Test c3d93 Description sheet
Test name
c3d93
Calculation type
3D SCALAR POTENTIAL COMPUTATION OF MAGNETIC FIELD
Non Linear Material.
2 Scalar potentials method (see Trowbridge - Simkin)
Finite element type
CUB8 or CU20
Topic
A circular coil of rectangular cross section is embeded in an iron box.
Goal
Calculate scalar potential and field in the cavity.
Reference
Analytical solution.
Version
97' customer version
Model description
Soft iron curve for B(H).
Test c3d93 Results
CASTEM FIGURES
**************************************************************
* 3D MAGNETIC FIELD COMPUTATION 2 POTENTIALS METHOD
*
* REDUCED POTENTIAL (VOLUME CONTAINING INDUCTORS)
* TOTAL POTENTIAL (VOLUME WHITHOUT CURRENTS )
*
**************************************************************
option echo 1 ;
TYPEL = 2 ;
GRAPH = N ;
si ( ega typel 2 ) ;
OPTION DIME 2 ELEM QUA8 COUL VERT echo 0 ;
sinon ;
OPTION DIME 2 ELEM QUA4 COUL VERT echo 0 ;
finsi ;
*---------------------------MESH -----------------------------------
R1 =20. ; R2= 25. ; R3= 27. ; R4= 29. ; R5=39.;R6 = 130.;
Z1= 2.5; Z2= 5. ; Z3= 20. ; Z4= 130.;Z31=30.;Z32=50.;
DI1= 1.; DI2=5.;DI3=60. ;DI4= 10.;NET2= 6;
DENS DI1 ;
OZ3= 0. Z3; OZ2= 0. Z2;OZ1= 0. Z1;OZ4=0. Z4;
OO= 0. 0.;R0Z0= DI1 0 ;
R1Z0= R1 0. ;R2Z0= R2 0. ;R3Z0 = R3 0. ;R4Z0 = R4 0.;
R0Z2= DI1 Z2 ; R4Z2 = R4 Z2 ;
DENS DI2 ;
R5Z0= R5 0. ;R5Z3= R5 Z3 ;R0Z3 =DI2 Z3 ;OZ3 = 0. Z3 ;
DENS DI3 ;
R6Z0=R6 0.; R6Z4=R6 Z4 ;
DENS 10 ;
R2Z3= R2 Z3 ; R1Z3= R1 Z3; R4Z1 = R4 Z1;
R3Z1= R3 Z1 ;
DENSITE DI4 ;
R0Z4 = DI4 Z4 ; OZ4 = 0. Z4 ;
NTRA= 1;
FLAN1 =( D OO R0Z0 D R1Z0 ) TRAN DINI DI1 DFIN DI1 ( OZ1 MOINS OO )
TRAN DINI DI1 DFIN DI1 ( OZ2 MOINS OZ1) COUL VERT ;
BOBI =( D R1Z0 R2Z0 ) TRAN DINI DI1 DFIN DI1 ( OZ1 MOINS OO )
COUL BLEU ;
FLAN2 =(INVE( BOBI COTE 3)) TRAN DINI DI1 DFIN DI1
( OZ2 MOINS OZ1) COUL VERT ;
FLAN3 =( D R2Z0 R3Z0 ) TRAN DINI DI1 DFIN DI1 ( OZ1 MOINS OO )
TRAN DINI DI1 DFIN DI1 ( OZ2 MOINS OZ1) COUL VERT ;
FLAN4 =( D R3Z0 R4Z0 ) TRAN DINI DI1 DFIN DI1 ( OZ1 MOINS OO )
TRAN DINI DI1 DFIN DI1 ( OZ2 MOINS OZ1) COUL VERT ;
FER = (D OZ2 R0Z2 D R4Z2 D 6 R4Z0 D R5Z0 D R5Z3 D R0Z3 D OZ3 D OZ2 )
SURF PLANE COUL ROUG ;
FLAN5 = ( D R5Z0 R5Z3 D R6Z4 D R6Z0 D R5Z0 ) SURF PLANE ;
*
FLAN6 =( D R0Z3 R5Z3 D R6Z4 D R0Z4 D R0Z3 ) SURF PLANE
COUL VERT ;
TUB6 = (D OZ3 R0Z3 D R0Z4 D OZ4 D OZ3) SURF PLANE COUL VERT ;
AIREXT =( FLAN6 ET TUB6 ET FLAN5 ) coul blan ;
AIRIN =(FLAN1 ET FLAN2 ET FLAN3 ET BOBI ET FLAN4) coul vert ;
TFLAN = AIRIN ET FER ET AIREXT ;ELIM .1 TFLAN ;
PTAX = TFLAN POINT DROITE OO ( 0 1. ) .01 ;
TU1 = TFLAN ELEM APPU LARG PTAX ;
TOUT = DIFF TFLAN TU1 ;
*
C1 = (TOUT CONT ) COMPRIS R0Z4 R0Z0 ;
C2 = C1 PROJETER (1 0 ) DROITE OO OZ4 ;
OZ4 = C2 POINT PROCHE OZ4 ;
OO = C2 POINT PROCHE OO ;
TU1 = DALLER C1 ( D 1 R0Z0 OO ) C2 (D OZ4 R0Z4 ) PLAN ;
TUA = (COOR 2 TU1) POINT SUPER Z3 ;
TUA = (TU1 ELEM APPU LARG TUA ) COUL BLAN ;
TUB = (COOR 2 TU1) POINT INFER Z2 ;
TUB= (TU1 ELEM APPU LARG TUB ) COUL VERT ;
TUF = DIFF TU1 ( TUA ET TUB ) COUL ROUG ;
AIRIN = (TOUT ELEM VERT ) ET TUB ;
FER = (TOUT ELEM ROUG ) ET TUF ;
AIREXT = ( TOUT ELEM BLAN) ET TUA ;
* TRAC (AIRIN ET FER ET AIREXT ) FACE ;
*-----------
*------------------ SHIFT TO 3D --------------------------------
*------------
OPTION ELEM CUB8 ;
SI ( EGA TYPEL 2 )
OPTION DIME 3 ELEM CU20 ;
FINSI ;
ANG = 20. ;
*
*------------- DEFINITION OF THE 2 DOMAINS -----------
*------ REDUCED POTENTIAL VOLUME --------------------------
DPHI = AIRIN VOLU 1 ROTA ANG (0 0 0 ) (0 1 0 ) ;
**------ TOTAL POTENTIAL VOLUME --------------------------
DPSI = (AIREXT ET FER) VOLU 1 ROTA ANG (0 0 0 ) (0 1 0 ) ;
*
ELIM .001 DPHI ; DPHI = REGE DPHI ;
ELIM .001 DPSI ; DPSI = REGE DPSI ;
ELIM .001 ( DPHI ET DPSI) ;
*---- ---------SEPARATION SURFACE IDENTIFICATION -------------
* ---------- BELONGS TO REDUCED POTENTIAL VOLUME ---------------
SEP_PHI = INTE ( DPSI ENVEL ) ( DPHI ENVEL ) ;
*------------- SPLITTING OF THE 2 DOMAINS ------------------
DPSI = DPSI PLUS ( 0 0 0 ) ;
SEP_PSI = SEP_PHI PLUS ( 0 0 0 ) ; ELIM .01 DPSI SEP_PSI ;
*--------------------IRON-------------------------------------
DFER = DPSI ELEM ROUG ;
*
VOL1 = DPHI ET DPSI ;
DAIR = DPSI ELEM BLAN ;
AA = DPHI POINT PLAN (0 0 0 ) ( 10 0 0 ) (0 0 10 ) .00001 ;
AB =( DPHI ENVEL ) ELEM APPU STRIC AA ;
AA = (AB ENVEL ) POINT DROITE (0 0 0 ) ( 10 0 0 ) .00001 ;
AA = ( (AB CONTOUR ) ELEM APPU STRIC AA );
deplacer vol1 tourner 90 ( 0 0 0 ) ( 1 0 0 ) ;
*
ORIG= SEP_PHI POINT PROCHE (29. 0 0 ) ;
BANTI= SEP_PHI POINT PLAN (0. 0. 0.) (10. 0. 0.) (0. 10. 0.) .1 ;
geomed = (dpsi et dphi ) point plan (0 0 0) ( 1 0 0) (0 1 0 ) .1 ;
MU0 = 4. * PI * 1.E-4 ;
RINT = 20. ;REXT =25. ; HAUT = 5. ; J = 800. ;
C1 = 0. 0. 0. ; ZP1 = 20. 0. 0. ;ZP2 = 0. 20. 0. ;
E = Z1 * 4 ;
UNIT = M ;
si ( ega UNIT M) ;
deplacer vol1 homo .001 (0. 0. 0.) ;
MU0 = 4. * PI * 1.E-7 ;
RINT = RINT/1000; REXT = REXT/1000 ; HAUT = HAUT/1000 ;
ZP1 = ZP1/1000;ZP2 = ZP2 / 1000 ;J = J*1.E6 ;
E = E /1000 ;
finsi ;
option echo 1 ;
*-------
*-- BIOT and SAVART COMPUTATION of Hs ON REDUCED POTENTIAL DOMAIN
*-------
BS = BIOT SEP_PHI CERC C1 ZP1 ZP2 RINT REXT HAUT J MU0 ;
HS = BS / MU0 ;
SI (NEG GRAPH 'N') ;
OEIL = 1000 1000 500 ;
TITRE ' HS ON SEPARATION SURFACE ' ;
VVVV = VECTEUR BS 1.e-3 'BX' 'BY' 'BZ' ROUG ;
TRAC OEIL SEP_PHI VVVV ;
option donn 5 ;
FINSI ;
*---------------- FILLING OF A TABLE -----------------------------
*-in this computation there is only one isotropic material but it
* is shown how to coope with multi-material (even orthotropic )
*------------------------------------------------------------------
TABB= TABLE ;
*
FER1 = DFER ELEM CU20 ;
FER2 = DFER ELEM PR15 ;
*
KEVOL1 = H_B MU0 ;
KEVOL2 = H_B MU0 ;
OBFER1 = FER1 MODE THERMIQUE ISOTROPE ;
OBFER2 = FER2 MODE THERMIQUE ORTHOTROPE ;
TABDEF = TABLE ;
*----------------- isotropic material -----------------
STN = TABLE ;
STN.'EV1' = KEVOL1 ;
TABDEF.OBFER1 = STN ;
*------------- orthotropic material -------------------
STN = TABLE ;
DI1 = (0 1 0 ) ;DI2 = (1 0 1 ) ;
STN.'EV1' = KEVOL1 ;STN.'DIR1' = DI1 ;
STN.'EV2' = KEVOL2 ;STN.'DIR2' = DI2 ;
TABDEF.OBFER2 = STN ;
TABB.'TABNUSEC'= TABDEF;
*----------------------------------------------------------------
TABB.'BIOT'=HS ;
*----------------- REDUCED POTENTIAL AREA ----------------
*---
TABB.'DPHI' = DPHI ;
imet = 0 ;
si (ega imet 1 ) ;
MOD1 = DPHI MODE THERMIQUE ISOTROPE ;
MAT1 = MATE MOD1 'K' MU0 ;
RIGC1 = CONDUC MOD1 MAT1 ;
TABB.'RIGCON' = RIGC1 ;
finsi ;
*
TABB.'SEPPHI' = SEP_PHI ;
TABB.'ORIG' = ORIG ;
TABB.'MUAIR' = MU0;
*
*------------------- TOTAL POTENTIAL AREA --------------------
*---------
TABB.'DPSI' = DPSI ;
TABB.'AIRPSI' = DPSI ELEM BLAN ;
si ( ega imet 1 ) ;
MOD2 = DAIR MODE THERMIQUE ISOTROPE ;
MAT2 = MATE MOD2 'K' MU0 ;
RIGC2 = CONDUC MOD2 MAT2 ;
TABB.'RIGCPSI' = RIGC2 ;
finsi ;
* TABB.'SEP_PSI' = SEP_PSI ;
*------------------ GENERAL BOUBDARY CONDITIONS ---------
TABB.'BLOQUE' = BLOQUER 'T' GEOMED ;
*
*------ BOUNDARY CONDITION LINKED TO POTENTIAL JUMP ------------
*
TABA = TABLE ;
STN = TABLE ;TABA.1 = STN ;
STN.'LGEO' = BANTI ;STN.'MTYP' = 'TBLOQ' ;
TABB.'POTSYM'= TABA ;
TABB.ISTEP = 1 ;
*-------------------- FIRST STEP POTENTIALS COMPUTATION ----------
POT_SCAL TABB 'SOLIN';
*-------------------------------------------------------------------
SOL1= TABB.'POTENTIEL';
PREF= 0. 0. 0. ;
*----------- FIELD COMPUTATION (B) -----------------------
OBJM= MODL DPHI THERMIQUE ISOTROPE ;
BA= CHAN CHPO ( GRAD OBJM SOL1 ) OBJM ;
BA= BA * -1. * MU0 ;
BM= EXTR BA 'T,Z' OO ;
option echo 0 ;
SAUTER 5 LIGNES ;
MESS '***********************************************************';
MESS ' CIRCULAR COIL INTERNAL RADIUS' RINT 'mm *';
MESS '* CROSS SECTION ' ( REXT - RINT) '*' HAUT 'mm2';
MESS '* CURRENT DENSITY ' J 'A/mm2 *';
MESS '***********************************************************';
BS = BIOT AA CERC C1 ZP1 ZP2 RINT REXT HAUT J MU0 ;
MESS '* INDUCTION ON AXIS WITHOUT IRON (BIOT SAVART )';
BS0= EXTR BS 'BZ' OO ;
MESS '**************************************************************';
MESS '* AMPERE mufer >> muo ALL AMPERE*TURNS IN THE GAP ';
MESS '* GAP = ' E 'mm ';
MESS '* J * EP * HAUT = B/ MU0 * e ';
MESS '**************************************************************';
BTH = MU0 * J * (REXT - RINT ) * HAUT / E ; BCAL = BM + BS0 ;
MESS '**************************************************************';
MESS ' BIOT ET SAVART ' BS0 ;
MESS ' TOTAL B on AXIS ( z=0 ) EXPECTED ' BTH ;
MESS ' COMPUTED ' BCAL ;
*******************************************************************
SI (NEG GRAPH 'N' ) ;
TABLEG= TABLE ;TATT = TABLE ;
TABLEG.1 = 'MARQ CROI' ;TATT.1= 'B_COIL' ;
TABLEG.2 = 'MARQ PLUS' ;TATT.2= 'B_IRON' ;
TABLEG.3 = 'MARQ CARR' ;TATT.3= 'B_TOTAL ' ;
TABLEG.TITRE = TATT ;
BRBIO = ( EXCO BS 'BZ') NOMC 'SCAL' ;
BMRAY = EXCO (REDU BA AA) 'T,Z';
EVBI = EVOL ROUG CHPO BRBIO 'SCAL' AA ;
EVBM = EVOL VERT CHPO BMRAY 'SCAL' AA ;
EVBT = EVOL TURQ CHPO (BRBIO + BMRAY ) 'SCAL' AA ;
TITRE ' BZ(R) for Z=0 ' ;
DESS (EVBI ET EVBM ET EVBT ) LEGE TABLEG TITY TESLAS ;
FINSI ;
RAP = ABS ((BCAL - BTH ) / BTH );
SI ( RAP > .01 ) ; ERREUR 5 ; FINSI ;
*-----------------------------------------------------------------
* NON LINEAR COMPUTATION
*-----------------------------------------------------------------
TABB.SOUSTYPE = THERMIQUE ;
TABB.CRITERE =1.E-4 ;
TABB.NITER =1;
TABB.'OME'= .99 ;
* ----------2 itérations only for the test ------------------------
TABB.ITERMAX=2;
TABB.NIVEAU =1;
*-----------------------------------------------------------------
MAG_NLIN TABB ;
*-----------------------------------------------------------------
SOL2 = TABB.'POTENTIEL';
BA= CHAN CHPO ( GRAD OBJM SOL2 ) OBJM ;
BA= BA * -1. * MU0 ;
BM= EXTR BA 'T,Z' OO ;
*---------------
ITEST = 1 ;
SI ( EGA ITEST 1 ) ;
MESS '***********************************************************';
MESS ' VERIFICATION AU CENTRE ';
MESS ' CONTRIBUTION FER ATTENDUE 1.9496 CALCULEE ' BM ;
*****************************************************************
BAT = 1.9496 ;
*******************************************************************
RAP = ABS ((BM - BAT ) / BAT );
SI ( RAP > .01 ) ; ERREUR 5 ; FINSI ;
*******************************************************************
FIN ;
FINSI ;
*------------
*------ CONTINUATION TILL CONVERGENCE OR UP TO 100 ITERATION ---
*----------
TABB.ITERMAX=100 ;
*------------------------------------------------------------------
MAG_NLI3 TABB ;
*------------------------------------------------------------------
SOL2 = TABB.'POTENTIEL';
BA= CHAN CHPO ( GRAD OBJM SOL2 ) OBJM ;
BA= BA * -1. * MU0 ;
BM= EXTR BA 'T,Z' OO ;
BCAL = BM + BS0 ;
MESS '***********************************************************';
MESS ' CHECK AT CENTER OF THE DEVICE ';
MESS ' EXPECTED IRON CONTRIBUTION 1.9059 COMPUTED ' BM ;
MESS ' TOTAL BZ COMPUTED AT CENTER ' BCAL ;
MESS '***********************************************************';
FIN;