Code_Aster ®
Version
5.0
Titrate:
TPLL101 Chauffage by Joule effect of a hollow roll

Date:
19/10/01
Author (S):
Key S. TAHERI
:
V4.02.101-B Page:
1/6

Organization (S): EDF/MTI/MN

Handbook of Validation
V4.02 booklet: Stationary thermics of the linear structures
Document: V4.02.101

TPLL101 - Chauffage by Joule effect of a cylinder
hollow

Summary:

One imposes electrical currents inside and outside a hollow roll finite length, then one
calculate the temperature established under the effect of a heat source produced by Joule effect. The solution of
reference is analytical.

The applicability is it thermal linear stationary.

The model is axisymmetric.

The test is carried out on elements QUAD8 and TRIA6.
Handbook of Validation
V4.02 booklet: Stationary thermics of the linear structures
HI-75/01/010/A

Code_Aster ®
Version
5.0
Titrate:
TPLL101 Chauffage by Joule effect of a hollow roll

Date:
19/10/01
Author (S):
Key S. TAHERI
:
V4.02.101-B Page:
2/6

1
Problem of reference

1.1 Geometry

Axisymmetric

Z
D
C
R1
R0
+ M
R
With
B


WITH B
C
D
M
R 1.
2.7182
2.7182
1.
1.8591
Z 0.
0.
0.1 0.1
0.025

1.2 Properties
of
materials

Electric characteristic: electric conductivity = 1.
­ 1 ­ 1
m

Thermal characteristics: = 2. 10­2W/m°C CP = 0.

1.3
Boundary conditions and loadings

Electric calculation:

j.n = ­ 10.
on DA
j.n =.
3 6787944 on BC

Thermal calculation

T = 0. on DA

T = 0. on BC

FLUX = 0. on AB

FLUX = 0. on CD

1.4 Conditions
initial

Stationary calculation.
Handbook of Validation
V4.02 booklet: Stationary thermics of the linear structures
HI-75/01/010/A

Code_Aster ®
Version
5.0
Titrate:
TPLL101 Chauffage by Joule effect of a hollow roll

Date:
19/10/01
Author (S):
Key S. TAHERI
:
V4.02.101-B Page:
3/6

2
Reference solution

2.1
Method of calculation used for the reference solution

· Problem elastostatic V potential electric

In volume V = 0.

j.n =.
0
on CD and AB

Boundary conditions NEUMANN j.n = ­ 10.
on AD

j.n

=.
3 6787944 on BC

electric conductivity = 1.

j.n = ­ V

Axisymmetric solution

1
V

R
R
= 0 V = 0
V L

R R R
og

With

The boundary conditions on AD and BC impose:

V0 = 10.

Note:

The knowledge of A is not necessary for thermal calculation.

· Thermal problem T the temperature

­ T = S with a voluminal source S = (V) 2

Boundary conditions: T = 0. on DA and BC ­.
T N = 0 on cd. and AB

Axisymmetric solution:

1
2
T
v0
R
= ­
Taking into account the boundary conditions
R R R
1 2
R

2
v
R
R
T (R)
1
0
= ­
L
L

2
og
og

0
R
1
R

2.2
Results of reference

T = 5.889313 102 (temperature at the point M).

2.3
Uncertainty on the solution

Analytical solution.
Handbook of Validation
V4.02 booklet: Stationary thermics of the linear structures
HI-75/01/010/A

Code_Aster ®
Version
5.0
Titrate:
TPLL101 Chauffage by Joule effect of a hollow roll

Date:
19/10/01
Author (S):
Key S. TAHERI
:
V4.02.101-B Page:
4/6

3 Modeling
With

3.1
Characteristics of modeling

Element THAXTR6

Not M: N200

3.2 Characteristics

grid

A number of nodes: 305

A number of elements: 120

3.3 Functionalities
tested

Commands
Key word factor
Single-ended spanner word
Argument
AFFE_MODELE
AFFE
MODELING AXIS
% calculation electric



AFFE_CHAR_THER FLUX_REP


THER_LINEAIRE


CALC_CHAM_ELEM OPTION “SOUR_ELGA_ELEC”

% calculation thermal



AFFE_CHAR_THER TEMP_IMPO


FLUX_REP


SOURCE
SOUR_CALCULEE

THER_LINEAIRE



4
Results of modeling A

4.1 Values
tested

Identification Reference
Aster %
difference
Temperature at the point Mr. N200
5.889313 102 5.891298
102
0.034

4.2 Remarks

The boundary conditions of the electric problem are all of the conditions of NEUMANN.
Nevertheless, the analytical solution is found.

4.3 Parameters
of execution

Version: 5.4.17



Machine: SGI O-2000

System:
IRIX 64
Obstruction memory:
32 Mo
Time CPU To use:
2.0 seconds
Handbook of Validation
V4.02 booklet: Stationary thermics of the linear structures
HI-75/01/010/A

Code_Aster ®
Version
5.0
Titrate:
TPLL101 Chauffage by Joule effect of a hollow roll

Date:
19/10/01
Author (S):
Key S. TAHERI
:
V4.02.101-B Page:
5/6

5 Modeling
B

5.1
Characteristics of modeling

Element THAXQU8

Not M: N186

5.2 Characteristics

grid

A number of nodes: 245

A number of elements: 60

5.3 Functionalities
tested

Commands
Key word factor
Single-ended spanner word
Argument
AFFE_MODELE
AFFE
MODELING AXIS
% calculation electric



AFFE_CHAR_THER FLUX_REP

THER_LINEAIRE


CALC_CHAM_ELEM OPTION
“SOUR_ELGA_ELEC”

% calculation thermal



AFFE_CHAR_THER TEMP_IMPO


FLUX_REP


SOURCE
SOUR_CALCULEE

THER_LINEAIRE



6
Results of modeling B

6.1 Values
tested

Identification Reference Aster %
difference
Temperature at the point Mr. N186
5.889313 102 5.892292
102
0.051


6.2 Parameters
of execution

Version: 5.4.17
Machine: SGI O-2000

System:
IRIX 64
Obstruction memory:
64 Mo
Time CPU To use:
2.00 seconds
Handbook of Validation
V4.02 booklet: Stationary thermics of the linear structures
HI-75/01/010/A

Code_Aster ®
Version
5.0
Titrate:
TPLL101 Chauffage by Joule effect of a hollow roll

Date:
19/10/01
Author (S):
Key S. TAHERI
:
V4.02.101-B Page:
6/6

7
Summary of the results

In addition to the test presented, one carried out a calculation on structure (COTHAA). The results obtained have
summer compared with those obtained using Code CASTEM 2000. One obtains results very
close relations.
Handbook of Validation
V4.02 booklet: Stationary thermics of the linear structures
HI-75/01/010/A

Outline document