Code_Aster
®
Version
5.0
Titrate:
Orthotropic Cubic TPLV07
Date:
20/09/02
Author (S):
C. DURAND, E. SCREW, F. LEBOUVIER
Key
:
V4.04.007-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
V4.04.007 document
TPLV07 - Cubic orthotropic
Summary:
This test results from the validation independent of version 3 in linear stationary thermics.
It validates the voluminal thermal elements under conditions of imposed flow, of convection but also of
linear variation of the outside air temperature.
The results are compared with an analytical solution (VPCS).
Code_Aster
®
Version
5.0
Titrate:
Orthotropic Cubic TPLV07
Date:
20/09/02
Author (S):
C. DURAND, E. SCREW, F. LEBOUVIER
Key
:
V4.04.007-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
has
X
y
Z
O
Cubic of edge = 0.2 m has
Center cube = (0., 0., 0.)
1.2
Properties of material
X
= 1.0 W/m.°C thermal Conductivity along axis X
y
= 0.75 W/m.°C thermal Conductivity along the axis y
Z
= 0.50 W/m.°C thermal Conductivity along axis Z
1.3
Boundary conditions and loadings
·
density flux normal:
-
N
= 60 W/m ² face y =
-
0.1 (entering flow),
-
N
= - 60 W/m ² face y = 0.1 (outgoing flow),
-
N
= 30 W/m ² face Z =
-
0.1 (entering flow),
-
N
= - 30 W/m ² face Z = 0.1 (outgoing flow),
·
convection on the faces X = 0.1 and X = 0.1: H = 15 W/m
2
°C,
·
linear variation of the outside air temperatures,
- T
ext.
= 30 - 80y - 60z face X =
-
0.1,
- T
ext.
= 15 - 80y - 60z face X =
0.1.
1.4 Conditions
initial
Without object.
Code_Aster
®
Version
5.0
Titrate:
Orthotropic Cubic TPLV07
Date:
20/09/02
Author (S):
C. DURAND, E. SCREW, F. LEBOUVIER
Key
:
V4.04.007-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 TPLV07/89 of guide VPCS.
Analytical solution.
T (X, y, Z) = ax + by + cz + D
=
-
45x - 80y
-
60z + 22.5
I
With
NR
J
B
P
K
C
Q
L
D
R
M
S
H O
F
E
G
Not T (°C)
O
22.5
With
35.0
B
26.0
C
10.0
D
19.0
E
30.5
F
18.0
G
14.5
H
27.0
I
29.0
J
20.0
K
4.0
L
13.0
M
16.5
NR
41.0
P
32.0
Q
16.0
R
25.0
S
28.5
X
= 45 W/m ² = constant
y
= 60 W/m ² = constant
Z
= 30 W/m ² = constant
Z
y
X
2.2
Results of reference
Temperature at the points quoted in the table above.
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:
Orthotropic Cubic TPLV07
Date:
20/09/02
Author (S):
C. DURAND, E. SCREW, F. LEBOUVIER
Key
:
V4.04.007-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:
- face NPJI
N
= 60 W/m ²
- face RQKL
N
= - 60 W/m ²
- face NPQR
N
= 30 W/m ²
- face IJKL
N
= - 30 W/m ²
- face NRLI
H = 15 W/m ² °C
T
ext.
= 30-80y-60z
- face PQKJ
H = 15 W/m ² °C
T
ext.
= 15-80y-60z
Cutting:
- 6 elements according to X
- 6 elements following y
- 6 elements according to Z
I
NR
K
Q
L
R
O
y
X
Z
J
P
3.2
Characteristics of the mesh
A number of nodes:
343
A number of meshs and types: 216 HEXA8 (and 216 QUAD8)
3.3 Functionalities
tested
Controls
DEFI_MATERIAU
THER_ORTH
AFFE_MODELE
THERMICS
3D
ALL
AFFE_CARA_ELEM
SOLID MASS
ANGLE_REP
0. 0. 0.
DEFI_NAPPE
AFFE_CHAR_THER_F
FLUX_REP
EXCHANGE
THER_LINEAIRE
CARA_ELEM
EXCIT
CALC_CHAM_ELEM
CARA_ELEM
FLUX_ELNO_TEMP
3.4 Remarks
Voluminal heat
C
p
does not intervene in this test, but must be declared for Code_Aster. One
takes
C
p
= 1.0 J/m
3
°C.
Code_Aster
®
Version
5.0
Titrate:
Orthotropic Cubic TPLV07
Date:
20/09/02
Author (S):
C. DURAND, E. SCREW, F. LEBOUVIER
Key
:
V4.04.007-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
Relative variation (%)
Deviation absolute (°C, W/m
2
)
difference
tolerance
difference
tolerance
Not
Node
T
(°C)
O
N169
22.5
22.500
0.000% 1.% 2.50E-7 0.5
°C
With
N5
35.0
35.000 0.000%
1.%
1.03E-7
0.5
B
N301
26.0
26.000 0.000%
1.%
-
7.12E-8
0.5
C
N337
10.0
10.000
0.000%
1.%
-
7.72E-8
0.5
D
N49
19.0
19.000
0.000%
1.%
1.00E-7
0.5
E
N151
30.5
30.500 0.000%
1.%
2.54E-7
0.5
F
N316
18.0
18.000
0.000%
1.%
-
7.42E-8
0.5
G
N196
14.5
14.500
0.000%
1.%
2.46E-7
0.5
H
N24
27.0
27.000
0.000%
1.%
1.02E-7
0.5
I
N1
29.0
29.000
0.000%
1.%
1.14E-7
0.5
J
N298
20.0
20.000
0.000% 1.% 4.97E-7 0.5
K
N340
4.0
4.000 0.000%
1.%
-
4.64E-8
0.5
L
N44
13.0
13.000
0.000%
1.%
1.07E-7
0.5
M
N172
16.5
16.500
0.000%
1.%
2.89E-7
0.5
NR
N2
41.0
41.000
0.000%
1.%
9.66E-8
0.5
P
N297
32.0
32.000 0.000%
1.%
-
8.30E-8
0.5
Q
N338
16.0
16.000
0.000%
1.%
-
8.38E-8
0.5
R
N43
25.0
25.000
0.000%
1.%
9.59E-8
0.5
S
N173
28.5
28.500 0.000%
1.%
2.37E-7
0.5
Not mall
E
Node
(W/m
2
)
X
K
m211 N340
45.0
45.000
0.000%
1.%
-
1.73E-6
0.5 W/m
2
X
F
m201 N316
45.0
45.000
0.000%
1.%
-
1.13E-6
0.5
X
O m129 N169
45.0
45.000
0.000%
1.%
-
1.36E-6
0.5
y
K
m211 N340
60.0
60.000
0.000%
1.%
-
2.43E-6
0.5
y
F
m201 N316
60.0
60.000
0.000% 1.% 2.96E-8 0.5
y
O m129 N169
60.0
60.000
0.000% 1.% 4.49E-8 0.5
Z
K
m211 N340
30.0
30.000
0.000% 1.% - 3.71E-7 0.5
Z
F
m201 N316
30.0
30.000
0.000%
1.%
-
2.40E-7
0.5
Z
O m129 N169
30.0
30.000
0.000%
1.%
-
2.03E-7
0.5
4.2 Parameters
of execution
Version: 5.03
Machine: SGI - ORIGIN 2000 - R12000
Overall dimension memory:
8 megawords
Time CPU To use: 3.30 seconds
Code_Aster
®
Version
5.0
Titrate:
Orthotropic Cubic TPLV07
Date:
20/09/02
Author (S):
C. DURAND, E. SCREW, F. LEBOUVIER
Key
:
V4.04.007-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 excellent. The computed values by Aster are identical to the values of
reference. That is “a normally awaited” result since the field solution which is linear
belongs to the space of interpolation of the element tested.
This test made it possible to test the following controls:
·
DEFI_NAPPE
allowing to define a variation in the external temperature according to
X-coordinate X and of the ordinate y,
·
DEFI_MATERIAU
associated the key word
THER_ORTH
,
allowing to define the characteristics of one
orthotropic material,
·
AFFE_CARA_ELEM
associated the key word
SOLID MASS
,
allowing to define the axes of orthotropism.