Code_Aster
®
Version
5.0
Titrate:
TPLA300 Plates circular subjected to a voluminal heat source
Date:
20/09/02
Author (S):
C. DURAND, E. SCREW, F. LEBOUVIER
Key
:
V4.01.300-A
Page:
1/6
Manual of Validation
V4.01 booklet: Stationary thermics of the axisymmetric structures
HT-66/02/001/A
Organization (S):
EDF/AMA, EDF/UTO/LOCATED, Delta CAD
Manual of Validation
V4.01 booklet: Stationary thermics of the axisymmetric structures
V4.01.300 document
TPLA300 - Plate circular subjected to a source
of voluminal heat
Summary:
This test results from the validation independent of version 3 in linear stationary thermics.
The interest of this case test plane 2D is to validate a thermal element under various boundary conditions
(imposed temperature, heat source).
This case test includes/understands two modelings 2D, one axisymmetric, the other planes.
The results are compared with an analytical solution.
Code_Aster
®
Version
5.0
Titrate:
TPLA300 Plates circular subjected to a voluminal heat source
Date:
20/09/02
Author (S):
C. DURAND, E. SCREW, F. LEBOUVIER
Key
:
V4.01.300-A
Page:
2/6
Manual of Validation
V4.01 booklet: Stationary thermics of the axisymmetric structures
HT-66/02/001/A
1
Problem of reference
1.1 Geometry
R=5.0
With
O
Q
1.2
Properties of material
= 0.04 W/m.°C thermal Conductivity
1.3
Boundary conditions and loadings
·
voluminal heat source Q = 1W/m
3
,
·
temperature imposed on surface outside (R = 5): T = 0°C.
1.4 Conditions
initial
Without object.
Code_Aster
®
Version
5.0
Titrate:
TPLA300 Plates circular subjected to a voluminal heat source
Date:
20/09/02
Author (S):
C. DURAND, E. SCREW, F. LEBOUVIER
Key
:
V4.01.300-A
Page:
3/6
Manual of Validation
V4.01 booklet: Stationary thermics of the axisymmetric structures
HT-66/02/001/A
2
Reference solution
2.1
Method of calculation used for the reference solution
Analytical solution:
T (R) = 6.25 (25
-
R
2
)
2.2
Results of reference
Temperature for R = 0., 0.625, 1.25, 1.875, 2.5, 3.125, 3.75, 4.375, 5.
2.3
Uncertainty on the solution
Analytical solution.
2.4 References
bibliographical
[1]
W.K. Liu, T. Belytschko, “Efficient linear and nonlinear heat conduction with has quadrilateral
element ", Int. J. num. Meth. Engng, flight 20, n°5, p 931-948, 1984.
Code_Aster
®
Version
5.0
Titrate:
TPLA300 Plates circular subjected to a voluminal heat source
Date:
20/09/02
Author (S):
C. DURAND, E. SCREW, F. LEBOUVIER
Key
:
V4.01.300-A
Page:
4/6
Manual of Validation
V4.01 booklet: Stationary thermics of the axisymmetric structures
HT-66/02/001/A
3 Modeling
With
3.1
Characteristics of modeling
PLAN (QUAD4)
y
C
X
B
With
Limiting conditions:
- dimensioned AB
= 0
- dimensioned CA
= 0
- dimensioned BC T = 0°C
N17
N15
N13
N11
N9
N7
N5
N3
N1
N45 N116 N171 N207
N79 N146 N191 N217
N108
N133
N168
N151
N184
3.2
Characteristics of the mesh
A number of nodes:
217
A number of meshs and types: 192 QUAD4
3.3 Functionalities
tested
Controls
AFFE_MODELE
THERMICS
PLAN
ALL
AFFE_CHAR_THER
TEMP_IMPO
SOURCE
THER_LINEAIRE
EXCIT
CHARGE
RECU_CHAMP
NUME_ORDRE
Code_Aster
®
Version
5.0
Titrate:
TPLA300 Plates circular subjected to a voluminal heat source
Date:
20/09/02
Author (S):
C. DURAND, E. SCREW, F. LEBOUVIER
Key
:
V4.01.300-A
Page:
5/6
Manual of Validation
V4.01 booklet: Stationary thermics of the axisymmetric structures
HT-66/02/001/A
4
Results of modeling A
4.1 Values
tested
Identification Reference
Aster %
difference
tolerance
temperatures (°C)
R = 0.000 (N1)
156.25
156.07
-
0.114
1%
R = 0.625 (N3)
153.81
153.63
-
0.116
1%
R = 0.625 (N45)
153.81
153.63
-
0.116
1%
R = 1.250 (N5)
146.48
146.31
-
0.117
1%
R = 1.250 (N79)
146.48
146.31
-
0.117
1%
R = 1.875 (N7)
134.28
134.10
-
0.131
1%
R = 1.875 (N116)
134.28
134.10
-
0.131
1%
R = 2.500 (N9)
117.19
116.98
-
0.182
1%
R = 2.500 (N108)
117.19
116.82
-
0.313
1%
R = 2.500 (N146)
117.19
116.98
-
0.182
1%
R = 3.125 (N11)
95.21
95.04
-
0.178
1%
R = 3.125 (N133)
95.21
95.00
-
0.216
1%
R = 3.125 (N171)
95.21
95.04
-
0.178
1%
R = 3.750 (N13)
68.36
68.23
-
0.191
1%
R = 3.750 (N151)
68.36
68.21
-
0.214
1%
R = 3.750 (N191)
68.36
68.23
-
0.191
1%
R = 4.375 (N15)
36.62
36.55
-
0.194
1%
R = 4.375 (N168)
36.62
36.54
-
0.211
1%
R = 4.375 (N207)
36.62
36.55
-
0.194
1%
R = 5.000 (N17)
0.00 *
0.00
0.00
1%
R = 5.000 (N217)
0.00 *
0.00
0.00
1%
R = 5.000 (N184)
0.00 *
0.00
0.00
1%
* Condition limiting
4.2 Parameters
of execution
Version: 5.03
Machine: SGI - ORIGIN 2000 - R12000
Overall dimension memory:
8 megawords
Time CPU To use: 1.98 seconds
Code_Aster
®
Version
5.0
Titrate:
TPLA300 Plates circular subjected to a voluminal heat source
Date:
20/09/02
Author (S):
C. DURAND, E. SCREW, F. LEBOUVIER
Key
:
V4.01.300-A
Page:
6/6
Manual of Validation
V4.01 booklet: Stationary thermics of the axisymmetric structures
HT-66/02/001/A
5
Summary of the results
The results obtained are very satisfactory, the maximum change is 0.313%.
Among the points of observation, the most important variation is noted with the N108 node which belongs to
the element more deformed mesh.
The mesh used is that proposed in the reference. A radial mesh with the same cutting and
with the same meshs should give better results.
This test made it possible to test the taking into account of a source term within meshs QUAD9 with one
modeling AXIS (
AFFE_CHAR_THER
associated the key word
SOURCE
).