Code_Aster
®
Version
5.0
Titrate:
TPLP302 Plates rectangular with imposed temperature
Date:
20/09/02
Author (S):
C. DURAND, E. SCREW, F. LEBOUVIER
Key
:
V4.05.302-A
Page:
1/6
Manual of Validation
V4.05 booklet: Stationary thermics of the plane structures
HT-66/02/001/A
Organization (S):
EDF/AMA, EDF/UTO/LOCATED, Delta CAD
Manual of Validation
V4.05 booklet: Stationary thermics of the plane structures
V4.05.302 document
TPLP302 - Rectangular plate with temperature
imposed
Summary:
This test results from the validation independent of version 3 in linear stationary thermics.
It is about a problem plane 2D represented by a modeling hull.
The functionalities tested are as follows:
·
thermal element hull,
·
limiting conditions: imposed temperature.
The results are compared with an analytical solution.
Code_Aster
®
Version
5.0
Titrate:
TPLP302 Plates rectangular with imposed temperature
Date:
20/09/02
Author (S):
C. DURAND, E. SCREW, F. LEBOUVIER
Key
:
V4.05.302-A
Page:
2/6
Manual of Validation
V4.05 booklet: Stationary thermics of the plane structures
HT-66/02/001/A
1
Problem of reference
1.1 Geometry
L
L
Y
X
With
B
D
C
L = 0.2 m
L = 2 m
= 0.05m has
has
E
H
F
I
has
J
G
K
Points
X
Y
E
0.05 0.05
F
0.05 0.10
G
0.05 0.15
H
0.10 0.05
I
0.10 0.10
J
0.10 0.15
K
0.10 0.20
1.2
Properties of material
=
1 W/m °C
Thermal conductivity
1.3
Boundary conditions and loadings
·
Imposed temperature:
-
dimensioned [BC] and [AD] T = 0°C,
-
dimensioned [AB] T
= 100°C.
·
Imposed flow:
-
dimensioned [CD]
= 0
1.4 Conditions
initial
Without object.
Code_Aster
®
Version
5.0
Titrate:
TPLP302 Plates rectangular with imposed temperature
Date:
20/09/02
Author (S):
C. DURAND, E. SCREW, F. LEBOUVIER
Key
:
V4.05.302-A
Page:
3/6
Manual of Validation
V4.05 booklet: Stationary thermics of the plane structures
HT-66/02/001/A
2
Reference solution
2.1
Method of calculation used for the reference solution
[
]
T X y
T
E
N
N
X
L
p
N
y L
N
(,)
.sin (
)
(
)
/
=
+
+
-
+
=
4
2
1
2
1
2
1
0
where X
: X-coordinate
y
:
ordinate
T
p
: temperature imposed on the with dimensions one [AB]
N = 0,1,2,3,…
The values of reference are obtained with N = 1000
2.2
Results of reference
Temperature at the points E, F, G, H, I, J, K
2.3
Uncertainty on the solution
Analytical solution.
2.4 References
bibliographical
[1]
J.R. Welty, E.C. Wicks, R.E. Wilson, “Fundamentals off momentum heat and farmhouse transfer”,
third edition, John Wiley & Sounds, 1983.
Code_Aster
®
Version
5.0
Titrate:
TPLP302 Plates rectangular with imposed temperature
Date:
20/09/02
Author (S):
C. DURAND, E. SCREW, F. LEBOUVIER
Key
:
V4.05.302-A
Page:
4/6
Manual of Validation
V4.05 booklet: Stationary thermics of the plane structures
HT-66/02/001/A
3 Modeling
With
3.1
Characteristics of modeling
HULL (TRIA6)
Limiting conditions:
- dimensioned Al
= 100°
C
- dimensioned AD
= 0°
C
- dimensioned LM
= 0
- dimensioned DM
= 0
Cutting:
- 4 elements
according to X
- 40 elements
according to y
Points
X
Y
Nodes
E
0.05 0.05
N21
F
0.05 0.10
N39
G
0.05 0.15
N57
H
0.10 0.05
N23
I
0.10 0.10
N41
J
0.10 0.15
N59
K
0.10 0.20
N77
y
X
With
L
D
M
.1
2.
3.2
Characteristics of the mesh
A number of nodes:
729
A number of meshs and types: 320 TRIA6
3.3 Functionalities
tested
Controls
AFFE_MODELE
THERMICS
HULL
ALL
AFFE_CHAR_THER_F
TEMP_IMPO
TEMP_SUP
TEMP_INF
TEMP
THER_LINEAIRE
CARA_ELEM
EXCIT
CHARGE
RECU_CHAMP
NUME_ORDRE
3.4 Remarks
Limiting conditions, T = 100°C on AB, and T = 0°C on AD, are incompatible at point A. It
Code_Aster applies a “law of overload” which, in this case, consists in taking into account
last condition limits entered. The command of assignment of the imposed temperatures thus has large
influence on the results obtained.
In the treated case, the temperature assigned to point A is of 0°C.
Code_Aster
®
Version
5.0
Titrate:
TPLP302 Plates rectangular with imposed temperature
Date:
20/09/02
Author (S):
C. DURAND, E. SCREW, F. LEBOUVIER
Key
:
V4.05.302-A
Page:
5/6
Manual of Validation
V4.05 booklet: Stationary thermics of the plane structures
HT-66/02/001/A
4
Results of modeling A
4.1 Values
tested
Identification Reference
Aster difference
tolerance
Temperature (°C)
N21
(surface_supérieure)
43.496
43.499
0.007
1%
N21
(surface_moyenne)
43.496
43.499
0.007
1%
N21
(surface_inférieure)
43.496
43.499
0.007
1%
N39
(surface_supérieure)
18.978
18.957
-
0.112
1%
N39
(surface_moyenne)
18.978
18.957
-
0.112
1%
N39
(surface_inférieure)
18.978
18.957
-
0.112
1%
N57
(surface_supérieure)
8.559
8.554
-
0.057
1%
N57
(surface_moyenne)
8.559
8.554
-
0.057
1%
N57 (
surface_inférieure)
8.559
8.554
-
0.057
1%
N23
(surface_supérieure)
54.467
54.514
0.087
1%
N23
(surface_moyenne)
54.467
54.514
0.087
1%
N23 (
surface_inférieure)
54.467
54.514
0.087
1%
N41
(surface_supérieure)
26.096
26.096
-
0.001
1%
N41
(surface_moyenne)
26.096
26.096
-
0.001
1%
N41 (
surface_inférieure)
26.096
26.096
-
0.001
1%
N59
(surface_supérieure)
12.032
12.025
-
0.061
1%
N59
(surface_moyenne)
12.032
12.025
-
0.061
1%
N59 (
surface_inférieure)
12.032
12.025
-
0.061
1%
N77
(surface_supérieure)
5.499
5.496
-
0.063
1%
N77
(surface_moyenne)
5.499
5.496
-
0.063
1%
N77 (
surface_inférieure)
5.499
5.496
-
0.063
1%
4.2 Parameters
of execution
Version: 5.03
Machine: SGI - ORIGIN 2000 - R12000
Overall dimension memory:
8 megawords
Time CPU To use: 3.19 seconds
Code_Aster
®
Version
5.0
Titrate:
TPLP302 Plates rectangular with imposed temperature
Date:
20/09/02
Author (S):
C. DURAND, E. SCREW, F. LEBOUVIER
Key
:
V4.05.302-A
Page:
6/6
Manual of Validation
V4.05 booklet: Stationary thermics of the plane structures
HT-66/02/001/A
5
Summary of the results
Modeling HULL with meshs TRIA6 gives very satisfactory results, the variation
maximum obtained is 0.11%. The interest of this test is of:
·
to test meshs TRIA6 in HULL,
·
to compare the results compared to an analytical solution.