Test c2d93 Description sheet
Test name
c2d93
Calculation type
2D AXISYMMETRIC VECTOR POTENTIAL
Computation of magnetic field with non linear material
Finite element type
TRI6 QUA8
Topic
A circular coil of rectangular cross section is embeded in an iron box.
Goal
Calculate vector potential and field in the cavity.
Reference
Analytical solution.
Version
97' customer version
Model description
Soft iron curve for B(H).
Test cd2d93 Results
CASTEM FIGURES
***********************************************************************
*
* 2D AXISYMMETRIC MAGNETIC FIELD COMPUTATION
*
* Formulation : VECTOR POTENTIAL
*
* NON LINEAR MATERIAL
*
***********************************************************************
OPTION DIME 2 ELEM TRI6 COUL VERT echo 1 ;
GRAPH ='N' ;
* ------------------------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 ;
*------------------------- COIL SURFACE -------------------------
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 ;
*---------------------IRON ------------------------------------------
FER = (D OZ2 R0Z2 D R4Z2 D 6 R4Z0 D R5Z0 D R5Z3 D R0Z3 D OZ3 D OZ2 )
SURF PLANE COUL ROUG ;
*---------------------EXTERNAL AIR BOX ------------------------------
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 FLAN4 ) coul vert) et BOBI ;
TOUT = AIRIN ET AIREXT ET FER ; ELIM .2 TOUT ;
*
*--------------- BOUNDARIES -----------------------------------------
*
ENPP = CONTOUR TOUT ;
CEXTR=ENPP POINTS DROITE (130. 0.) (130. 100.) .1 ;
CEXTH=ENPP POINTS DROITE ( 0. 130.) (10. 130.) .1 ;
AXE=ENPP POINTS DROITE ( 0. 0. ) ( 0. 100. ) .1 ;
AX1 = (AIRIN ET FER) POINT DROITE ( 0. 0. ) ( 0. 100. ) .1 ;
AX2 = DIFF ( CHAN POI1 AXE) (CHAN POI1 AX1) ;
*
*----------------------------------------------------------------------
* FORMER DESCRIPTION IN MILLIMETRES
*--------------- SHIFT FOR METERS ------------------------------------
*
deplacer tout homo .001 (0. 0.) ;
*
SI (NEG GRAPH N ) ;
TITRE ' MESH 2D ' ;
TRAC tout ;
FINSI ;
*----------------------------------------------------------------------
MU0= 4. * PI * 1.E-7 ;
*
*------------------CURENT DESCRIPTION ---------------------------------
TABCOUR= TABLE ;
DESCOUR TABCOUR 1 BOBI 'AMP' 800.E6 ;
TABB = TABLE ;
*----------------- AXISYMMETRIC PROBLEM ------------------------------
TABB.'AXI'= VRAI ;
NF = FER NBEL ;
FER1 = FER ELEM ( LECT 1 PAS 1 30 ) ;
FER2 = FER ELEM ( LECT 31 PAS 1 NF ) ;
*------------------MATERIALS -----------------------------------------
KEVOL = H_B MU0 ;
TABMAT = TABLE ;
OBFER1 = FER1 MODE THERMIQUE ISOTROPE ;
OBFER2 = FER2 MODE THERMIQUE ISOTROPE ;
STN = TABLE ; STN.EV1 = KEVOL ;
TABMAT.OBFER1 = STN ;
STN = TABLE ; STN.EV1 = KEVOL ;
TABMAT.OBFER2 = STN ;
TABB.'TABNUSEC' = TABMAT ;
TABB.'MUAIR' =MU0 ;
*------- LINEAR MATERIAL CAN BE TRAITED AS A SUPER ELEMENT OR NOT
*
isuper= 1 ;
'SI' ('EGA' isuper 1 ) ;
TABB.'AIRSUP' = AIREXT ;
TABB.'MAITRES' = ( FER CONTOUR) COMPRIS R5Z0 OZ3 ;
TABB.'ENCS' = CEXTR ET CEXTH ET AX2 ;
TABB.'BLOQUE' = BLOQUER 'T' AX1 ;
TABB.'AIR' = AIRIN ;
'SINON' ;
TABB.'AIR' = (AIRIN ET AIREXT) ;
TABB.'BLOQUE' = BLOQUER 'T' (CEXTR ET CEXTH ET AXE ) ;
'FINSI' ;
TABB.'COUR'= TABCOUR ;
*
* ------POTENTIAL COMPUTATION OR FIRST STEP IF NON LINEAR PROBLEM ---
*------
POT_VECT TABB 'SOLIN' ;
*-----
*------------------------------------------------------------------
SOL1 = (TABB.'POTENTIEL' ) ENLEVER LX ;
RAY = FLAN1 COTE 1 ;
RAY2 = D 10 (0. .0001) ( .020 .0001) ;
* -------------SOME POST TRAITMENT B COMPUTATION ----------------
BB = INDUCTIO AIRIN SOL1 VRAI ;
PREF = AIRIN POINT PROCHE ( 0. 0. ) ;
BY0 = EXTR BB 'BY' PREF ;
BY10 = EXTR BB 'BY' ( AIRIN POINT PROCHE ( .010 0.)) ;
TITRE ' COMPOSANTE BY AVANT ET APRES LISSAGE ' ;
EVB1 = EVOL ROUG CHPO BB 'BY' RAY ;
*---------- polynomial smothing if wanted --------------------
CHLIS = PROI POLY TOUT RAY2 SOL1 1 AXIS ;
BBY = (EXCO CHLIS 'BY' ) NOMC 'BY' ;
BY01 = EXTR BBY 'BY' (RAY2 POINT INITIAL) ;
BAT1 = 800.e6 * 5.e-3 * 5.e-3 * MU0 /10.e-3 ;
option echo 0 ;
MESS '**************************************************************';
MESS '* CIRCULAR COIL internal radius 20 mm ' ;
MESS '* total cross section 5*5 mm ' ;
MESS '* SYMMETRY BY HORIZONTAL PLANE ' ;
MESS '* AMPERE mufer >> muo all AMPERE*TURNS in the GAP of 10 mm ';
MESS '* ';
MESS '* J * EP * HAUT = B/ MU0 * e ';
MESS '* WAITED : By = ' bat1 ' TESLAS ';
MESS ' *************************************************************';
MESS ' NUMERICAL DERIVATION BY AU CENTRE ' BY0 ;
MESS ' SMOTHED SOLUTION BY AU CENTRE ' BY01 ;
MESS ' *****************************************';
*******************************************************************
RAP = ABS ((BY01 - bat1 ) / bat1 );
SI ( RAP > .01 ) ; ERREUR 5 ; FINSI ;
*******************************************************************
SI (NEG GRAPH N ) ;
TITRE ' POTENTIAL BEFORE AND AFTER SMOTHING ' ;
EVPO1 = EVOL ROUG CHPO SOL1 'T' RAY ;
EVPO2 = EVOL VERT CHPO CHLIS 'A' RAY2 ;
dess (evpo1 et evpo2) xbor 0. (R1 * 0.001 * .75);
TITRE ' BY COMPONENT BEFORE AND AFTER SMOTHING ' ;
EVB1 = EVOL ROUG CHPO BB 'BY' RAY ;
EVB2 = EVOL VERT CHPO CHLIS 'BY' RAY2 ;
dess (evb1 et evb2) xbor 0. (R1 * 0.001 * .75) ;
FINSI ;
*
**----------------- NON LINEAR COMPUTATION -------------------
* filling
TABB.SOUSTYPE='THERMIQUE' ;
TABB.CRITERE =1.E-4 ;
TABB.NITER =1;
TABB.'OME' = .1 ;
*----------- test shortened to 2 iterations ----------------------
TABB.ITERMAX=2;
TABB.NIVEAU =1;
*
*-------------------------------
MAG_NLIN TABB ;
*-------------------------------
*
SOL2 = enlever (TABB.'POTENTIEL' ) LX ;
BB = INDUCTIO AIRIN SOL2 VRAI ;
BY02 = EXTR BB 'BY' PREF ;
CHLIS = PROI POLY TOUT RAY2 SOL2 1 AXIS ;
BBY = (EXCO CHLIS 'BY' ) NOMC 'BY' ;
BY03 = EXTR BBY 'BY' (RAY2 POINT INITIAL) ;
BAT = 2.4106 ;
MESS ' *****************************************';
MESS ' EXPECTED SOLUTIONS AT CENTER BY ' BAT ;
MESS ' NUMERICAL DERIVATION BY ' BY02 ;
MESS ' SMOTHED SOLUTION BY ' BY03 ;
MESS ' *****************************************';
itest = 1 ;
*--------------------GOOD WORKING MESSAGE -----------------------
SI (EGA ITEST 1 ) ;
*------- test shortened ---------------------------------------
RAP = ABS ((BY03 - BAT ) / BAT);
SI ( RAP > .01 ) ; ERREUR 5 ; FINSI ;
*----------------------------------------------------------------
SINON ;
*------ COMPUTATION TILL CONVERGENCE OR UP TO 100 MORE ITERATION
TABB.ITERMAX=100;
MAG_NLIN TABB ;
*----------------------------------------------------------------
SOL2 = enlever (TABB.'POTENTIEL' ) LX ;
BB = INDUCTIO AIRIN SOL2 VRAI ;
BY02 = EXTR BB 'BY' PREF ;
CHLIS = PROI POLY TOUT RAY2 SOL2 1 AXIS ;
BBY = (EXCO CHLIS 'BY' ) NOMC 'BY' ;
BY03 = EXTR BBY 'BY' (RAY2 POINT INITIAL) ;
BAT = 2.3468 ;
MESS ' *****************************************';
MESS ' EXPECTED SOLUTION ON AXIS BY ' BAT ;
MESS ' NUMERICAL DERIVATION BY AU CENTRE ' BY02 ;
MESS ' SMOTHED SOLUTION BY AU CENTRE ' BY03 ;
MESS ' *****************************************';
*
*******************************************************************
RAP = ABS ((BY03 - BAT ) / BAT );
SI ( RAP > .01 ) ; ERREUR 5 ; FINSI ;
*******************************************************************
SI (NEG GRAPH N ) ;
TITRE ' POTENTIAL BEFORE AND AFTER SMOTHING ' ;
EVPO1 = EVOL ROUG CHPO SOL2 'T' RAY ;
EVPO2 = EVOL VERT CHPO CHLIS 'A' RAY2 ;
dess (evpo1 et evpo2) xbor 0. (R1 * 0.001 * .75);
TITRE ' BY COMPONENT BEFORE AND AFTER SMOTHING ' ;
EVB1 = EVOL ROUG CHPO BB 'BY' RAY ;
EVB2 = EVOL VERT CHPO CHLIS 'BY' RAY2 ;
dess (evb1 et evb2) xbor 0. (R1 * 0.001 * .75);
FINSI ;
FINSI ;
FIN ;
;