Code_Aster
®
Version
5.0
Titrate:
TPLV06 Release of power in a hollow sphere
Date:
20/09/02
Author (S):
C. DURAND, E. SCREW, F. LEBOUVIER
Key
:
V4.04.006-A
Page:
1/6
Manual of Validation
V4.04 booklet: Stationary thermics of the voluminal structures
HT-66/02/001/A
Organization (S):
EDF/AMA, EDF/UTO/LOCATED, Delta CAD
Manual of Validation
V4.04 booklet: Stationary thermics of the voluminal structures
V4.04.006 document
TPLV06 - Release of power in one
hollow sphere
Summary:
This test results from the validation independent of version 3 in linear stationary thermics.
It is about a three-dimensional problem which aims to validate the voluminal thermal element subjected to
a temperature imposed and on a heat source.
This case test includes/understands a modeling 3D. The results are compared with an analytical solution (VPCS).
Code_Aster
®
Version
5.0
Titrate:
TPLV06 Release of power in a hollow sphere
Date:
20/09/02
Author (S):
C. DURAND, E. SCREW, F. LEBOUVIER
Key
:
V4.04.006-A
Page:
2/6
Manual of Validation
V4.04 booklet: Stationary thermics of the voluminal structures
HT-66/02/001/A
1
Problem of reference
1.1 Geometry
R
E
R
O
R
I
Hollow sphere:
- Interior Radius R
I
= 1 m
- External Radius R
E
= 2 m
Q
1.2
Properties of material
=
1. W/m °C
Thermal conductivity
1.3
Boundary conditions and loadings
·
T
I
= T (R = R
I
) = 20°C,
·
T
E
= T (R = R
E
) = 20°C,
·
Q = 100 W/m
3
.
1.4 Conditions
initial
Without object.
Code_Aster
®
Version
5.0
Titrate:
TPLV06 Release of power in a hollow sphere
Date:
20/09/02
Author (S):
C. DURAND, E. SCREW, F. LEBOUVIER
Key
:
V4.04.006-A
Page:
3/6
Manual of Validation
V4.04 booklet: Stationary thermics of the voluminal structures
HT-66/02/001/A
2
Reference solution
2.1
Method of calculation used for the reference solution
The reference solution is that given in card TPLV06/89 of guide VPCS.
·
Temperature according to R:
(
)
(
)
T
T
Q
R
R
R
R
R
R
R
R
I
E
I
I
I
E
I
=
+
-
-
-
-
-
6
1
1
1
1
2
2
2
2
·
Density flux according to R:
(
)
= -
= -
-
-
-
4
2
3
1
1
2
2
2
2
3
R
dT
Dr.
Q
R
R
R
R
R
E
I
I
E
2.2
Results of reference
Temperature in R = 1.25; 1.5 and 1.75 m
2.3
Uncertainty on the solution
Analytical solution.
2.4 References
bibliographical
[1]
Guide validation of the software packages of structural analysis. French company of
Mechanics, AFNOR 1990 ISBN 2-12-486611-7
Code_Aster
®
Version
5.0
Titrate:
TPLV06 Release of power in a hollow sphere
Date:
20/09/02
Author (S):
C. DURAND, E. SCREW, F. LEBOUVIER
Key
:
V4.04.006-A
Page:
4/6
Manual of Validation
V4.04 booklet: Stationary thermics of the voluminal structures
HT-66/02/001/A
3 Modeling
With
3.1
Characteristics of modeling
3D (HEXA8)
Limiting conditions:
- faces ABCD, EFGH,
ABFE, DCGH
= 0
- faces ADHE, BCGF T = 20°C
C
E
X
y
Z
30°
30°
N20
N15
N10
N5
N25
N120
N115
N110
N105
N125
N116
N106
N111
N101
N121
N16
N11
N6
N1
N21
With
B
D
C
H
F
G
3.2
Characteristics of the mesh
A number of nodes:
125
A number of meshs and types: 64 HEXA8
3.3 Functionalities
tested
Controls
AFFE_MODELE
THERMICS
3D
ALL
AFFE_CHAR_THER
TEMP_IMPO
SOURCE
THER_LINEAIRE
EXCIT
CHARGE
RECU_CHAMP
NUME_ORDRE
Code_Aster
®
Version
5.0
Titrate:
TPLV06 Release of power in a hollow sphere
Date:
20/09/02
Author (S):
C. DURAND, E. SCREW, F. LEBOUVIER
Key
:
V4.04.006-A
Page:
5/6
Manual of Validation
V4.04 booklet: Stationary thermics of the voluminal structures
HT-66/02/001/A
4
Results of modeling A
4.1 Values
tested
Identification Reference
Aster %
difference
tolerance
Temperature (°C)
R = 1.25 (N16)
30.625
30.471
-
0.504
1%
R = 1.25 (N116)
30.625
30.471
-
0.504
1%
R = 1.25 (N20)
30.625
30.462
-
0.532
1%
R = 1.25 (N120)
30.625
30.462
-
0.532
1%
R = 1.50 (N11)
32.500
32.337
-
0.500
1%
R = 1.50 (N111)
32.500
32.337
-
0.500
1%
R = 1.50 (N15)
32.500
32.335
-
0.507
1%
R = 1.50 (N115)
32.500
32.335
-
0.507
1%
R = 1.75 (N6)
28.482
28.379
-
0.362
1%
R = 1.75 (N106)
28.482
28.379
-
0.362
1%
R = 1.75 (N10)
28.482
28.382
-
0.351
1%
R = 1.75 (N110)
28.482
28.382
-
0.351
1%
4.2 Parameters
of execution
Version: 5.03
Machine: SGI - ORIGIN 2000 - R12000
Overall dimension memory:
8 megawords
Time CPU To use: 2.00 seconds
Code_Aster
®
Version
5.0
Titrate:
TPLV06 Release of power in a hollow sphere
Date:
20/09/02
Author (S):
C. DURAND, E. SCREW, F. LEBOUVIER
Key
:
V4.04.006-A
Page:
6/6
Manual of Validation
V4.04 booklet: Stationary thermics of the voluminal structures
HT-66/02/001/A
5
Summary of the results
The results obtained are satisfactory, the maximum change obtained is 0.53%.
Modeling 3D used to modelize this sphere is correct.
The quality of the results could be still improved in:
·
carrying out a finer mesh of the portion of sphere,
·
choosing quadratic elements for better approximating the reference solution.