background image
Code_Aster
®
Version
5.0
Titrate:
Thermal TTLL303 Transfer in a bar with generation of heat
Date:
20/09/02
Author (S):
C. DURAND, E. SCREW, F. LEBOUVIER
Key
:
V4.21.303-A
Page:
1/6
Manual of Validation
V4.21 booklet: Transitory thermics of the linear structures
HT-66/02/001/A
Organization (S):
EDF/AMA, EDF/UTO/LOCATED, Delta CAD















Manual of Validation
V4.21 booklet: Transitory thermics of the linear structures
V4.21.303 document



TTLL303 - Thermal transfer 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.
background image
Code_Aster
®
Version
5.0
Titrate:
Thermal TTLL303 Transfer in a bar with generation of heat
Date:
20/09/02
Author (S):
C. DURAND, E. SCREW, F. LEBOUVIER
Key
:
V4.21.303-A
Page:
2/6
Manual of Validation
V4.21 booklet: Transitory thermics of the linear structures
HT-66/02/001/A
1
Problem of reference
1.1 Geometry
2L = 0.2 m
C
D
B
With
y
X
With
Q
0.05 m
E
F

1.2
Properties of material
=
100 W/m °C
thermal conductivity
C
p
= 7000
J/m
3
°C voluminal heat

1.3
Boundary conditions and loadings
·
Heat source interns Q = 10
6
W/m
3
,
·
[AB], [CD]
= 0,
·
[BC], [DA] T = 0 °C.

1.4 Conditions
initial
T (T = 0) = 0°C
background image
Code_Aster
®
Version
5.0
Titrate:
Thermal TTLL303 Transfer in a bar with generation of heat
Date:
20/09/02
Author (S):
C. DURAND, E. SCREW, F. LEBOUVIER
Key
:
V4.21.303-A
Page:
3/6
Manual of Validation
V4.21 booklet: Transitory thermics of the linear structures
HT-66/02/001/A
2
Reference solution
2.1
Method of calculation used for the reference solution
T
QL
X
L
I
I
L
C
I
L
T
I
I
=
-


-
-
+
+




-
+














=
2
2
3
3
2
0
2
1
32
1
2
1
2
1
2
2
1
2
()
(
) cos
exp
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.
background image
Code_Aster
®
Version
5.0
Titrate:
Thermal TTLL303 Transfer in a bar with generation of heat
Date:
20/09/02
Author (S):
C. DURAND, E. SCREW, F. LEBOUVIER
Key
:
V4.21.303-A
Page:
4/6
Manual of Validation
V4.21 booklet: Transitory thermics of the linear structures
HT-66/02/001/A
3 Modeling
With
3.1
Characteristics of modeling
PLAN (TRIA6, QUAD8)
G
B
E
X
Limiting conditions:
- dimensioned EB, CG, GE
= 0
- dimensioned BC
T = 0 °C
C
Y
y
X
0.05
0.1
0.03
=15°
N163
N151
N152
N154
N156
N158
N161
N19
N1
N4
N7
N10
N13
N16
3.2
Characteristics of the mesh
A number of nodes:
314
A number of meshs and types: 97 (20 TRIA6, 77QUAD8)
3.3 Functionalities
tested
Controls
AFFE_MODELE
THERMICS
PLAN
AFFE_CHAR_THER_F
SOURCE
TEMP_IMPO
ALL
THER_LINEAIRE
TEMP_INIT
VALE
LIST_INST
RECU_CHAMP
INST
3.4 Remarks
The discretization in pitch of time is as follows:
50 pitches for [0. , 0.50] are
T = 1.D-2
background image
Code_Aster
®
Version
5.0
Titrate:
Thermal TTLL303 Transfer in a bar with generation of heat
Date:
20/09/02
Author (S):
C. DURAND, E. SCREW, F. LEBOUVIER
Key
:
V4.21.303-A
Page:
5/6
Manual of Validation
V4.21 booklet: Transitory thermics of the linear structures
HT-66/02/001/A
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
Overall dimension memory:
8 megawords
Time CPU To use: 4.04 seconds
background image
Code_Aster
®
Version
5.0
Titrate:
Thermal TTLL303 Transfer in a bar with generation of heat
Date:
20/09/02
Author (S):
C. DURAND, E. SCREW, F. LEBOUVIER
Key
:
V4.21.303-A
Page:
6/6
Manual of Validation
V4.21 booklet: Transitory thermics of the linear structures
HT-66/02/001/A
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 control
AFFE_CHAR_THER_F
with the operand
SOURCE
.