Code_Aster
®
Version
5.0
Titrate:
TPNL300 unidimensional Transfer of heat with radiation
Date:
20/09/02
Author (S):
C. DURAND,
E. SCREWS, F. LEBOUVIER
Key
:
V4.42.300-A
Page:
1/8
Manual of Validation
V4.42 booklet: Nonlinear stationary thermics of the linear structures
HT-66/02/001/A
Organization (S):
EDF/AMA, EDF/UTO/LOCATED, Delta CAD
Manual of Validation
V4.42 booklet: Nonlinear stationary thermics of the linear structures
V4.42.300 document
TPNL300 - Unidimensional transfer of heat
with radiation
Summary:
This test results from the validation independent of version 3 in nonlinear stationary thermics.
It is about a linear problem 1D represented by two modelings, one planes, the other voluminal one.
The functionalities tested are as follows:
·
plane thermal element,
·
voluminal thermal element,
·
limiting conditions: (imposed temperatures, radiation).
The interest of the test lies in the taking into account of the radiation.
The results are compared with those provided by NAFEMS.
Code_Aster
®
Version
5.0
Titrate:
TPNL300 unidimensional Transfer of heat with radiation
Date:
20/09/02
Author (S):
C. DURAND,
E. SCREWS, F. LEBOUVIER
Key
:
V4.42.300-A
Page:
2/8
Manual of Validation
V4.42 booklet: Nonlinear stationary thermics of the linear structures
HT-66/02/001/A
1
Problem of reference
1.1 Geometry
0.1 m
With
B
X
1.2
Properties of material
= 55.6 W/m.°C
Thermal conductivity
C
= 460 J/kg.°C
Specific heat
= 7850 kg/m
3
Mass
voluminal
1.3
Boundary conditions and loadings
·
temperature imposed on point a: T
With
= 726.85°C,
·
exchange by radiation at point b:
-
outside air temperature = 26.85°C,
-
= 0.98 emissivity,
-
= 5.67x10
- 8
W/m ² K
4
(constant of Stefan-Boltzmann).
1.4 Conditions
initial
Without object.
Code_Aster
®
Version
5.0
Titrate:
TPNL300 unidimensional Transfer of heat with radiation
Date:
20/09/02
Author (S):
C. DURAND,
E. SCREWS, F. LEBOUVIER
Key
:
V4.42.300-A
Page:
3/8
Manual of Validation
V4.42 booklet: Nonlinear stationary thermics of the linear 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 the card “TEST n°2” of the tests of reference published by
NAFEMS.
2.2
Results of reference
Temperature at point b: T = 653.85°C
2.3
Uncertainty on the solution
Nonavailable on card NAFEMS.
2.4 References
bibliographical
[1]
NAFEMS (the National Agency for Finite Element Methods Standard and (the U.K.)): “The
standard NAFEMS Benchmarcks ", TNSB rév 3, October 1990.
Code_Aster
®
Version
5.0
Titrate:
TPNL300 unidimensional Transfer of heat with radiation
Date:
20/09/02
Author (S):
C. DURAND,
E. SCREWS, F. LEBOUVIER
Key
:
V4.42.300-A
Page:
4/8
Manual of Validation
V4.42 booklet: Nonlinear stationary thermics of the linear structures
HT-66/02/001/A
3 Modeling
With
3.1
Characteristics of modeling
PLAN (TRIA3, QUAD4)
Boundary conditions:
- Dimensioned AD:
T = 726.85°C
- Dimensioned AB, CD:
= 0
- Dimensioned BC:
T
ext.
=26.85°C
= 0.98
0.02m
With
B
D
C
y
X
N51
N53
N55
3.2
Characteristics of the mesh
A number of nodes:
55
A number of meshs and types: 60: (20 QUAD4, 40 TRIA3)
3.3 Functionalities
tested
Controls
AFFE_MODELE
THERMICS
PLAN
ALL
DEFI_MATERIAU
THER_NL
AFFE_CHAR_THER_F
FLUX_NL
TEMP_IMPO
THER_NON_LINE
TEMP_INIT
STATIONARY
“YES”
EXCIT
CHARGE
RECU_CHAMP
INST
0.
Code_Aster
®
Version
5.0
Titrate:
TPNL300 unidimensional Transfer of heat with radiation
Date:
20/09/02
Author (S):
C. DURAND,
E. SCREWS, F. LEBOUVIER
Key
:
V4.42.300-A
Page:
5/8
Manual of Validation
V4.42 booklet: Nonlinear stationary thermics of the linear structures
HT-66/02/001/A
4
Results of modeling A
4.1 Values
tested
Identification Reference
Aster %
difference
tolerance
Temperature at the point B
in °C
N51 653.85
653.87
0.003
2%
N53 653.85
653.87
0.003
2%
N55 653.85
653.87
0.003
2%
4.2 Parameters
of execution
Version: 5.03
Machine: SGI - ORIGIN 2000 - R12000
Overall dimension memory:
8 megawords
Time CPU To use: 2.64 seconds
Code_Aster
®
Version
5.0
Titrate:
TPNL300 unidimensional Transfer of heat with radiation
Date:
20/09/02
Author (S):
C. DURAND,
E. SCREWS, F. LEBOUVIER
Key
:
V4.42.300-A
Page:
6/8
Manual of Validation
V4.42 booklet: Nonlinear stationary thermics of the linear structures
HT-66/02/001/A
5 Modeling
B
5.1
Characteristics of modeling
3D (HEXA8)
Boundary conditions:
- face X = 0
T=726.85°C
- face X = 0.1
T
ext.
=26.85°C
= 0.98
- others faces
= 0
Z
X
y
0.02m
0.02m
N91
N98
N97
N92
5.2
Characteristics of the mesh
A number of nodes:
99
A number of meshs and types: 40 HEXA8
5.3 Functionalities
tested
Controls
AFFE_MODELE
THERMICS
PLAN
ALL
DEFI_MATERIAU
THER_NL
AFFE_CHAR_THER_F
FLUX_NL
TEMP_IMPO
THER_NON_LINE
TEMP_INIT
STATIONARY
“YES”
EXCIT
CHARGE
RECU_CHAMP
INST
0.
Code_Aster
®
Version
5.0
Titrate:
TPNL300 unidimensional Transfer of heat with radiation
Date:
20/09/02
Author (S):
C. DURAND,
E. SCREWS, F. LEBOUVIER
Key
:
V4.42.300-A
Page:
7/8
Manual of Validation
V4.42 booklet: Nonlinear stationary thermics of the linear structures
HT-66/02/001/A
6
Results of modeling B
6.1 Values
tested
Identification Reference
Aster %
difference
tolerance
Temperature at the point B
in °C
N91 653.85
653.87
0.003
2%
N92 653.85
653.87
0.003
2%
N97 653.85
653.87
0.003
2%
N98 653.85
653.87
0.003
2%
6.2 Parameters
of execution
Version: 5.03
Machine: SGI - ORIGIN 2000 - R12000
Overall dimension memory:
8 megawords
Time CPU To use: 2.66 seconds
Code_Aster
®
Version
5.0
Titrate:
TPNL300 unidimensional Transfer of heat with radiation
Date:
20/09/02
Author (S):
C. DURAND,
E. SCREWS, F. LEBOUVIER
Key
:
V4.42.300-A
Page:
8/8
Manual of Validation
V4.42 booklet: Nonlinear stationary thermics of the linear structures
HT-66/02/001/A
7
Summary of the results
This test is recommended by NAFEMS (but with another type of mesh).
Two modelings give very satisfactory results, the maximum change obtained is of
0.003%.
For modeling PLAN, in spite of the not-symmetry of the mesh, one notes that the temperature with
nodes (points of observation) pertaining to the TRIA3 and the QUAD4 is identical.
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 case of) modelings PLAN and 3D.