Code_Aster ®
Version
5.0
Titrate:
Orthotropic TPLA07 hollow Cylindre
Date:
20/09/02
Author (S):
C. DURAND, E. SCREW, F. LEBOUVIER Clé
:
V4.01.007-A Page:
1/6
Organization (S): EDF/AMA, EDF/UTO/LOCATED, Delta CAD
Handbook of Validation
V4.01 booklet: Stationary thermics of the axisymmetric structures
V4.01.007 document
TPLA07 - Orthotropic hollow Cylindre
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 three-dimensional one,
second axisymmetric 2D.
The interest of this case test is to test an orthotropic material subjected to various boundary conditions (flow
imposed, convection, linear variation of the outside temperatures).
The results resulting from this case test are compared with those provided by VPCS.
Handbook of Validation
V4.01 booklet: Stationary thermics of the axisymmetric structures
HT-66/02/001/A
Code_Aster ®
Version
5.0
Titrate:
Orthotropic TPLA07 hollow Cylindre
Date:
20/09/02
Author (S):
C. DURAND, E. SCREW, F. LEBOUVIER Clé
:
V4.01.007-A Page:
2/6
1
Problem of reference
1.1 Geometry
Z
Re
IH
Interior radius IH = 0.03 m
External radius Re = 0.05 m
Height L = 0.40 m
L
R
1.2
Properties of material
R = 2.89 W/m.°C
thermal conductivity along the axis R
Z = 40.0 W/m.°C
thermal conductivity along axis Z
circumferential:
unspecified
1.3
Boundary conditions and loadings
· density flux = - 500 W/m ² through surface Z = 0. (outgoing flow),
· density flux = +500 W/m ² through surface Z = 0.4 (entering flow),
· convection on interior surface: H = 377.0 W/m2 °C,
· convection on external surface: H = 339.3 W/m2 °C,
· linear variation of the outside temperatures:
-
on surface R
E
E
E
I: Ti = 130°C in Z = 0. ; Ti = 135°C in Z = 0.4 (Ti = 130 + 12.5z),
-
on surface R
E
E
E
E: Te = 20°C in Z = 0. ; Ti = 25°C in Z = 0.4 (Te = 20 + 12.5z).
1.4 Conditions
initial
Without object.
Handbook of Validation
V4.01 booklet: Stationary thermics of the axisymmetric structures
HT-66/02/001/A
Code_Aster ®
Version
5.0
Titrate:
Orthotropic TPLA07 hollow Cylindre
Date:
20/09/02
Author (S):
C. DURAND, E. SCREW, F. LEBOUVIER Clé
:
V4.01.007-A Page:
3/6
2
Reference solution
2.1
Method of calculation used for the reference solution
The reference solution is that given in card TPLA07/89 of guide VPCS.
Temperature: T (R, Z) = - 117.46 Log R + 12.5z - 311.87
2.2
Results of reference
· temperature in R = 0.03, 0.035, 0.04 and 0.05 and for Z = 0., 0.2 and 0.4,
· density flux on interior and external surface,
· density flux following axis Z.
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
V4.01 booklet: Stationary thermics of the axisymmetric structures
HT-66/02/001/A
Code_Aster ®
Version
5.0
Titrate:
Orthotropic TPLA07 hollow Cylindre
Date:
20/09/02
Author (S):
C. DURAND, E. SCREW, F. LEBOUVIER Clé
:
V4.01.007-A Page:
4/6
3 Modeling
With
3.1
Characteristics of modeling
AXIS (TRIA3)
y (Z)
Limiting conditions:
D
C
- dimensioned AB
=
500. W/m ²
- dimensioned CD
=
- 500. W/m ²
- dimensioned DA
H =
377. W/m ² °C
Tei = 130+12.5z
- dimensioned BC
H =
339.3 W/m ² °C
Tee = 20+12.5z
Cutting:
X (R)
- 40 elements
according to y
- 4 elements
according to X
With
B
z=0.
z=0.2
M42
N201 N202 z=0.4 N204 N205
M282
M2
M242
M41
M281
M80
M320
N101
N102
N104
N105
M1
M241
M40
R
M280
M79
M319
N1
N2
N4
N5
M39
M279
r=0.03 r=0.05 r=0.03 r=0.05 r=0.03 r=0.05
3.2
Characteristics of the grid
A number of nodes:
205
A number of meshs and types: 408 TRIA3 (and 88 SEG2)
3.3 Functionalities
tested
Commands
AFFE_MODELE
THERMIQUE
AXIS
DEFI_MATERIAU
THER_ORTH
AFFE_CARA_ELEM
MASSIF
ANGL_REP
AFFE_CHAR_THER_F
ECHANGE
FLUX_REP
THER_LINEAIRE
CARA_ELEM
CALC_CHAM_ELEM
CARA_ELEM
3.4 Remarks
Voluminal heat CP does not intervene in this test, but must obligatorily be declared. One
takes .cp = 1.0 J/m3 °C.
The condition limits = 0. is implicit on the free edges.
Handbook of Validation
V4.01 booklet: Stationary thermics of the axisymmetric structures
HT-66/02/001/A
Code_Aster ®
Version
5.0
Titrate:
Orthotropic TPLA07 hollow Cylindre
Date:
20/09/02
Author (S):
C. DURAND, E. SCREW, F. LEBOUVIER Clé
:
V4.01.007-A Page:
5/6
4
Results of modeling A
4.1 Values
tested
Identification Reference
Aster %
difference
tolerance
Temperature (°C)
Z = 0. R = 0.030 (N1)
100.01
99.829
- 0.181%
1.%
R = 0.035 (N2)
81.90
81.867
- 0.040%
1.%
R = 0.040 (N3)
66.22
66.229
0.014%
1.%
R = 0.045 (N4)
52.38
52.422
0.081%
1.%
R = 0.050 (N5)
40.01
40.095
0.212%
1.%
Z = 0.2 R = 0.030 (N101)
102.51
102.469
- 0.040%
1.%
R = 0.035 (N102)
84.40
84.388
- 0.014%
1.%
R = 0.040 (N103)
68.72
68.718
- 0.003%
1.%
R = 0.045 (N104)
54.88
54.892
0.021%
1.%
R = 0.050 (N105)
42.51
42.521
0.025%
1.%
Z = 0.4 R = 0.030 (N201)
105.01
105.111
0.096%
1.%
R = 0.035 (N202)
86.90
86.909
0.010%
1.%
R = 0.040 (N203)
71.22
71.207
- 0.018%
1.%
R = 0.045 (N204)
57.38
57.361
- 0.033%
1.%
R = 0.050 (N205)
45.01
44.946
- 0.142%
1.%
Density flux (W/m ²)
Z (z=0.) M1/N1
- 500.
- 511.97
2.395
1.%
Z (z=0.) m2/N1
- 500.
- 824.47
64.894
1.%
Z (z=0.) M241/N5
- 500.
- 346.66
- 30.668
1.%
Z (z=0.2) M40/N101
- 500.
- 499.95
- 0.009
1.%
Z (z=0.2) M41/N101
- 500.
- 499.93
- 0.013
1.%
Z (z=0.2) M280/N105
- 500.
- 499.93
- 0.014
1.%
Z (z=0.4) M80/N201
- 500.
- 828.51
65.701
1.%
Z (z=0.4) M319/N205
- 500.
- 345.65
- 30.869
1.%
Z (z=0.4) M320/N205
- 500.
- 468.64
- 6.271
1.%
IH (z=0.) M1/N1
11310.
10381.98
- 8.205
1.%
IH (z=0.2) M40/N101
11310.
10450.74
- 7.597
1.%
IH (z=0.4) M80/N201
11310.
10520.67
- 6.979
1.%
IH (z=0.) M241/N5
6786.
7125.41
5.002
1.%
IH (z=0.2) M280/N105
6786.
7150.5
5.371
1.%
IH (z=0.4) M320/N205
6786.
7175.83
5.745
1.%
4.2 Parameters
of execution
Version: 5.03
Machine: SGI - ORIGIN 2000 - R12000
Obstruction memory:
8 megawords
Time CPU To use: 2.56 seconds
Handbook of Validation
V4.01 booklet: Stationary thermics of the axisymmetric structures
HT-66/02/001/A
Code_Aster ®
Version
5.0
Titrate:
Orthotropic TPLA07 hollow Cylindre
Date:
20/09/02
Author (S):
C. DURAND, E. SCREW, F. LEBOUVIER Clé
:
V4.01.007-A Page:
6/6
5
Summary of the results
The results obtained are satisfactory in temperature but far away from the reference solution to
level of flows (especially for flow along axis Z). The maximum departures obtained are as follows:
· 0.212% in temperature,
· 65.701% for flow along axis Z,
· - 8.205 for flow according to the radius.
Flow following the axis: the flow of reference is constant, the variations observed are more important with
ends of the cylinder, on the other hand with semi height these variations are very weak (lower than the tolerance).
Flow following the radius: The variations according to the radius are higher than the tolerance, but they could
to be minimized by increasing the discretization along axis R.
Following these results, an anomaly software was emitted under the n° 96-176.
Handbook of Validation
V4.01 booklet: Stationary thermics of the axisymmetric structures
HT-66/02/001/A
Outline document