Code_Aster ®
Version
5.0
Titrate:
TTLV300 Parallélépipède subjected to a density flux on its faces
Date:
20/09/02
Author (S):
C. DURAND, E. SCREW, F. LEBOUVIER Clé
:
V4.25.300-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
V4.25.300 document

TTLV300 - Parallélépipède subjected to a density of
flow 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 a modeling 3D.

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

The results are compared with a three-dimensional 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:
TTLV300 Parallélépipède subjected to a density flux on its faces
Date:
20/09/02
Author (S):
C. DURAND, E. SCREW, F. LEBOUVIER Clé
:
V4.25.300-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
- L2 = 1.6 m
- L3 = 2.0 m
L2

Not O (0., 0., 0.)
X
C O
Not H (0.5, 0.8, 1.0)
Not C (1.0, 1.6, 2.0)
H
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

Flow imposed on the 6 faces Q = 0.5 W/m2 = qw

1.4 Conditions
initial

T (T = 0) = 1°C = T0

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

Code_Aster ®
Version
5.0
Titrate:
TTLV300 Parallélépipède subjected to a density flux on its faces
Date:
20/09/02
Author (S):
C. DURAND, E. SCREW, F. LEBOUVIER Clé
:
V4.25.300-A Page:
3/6

2
Reference solution

2.1
Method of calculation used for the reference solution

.t
T (X, y, Z, T) = T0 + 2qw
(A + B + C)
with:



(2m -)
1 L1 + X
(2m -)
1 L1 - X
With = i.erfc
+ i.erfc



=0
2 .t


2 .t

m


(2m -)
1 L2 + y
(2m -)
1 L2 - y
B = i.erfc
+ i.erfc



=0
2 .t


2 .t

m


(2m -)
1 L
Z
(2m -)

3 +
1 L - Z
C = i.erfc
+ i.erfc
3




=
2
.t


2
.t

m 0




= .cp

The values of reference are obtained with m = 1000.

2.2
Results of reference

Temperature at the points: O (0,0,0), H (0.5, 0.8, 1.) and C (1., 1.6, 2.)

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:
TTLV300 Parallélépipède subjected to a density flux on its faces
Date:
20/09/02
Author (S):
C. DURAND, E. SCREW, F. LEBOUVIER Clé
:
V4.25.300-A Page:
4/6

3 Modeling
With

3.1
Characteristics of modeling

3D (HEXA8, PENTA6)

Z
Modeling 1/8 of the parallelepiped
G
F
Grid:
- 6 elements according to X
L2
- 8 elements following y
- 10 elements according to Z
Limiting conditions:
D
C
- faces [ABCD], [BEFC], [DCFG]: qw = 0.5
H
- faces [ABEO], [AOGD], [OEFG]:
E X
= 0.
L3
O
3
L 2
Points
X
y
Z
Node
O
0.00
0.00
0.00
N2
H
0.50
0.8
1.00
N409
C
1.00
1.6
2.00
N814
With
B
L
y
1


3.2
Characteristics of the grid

A number of nodes:
819
A number of meshs and types: 288 HEXA8, 576 PENTA6 (168 QUAD4, 96 TRIA3)

3.3 Functionalities
tested

Commands




AFFE_MODELE
THERMIQUE
3D

AFFE_CHAR_THER
FLUX_REP

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: 36 intervals, between 0 and 10 seconds (of 0.005 S with 1.s by interval).
Handbook of Validation
V4.25 booklet: Transitory thermics of the voluminal structures
HT-66/02/001/A

Code_Aster ®
Version
5.0
Titrate:
TTLV300 Parallélépipède subjected to a density flux on its faces
Date:
20/09/02
Author (S):
C. DURAND, E. SCREW, F. LEBOUVIER Clé
:
V4.25.300-A Page:
5/6

4
Results of modeling A

4.1 Values
tested

Identification
Reference
Aster %
difference
Tolerance
Not O




(N2) T = 0.05 S
1.0001
1.00000443
- 0.010
1%
T = 0.1 S
1.00398
1.003172
- 0.080
1%
T = 0.2 S
1.03331
1.03127
- 0.198
1%
T = 0.3 S
1.08533
1.08227
- 0.282
1%
T = 0.5 S
1.23086
1.2266
- 0.345
1%
T = 1. S
1.69979
1.6945
- 0.311
1%
T = 5. S
5.9292
5.9234
- 0.098
1%
T = 10. S
11.242
11.236
- 0.054
1%





Not H




(N409) T = 0.05 S
1.0083
1.006472
- 0.181
1%
T = 0.1 S
1.03819
1.03573
- 0.237
1%
T = 0.2 S
1.12556
1.1229
- 0.235
1%
T = 0.3 S
1.22594
1.2233
- 0.217
1%
T = 0.5 S
1.43580
1.4331
- 0.188
1%
T = 1. S
1.96667
1.9639
- 0.140
1%
T = 5. S
6.2167
6.2139
- 0.045
1%
T = 10. S
11.529
11.526
- 0.023
1%





Not C




(N814) T = 0.05 S
1.3785
1.3726
- 0.429
1%
T = 0.1 S
1.5352
1.5308
- 0.290
1%
T = 0.2 S
1.7572
1.7536
- 0.206
1%
T = 0.3 S
1.9295
1.9261
- 0.176
1%
T = 0.5 S
2.2142
2.2110
- 0.146
1%
T = 1. S
2.8085
2.8054
- 0.112
1%
T = 5. S
7.0792
7.0762
- 0.043
1%
T = 10. S
12.392
12.389
- 0.027
1%

4.2 Parameters
of execution

Version: 5.03


Machine: SGI - ORIGIN 2000 - R12000

Obstruction memory:
8 megawords
Time CPU To use: 7.07 seconds
Handbook of Validation
V4.25 booklet: Transitory thermics of the voluminal structures
HT-66/02/001/A

Code_Aster ®
Version
5.0
Titrate:
TTLV300 Parallélépipède subjected to a density flux on its faces
Date:
20/09/02
Author (S):
C. DURAND, E. SCREW, F. LEBOUVIER Clé
:
V4.25.300-A Page:
6/6

5
Summary of the results

The results obtained are satisfactory. The maximum change (0.43%), is located on external surface
parallelepiped (Point C) at the moment T weakest. At the end of 10 S, this variation decreases, the maximum
is then of 0.054% (not O: center parallelepiped).

This test made it possible to test in linear transient modeling 3D with meshs HEXA8 and
PENTA6.

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

Outline document