Code_Aster
®
Version
5.0
Titrate:
Orthotropic TPLA07 Hollow roll
Date:
20/09/02
Author (S):
C. DURAND, E. SCREW, F. LEBOUVIER
Key
:
V4.01.007-A
Page:
1/6
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
V4.01.007 document
TPLA07 - Orthotropic hollow roll
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 air temperatures).
The results resulting from this case test are compared with those provided by VPCS.
Code_Aster
®
Version
5.0
Titrate:
Orthotropic TPLA07 Hollow roll
Date:
20/09/02
Author (S):
C. DURAND, E. SCREW, F. LEBOUVIER
Key
:
V4.01.007-A
Page:
2/6
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
R
E
R
I
Interior radius R
I
= 0.03 m
External radius R
E
= 0.05 m
Height L = 0.40 m
L
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/m
2
°C,
·
convection on external surface: H = 339.3 W/m
2
°C,
·
linear variation of the outside air temperatures:
-
on surface R
I
:
T
IE
= 130°C in Z = 0. ;
T
IE
= 135°C in Z = 0.4 (
T
IE
= 130 + 12.5z),
-
on surface R
E
:
T
ee
= 20°C in Z = 0. ;
T
IE
= 25°C in Z = 0.4 (
T
ee
= 20 + 12.5z).
1.4 Conditions
initial
Without object.
Code_Aster
®
Version
5.0
Titrate:
Orthotropic TPLA07 Hollow roll
Date:
20/09/02
Author (S):
C. DURAND, E. SCREW, F. LEBOUVIER
Key
:
V4.01.007-A
Page:
3/6
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 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
Code_Aster
®
Version
5.0
Titrate:
Orthotropic TPLA07 Hollow roll
Date:
20/09/02
Author (S):
C. DURAND, E. SCREW, F. LEBOUVIER
Key
:
V4.01.007-A
Page:
4/6
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
AXIS (TRIA3)
X (R)
y (Z)
D
B
With
Limiting conditions:
- dimensioned AB
=
500. W/m ²
- dimensioned CD
=
- 500. W/m ²
- dimensioned DA
H =
377. W/m ² °C
T
I
E
= 130+12.5z
- dimensioned BC
H =
339.3 W/m ² °C
T
E
E
=
20+12.5z
Cutting:
- 40 elements
according to y
- 4 elements
according to X
C
N1
N2
M2
M1
N4
N5
M242
M241 R
z=0.
N101
N102
M40
N104
N105
M280
M41
M281
M39
M279
M42
M282
z=0.2
N201 N202
M80
M79
N204 N205
M320
M319
z=0.4
r=0.03 r=0.05 r=0.03 r=0.05 r=0.03 r=0.05
3.2
Characteristics of the mesh
A number of nodes:
205
A number of meshs and types: 408 TRIA3 (and 88 SEG2)
3.3 Functionalities
tested
Controls
AFFE_MODELE
THERMICS
AXIS
DEFI_MATERIAU
THER_ORTH
AFFE_CARA_ELEM
SOLID MASS
ANGL_REP
AFFE_CHAR_THER_F
EXCHANGE
FLUX_REP
THER_LINEAIRE
CARA_ELEM
CALC_CHAM_ELEM
CARA_ELEM
3.4 Remarks
Voluminal heat
C
p
does not intervene in this test, but must obligatorily be declared. 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:
Orthotropic TPLA07 Hollow roll
Date:
20/09/02
Author (S):
C. DURAND, E. SCREW, F. LEBOUVIER
Key
:
V4.01.007-A
Page:
5/6
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. 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
Overall dimension memory:
8 megawords
Time CPU To use: 2.56 seconds
Code_Aster
®
Version
5.0
Titrate:
Orthotropic TPLA07 Hollow roll
Date:
20/09/02
Author (S):
C. DURAND, E. SCREW, F. LEBOUVIER
Key
:
V4.01.007-A
Page:
6/6
Manual of Validation
V4.01 booklet: Stationary thermics of the axisymmetric structures
HT-66/02/001/A
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, a fault software was emitted under the n° 96-176.