Code_Aster
®
Version
5.0
Titrate:
TPLA06 Bars cylindrical with convection
Date:
20/09/02
Author (S):
C. DURAND,
E. SCREWS, F. LEBOUVIER
Key
:
V4.01.006-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
V4.01.006 document
TPLA06 - Cylindrical bar with convection
Summary:
This test results from the validation independent of version 3 in linear stationary thermics.
It is about an axisymmetric problem 2D represented by two modelings, the first using of the elements
voluminal, the second of the axisymmetric elements 2D.
Boundary conditions in imposed temperature and of convection are taken into account.
The results resulting from this case test are compared with those provided by VPCS.
Code_Aster
®
Version
5.0
Titrate:
TPLA06 Bars cylindrical with convection
Date:
20/09/02
Author (S):
C. DURAND,
E. SCREWS, F. LEBOUVIER
Key
:
V4.01.006-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.,
·
Convection on cylindrical surface,
-
H = 10 W/m
2
°C,
- T
E
= 0 °C (outside air temperature).
1.4 Conditions
initial
Without object.
Code_Aster
®
Version
5.0
Titrate:
TPLA06 Bars cylindrical with convection
Date:
20/09/02
Author (S):
C. DURAND,
E. SCREWS, F. LEBOUVIER
Key
:
V4.01.006-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 TPLA06/89 of guide VPCS
Z
R
L>> R
O
·
Temperature according to Z:
T Z
T
az
Al
()
sinh ()
sinh ()
=
1
,
where
has
H
R
=
2
·
T (Z = 0) =0 T (Z = L) = T
1
.
2.2
Results of reference
Temperature in Z = 0., 0.1, 0.2,…, 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:
TPLA06 Bars cylindrical with convection
Date:
20/09/02
Author (S):
C. DURAND,
E. SCREWS, F. LEBOUVIER
Key
:
V4.01.006-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 (PENTA6, HEXA8)
Limiting conditions:
- faces ABCD, ABEF
=
0.
- face DCEF
H = 10.W/m ² °C
T
ext.
= 0°C
- face ADF
T =
0°C
- face ECB
T = 500°C
Cutting:
- 100 elements according to Z
- 3 elements according to
- 3 elements according to X
= 30°
X (R)
Z
y
C
B
E
With
D
F
3.2
Characteristics of the mesh
A number of nodes:
1313
A number of meshs and types: 300 PENTA6, 600 HEXA8 (and 300 QUAD4)
3.3 Functionalities
tested
Controls
AFFE_MODELE
AFFE
THERMICS
3D
AFFE_CHAR_THER
TEMP_IMPO
EXCHANGE
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:
TPLA06 Bars cylindrical with convection
Date:
20/09/02
Author (S):
C. DURAND,
E. SCREWS, F. LEBOUVIER
Key
:
V4.01.006-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)
0.0000
0.0000
0.0000 *
.00001
R = .01 (n13:D)
0.0000
0.0000
0.0000 *
.00001
Z = 0.1 R = .0 (n131)
0.3694
0.3654
-
1.084%
1%
R = .01 (n143)
0.3694
0.3648
-
1.240%
1%
Z = 0.2 R = .0 (n261)
0.9718
0.9621
-
0.998%
1%
R = .01 (n273)
0.9718
0.9606
-
1.154%
1%
Z = 0.3 R = .0 (n391)
2.1870
2.1679
-
0.875%
1%
R = .01 (n403)
2.1870
2.1644
-
1.031%
1%
Z = 0.4 R = .0 (n521)
4.7815
4.7460
-
0.743%
1%
R = .01 (n533)
4.7815
4.7385
-
0.899%
1%
Z = 0.5 R = .0 (n651)
10.392
10.329
-
0.611%
1%
R = .01 (n663)
10.392
10.312
-
0.768%
1%
Z = 0.6 R = .0 (n781)
22.555
22.450
-
0.468%
1%
R = .01 (n793)
22.555
22.414
-
0.625%
1%
Z = 0.7 R = .0 (n911)
48.944
48.782
-
0.331%
1%
R = .01 (n923)
48.944
48.705
-
0.488%
1%
Z = 0.8 R = .0 (n1041)
106.20
106.00
-
0.192%
1%
R = .01 (n1053)
106.20
105.83
-
0.349%
1%
Z = 0.9 R = .0 (n1171)
230.44
230.31
-
0.056%
1%
R = .01 (n1183)
230.44
229.95
-
0.214%
1%
Z = 1.0 R = .0 (n1301:B)
500.00
500.00
0.0000 *
.00001
R = .01 (n1313:C)
500.00
500.00
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: 3.10 seconds
Code_Aster
®
Version
5.0
Titrate:
TPLA06 Bars cylindrical with convection
Date:
20/09/02
Author (S):
C. DURAND,
E. SCREWS, F. LEBOUVIER
Key
:
V4.01.006-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 (TRIA3)
Limiting conditions:
- dimensioned CD
H = 10.W/m ² °C
T
ext.
= 10°C
- dimensioned AD
T =
0°C
- dimensioned BC
T = 500°C
Cutting:
- 150 elements following y
- 3 elements according to X
X (R)
y (Z)
D
B
With
C
5.2
Characteristics of the mesh
A number of nodes:
604
A number of meshs and types: 900 TRIA3 (and 150 SEG2)
5.3 Functionalities
tested
Controls
AFFE_MODELE
AFFE
THERMICS
AXIS
AFFE_CHAR_THER
TEMP_IMPO
EXCHANGE
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.
Code_Aster
®
Version
5.0
Titrate:
TPLA06 Bars cylindrical with convection
Date:
20/09/02
Author (S):
C. DURAND,
E. SCREWS, F. LEBOUVIER
Key
:
V4.01.006-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)
0.0000
0.0000
0.0000 *
.00001
R = .01 (n4:D)
0.0000
0.0000
0.0000 *
.00001
Z = 0.1 R = .0 (n61)
0.3694
0.3703
0.254%
1%
R = .01 (n64)
0.3694
0.3697
0.095%
1%
Z = 0.2 R = .0 (n121)
0.9718
0.9741
0.237%
1%
R = .01 (n124)
0.9718
0.9726
0.079%
1%
Z = 0.3 R = .0 (n181)
2.1870
2.1919
0.224%
1%
R = .01 (n184)
2.1870
2.1884
0.065%
1%
Z = 0.4 R = .0 (n241)
4.7815
4.7913
0.205%
1%
R = .01 (n244)
4.7815
4.7837
0.046%
1%
Z = 0.5 R = .0 (n301)
10.392
10.411
0.181%
1%
R = .01 (n304)
10.392
10.394
0.022%
1%
Z = 0.6 R = .0 (n361)
22.555
22.593
0.167%
1%
R = .01 (n364)
22.555
22.557
0.008%
1%
Z = 0.7 R = .0 (n421)
48.944
49.015
0.145%
1%
R = .01 (n424)
48.944
48.937
-
0.013%
1%
Z = 0.8 R = .0 (n481)
106.20
106.33
0.126%
1%
R = .01 (n484)
106.20
106.16
-
0.033%
1%
Z = 0.9 R = .0 (n541)
230.44
230.68
0.103%
1%
R = .01 (n544)
230.44
230.31
-
0.056%
1%
Z = 1.0 R = .0 (n601:B)
500.00
500.00
0.0000 *
.00001
R = .01 (n604:C)
500.00
500.00
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: 2.60 seconds
Code_Aster
®
Version
5.0
Titrate:
TPLA06 Bars cylindrical with convection
Date:
20/09/02
Author (S):
C. DURAND,
E. SCREWS, F. LEBOUVIER
Key
:
V4.01.006-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 modeling A, carried out in 3D with linear meshs (PENTA15, HEXA8), gives
results whose four values (out of 22) exceed the tolerance fixed initially. The maximum change
obtained is 1.24% for a tolerance of 1%. This going beyond of the tolerance is observed for
values of the temperature close to 0.
By account modeling B, carried out in AXIS with linear meshs (TRIA3), gives
satisfactory results, the maximum change obtained is 0.25%.
Modeling AXIS is adapted to modelize this cylindrical bar than modeling
3D. Cutting circonférenciel in 3D is not enough dense to represent the cylinder, and one
finer cutting would improve the results.
The results obtained by modeling 3D are regarded as acceptable taking into account
mesh used.
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.