Code_Aster
®
Version
5.0
Titrate:
TPLL101 Joule effect heating of a hollow roll
Date:
19/10/01
Author (S):
S. TAHERI
Key
:
V4.02.101-B
Page:
1/6
Manual of Validation
V4.02 booklet: Stationary thermics of the linear structures
HI-75/01/010/A
Organization (S):
EDF/MTI/MN
Manual of Validation
V4.02 booklet: Stationary thermics of the linear structures
Document: V4.02.101
TPLL101 - Joule effect heating 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.
Code_Aster
®
Version
5.0
Titrate:
TPLL101 Joule effect heating of a hollow roll
Date:
19/10/01
Author (S):
S. TAHERI
Key
:
V4.02.101-B
Page:
2/6
Manual of Validation
V4.02 booklet: Stationary thermics of the linear structures
HI-75/01/010/A
1
Problem of reference
1.1 Geometry
Axisymmetric
Z
R
0
C
R
1
D
+ 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 10
0
.
/
.
2
W m C C
p
1.3
Boundary conditions and loadings
Electric calculation:
J N
J N
.
10.
.
.
=
=
on DA
on BC
3 6787944
Thermal calculation
T = 0. on DA
T = 0. on BC
FLOW = 0. on AB
FLOW = 0. on CD
1.4 Conditions
initial
Stationary calculation.
Code_Aster
®
Version
5.0
Titrate:
TPLL101 Joule effect heating of a hollow roll
Date:
19/10/01
Author (S):
S. TAHERI
Key
:
V4.02.101-B
Page:
3/6
Manual of Validation
V4.02 booklet: Stationary thermics of the linear structures
HI-75/01/010/A
2
Reference solution
2.1
Method of calculation used for the reference solution
·
Problem elastostatic V potential electric
In volume
V
=
0.
Boundary conditions NEUMANN
J N
J N
J N
.
.
.
10.
.
.
=
=
=
0
3 6787944
on CD and AB
on AD
on BC
electric conductivity = 1.
J N
V
.
=
Axisymmetric solution
1
0
0
R
R R
V
R
V
V L
R
With
og
=
=
The boundary conditions on AD and BC impose:
V
0
10
=
.
Note:
The knowledge of
With
is not necessary for thermal calculation.
·
Thermal problem T the temperature
(
)
T
S
S
=
=
with a voluminal source
V
2
Boundary conditions:
T
=
=
0
0
.
.
on DA and BC
on cd. and AB
T N
Axisymmetric solution:
()
1
1
1
2
02
2
02
0
1
R
R R
T
R
v
R
T R
v L
R
R
L
R
R
og
og
=
=
Taking into account the boundary conditions
2.2
Results of reference
T
= 5.889313 10
2
(temperature at the point M).
2.3
Uncertainty on the solution
Analytical solution.
Code_Aster
®
Version
5.0
Titrate:
TPLL101 Joule effect heating of a hollow roll
Date:
19/10/01
Author (S):
S. TAHERI
Key
:
V4.02.101-B
Page:
4/6
Manual of Validation
V4.02 booklet: Stationary thermics of the linear structures
HI-75/01/010/A
3 Modeling
With
3.1
Characteristics of modeling
Element THAXTR6
Not M: N200
3.2 Characteristics
mesh
A number of nodes: 305
A number of elements: 120
3.3 Functionalities
tested
Controls
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 10
2
5.891298
10
2
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
Overall dimension memory:
32 Mo
Time CPU To use:
2.0 seconds
Code_Aster
®
Version
5.0
Titrate:
TPLL101 Joule effect heating of a hollow roll
Date:
19/10/01
Author (S):
S. TAHERI
Key
:
V4.02.101-B
Page:
5/6
Manual of Validation
V4.02 booklet: Stationary thermics of the linear structures
HI-75/01/010/A
5 Modeling
B
5.1
Characteristics of modeling
Element THAXQU8
Not M: N186
5.2 Characteristics
mesh
A number of nodes: 245
A number of elements: 60
5.3 Functionalities
tested
Controls
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 10
2
5.892292
10
2
0.051
6.2 Parameters
of execution
Version: 5.4.17
Machine: SGI O-2000
System:
IRIX 64
Overall dimension memory:
64 Mo
Time CPU To use:
2.00 seconds
Code_Aster
®
Version
5.0
Titrate:
TPLL101 Joule effect heating of a hollow roll
Date:
19/10/01
Author (S):
S. TAHERI
Key
:
V4.02.101-B
Page:
6/6
Manual of Validation
V4.02 booklet: Stationary thermics of the linear structures
HI-75/01/010/A
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.