g17,g21}; s.name={'SQ5','SQ1','SQ2','SQ3','SQ4','R1','R2'}; s.tags={'g7','g12','g14','g15','g16','g17','g21'}; fem.draw=struct('s',s); fem.geom=geomcsg(fem); tclear mfile clear vrsn vrsn.name = 'COMSOL 3.5'; vrsn.ext = ''; vrsn.major = 0; vrsn.build = 494; vrsn.rcs = '$Name: $'; vrsn.date = '$Date: 2008/09/19 16:09:48 $'; mfile.version=vrsn; mfile.fem='fem'; mfile.stored={'fem0','fem1'}; mfile.tags={}; mfile.types={}; x

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