Code_Aster ®
Version
5.0
Titrate:
Orthotropic TPLV07 Cube


Date:
20/09/02
Author (S):
C. DURAND, E. SCREW, F. LEBOUVIER Clé
:
V4.04.007-A Page:
1/6

Organization (S): EDF/AMA, EDF/UTO/LOCATED, Delta CAD
Handbook of Validation
V4.04 booklet: Stationary thermics of the voluminal structures
V4.04.007 document

TPLV07 - Orthotropic Cube

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 temperature.

The results are compared with an analytical solution (VPCS).

Handbook of Validation
V4.04 booklet: Stationary thermics of the voluminal structures
HT-66/02/001/A

Code_Aster ®
Version
5.0
Titrate:
Orthotropic TPLV07 Cube


Date:
20/09/02
Author (S):
C. DURAND, E. SCREW, F. LEBOUVIER Clé
:
V4.04.007-A Page:
2/6

1
Problem of reference

1.1 Geometry
has
Cubic of edge = 0.2 m has
Center cube = (0., 0., 0.)
Z
y
X
O


1.2
Properties of material

X = 1.0 W/m.°C thermal Conductivité following axis X
y = 0.75 W/m.°C thermal Conductivité following the axis y
Z = 0.50 W/m.°C thermal Conductivité following 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/m2 °C,

· linear variation of the outside temperatures,
- Text = 30 - 80y - 60z face X = - 0.1,
- Text = 15 - 80y - 60z face X =
0.1.

1.4 Conditions
initial

Without object.

Handbook of Validation
V4.04 booklet: Stationary thermics of the voluminal structures
HT-66/02/001/A

Code_Aster ®
Version
5.0
Titrate:
Orthotropic TPLV07 Cube


Date:
20/09/02
Author (S):
C. DURAND, E. SCREW, F. LEBOUVIER Clé
:
V4.04.007-A Page:
3/6

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

Z
Not T (°C)
L
K
O
22.5
M
With
35.0
B
26.0
I
y
J
C
10.0
G
D
C
D
19.0
E
30.5
H O F X
F
18.0
E
G
14.5
With
B
H
27.0
R
Q
I
29.0
S
J
20.0
K
4.0
L
13.0
NR
P
M
16.5
NR
41.0
P
32.0
X = 45 W/m ² = constant
Q
16.0
R
25.0
y = 60 W/m ² = constant
S
28.5
Z = 30 W/m ² = constant


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
Handbook of Validation
V4.04 booklet: Stationary thermics of the voluminal structures
HT-66/02/001/A

Code_Aster ®
Version
5.0
Titrate:
Orthotropic TPLV07 Cube


Date:
20/09/02
Author (S):
C. DURAND, E. SCREW, F. LEBOUVIER Clé
:
V4.04.007-A Page:
4/6

3 Modeling
With

3.1
Characteristics of modeling

3D (HEXA8)

Limiting conditions:
Z
- face NPJI
L
K
N = 60 W/m ²
- face RQKL
N = - 60 W/m ²
- face NPQR
I
J
N = 30 W/m ²
- face IJKL
N = - 30 W/m ²
y
- face NRLI
H = 15 W/m ² °C
T
X
ext. = 30-80y-60z
O
- face PQKJ
H = 15 W/m ² °C
Text = 15-80y-60z
Cutting:
R
Q
- 6 elements according to X
- 6 elements following y
NR
P
- 6 elements according to Z


3.2
Characteristics of the grid

A number of nodes:
343
A number of meshs and types: 216 HEXA8 (and 216 QUAD8)

3.3 Functionalities
tested

Commands




DEFI_MATERIAU
THER_ORTH

AFFE_MODELE
THERMIQUE
3D
TOUT
AFFE_CARA_ELEM
MASSIF
ANGLE_REP
0. 0. 0.

DEFI_NAPPE

AFFE_CHAR_THER_F
FLUX_REP
ECHANGE

THER_LINEAIRE
CARA_ELEM
EXCIT

CALC_CHAM_ELEM
CARA_ELEM
FLUX_ELNO_TEMP


3.4 Remarks

Voluminal heat CP does not intervene in this test, but must be declared for Code_Aster. One
takes CP = 1.0 J/m3 °C.

Handbook of Validation
V4.04 booklet: Stationary thermics of the voluminal structures
HT-66/02/001/A

Code_Aster ®
Version
5.0
Titrate:
Orthotropic TPLV07 Cube


Date:
20/09/02
Author (S):
C. DURAND, E. SCREW, F. LEBOUVIER Clé
:
V4.04.007-A Page:
5/6

4
Results of modeling A

4.1 Values
tested

Identification Reference
Aster
Relative variation (%)
Absolute deviation (°C, W/m2)


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
Node
(W/m2)





E
X K m211 N340
45.0
45.000
0.000%
1.%
- 1.73E-6
0.5 W/m2
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

Obstruction memory:
8 megawords
Time CPU To use: 3.30 seconds
Handbook of Validation
V4.04 booklet: Stationary thermics of the voluminal structures
HT-66/02/001/A

Code_Aster ®
Version
5.0
Titrate:
Orthotropic TPLV07 Cube


Date:
20/09/02
Author (S):
C. DURAND, E. SCREW, F. LEBOUVIER Clé
:
V4.04.007-A Page:
6/6

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 commands:

· DEFI_NAPPE allowing to define a variation in the external temperature according to
X-coordinate X and of the ordinate y,
· DEFI_MATERIAU associated with key word THER_ORTH, allowing to define the characteristics of one
orthotropic material,
· AFFE_CARA_ELEM associated with key word MASSIF, allowing to define the axes of orthotropism.

Handbook of Validation
V4.04 booklet: Stationary thermics of the voluminal structures
HT-66/02/001/A

Outline document