Code_Aster
®
Version
5.0
Titrate:
TPNV01 hollow Sphere: convection, radiation
Date:
20/09/02
Author (S):
C. DURAND,
E. SCREWS, F. LEBOUVIER
Key
:
V4.43.001-A
Page:
1/8
Manual of Validation
V4.43 booklet: Nonlinear stationary thermics of the voluminal structures
HT-66/02/001/A
Organization (S):
EDF/AMA, EDF/UTO/LOCATED, Delta CAD
Manual of Validation
V4.43 booklet: Nonlinear stationary thermics of the voluminal structures
V4.43.001 document
TPNV01 - Hollow sphere: convection, radiation
Summary:
This test results from the validation independent of version 3 in nonlinear stationary thermics.
It is about a voluminal problem represented by two modelings, one 3D, the other axisymmetric one.
The functionalities tested are as follows:
·
thermal element 3D,
·
axisymmetric thermal element,
·
conditions limit convection and of radiation.
The interest of the test lies in the taking into account of the radiation.
The results are compared with an analytical solution on a test VPCS.
Code_Aster
®
Version
5.0
Titrate:
TPNV01 hollow Sphere: convection, radiation
Date:
20/09/02
Author (S):
C. DURAND,
E. SCREWS, F. LEBOUVIER
Key
:
V4.43.001-A
Page:
2/8
Manual of Validation
V4.43 booklet: Nonlinear stationary thermics of the voluminal structures
HT-66/02/001/A
1
Problem of reference
1.1 Geometry
R
I
R
E
R
B
With
O
Interior radius R
I
= 0.300 m
External radius R
E
= 0.392 m
1.2
Properties of material
= 40 W/m °C
Thermal conductivity
C = 1 J/m
3
°C
Voluminal heat
1.3
Boundary conditions and loadings
·
Surface intern: radiation,
= 0.6 (coefficient of gray body),
T
IE
= 500.0°C,
·
External surface: convection, H
E
= 133.5 W/m
2
°C,
T
ee
= 20.0°C.
1.4 Conditions
initial
Without object.
Code_Aster
®
Version
5.0
Titrate:
TPNV01 hollow Sphere: convection, radiation
Date:
20/09/02
Author (S):
C. DURAND,
E. SCREWS, F. LEBOUVIER
Key
:
V4.43.001-A
Page:
3/8
Manual of Validation
V4.43 booklet: Nonlinear stationary thermics of the voluminal structures
HT-66/02/001/A
2
Reference solution
2.1
Method of calculation used for the reference solution
T R
T
T
R
R
R
T
R
T
R
R
R
E
I
E
I
I
E
E
I
E
I
()
=
-
-
+
-
-
1
1
1
1
1
(
)
E
E
E
ee
E E
E
ee
H T
T
R H T
T
=
-
=
-
(
)
4
2
éq
2.1-1
(
)
(
)
(
)
(
)
I
IE
I
I
IE
I
T
T
T
T
=
+
-
+
+
-
+
.
.
.
R
.
.
.
273 15
273 15
273 15
273 15
4
4
2
4
4
= 4
éq
2.1-2
=
=
=
-
-
4
4
1
1
2
R
T
T
R
R
E
I
E
I
C O N S your N you
éq
2.1-3
=
-
5 7 3 1 0
8
4
.
/
²
X
W
m K
(constant of Stefan) with T in °C
The temperatures of reference are obtained while solving numerically by the method of Newton
an equation of the 4
ème
degree in
T
I
obtained starting from the equations [éq 2.1-1] [éq 2.1-2] and [éq 2.1-3].
2.2
Results of reference
in a:
in b:
Temperatures
T
I
= 91.77°C
T
E
= 71.22°C
Densities flux
I
= 11675. W/m
2
E
= 6838. W/m
2
2.3
Uncertainty on the solution
Analytical solution.
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
Code_Aster
®
Version
5.0
Titrate:
TPNV01 hollow Sphere: convection, radiation
Date:
20/09/02
Author (S):
C. DURAND,
E. SCREWS, F. LEBOUVIER
Key
:
V4.43.001-A
Page:
4/8
Manual of Validation
V4.43 booklet: Nonlinear stationary thermics of the voluminal structures
HT-66/02/001/A
3 Modeling
With
3.1
Characteristics of modeling
3D (HEXA20, PENTA15, QUAD8)
Limiting conditions:
- external face
H = 133.5 W/m ² °C
T
ext.
= 20°C
- internal face
= 0.6
T
ext.
= 500°C
- other faces
= 0
30°
Z
y
X
30°
R
E
= 0.392
R
I
= 0.3
N184
N46
N93
N145
N38
N460
N453
N440
N443
N463
m8
m2
3.2
Characteristics of the mesh
A number of nodes:
465
A number of meshs and types: 96 (32 HEXA20, 64 PENTA15)
3.3 Functionalities
tested
Controls
AFFE_MODELE
THERMICS
3D
ALL
DEFI_MATERIAU
THER_NL
AFFE_CHAR_THER_F
EXCHANGE
FLUX_NL
THER_NON_LINE
TEMP_INIT
STATIONARY
“YES”
EXCIT
CHARGE
RECU_CHAMP
INST
0.
Code_Aster
®
Version
5.0
Titrate:
TPNV01 hollow Sphere: convection, radiation
Date:
20/09/02
Author (S):
C. DURAND,
E. SCREWS, F. LEBOUVIER
Key
:
V4.43.001-A
Page:
5/8
Manual of Validation
V4.43 booklet: Nonlinear stationary thermics of the voluminal structures
HT-66/02/001/A
4
Results of modeling A
4.1 Values
tested
Identification Reference
Aster %
difference
tolerance
Temperature (°C)
N184 91.77
91.75
-
0.026
1%
N145 91.77
91.75
-
0.026
1%
N93 91.77
91.75
-
0.018
1%
N46 91.77
91.76
-
0.016
1%
N38 91.77
91.76
-
0.016
1%
N460 71.22
71.21
-
0.011
1%
N443 71.22
71.21
-
0.011
1%
N440 71.22
71.21
-
0.017
1%
N453 71.22
71.21
-
0.021
1%
N463 71.22
71.20
-
0.022
1%
Density flux (W/m ²)
Net m8, N184
11675.
11677.
0.016
2%
Net m2, N460
6838.
6843.
0.076
2%
4.2 Remarks
The boundary condition of the radiation type is provided in the form of a function of
temperature interpolated linearly between each point (one discretized the curve in 101 points).
4.3 Parameters
of execution
Version: 5.03
Machine: SGI - ORIGIN 2000 - R12000
Overall dimension memory:
8 megawords
Time CPU To use: 6.33 seconds
Code_Aster
®
Version
5.0
Titrate:
TPNV01 hollow Sphere: convection, radiation
Date:
20/09/02
Author (S):
C. DURAND,
E. SCREWS, F. LEBOUVIER
Key
:
V4.43.001-A
Page:
6/8
Manual of Validation
V4.43 booklet: Nonlinear stationary thermics of the voluminal structures
HT-66/02/001/A
5 Modeling
B
5.1
Characteristics of modeling
AXIS (TRIA6, QUAD8, SEG3)
B
y
30°
With
Limiting conditions:
- dimensioned AB, CD
= 0
- dimensioned BC
H
=
133.5 W/m ² °C
T
ext.
= 20°C
- dimensioned AD
=
0.6
T
ext.
= 500°C
D
C
N57
N47
N30
N12
N1
N72
N55
N35
N25
N16
X
m8
m2
5.2
Characteristics of the mesh
A number of nodes:
73
A number of meshs and types: 24: (16 TRIA6, 8 QUAD8)
5.3 Functionalities
tested
Controls
AFFE_MODELE
THERMICS
AXIS
ALL
DEFI_MATERIAU
THER_NL
AFFE_CHAR_THER_F
EXCHANGE
FLUX_NL
THER_NON_LINE
TEMP_INIT
STATIONARY
“YES”
EXCIT
CHARGE
RECU_CHAMP
INST
0.
Code_Aster
®
Version
5.0
Titrate:
TPNV01 hollow Sphere: convection, radiation
Date:
20/09/02
Author (S):
C. DURAND,
E. SCREWS, F. LEBOUVIER
Key
:
V4.43.001-A
Page:
7/8
Manual of Validation
V4.43 booklet: Nonlinear stationary thermics of the voluminal structures
HT-66/02/001/A
6
Results of modeling B
6.1 Values
tested
Identification Reference
Aster %
difference
tolerance
Temperature (°C)
N1 91.77
91.75
-
0.019
1%
N12 91.77
91.75
-
0.018
1%
N30 91.77
91.75
-
0.021
1%
N47 91.77
91.75
-
0.022
1%
N57 91.77
91.75
-
0.020
1%
N16 71.22
71.21
-
0.017
1%
N25 71.22
71.21
-
0.017
1%
N35 71.22
71.21
-
0.016
1%
N55 71.22
71.21
-
0.014
1%
N72 71.22
71.21
-
0.012
1%
Density flux (W/m ²)
Net m8, N1
11675.
11656.
-
0.163
2%
Net m2, N16
6838.
6834.
-
0.062
2%
6.2 Remarks
The boundary condition of the radiation type is provided in the form of a function of
temperature interpolated linearly between each point (one discretized the curve in 101 points).
6.3 Parameters
of execution
Version: 5.03
Machine: SGI - ORIGIN 2000 - R12000
Overall dimension memory:
8 megawords
Time CPU To use: 2.63 seconds
Code_Aster
®
Version
5.0
Titrate:
TPNV01 hollow Sphere: convection, radiation
Date:
20/09/02
Author (S):
C. DURAND,
E. SCREWS, F. LEBOUVIER
Key
:
V4.43.001-A
Page:
8/8
Manual of Validation
V4.43 booklet: Nonlinear stationary thermics of the voluminal structures
HT-66/02/001/A
7
Summary of the results
The results of reference provided by VPCS are incorrect. New results of reference have
summer determined starting from an analytical approach.
The results obtained are satisfactory. The maximum change is of:
·
modeling A (
3D
:
HEXA20
,
PENTA15
): 0.026% for the temperature and of 0.076% for
flow,
·
modeling B (
AXIS
:
QUAD4
,
TRIA3
): 0.022% for the temperature and of 0.16% for
flow.
The limiting condition of radiation was imposed via a nonlinear loading of flow (flow function
temperature). In this test the taking into account of the radiation is completely correct.
This test with license to test the control
AFFE_CHAR_THER_F
(associate with the operand
FLUX_NL
who
allows to affect a flow non_linéaire) in the cases of modeling AXIS and 3D.