Code_Aster ®
Version
5.0
Titrate:
TTLV301 Parallélépipède subjected to a temperature imposed on its Date faces:
20/09/02
Author (S):
C. DURAND, E. SCREW, F. LEBOUVIER Clé
:
V4.25.301-A Page:
1/6

Organization (S): EDF/AMA, EDF/UTO/LOCATED, Delta CAD
Handbook of Validation
V4.25 booklet: Transitory thermics of the voluminal structures
V4.25.301 document

TTLV301 - Parallélépipède subjected to one
temperature imposed on its faces

Summary:

This test results from the validation independent of version 3 in linear transitory thermics.

It is about a voluminal problem represented by only one modeling (3D).

The functionalities tested are as follows:
· voluminal thermal element,
· transitory algorithm of thermics,
· limiting conditions: imposed temperature.

The results are compared with an analytical solution.

Handbook of Validation
V4.25 booklet: Transitory thermics of the voluminal structures
HT-66/02/001/A

Code_Aster ®
Version
5.0
Titrate:
TTLV301 Parallélépipède subjected to a temperature imposed on its Date faces:
20/09/02
Author (S):
C. DURAND, E. SCREW, F. LEBOUVIER Clé
:
V4.25.301-A Page:
2/6

1
Problem of reference

1.1 Geometry

Z
Dimensions of the parallelepiped: 2m X 3.2m X 4m
- L1 = 1.0 m
- L
L2
2 = 1.6 m
- L3 = 2.0 m
O
X
Not O (0., 0., 0.)
H
Not H (0.5, 0.8, 1.0)
L3
Y
L1


1.2
Properties of material


=
1. W/m °C
thermal conductivity
CP
=
1. J/kg °C
specific heat

1.
kg/m3 masses
voluminal

1.3
Boundary conditions and loadings

Temperature imposed on the 6 faces T = 2 °C = Tw

1.4 Conditions
initial

T (T = 0) = 1°C = To

Handbook of Validation
V4.25 booklet: Transitory thermics of the voluminal structures
HT-66/02/001/A

Code_Aster ®
Version
5.0
Titrate:
TTLV301 Parallélépipède subjected to a temperature imposed on its Date faces:
20/09/02
Author (S):
C. DURAND, E. SCREW, F. LEBOUVIER Clé
:
V4.25.301-A Page:
3/6

2
Reference solution

2.1
Method of calculation used for the reference solution




(2m
2
-)
1 X

(2n -) 1 y

(2l -)
1 Z

T (X, y, Z, T) = T + has
exp (-
.t




W
nml
mnl
) .cos
cos
cos

2L1





m=1 n=1 l=1

2L2


2L3
(
64 T0 - Tw)
(2m -)
1
(2n -)
1
(2l -)
1
amnl = 3
(
sin
sin
sin
2m -)
1 (2n -)
1 (2l -)
1


2




2




2


2
2
2
m

N

L

2
(2 -) 1
(2 -) 1
(2 -) 1
mnl =
+
+

2L
2L
2

1


2


3
L


= .cp

The values of reference are obtained with m = N = L = 100.

2.2
Results of reference

Temperature at the points: O (0,0,0) and H (0.5, 0.8, 1.)

2.3
Uncertainty on the solution

Analytical solution.

2.4 References
bibliographical

[1]
Mr. J Chang, L.C Chow, W.S Chang, “Improved alternating direction implicit for solving
transient three dimensional heat diffusion problems ", Numerical Heat Transfer, flight 19, p 69-
84, 1991.
Handbook of Validation
V4.25 booklet: Transitory thermics of the voluminal structures
HT-66/02/001/A

Code_Aster ®
Version
5.0
Titrate:
TTLV301 Parallélépipède subjected to a temperature imposed on its Date faces:
20/09/02
Author (S):
C. DURAND, E. SCREW, F. LEBOUVIER Clé
:
V4.25.301-A Page:
4/6

3 Modeling
With

3.1
Characteristics of modeling

3D (HEXA27)

Z
Modeling 1/8 of the parallelepiped
G
F
Grid:
- 5 elements according to X
L2
- 8 elements following y
- 10 elements according to Z
Limiting conditions:
D
C
- faces [ABCD], [BEFC], [DCFG]: T = 2°C
- faces [ABEO], [AOGD], [OEFG]: = 0.
H
E X
L3
O
Points
X
y
Z
Node
O
0.00
0.00
0.00
N5
H
0.50
0.80
1.00
N1075
With
B
L
y
1


3.2
Characteristics of the grid

A number of nodes:
3927
A number of meshs and types: 400 HEXA27

3.3 Functionalities
tested

Commands




AFFE_MODELE
THERMIQUE
3D

AFFE_CHAR_THER
TEMP_IMPO

THER_LINEAIRE
TEMP_INIT
VALE

LIST_INST

RECU_CHAMP
INST


3.4 Remarks

The condition limits = 0. is implicit on the free edges.

Discretization of time: 24 intervals between 0. and 1.2 seconds:

T = 0.00
with T = 0.02
: 4 0.005 seconds intervals.
T = 0.02
with T = 0.05
: 3 intervals of 0.01
seconds.
T = 0.05
with T = 0.15
: 4 0.025 seconds intervals.
T = 0.15
with T = 0.4
: 5 intervals of 0.05
seconds.
T = 0.4
with T = 1.2
: 8 intervals of 0.1
seconds.
Handbook of Validation
V4.25 booklet: Transitory thermics of the voluminal structures
HT-66/02/001/A

Code_Aster ®
Version
5.0
Titrate:
TTLV301 Parallélépipède subjected to a temperature imposed on its Date faces:
20/09/02
Author (S):
C. DURAND, E. SCREW, F. LEBOUVIER Clé
:
V4.25.301-A Page:
5/6

4
Results of modeling A

4.1 Values
tested

Identification
Reference
Aster %
difference
Tolerance
Not O




N5 (0., 0., 0.)




T = 0.1 S
1.05137
1.04934
- 0.193
1%
T = 0.2 S
1.24768
1.24181
- 0.471
1%
T = 0.3 S
1.45136
1.44378
- 0.522
1%
T = 0.5 S
1.73684
1.72955
- 0.420
1%
T = 0.7 S
1.88010
1.87516
- 0.263
1%
T = 1.0 S
1.96406
1.96191
- 0.110
1%
T = 1.2 S
1.98398
1.98282
- 0.059
1%





Not H




N1075 (0.5, 0.8, 1.0)




T = 0.1 S
1.33579
1.32490
- 0.816
1%
T = 0.2 S
1.61081
1.60337
- 0.462
1%
T = 0.3 S
1.75959
1.75424
- 0.304
1%
T = 0.5 S
1.90017
1.89718
- 0.157
1%
T = 0.7 S
1.95657
1.95478
- 0.091
1%
T = 1.0 S
1.98723
1.98646
- 0.039
1%
T = 1.2 S
1.99433
1.99391
- 0.021
1%

4.2 Parameters
of execution

Version: 5.03


Machine: SGI - ORIGIN 2000 - R12000

Obstruction memory:
8 megawords
Time CPU To use: 16.36 seconds
Handbook of Validation
V4.25 booklet: Transitory thermics of the voluminal structures
HT-66/02/001/A

Code_Aster ®
Version
5.0
Titrate:
TTLV301 Parallélépipède subjected to a temperature imposed on its Date faces:
20/09/02
Author (S):
C. DURAND, E. SCREW, F. LEBOUVIER Clé
:
V4.25.301-A Page:
6/6

5
Summary of the results

The results obtained are satisfactory. The maximum change obtained (0.816%), is located at the point H placed
halfway enters surface external and the center of the parallelepiped. At the end of 1.2s, this variation
decrease, the maximum obtained is then of 0.059% (not O: center parallelepiped).

This test made it possible to test in linear transient modeling 3D with meshs HEXA27.

Handbook of Validation
V4.25 booklet: Transitory thermics of the voluminal structures
HT-66/02/001/A

Outline document