background image
Code_Aster
®
Version
5.0
Titrate:
TTLV01 Sphere: heat transfer by convection
Date:
20/09/02
Author (S):
C. DURAND,
E. SCREWS, F. LEBOUVIER
Key
:
V4.25.001-A
Page:
1/12
Manual of Validation
V4.25 booklet: Transitory thermics of the voluminal structures
HT-66/02/001/A
Organization (S):
EDF/AMA, EDF/UTO/LOCATED, Delta CAD















Manual of Validation
V4.25 booklet: Transitory thermics of the voluminal structures
V4.25.001 document



TTLV01 - Sphere: heat transfer by
convection




Summary:

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

It is about a three-dimensional problem represented by four modelings, one voluminal, the three others
axisymmetric.

The functionalities tested are as follows:
·
voluminal thermal elements,
·
axisymmetric thermal elements,
·
transitory algorithm of thermics,
·
limiting conditions: convection.

The results are compared with those provided by VPCS.
background image
Code_Aster
®
Version
5.0
Titrate:
TTLV01 Sphere: heat transfer by convection
Date:
20/09/02
Author (S):
C. DURAND,
E. SCREWS, F. LEBOUVIER
Key
:
V4.25.001-A
Page:
2/12
Manual of Validation
V4.25 booklet: Transitory thermics of the voluminal structures
HT-66/02/001/A
1
Problem of reference
1.1 Geometry
D
R
O
D = 0.2m
H
E
, T
E

1.2
Properties of material
=
48.822 W/m °C conductivity thermal
C
p
=
669.0 J/kg °C specific heat
7200 kg/m
3
mass
voluminal

1.3
Boundary conditions and loadings
Convection on external surface with air:
·
H
E
= 232.5 W/m
2
°C,
·
T
E
= 1000 °C.

1.4 Conditions
initial
Initial temperature: T (T = 0) = 20 °C
background image
Code_Aster
®
Version
5.0
Titrate:
TTLV01 Sphere: heat transfer by convection
Date:
20/09/02
Author (S):
C. DURAND,
E. SCREWS, F. LEBOUVIER
Key
:
V4.25.001-A
Page:
3/12
Manual of Validation
V4.25 booklet: Transitory thermics of the voluminal structures
HT-66/02/001/A
2
Reference solution
2.1
Method of calculation used for the reference solution
The reference solution is that given in card TTLV01/89 of guide VPCS.
·
calculation of the coefficients,
·
reading on abacus of Gurney-Lurie.

2.2
Results of reference
Temperature on the surface and in the center of the sphere for T ranging between 400 S and 2400 S

2.3
Uncertainty on the solution
< 2%
In 600 second old lower part, uncertainty increases (difficult reading of the abacuses).

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
background image
Code_Aster
®
Version
5.0
Titrate:
TTLV01 Sphere: heat transfer by convection
Date:
20/09/02
Author (S):
C. DURAND,
E. SCREWS, F. LEBOUVIER
Key
:
V4.25.001-A
Page:
4/12
Manual of Validation
V4.25 booklet: Transitory thermics of the voluminal structures
HT-66/02/001/A
3 Modeling
With
3.1
Characteristics of modeling
3D (PENTA6 and TETRA4)
15°
Limiting conditions:
- faces OAB, OAD,
ODC, OBC
= 0
- face ABCD
H = 232.5 W/m ² °C
T
ext.
=1000°C
Not
Node
O
N291
With
N292
B
N345
C
N234
D
N179
E
N254
F
N133
G
N5
H
N198
C
B
O
X
y
Z
30°
30°
D
22,5°
With
G
H
E
F
3.2
Characteristics of the mesh
A number of nodes:
361
A number of meshs and types: 450 PENTA6, 50 TETRA4 (and 50 TRIA3)
3.3 Functionalities
tested
Controls
AFFE_MODELE
AFFE
THERMICS
3D
AFFE_CHAR_THER_F
EXCHANGE
THER_LINEAIRE
TEMP_INIT
VALE
INCREMENT
LIST_INST
RECU_CHAMP
INST
3.4 Remarks
One takes, for voluminal heat, CP =
C
p
= 4816800.0 J/m
3
°C.
The limiting condition
= 0. are implicit on the free edges.
Discretization of time: (36 intervals)
of
0 to 100 seconds: 8 intervals of 12.5 S.
of
100 to 300 seconds: 8 intervals of 25.0 S.
of
300 to 700 seconds: 8 intervals of 50.0 S.
of
700 to 1400 seconds: 7 intervals of 100.0 S.
of
1400 to 2400 seconds: 5 intervals of 200.0 S.
background image
Code_Aster
®
Version
5.0
Titrate:
TTLV01 Sphere: heat transfer by convection
Date:
20/09/02
Author (S):
C. DURAND,
E. SCREWS, F. LEBOUVIER
Key
:
V4.25.001-A
Page:
5/12
Manual of Validation
V4.25 booklet: Transitory thermics of the voluminal structures
HT-66/02/001/A
4
Results of modeling A
4.1 Values
tested
Identification Reference
Aster
Relative variation (%)
Absolute deviation (°C)
difference
tolerance
difference
tolerance
Temperatures:
In the center (O: N291)
T (°C)
T = 400 S
334
340.56
1.965%
5.%
6.56
20.
T = 600 S
500
493.15
-
1.371%
5.%
-
6.85
20.
T = 800 S
618
610.27
-
1.252%
5.%
-
7.73
20.
T = 1000 S
706
700.18
-
0.824%
5.%
-
5.82
20.
T = 1200 S
774
769.35
-
0.600%
5.%
-
4.65
20.
T = 1400 S
828
822.57
-
0.656%
5.%
-
5.43
20.
T = 1600 S
872
863.33
-
0.994%
5.%
-
8.67
20.
T = 1800 S
902
894.73
-
0.806%
5.%
-
7.27
20.
T = 2000 S
923
918.91
-
0.443%
5.%
-
4.09
20.
T = 2200 S
942
937.54
-
0.474%
5.%
-
4.46
20.
T = 2400 S
956
951.89
-
0.430%
5.%
-
4.11
20.
On the surface (a: N292)
T (°C)
T = 400 S
461
474.82
2.998%
5.%
13.8
20.
T = 600 S
608
596.37
-
1.913%
5.%
-
11.6
20.
T = 800 S
696
689.64
-
0.914%
5.%
-
6.36
20.
T = 1000 S
774
761.24
-
1.648%
5.%
-
12.8
20.
T = 1200 S
828
816.33
-
1.410%
5.%
-
11.7
20.
T = 1400 S
868
858.70
-
1.071%
5.%
-
9.30
20.
T = 1600 S
902
891.16
-
1.202%
5.%
-
10.8
20.
T = 1800 S
923
916.17
-
0.741%
5.%
-
6.83
20.
T = 2000 S
942
935.42
-
0.698%
5.%
-
6.58
20.
T = 2200 S
956
950.26
-
0.601%
5.%
-
5.74
20.
T = 2400 S
962
961.69
-
0.033%
5.%
-
0.314
20.

4.2 Remarks
The relative variations are higher than 2% for T = 400. S, inferiors for T
600. S
On the surface, the results calculated by Code_Aster are symmetrical compared to the diagonal AC.
The maximum variation observed, into relative as in absolute, is 0.29% is 1,4°C, between point A (N291)
and the point D (N179) at the moment T = 400. S. These variations decrease in absolute value when time
increase.

4.3 Parameters
of execution
Version: 5.03
Machine: SGI - ORIGIN 2000 - R12000
Overall dimension memory:
8 megawords
Time CPU To use: 5.76 seconds
background image
Code_Aster
®
Version
5.0
Titrate:
TTLV01 Sphere: heat transfer by convection
Date:
20/09/02
Author (S):
C. DURAND,
E. SCREWS, F. LEBOUVIER
Key
:
V4.25.001-A
Page:
6/12
Manual of Validation
V4.25 booklet: Transitory thermics of the voluminal structures
HT-66/02/001/A
5 Modeling
B
5.1
Characteristics of modeling
AXIS (TRIA3, QUAD4)
Limiting conditions:
- dimensioned AB, AC
= 0
- dimensioned BC
H = 232.5 W/m ² °C
T
ext.
=1000°C
Not
Node
With
N1
B
N56
C
N61
X
With
(R)
15°
30°
C
N1
B
y
(Z)
N61
N60
N59
N58
N57
N56
5.2
Characteristics of the mesh
A number of nodes:
61
A number of meshs and types: 45 QUAD4, 5 TRIA3 (and 5 SEG2)
5.3 Functionalities
tested
Controls
AFFE_MODELE
AFFE
THERMICS
AXIS
AFFE_CHAR_THER
EXCHANGE
THER_LINEAIRE
TEMP_INIT
VALE
INCREMENT
LIST_INST
RECU_CHAMP
INST
5.4 Remarks
One takes, for voluminal heat, CP =
C
p
= 4816800.0 J/m
3
°C.
The limiting condition
= 0. are implicit on the free edges.
Discretization of time: (36 intervals)
of
0 to 100 seconds: 8 intervals of 12.5 S.
of
100 to 300 seconds: 8 intervals of 25.0 S.
of
300 to 700 seconds: 8 intervals of 50.0 S.
of
700 to 1400 seconds: 7 intervals of 100.0 S.
of
1400 to 2400 seconds: 5 intervals of 200.0 S.
background image
Code_Aster
®
Version
5.0
Titrate:
TTLV01 Sphere: heat transfer by convection
Date:
20/09/02
Author (S):
C. DURAND,
E. SCREWS, F. LEBOUVIER
Key
:
V4.25.001-A
Page:
7/12
Manual of Validation
V4.25 booklet: Transitory thermics of the voluminal structures
HT-66/02/001/A
6
Results of modeling B
6.1 Values
tested
Identification Reference
Aster
Relative variation (%)
Absolute deviation (°C)
difference
tolerance
difference
tolerance
Temperatures:
In center (a: N1)
T (°C)
T = 400 S
334
339.95
1.780%
5.%
5.95
20.
T = 600 S
500
492.47
-
1.506%
5.%
-
7.53
20.
T = 800 S
618
609.59
-
1.361%
5.%
-
8.41
20.
T = 1000 S
706
699.55
-
0.914%
5.%
-
6.45
20.
T = 1200 S
774
768.78
-
0.675%
5.%
-
5.22
20.
T = 1400 S
828
822.05
-
0.718%
5.%
-
5.95
20.
T = 1600 S
872
862.88
-
1.046%
5.%
-
9.12
20.
T = 1800 S
902
894.34
-
0.849%
5.%
-
7.66
20.
T = 2000 S
923
918.58
-
0.479%
5.%
-
4.42
20.
T = 2200 S
942
937.26
-
0.503%
5.%
-
4.74
20.
T = 2400 S
956
951.65
-
0.455%
5.%
-
4.35
20.
On the surface (NR: N56)
T (°C)
T = 400 S
461
475.14
3.068%
5.%
14.1
20.
T = 600 S
608
596.46
-
1.899%
5.%
-
11.5
20.
T = 800 S
696
689.58
-
0.922%
5.%
-
6.42
20.
T = 1000 S
774
761.11
-
1.666%
5.%
-
12.9
20.
T = 1200 S
828
816.15
-
1.431%
5.%
-
11.8
20.
T = 1400 S
868
858.51
-
1.093%
5.%
-
9.49
20.
T = 1600 S
902
890.97
-
1.223%
5.%
-
11.0
20.
T = 1800 S
923
915.99
-
0.760%
5.%
-
7.01
20.
T = 2000 S
942
935.26
-
0.715%
5.%
-
6.74
20.
T = 2200 S
956
950.11
-
0.616%
5.%
-
5.89
20.
T = 2400 S
962
961.56
-
0.046%
5.% - 0.441
20.

6.2 Remarks
The relative variations are higher than 2% for T = 400. S, inferiors for T
600. S
The maximum variation observed between two nodes on surface, into relative as in absolute, is 0.012%
that is to say 0,055°C, between the point B (N56) and the point C (N61) at the moment T = 400. S. These variations decrease in
absolute value when time increases.

6.3 Parameters
of execution
Version: 5.03
Machine: SGI - ORIGIN 2000 - R12000
Overall dimension memory:
8 megawords
Time CPU To use: 4.03 seconds
background image
Code_Aster
®
Version
5.0
Titrate:
TTLV01 Sphere: heat transfer by convection
Date:
20/09/02
Author (S):
C. DURAND,
E. SCREWS, F. LEBOUVIER
Key
:
V4.25.001-A
Page:
8/12
Manual of Validation
V4.25 booklet: Transitory thermics of the voluminal structures
HT-66/02/001/A
7 Modeling
C
7.1
Characteristics of modeling
AXIS (TRIA6, QUAD8)
Limiting conditions:
- dimensioned AB, AC
= 0
- dimensioned BC
H = 232.5 W/m ² °C
T
ext.
=1000°C
Not
Node
With
N1
B
N163
C
N171
X
With
(R)
15°
30°
C
y
(Z)
B
N1
N171
N170
N169
N168
N167
N166
N165
N158
N164
N156
N163
7.2
Characteristics of the mesh
A number of nodes:
171
A number of meshs and types: 45 QUAD8, 5 TRIA6 (and 5 SEG3)
7.3 Functionalities
tested
Controls
AFFE_MODELE
AFFE
THERMICS
AXIS
AFFE_CHAR_THER
EXCHANGE
THER_LINEAIRE
TEMP_INIT
VALE
INCREMENT
LIST_INST
RECU_CHAMP
INST
7.4 Remarks
One takes, for voluminal heat, CP =
C
p
= 4816800.0 J/m
3
°C.
The limiting condition
= 0. are implicit on the free edges.
Discretization of time: (36 intervals)
of
0 to 100 seconds: 8 intervals of 12.5 S.
of
100 to 300 seconds: 8 intervals of 25.0 S.
of
300 to 700 seconds: 8 intervals of 50.0 S.
of
700 to 1400 seconds: 7 intervals of 100.0 S.
of
1400 to 2400 seconds: 5 intervals of 200.0 S.
background image
Code_Aster
®
Version
5.0
Titrate:
TTLV01 Sphere: heat transfer by convection
Date:
20/09/02
Author (S):
C. DURAND,
E. SCREWS, F. LEBOUVIER
Key
:
V4.25.001-A
Page:
9/12
Manual of Validation
V4.25 booklet: Transitory thermics of the voluminal structures
HT-66/02/001/A
8
Results of modeling C
8.1 Values
tested
Identification Reference
Aster
Relative variation (%)
Absolute deviation (°C)
difference
tolerance
difference
tolerance
Temperatures:
In center (a: N1)
T (°C)
T = 400 S
334
341.10
2.126%
5.%
7.10
20.
T = 600 S
500
493.15
-
1.370%
5.%
-
6.85
20.
T = 800 S
618
609.65
-
1.303%
5.%
-
8.05
20.
T = 1000 S
706
699.70
-
0.893%
5.%
-
6.30
20.
T = 1200 S
774
768.80
-
0.672%
5.%
-
5.20
20.
T = 1400 S
828
822.00
-
0.725%
5.%
-
6.00
20.
T = 1600 S
872
862.78
-
1.058%
5.%
-
9.22
20.
T = 1800 S
902
894.22
-
0.863%
5.%
-
7.78
20.
T = 2000 S
923
918.45
-
0.493%
5.%
-
4.55
20.
T = 2200 S
942
937.14
-
0.516%
5.%
-
4.86
20.
T = 2400 S
956
951.54
-
0.467%
5.%
-
4.46
20.
On the surface (NR: N163)
T (°C)
T = 400 S
461
474.78
2.989%
5.%
13.8
20.
T = 600 S
608
596.02
-
1.971%
5.%
-
12.0
20.
T = 800 S
696
689.12
-
0.989%
5.% - 6.88
20.
T = 1000 S
774
760.65
-
1.725%
5.%
-
13.3
20.
T = 1200 S
828
815.72
-
1.483%
5.%
-
12.3
20.
T = 1400 S
868
858.12
-
1.138%
5.% - 9.88
20.
T = 1600 S
902
890.63
-
1.261%
5.%
-
11.4
20.
T = 1800 S
923
915.69
-
0.792%
5.%
-
7.31
20.
T = 2000 S
942
935.00
-
0.743%
5.%
-
7.00
20.
T = 2200 S
956
949.90
-
0.639%
5.%
-
6.10
20.
T = 2400 S
962
961.37
-
0.065%
5.%
-
0.625
20.

8.2 Remarks
The relative variations are higher than 2% for T = 400. S, inferiors for T
600. S
Variations observed between the results calculated by Code_Aster on two nodes of surface
external, are lower than 0,011°C (either 0.002%).

8.3 Parameters
of execution
Version: 5.03
Machine: SGI - ORIGIN 2000 - R12000
Overall dimension memory:
8 megawords
Time CPU To use: 4.50 seconds
background image
Code_Aster
®
Version
5.0
Titrate:
TTLV01 Sphere: heat transfer by convection
Date:
20/09/02
Author (S):
C. DURAND,
E. SCREWS, F. LEBOUVIER
Key
:
V4.25.001-A
Page:
10/12
Manual of Validation
V4.25 booklet: Transitory thermics of the voluminal structures
HT-66/02/001/A
9 Modeling
D
9.1
Characteristics of modeling
AXIS (TRIA6, QUAD9)
Limiting conditions:
- dimensioned AB, AC
= 0
- dimensioned BC
H = 232.5 W/m ² °C
T
ext.
=1000°C
Not
Node
With
N1
B
N207
C
N216
X
With
(R)
15°
30°
C
N1
y
(Z)
B
N216
N215
N214
N213
N212
N211
N210
N209
N208
N65
N207
9.2
Characteristics of the mesh
A number of nodes:
216
A number of meshs and types: 45 QUAD9, 5 TRIA6 (and 5 SEG3)
9.3 Functionalities
tested
Controls
AFFE_MODELE
AFFE
THERMICS
AXIS
AFFE_CHAR_THER
EXCHANGE
THER_LINEAIRE
TEMP_INIT
VALE
INCREMENT
LIST_INST
RECU_CHAMP
INST
9.4 Remarks
One takes, for voluminal heat, CP =
C
p
= 4816800.0 J/m
3
°C.
The limiting condition
= 0. are implicit on the free edges.
Discretization of time: (36 intervals)
of
0 to 100 seconds: 8 intervals of 12.5 S.
of
100 to 300 seconds: 8 intervals of 25.0 S.
of
300 to 700 seconds: 8 intervals of 50.0 S.
of
700 to 1400 seconds: 7 intervals of 100.0 S.
of
1400 to 2400 seconds: 5 intervals of 200.0 S.
background image
Code_Aster
®
Version
5.0
Titrate:
TTLV01 Sphere: heat transfer by convection
Date:
20/09/02
Author (S):
C. DURAND,
E. SCREWS, F. LEBOUVIER
Key
:
V4.25.001-A
Page:
11/12
Manual of Validation
V4.25 booklet: Transitory thermics of the voluminal structures
HT-66/02/001/A
10 Results of modeling D
10.1 Values
tested
Identification Reference
Aster
Relative variation (%)
Absolute deviation (°C)
difference
tolerance
difference
tolerance
Temperatures:
In center (a: N1)
T (°C)
T = 400 S
334
341.10
2.125%
5.%
7.10
20.
T = 600 S
500
493.14
-
1.371%
5.%
-
6.86
20.
T = 800 S
618
609.95
-
1.303%
5.%
-
8.05
20.
T = 1000 S
706
699.70
-
0.893%
5.%
-
6.30
20.
T = 1200 S
774
768.79
-
0.673%
5.%
-
5.21
20.
T = 1400 S
828
821.99
-
0.726%
5.%
-
6.01
20.
T = 1600 S
872
862.78
-
1.058%
5.%
-
9.22
20.
T = 1800 S
902
894.22
-
0.863%
5.%
-
7.78
20.
T = 2000 S
923
918.45
-
0.493%
5.%
-
4.55
20.
T = 2200 S
942
937.13
-
0.516%
5.%
-
4.87
20.
T = 2400 S
956
951.54
-
0.467%
5.%
-
4.46
20.
On the surface (NR: N207)
T (°C)
T = 400 S
461
474.78
2.989%
5.%
13.8
20.
T = 600 S
608
596.01
-
1.971%
5.%
-
12.0
20.
T = 800 S
696
689.12
-
0.989%
5.% - 6.88
20.
T = 1000 S
774
760.65
-
1.725%
5.%
-
13.4
20.
T = 1200 S
828
815.72
-
1.483%
5.%
-
12.3
20.
T = 1400 S
868
858.12
-
1.138%
5.%
-
9.88
20.
T = 1600 S
902
890.63
-
1.261%
5.%
-
11.4
20.
T = 1800 S
923
915.69
-
0.792%
5.%
-
7.31
20.
T = 2000 S
942
935.00
-
0.743%
5.%
-
7.00
20.
T = 2200 S
956
949.89
-
0.639%
5.%
-
6.11
20.
T = 2400 S
962
961.37
-
0.065%
5.%
-
0.626
20.

10.2 Remarks
The relative variations are higher than 2% for T = 400. S, inferiors for T
600. S
The results calculated by Code_Aster on the nodes of external surface are almost
identical (maximum: 5.10
­ 5
°C is 10
­ 7
into relative).

10.3 Parameters
of execution
Version: 5.03
Machine: SGI - ORIGIN 2000 - R12000
Overall dimension memory:
8 megawords
Time CPU To use: 4.34 seconds
background image
Code_Aster
®
Version
5.0
Titrate:
TTLV01 Sphere: heat transfer by convection
Date:
20/09/02
Author (S):
C. DURAND,
E. SCREWS, F. LEBOUVIER
Key
:
V4.25.001-A
Page:
12/12
Manual of Validation
V4.25 booklet: Transitory thermics of the voluminal structures
HT-66/02/001/A
11 Summary of the results
The results obtained are satisfactory. The maximum change obtained (3%) is on surface
external of the sphere for the weakest moment the T. This variation decreases when the moment T increases.
Whatever the modeling, the results are increasingly more precise in the center than on the surface
external of the sphere.
With identical cutting the results between the linear and quadratic elements are appreciably them
same.