Code_Aster
®
Version
6.4
Titrate:
TPNA01 - Stationary axisymmetric problem with radiation
Date
:
02/06/03
Author (S):
J.P. LEFEBVRE
Key
:
V4.41.001-C
Page:
1/8
Manual of Validation
V4.41 booklet: Stationary thermics with radiation
HT-66/03/008/A
Organization (S):
EDF-R & D/AMA
Manual of Validation
V4.41 booklet: Stationary thermics with radiation
Document: V4.41.001
TPNA01 - Stationary axisymmetric problem
with radiation
Summary:
This elementary test makes it possible to deal with axisymmetric problem in stationary thermics with a condition
with the limits of the radiation type. The solution is analytical. The problem is dealt with into axisymmetric and in
voluminal.
For modelings presented here, the variations of the results obtained by Code_Aster range between 1 and
2% of the analytically calculated reference.
Code_Aster
®
Version
6.4
Titrate:
TPNA01 - Stationary axisymmetric problem with radiation
Date
:
02/06/03
Author (S):
J.P. LEFEBVRE
Key
:
V4.41.001-C
Page:
2/8
Manual of Validation
V4.41 booklet: Stationary thermics with radiation
HT-66/03/008/A
1
Problem of reference
1.1 Geometry
Z
Re = 0.300 m
Re = 0.391 m
R
The hollow roll is supposed infinitely long.
1.2
Material properties
Only the coefficient of conductivity intervenes. Code_Aster makes compulsory the supply of a function
representing the given voluminal enthalpy starting from the voluminal coefficient of heat.
voluminal heat
1.00 J/m
C
thermal conductivity
40 W/m C
C
p
=
=
°
°
3
K
1.3
Boundary conditions and loadings
Condition of the radiation type on surface interns cylinder, condition of the convection type
(exchange with the external medium) on external surface.
No the boundary condition on the ends of the cylinder (what amounts imposing a null flow).
(
)
(
)
[
]
C
20.0
and
C
142.0
with
external
surface
Centigrade
in
expressed
C,
500.0
and
/
10
5.73
,
0.6
with
273.15
273.15
intern
surface
2
4
2
8
4
4
°
°
°
°
=
=
-
=
=
=
=
-
+
=
-
+
E
ext.
E
E
ext.
E
iext
iext
T
W/m
H
T
T
H
N
T
K
T
T
K
m
W
T
T
T
K
N
Code_Aster
®
Version
6.4
Titrate:
TPNA01 - Stationary axisymmetric problem with radiation
Date
:
02/06/03
Author (S):
J.P. LEFEBVRE
Key
:
V4.41.001-C
Page:
3/8
Manual of Validation
V4.41 booklet: Stationary thermics with radiation
HT-66/03/008/A
2
Reference solution
2.1
Method of calculation used for the reference solution
One in the case of lays out of an analytical solution a cylinder infinite length:
Log (IH)
-
Log (Re)
Log (IH)
T
-
Log (Re)
T
R
Log
Log
T
T
T (R)
E
I
I
E
+
)
(
-
=
IH
Re
2.2
Results of reference
R (m)
T (°C)
.30000
105.55
.32275
99.21
.34550
93.30
.36825
87.76
.39100
82.56
Value of the temperature according to R
R (m)
(W/m)
2
.300
11577.49
.391
8822.98
Value of flow according to R
2.3
Uncertainty on the solution
Exact solution.
2.4 References
bibliographical
[1]
Guide validation of the software packages of structural analysis. French company of the Mechanics
AFNOR 1990 ISBN 2-12-486611-7
Code_Aster
®
Version
6.4
Titrate:
TPNA01 - Stationary axisymmetric problem with radiation
Date
:
02/06/03
Author (S):
J.P. LEFEBVRE
Key
:
V4.41.001-C
Page:
4/8
Manual of Validation
V4.41 booklet: Stationary thermics with radiation
HT-66/03/008/A
3 Modeling
With
3.1
Characteristics of modeling
Modeling 2D:
N1
N3
N6
N11
N9
3.2
Characteristics of the mesh
2 QUAD8
3.3
Functionalities tested
Order Mot-clé
factor
Key word
simple
Argument
DEFI_MATERIAU THER_NL
LAMBDA
BETA
THER_NON_LINE TEMP_INIT
STATIONARY “YES”
CONVERGENCE
RESI_GLOB_RELA
1.E-2
ITER_GLOB_MAXI
9
CRIT_LAGR_RELA
1.E-3
OPTION
“FLUX_ELNO_TEMP”
Code_Aster
®
Version
6.4
Titrate:
TPNA01 - Stationary axisymmetric problem with radiation
Date
:
02/06/03
Author (S):
J.P. LEFEBVRE
Key
:
V4.41.001-C
Page:
5/8
Manual of Validation
V4.41 booklet: Stationary thermics with radiation
HT-66/03/008/A
4
Results of modeling A
4.1 Values
tested
The nodes observed have as a co-ordinate Z = 0.0
Identification
temperature
Reference
Aster %
difference
N1 (r=.30000)
105.55
105.52
0.03
N3 (r=.32275)
99.21
99.17
0.04
N6 (r=.34550)
93.30
93.26
0.04
N11 (r=.36825)
87.76
87.73
0.04
N9 (r=.39100)
82.56
82.53
0.04
Identification
flow
Reference
Aster %
difference
net M1 N1 node
11577.49
11533.37
0.38
net m2 N9 node
8822.98
8855.97
0.37
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 using 101 here
points).
Code_Aster
®
Version
6.4
Titrate:
TPNA01 - Stationary axisymmetric problem with radiation
Date
:
02/06/03
Author (S):
J.P. LEFEBVRE
Key
:
V4.41.001-C
Page:
6/8
Manual of Validation
V4.41 booklet: Stationary thermics with radiation
HT-66/03/008/A
5 Modeling
B
5.1
Characteristics of modeling
Modeling 3D:
5.2
Characteristics of the mesh
32 HEXA20
5.3
Functionalities tested
Order Mot-clé
factor
Key word
simple
Argument
DEFI_MATERIAU THER_NL
LAMBDA
BETA
THER_NON_LINE TEMP_INIT
STATIONARY
“YES”
CONVERGENCE
RESI_GLOB_RELA
1.E-2
ITER_GLOB_MAXI
10
CRIT_LAGR_RELA
1.E-3
OPTION
“FLUX_ELNO_TEMP”
Code_Aster
®
Version
6.4
Titrate:
TPNA01 - Stationary axisymmetric problem with radiation
Date
:
02/06/03
Author (S):
J.P. LEFEBVRE
Key
:
V4.41.001-C
Page:
7/8
Manual of Validation
V4.41 booklet: Stationary thermics with radiation
HT-66/03/008/A
6
Results of modeling B
6.1 Values
tested
The nodes observed have as co-ordinates: y = Z = 0.0
Identification
temperature
Reference
Aster
% difference
NO106 (x=.30000)
105.55
105.51
0.03
NO105 (x=.32275)
99.21
99.17
0.04
NO115 (x=.34550)
93.30
93.26
0.04
NO125 (x=.36825)
87.76
87.73
0.04
NO123 (x=.39100)
82.56
82.52
0.04
Identification
flow
Reference
Aster
% difference
net MA17 node NO106
11577.49
11680.50
+0.89
net MA16 node NO123
8822.98
8968.85
+1.65
6.2 Remarks
The function of flow used in modeling A is also used here.
Code_Aster
®
Version
6.4
Titrate:
TPNA01 - Stationary axisymmetric problem with radiation
Date
:
02/06/03
Author (S):
J.P. LEFEBVRE
Key
:
V4.41.001-C
Page:
8/8
Manual of Validation
V4.41 booklet: Stationary thermics with radiation
HT-66/03/008/A
7
Summaries of the results
The taking into account of the conditions of radiation is completely correct in this stationary case.
Let us note that this test utilized a coefficient of thermal conductivity constant, only
non-linearity thus relates to the boundary conditions.
The errors are higher on the calculation of flow, which one can explain by the use of
smoothings with the nodes, carried out starting from the computed values at the points of integration (points of
GAUSS).