Code_Aster ®
Version
5.0
Titrate:
Hollow TPNV01 Sphère: convection, radiation


Date:
20/09/02
Author (S):
C. DURAND, E. SCREW, F. LEBOUVIER Clé
:
V4.43.001-A Page:
1/8

Organization (S): EDF/AMA, EDF/UTO/LOCATED, Delta CAD
Handbook of Validation
V4.43 booklet: Nonlinear stationary thermics of the voluminal structures
V4.43.001 document

TPNV01 - Hollow Sphère: 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.

Handbook of Validation
V4.43 booklet: Nonlinear stationary thermics of the voluminal structures
HT-66/02/001/A

Code_Aster ®
Version
5.0
Titrate:
Hollow TPNV01 Sphère: convection, radiation


Date:
20/09/02
Author (S):
C. DURAND, E. SCREW, F. LEBOUVIER Clé
:
V4.43.001-A Page:
2/8

1
Problem of reference

1.1 Geometry
Interior radius IH = 0.300 m
External radius Re = 0.392 m
IH
With
B
O
R
Re


1.2
Properties of material


= 40 W/m °C
Thermal conductivity
C = 1 J/m3 °C
Voluminal heat

1.3
Boundary conditions and loadings

· Surface intern: radiation, = 0.6 (coefficient of gray body), T E
I = 500.0°C,
· External surface: convection, H
E
E = 133.5 W/m2 °C, Te = 20.0°C.

1.4 Conditions
initial

Without object.

Handbook of Validation
V4.43 booklet: Nonlinear stationary thermics of the voluminal structures
HT-66/02/001/A

Code_Aster ®
Version
5.0
Titrate:
Hollow TPNV01 Sphère: convection, radiation


Date:
20/09/02
Author (S):
C. DURAND, E. SCREW, F. LEBOUVIER Clé
:
V4.43.001-A Page:
3/8

2
Reference solution

2.1
Method of calculation used for the reference solution

T
T
I
E
-
T - T1
R
R
T (R
E
I
E
I
) =
+
1
1 R
1
1
-
-
R
R
R
R
E
I
E
I


E
E
E = E
H (E
T - E
T)
=
4
2
E
R E
H (E
T - E
T)
éq
2.1-1



E
4
4
I =. (I
T +
.
273 15) - (iT +
.
273
)
15

éq
2.1-2
= 4 2

E
4
4
R I.(iT +
.
273 1)
5
- (iT + 2.
73 15)

2
Te -

T
= 4 R = Co N sta N you
= 4
I
1

éq
2.1-3
- 1
R
R
E
I

=
-
5 7 3 x1 0 8
4
.
W/m ² 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 4th degree out of Ti 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
Ti = 91.77°C
Te = 71.22°C
Densities flux
I = 11675. W/m2
E = 6838. W/m2

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
Handbook of Validation
V4.43 booklet: Nonlinear stationary thermics of the voluminal structures
HT-66/02/001/A

Code_Aster ®
Version
5.0
Titrate:
Hollow TPNV01 Sphère: convection, radiation


Date:
20/09/02
Author (S):
C. DURAND, E. SCREW, F. LEBOUVIER Clé
:
V4.43.001-A Page:
4/8

3 Modeling
With

3.1
Characteristics of modeling

3D (HEXA20, PENTA15, QUAD8)

Z
y
N38
N463
30°
N46
N453
30°
N93
N440
Limiting conditions:
N145
N184
N443
- external face
H = 133.5 W/m ² °C
R
T
I = 0.3
ext. = 20°C
N460
- internal face
= 0.6
T
m8
ext. = 500°C
Re = 0.392
m2
- other faces
= 0
X


3.2
Characteristics of the grid

A number of nodes:
465
A number of meshs and types: 96 (32 HEXA20, 64 PENTA15)

3.3 Functionalities
tested

Commands




AFFE_MODELE
THERMIQUE
3D
TOUT
DEFI_MATERIAU
THER_NL
AFFE_CHAR_THER_F
ECHANGE
FLUX_NL
THER_NON_LINE
TEMP_INIT
STATIONNAIRE
“OUI”
EXCIT
CHARGE
RECU_CHAMP
INST
0.


Handbook of Validation
V4.43 booklet: Nonlinear stationary thermics of the voluminal structures
HT-66/02/001/A

Code_Aster ®
Version
5.0
Titrate:
Hollow TPNV01 Sphère: convection, radiation


Date:
20/09/02
Author (S):
C. DURAND, E. SCREW, F. LEBOUVIER Clé
:
V4.43.001-A Page:
5/8

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

Obstruction memory:
8 megawords
Time CPU To use: 6.33 seconds

Handbook of Validation
V4.43 booklet: Nonlinear stationary thermics of the voluminal structures
HT-66/02/001/A

Code_Aster ®
Version
5.0
Titrate:
Hollow TPNV01 Sphère: convection, radiation


Date:
20/09/02
Author (S):
C. DURAND, E. SCREW, F. LEBOUVIER Clé
:
V4.43.001-A Page:
6/8

5 Modeling
B

5.1
Characteristics of modeling

AXIS (TRIA6, QUAD8, SEG3)

C
Limiting conditions:
N72
- dimensioned AB, CD
= 0
D
- dimensioned BC
H
=
133.5 W/m ² °C
N55
Text
= 20°C
N57
- dimensioned AD

=
0.6
Text
= 500°C
N47
N35
N30
y
N25
N12
30°
m8
m2
N1
N16
With
B
X

5.2
Characteristics of the grid

A number of nodes:
73
A number of meshs and types: 24: (16 TRIA6, 8 QUAD8)

5.3 Functionalities
tested

Commands




AFFE_MODELE
THERMIQUE
AXIS
TOUT
DEFI_MATERIAU
THER_NL
AFFE_CHAR_THER_F
ECHANGE
FLUX_NL
THER_NON_LINE
TEMP_INIT
STATIONNAIRE
“OUI”
EXCIT
CHARGE
RECU_CHAMP
INST
0.


Handbook of Validation
V4.43 booklet: Nonlinear stationary thermics of the voluminal structures
HT-66/02/001/A

Code_Aster ®
Version
5.0
Titrate:
Hollow TPNV01 Sphère: convection, radiation


Date:
20/09/02
Author (S):
C. DURAND, E. SCREW, F. LEBOUVIER Clé
:
V4.43.001-A Page:
7/8

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

Obstruction memory:
8 megawords
Time CPU To use: 2.63 seconds

Handbook of Validation
V4.43 booklet: Nonlinear stationary thermics of the voluminal structures
HT-66/02/001/A

Code_Aster ®
Version
5.0
Titrate:
Hollow TPNV01 Sphère: convection, radiation


Date:
20/09/02
Author (S):
C. DURAND, E. SCREW, F. LEBOUVIER Clé
:
V4.43.001-A Page:
8/8

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 command AFFE_CHAR_THER_F (associate with the operand FLUX_NL which
allows to affect a flow non_linéaire) in the cases of modeling AXIS and 3D.

Handbook of Validation
V4.43 booklet: Nonlinear stationary thermics of the voluminal structures
HT-66/02/001/A

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