Code_Aster
®
Version
5.0
Titrate:
TPLA05 Bars cylindrical with density flux
Date:
20/09/02
Author (S):
C. DURAND,
E. SCREWS, F. LEBOUVIER
Key
:
V4.01.005-A
Page:
1/8
Manual of Validation
V4.01 booklet: Stationary thermics of the axisymmetric structures
HT-66/02/001/A
Organization (S):
EDF/AMA, EDF/UTO/LOCATED, Delta CAD
Manual of Validation
V4.01 booklet: Stationary thermics of the axisymmetric structures
Document V4.01 005
TPLA05 - Cylindrical bar with density flux
Summary:
This test results from the validation independent of version 3 in linear stationary thermics.
It includes/understands two modelings, the first which tests the voluminal elements, the second, the elements 2D
axisymmetric.
Boundary conditions in imposed temperature and of density flux are taken into account.
The results resulting from this case test are compared with those provided by VPCS.
Code_Aster
®
Version
5.0
Titrate:
TPLA05 Bars cylindrical with density flux
Date:
20/09/02
Author (S):
C. DURAND,
E. SCREWS, F. LEBOUVIER
Key
:
V4.01.005-A
Page:
2/8
Manual of Validation
V4.01 booklet: Stationary thermics of the axisymmetric structures
HT-66/02/001/A
1
Problem of reference
1.1 Geometry
Z
R
L
O
R = 0.01 m (radius of the cylinder)
L = 1 m
1.2
Properties of material
= 33.33 W/m °C
Thermal conductivity
1.3
Boundary conditions and loadings
·
Imposed temperatures,
-
T = 0°C in Z = 0.,
-
T = 500°C in Z = 1.,
·
Constant density flux on cylindrical surface:
= 200 W/m
2
(outgoing flow).
1.4 Conditions
initial
Without object.
Code_Aster
®
Version
5.0
Titrate:
TPLA05 Bars cylindrical with density flux
Date:
20/09/02
Author (S):
C. DURAND,
E. SCREWS, F. LEBOUVIER
Key
:
V4.01.005-A
Page:
3/8
Manual of Validation
V4.01 booklet: Stationary thermics of the axisymmetric 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 TPLA05/89 of guide VPCS
Z
R
L
O
·
Temperature according to Z:
T Z
R Z Z L
T zL
()
(
)
.
= -
-
+
1
,
·
T (z=0) =0 T (z=L) = T
1
.
The cylinder is supposed infinitely long (L>>r)
The temperature minimum is of
-
4.17 °C in Z = 0.083 m
2.2
Results of reference
Temperature in Z = 0., 0.1,…, 0.8, 0.9, 1.0
2.3
Uncertainty on the solution
< 1%
Approximate analytical solution (approximation: T = cte, for any R)
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:
TPLA05 Bars cylindrical with density flux
Date:
20/09/02
Author (S):
C. DURAND,
E. SCREWS, F. LEBOUVIER
Key
:
V4.01.005-A
Page:
4/8
Manual of Validation
V4.01 booklet: Stationary thermics of the axisymmetric structures
HT-66/02/001/A
3 Modeling
With
3.1
Characteristics of modeling
3D (PENTA15, HEXA20)
= 30°
X (R)
Z
y
F
D
C
B
With
E
Limiting conditions:
- faces ABCD, ABEF
= 0
- face DFEC
= - 200 W/m ²
- face AFD
T= 0°C
- face NOZZLE
T= 500°C
Cutting:
- 80 elements
according to Z
- 2 elements according to
- 2 elements according to X
3.2
Characteristics of the mesh
A number of nodes:
1937
A number of meshs and types: 160 PENTA15, 160 HEXA20 (and 160 QUAD8)
3.3 Functionalities
tested
Controls
AFFE_MODELE
AFFE
THERMICS
3D
AFFE_CHAR_THER
TEMP_IMPO
FLUX_REP
THER_LINEAIRE
EXCIT
CHARGE
RECU_CHAMP
NUME_ORDRE
3.4 Remarks
Voluminal heat
C
p
does not intervene in this test, but must be declared for Code_Aster. One
takes
C
p
= 1.0 J/m
3
°C.
The limiting condition
= 0. are implicit on the free edges.
Code_Aster
®
Version
5.0
Titrate:
TPLA05 Bars cylindrical with density flux
Date:
20/09/02
Author (S):
C. DURAND,
E. SCREWS, F. LEBOUVIER
Key
:
V4.01.005-A
Page:
5/8
Manual of Validation
V4.01 booklet: Stationary thermics of the axisymmetric structures
HT-66/02/001/A
4
Results of modeling A
4.1 Values
tested
Identification Reference
Aster %
difference
tolerance
Temperature (°C)
Z = 0.0 R = .0 (n1:With)
0.00
0.000
0.0000 *
.00001
R = .01 (n17:D)
0.00
0.000
0.0000 *
.00001
Z = 0.1 R = .0 (n193)
-
4.00
-
3.991
-
0.234%
1%
R = .01 (n209)
-
4.00
-
4.021
0.517% 1%
Z = 0.2 R = .0 (n385)
4.00
4.005
0.123%
1%
R = .01 (n401)
4.00
3.975
-
0.627%
1%
Z = 0.3 R = .0 (n577)
24.00
24.002
0.007%
1%
R = .01 (n593)
24.00
23.972
-
0.118%
1%
Z = 0.4 R = .0 (n769)
56.00
56.000
0.000
1%
R = .01 (n785)
56.00
55.970
-
0.054%
1%
Z = 0.5 R = .0 (n961)
100.00
99.999
-
0.001%
1%
R = .01 (n977)
100.00
99.969
-
0.031%
1%
Z = 0.6 R = .0 (n1153)
156.00
156.000
0.000%
1%
R = .01 (n1169)
156.00
155.970
-
0.019%
1%
Z = 0.7 R = .0 (n1345)
224.00
224.002
0.001%
1%
R = .01 (n1361)
224.00
223.972
-
0.013%
1%
Z = 0.8 R = .0 (n1537)
304.00
304.005
0.002%
1%
R = .01 (n1553)
304.00
303.975
-
0.008%
1%
Z = 0.9 R = .0 (n1729)
396.00
396.009
0.002%
1%
R = .01 (n1745)
396.00
395.979
-
0.005%
1%
Z = 1.0 R = .0 (n1921:B)
500.00
500.000
0.0000 *
.00001
R = .01 (n1937:C)
500.00
500.000
0.0000 *
.00001
(*: Imposed temperature)
4.2 Parameters
of execution
Version: 5.03
Machine: SGI - ORIGIN 2000 - R12000
Overall dimension memory:
8 megawords
Time CPU To use: 3.21 seconds
Code_Aster
®
Version
5.0
Titrate:
TPLA05 Bars cylindrical with density flux
Date:
20/09/02
Author (S):
C. DURAND,
E. SCREWS, F. LEBOUVIER
Key
:
V4.01.005-A
Page:
6/8
Manual of Validation
V4.01 booklet: Stationary thermics of the axisymmetric structures
HT-66/02/001/A
5 Modeling
B
5.1
Characteristics of modeling
AXIS (TRIA6)
X (R)
y (Z)
D
B
With
Limiting conditions:
- dimensioned CD
= - 200.W/m ²
- dimensioned AD
T =
0°C
- dimensioned BC
T =
500°C
Cutting:
- 80 elements
according to y
- 2 elements according to X
C
5.2
Characteristics of the mesh
A number of nodes:
805
A number of meshs and types: 320 TRIA6 (and 80 SEG3)
5.3 Functionalities
tested
Controls
AFFE_MODELE
AFFE
THERMICS
AXIS
AFFE_CHAR_THER
TEMP_IMPO
FLUX_REP
THER_LINEAIRE
EXCIT
CHARGE
RECU_CHAMP
NUME_ORDRE
5.4 Remarks
Voluminal heat
C
p
does not intervene in this test, but must be declared for Code_Aster. One
takes
C
p
= 1.0 J/m
3
°C.
The limiting condition
= 0. are implicit on the free edges.
Code_Aster
®
Version
5.0
Titrate:
TPLA05 Bars cylindrical with density flux
Date:
20/09/02
Author (S):
C. DURAND,
E. SCREWS, F. LEBOUVIER
Key
:
V4.01.005-A
Page:
7/8
Manual of Validation
V4.01 booklet: Stationary thermics of the axisymmetric structures
HT-66/02/001/A
6
Results of modeling A
6.1 Values
tested
Identification Reference
Aster %
difference
tolerance
Temperature (°C)
Z = 0.0 R = .0 (n1:With)
0.00
0.000
0.0000 *
00001
R = .01 (n5:D)
0.00
0.000
0.0000 *
00001
Z = 0.1 R = .0 (n81)
-
4.00
-
3.990
-
0.257%
1%
R = .01 (n85)
-
4.00
-
4.021
0.513% 1%
Z = 0.2 R = .0 (n161)
4.00
4.006
0.152%
1%
R = .01 (n165)
4.00
3.976
-
0.618%
1%
Z = 0.3 R = .0 (n241)
24.00
24.003
0.013%
1%
R = .01 (n245)
24.00
23.972
-
0.116%
1%
Z = 0.4 R = .0 (n321)
56.00
56.001
0.002
1%
R = .01 (n325)
56.00
55.970
-
0.053%
1%
Z = 0.5 R = .0 (n401)
100.00
100.001
0.001%
1%
R = .01 (n405)
100.00
99.970
-
0.030%
1%
Z = 0.6 R = .0 (n481)
156.00
156.001
0.001%
1%
R = .01 (n485)
156.00
155.970
-
0.019%
1%
Z = 0.7 R = .0 (n561)
224.00
224.003
0.001%
1%
R = .01 (n565)
224.00
223.972
-
0.012%
1%
Z = 0.8 R = .0 (n641)
304.00
304.006
0.002%
1%
R = .01 (n645)
304.00
303.975
-
0.008%
1%
Z = 0.9 R = .0 (n721)
396.00
396.010
0.003%
1%
R = .01 (n725)
396.00
395.979
-
0.005%
1%
Z = 1.0 R = .0 (n801:B)
500.00
500.000
0.0000 *
00001
R = .01 (n805:C)
500.00
500.000
0.0000 *
00001
(*: Imposed temperature)
6.2 Parameters
of execution
Version: 5.03
Machine: SGI - ORIGIN 2000 - R12000
Overall dimension memory:
8 megawords
Time CPU To use: 2.28 seconds
Code_Aster
®
Version
5.0
Titrate:
TPLA05 Bars cylindrical with density flux
Date:
20/09/02
Author (S):
C. DURAND,
E. SCREWS, F. LEBOUVIER
Key
:
V4.01.005-A
Page:
8/8
Manual of Validation
V4.01 booklet: Stationary thermics of the axisymmetric structures
HT-66/02/001/A
7
Summary of the results
The results obtained are satisfactory, the maximum change is 0.63%. Modeling 3D (with
meshs PENTA15, HEXA20) and modeling AXIS (with meshs TRIA6) give appreciably
same results (the mesh and the degree of interpolation are identical).
The analytical solution which is an approached solution, supposes that the ratio R/L is much higher than
1. For this numerical test, the ratio R/L was taken equal to 100.