Code_Aster ®
Version
5.0
Titrate:
Thermal TTLL303 Transfert in a bar with generation of heat
Date:
20/09/02
Author (S):
C. DURAND, E. SCREW, F. LEBOUVIER Clé
:
V4.21.303-A Page:
1/6

Organization (S): EDF/AMA, EDF/UTO/LOCATED, Delta CAD
Handbook of Validation
V4.21 booklet: Transitory thermics of the linear structures
V4.21.303 document

TTLL303 - Thermal Transfert in a bar with
internal generation of heat

Summary:

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

It is about a problem plane 2D represented by only one modeling (plane).

The functionalities tested are as follows:
· plane thermal element,
· transitory algorithm of thermics,
· limiting conditions: heat source.

The interest of the test lies in the taking into account of a heat source.

The results are compared with an analytical solution.
Handbook of Validation
V4.21 booklet: Transitory thermics of the linear structures
HT-66/02/001/A

Code_Aster ®
Version
5.0
Titrate:
Thermal TTLL303 Transfert in a bar with generation of heat
Date:
20/09/02
Author (S):
C. DURAND, E. SCREW, F. LEBOUVIER Clé
:
V4.21.303-A Page:
2/6

1
Problem of reference

1.1 Geometry

y
D
C
Q
X
E
F
With
0.05 m
B
2L = 0.2 m


1.2
Properties of material


=
100 W/m °C
thermal conductivity
CP = 7000
J/voluminal m3 °C heat

1.3
Boundary conditions and loadings

· Heat source interns Q = 106 W/m3,
· [AB], [CD] = 0,
· [BC], [DA] T = 0 °C.

1.4 Conditions
initial

T (T = 0) = 0°C

Handbook of Validation
V4.21 booklet: Transitory thermics of the linear structures
HT-66/02/001/A

Code_Aster ®
Version
5.0
Titrate:
Thermal TTLL303 Transfert in a bar with generation of heat
Date:
20/09/02
Author (S):
C. DURAND, E. SCREW, F. LEBOUVIER Clé
:
V4.21.303-A Page:
3/6

2
Reference solution

2.1
Method of calculation used for the reference solution

QL2
X 2

I

32
(- 1)
2i + 1

2i + 1 2
T =

1 -
cos
exp

3

T
2



L -
3
= (2 1)
2


2
0
+




-






I
I
L
C
L


The values of reference are obtained with I = 1000.

2.2
Results of reference

Temperature at the points E and F at the moment T = 0.25 and 0.5 S

2.3
Uncertainty on the solution

Analytical solution.

2.4 References
bibliographical

[1]
B.M. Nicolaï, J. of Baerdemaeker, “Computation off heat conduction in materials with random
variable thermophysical properties ", Int. J. num. Meth. Engng, flight 36, p 523-536, 1993.
Handbook of Validation
V4.21 booklet: Transitory thermics of the linear structures
HT-66/02/001/A

Code_Aster ®
Version
5.0
Titrate:
Thermal TTLL303 Transfert in a bar with generation of heat
Date:
20/09/02
Author (S):
C. DURAND, E. SCREW, F. LEBOUVIER Clé
:
V4.21.303-A Page:
4/6

3 Modeling
With

3.1
Characteristics of modeling

PLAN (TRIA6, QUAD8)

Y
X
C
y
=15°
N151
0.03
N152
G
N154
X
N1
N156
N4
B
N158
N7
N161
N10
N163
N13
0.1
N16
0.05
N19
E
Limiting conditions:
- dimensioned EB, CG, GE = 0
- dimensioned BC
T = 0 °C


3.2
Characteristics of the grid

A number of nodes:
314
A number of meshs and types: 97 (20 TRIA6, 77QUAD8)

3.3 Functionalities
tested


Commands




AFFE_MODELE
THERMIQUE
PLAN
AFFE_CHAR_THER_F
SOURCE

TEMP_IMPO
TOUT

THER_LINEAIRE
TEMP_INIT
VALE

LIST_INST

RECU_CHAMP
INST


3.4 Remarks

The discretization in step of time is as follows:

50 steps for [0. , 0.50] are T = 1.D-2
Handbook of Validation
V4.21 booklet: Transitory thermics of the linear structures
HT-66/02/001/A

Code_Aster ®
Version
5.0
Titrate:
Thermal TTLL303 Transfert in a bar with generation of heat
Date:
20/09/02
Author (S):
C. DURAND, E. SCREW, F. LEBOUVIER Clé
:
V4.21.303-A Page:
5/6

4
Results of modeling A

4.1 Values
tested




Relative variation %
Absolute deviation
Identification Reference
Aster difference tolerance difference tolerance
Temperatures (°C)






X = 0, T = 0.25 S






N1 28.62
28.58
- 0.145
1%
- 0.042
0.05
N4 28.62
28.58
- 0.145
1%
- 0.042
0.05
N7 28.62
28.58
- 0.145
1%
- 0.042
0.05
N10 28.62
28.58
- 0.145
1%
- 0.042
0.05
N13 28.62
28.58
- 0.145
1%
- 0.042
0.05
N16 28.62
28.58
- 0.145
1%
- 0.042
0.05
N19 28.62
28.58
- 0.145
1%
- 0.042
0.05
X = 0.05, T = 0.25 S






N151 22.38
22.35
- 0.127
1%
- 0.028
0.05
N152 22.38
22.35
- 0.127
1%
- 0.028
0.05
N154 22.38
22.35
- 0.127
1%
- 0.028
0.05
N156 22.38
22.35
- 0.127
1%
- 0.028
0.05
N158 22.38
22.35
- 0.127
1%
- 0.028
0.05
N161 22.38
22.35
- 0.127
1%
- 0.028
0.05
N163 22.38
22.35
- 0.127
1%
- 0.028
0.05
X = 0, T = 0.50 S






N1 41.14
41.11
- 0.081
1%
- 0.033
0.05
N4 41.14
41.11
- 0.080
1%
- 0.033
0.05
N7 41.14
41.11
- 0.081
1%
- 0.033
0.05
N10 41.14
41.11
- 0.081
1%
- 0.033
0.05
N13 41.14
41.11
- 0.081
1%
- 0.033
0.05
N16 41.14
41.11
- 0.081
1%
- 0.033
0.05
N19 41.14
41.11
- 0.081
1%
- 0.033
0.05
X = 0.05, T = 0.50s






N151 31.24
31.21
- 0.091
1%
- 0.029
0.05
N152 31.24
31.21
- 0.091
1%
- 0.029
0.05
N154 31.24
31.21
- 0.091
1%
- 0.029
0.05
N156 31.24
31.21
- 0.091
1%
- 0.029
0.05
N158 31.24
31.21
- 0.091
1%
- 0.029
0.05
N161 31.24
31.21
- 0.091
1%
- 0.029
0.05
N163 31.24
31.21
- 0.091
1%
- 0.029
0.05

4.2 Parameters
of execution

Version: 5.03


Machine: SGI - ORIGIN 2000 - R12000

Obstruction memory:
8 megawords
Time CPU To use: 4.04 seconds
Handbook of Validation
V4.21 booklet: Transitory thermics of the linear structures
HT-66/02/001/A

Code_Aster ®
Version
5.0
Titrate:
Thermal TTLL303 Transfert in a bar with generation of heat
Date:
20/09/02
Author (S):
C. DURAND, E. SCREW, F. LEBOUVIER Clé
:
V4.21.303-A Page:
6/6

5
Summary of the results

The results obtained are satisfactory, the maximum change is of ­ 0.15%.

The points of observations, located at X = 0.05 and pertaining to meshs of the different types, have it
even result.

This test made it possible to test in linear transient (modeling PLAN), the command
AFFE_CHAR_THER_F with operand SOURCE.

Handbook of Validation
V4.21 booklet: Transitory thermics of the linear structures
HT-66/02/001/A

Outline document