Code_Aster
®
Version
5.0
Titrate:
TPLA04 Release of power in a hollow roll
Date:
20/09/02
Author (S):
C. DURAND,
E. SCREWS, F. LEBOUVIER
Key
:
V4.01.004-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
Document V4.01 004
TPLA04 - Release of power in one
hollow roll
Summary:
This test results from the validation independent of version 3 in linear stationary thermics.
It comprises an axisymmetric modeling 2D which tests the axisymmetric elements in thermics, them
boundary conditions in imposed temperature and the boundary conditions of the heat source type.
This test aims to validate the taking into account of the heat source by comparing the results obtained
with those provided by VPCS.
Code_Aster
®
Version
5.0
Titrate:
TPLA04 Release of power in a hollow roll
Date:
20/09/02
Author (S):
C. DURAND,
E. SCREWS, F. LEBOUVIER
Key
:
V4.01.004-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
Z
R
R
E
R
I
Interior radius R
I
= 1m
External radius R
E
= 2 m
Length L
Q
1.2
Properties of material
= 1.0 W/m°C
Thermal conductivity
1.3
Boundary conditions and loadings
·
Imposed temperatures:
-
Interior surface: T
I
= T (R = R
I
) = 20°C,
-
External surface: T
E
= T (R = R
E
) = 20°C,
·
Released power uniform Q = 100 W/m
3
.
1.4 Conditions
initial
Without object.
Code_Aster
®
Version
5.0
Titrate:
TPLA04 Release of power in a hollow roll
Date:
20/09/02
Author (S):
C. DURAND,
E. SCREWS, F. LEBOUVIER
Key
:
V4.01.004-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
The reference solution is that given in card TPLA04/89 of guide VPCS.
·
Temperature according to R:
T R
T
Q
R
R
R
R
R
R
R
R
I
E
I
I
E
I
I
()
(
)
ln (
)
ln (
)
(
)
= +
-
-
-
4
2
2
2
2
·
Density flux according to R:
()
(
)
ln (
)
R
dT
Dr.
Q
R
R
R
R
R
R
E
I
E
I
= -
= -
-
-
4
2
2
2
2
The cylinder is supposed infinitely long (l>>R
E
)
2.2
Results of reference
Temperature and density flux for R = 1.0, 1.2 and 1.5
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:
TPLA04 Release of power in a hollow roll
Date:
20/09/02
Author (S):
C. DURAND,
E. SCREWS, F. LEBOUVIER
Key
:
V4.01.004-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
AXIS (QUAD9)
Limiting conditions:
- dimensioned AD, BC T = 20 °C
- all
Q = 100 W/m
3
- dimensioned AB, CD
= 0. W/m
2
y (Z)
X (R)
0.1 m
With
R
I
= 1.m
R
E
= 2.m
1.2m
1.5m
E
D
m20
m17 m16
C
B
m1
m11 m10
F
Not
R
Z
Node
With
1.0
0.0
N1
D
1.0
0.1
N3
E
1.2
0.0
N25
F
1.5
0.0
N61
B
2.0
0.0
N121
C
2.0
0.1
N123
3.2
Characteristics of the mesh
A number of nodes:
123
A number of meshs and types: 20 QUAD9
3.3 Functionalities
tested
Controls
AFFE_MODELE
THERMICS
AXIS
ALL
AFFE_CHAR_THER
TEMP_IMPO
SOURCE
THER_LINEAIRE
EXCIT
CHARGE
RECU_CHAMP
NUME_ORDRE
CALC_CHAM_ELEM
FLUX_ELNO_TEMP
3.4 Remarks
Voluminal heat
C
p
does not intervene in this test, but must obligatorily be declared. One
takes
C
p
= 2.0 J/m
3
°C.
The limiting condition
= 0. are implicit on the free edges.
Code_Aster
®
Version
5.0
Titrate:
TPLA04 Release of power in a hollow roll
Date:
20/09/02
Author (S):
C. DURAND,
E. SCREWS, F. LEBOUVIER
Key
:
V4.01.004-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
Temperature (°C)
Node n1 (a: R = 1.0)
20.00
20.0000
0.000% *
1%
Node n25 (E: R = 1.2)
28.73
28.7276
-
0.008%
1%
Node n61 (F: R = 1.5)
32.62
32.6222
0.007%
1%
Density flux (W/m ²)
Net m20 n1 (R = 1.0)
-
58.20
-
58.1592
-
0.070%
1%
Net m17 n25 (R = 1.2)
-
30.17
-
30.1412
-
0.095%
1%
Net m16 n25 (R = 1.2)
-
30.17
-
30.1434
-
0.088%
1%
Net m11 n61 (R = 1.5)
2.87
2.8791
0.316%
1%
Net m10 n61 (R = 1.5)
2.87
2.8782
0.285%
1%
4.2 Parameters
of execution
Version: 5.03
Machine: SGI - ORIGIN 2000 - R12000
Overall dimension memory:
64 Mo
Time CPU To use: 1.98 seconds
Code_Aster
®
Version
5.0
Titrate:
TPLA04 Release of power in a hollow roll
Date:
20/09/02
Author (S):
C. DURAND,
E. SCREWS, F. LEBOUVIER
Key
:
V4.01.004-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 of
-
0.008% in temperature and of
0.316% in flow.
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
).