Code_Aster ®
Version
4.0
Titrate:
TTLP303 Transfert of heat in an orthotropic plate
Date: 01/12/98
Author (S)
:
E. SCREWS, F. LEBOUVIER
Key:
V4.23.303-A Page:
1/10
Organization (S): EDF/IMA/MN, Delta CAD
Handbook of Validation
V4.23 booklet: Transitory thermics of the plane systems
Document: V4.23.303
TTLP303 - Transfert of heat in a plate
orthotropic: imposed temperatures
Summary:
This test results from the validation independent of version 3 in thermics.
Analyze:
Linear transitory thermics
Problem:
plane 2D
Functionalities tested:
· thermal element hull
· plane thermal element
· orthotropic material
· transitory algorithm of thermics
· limiting conditions: imposed temperatures
Interest of the test:
· orthotropic material
· analytical solution
A number of modelings:
· 1 modeling hull
· 1 plane modeling
Handbook of Validation
V4.23 booklet: Transitory thermics of the plane systems
HI-75/98/040 - Ind A
Code_Aster ®
Version
4.0
Titrate:
TTLP303 Transfert of heat in an orthotropic plate
Date: 01/12/98
Author (S)
:
E. SCREWS, F. LEBOUVIER
Key:
V4.23.303-A Page:
2/10
1
Problem of reference
1.1 Geometry
y
D
C
To (X, y, 0) = - 1.111°C
Ly = 6 m
X
With
B
Lx = 3 m
1.2
Properties of material
=
1.319 W/m °C
thermal conductivity along axis X
X
=
0.659 W/m °C
thermal conductivity along the axis y
y
C
1899.1 J/m3 °C
voluminal heat
1.3
Boundary conditions and loadings
Contour ABCD: T = - 17.778°C
1.4 Conditions
initial
To (T = 0) = - 1.111°C
Handbook of Validation
V4.23 booklet: Transitory thermics of the plane systems
HI-75/98/040 - Ind A
Code_Aster ®
Version
4.0
Titrate:
TTLP303 Transfert of heat in an orthotropic plate
Date: 01/12/98
Author (S)
:
E. SCREWS, F. LEBOUVIER
Key:
V4.23.303-A Page:
3/10
2
Reference solution
2.1
Method of calculation used for the reference solution
2
2
nx
jy
N2 2
J
y
T (X, y, T) =
With
X
sin
sin
exp
-
2
+
T/C
N
2
L
Ly
=1
=1
L
L
N
J
X
X
y
(
4 T
I)
5
5
where A
N
J
=
- 1 - 1 - 1 - 1 - 3.
2
32
2
=
+
N
([)] ([)]
T
T
nj
I
O
9
9
Temperature in °C with T = 4320s
3.0
- 17.7778 - 17.5742 - 17.3905
- 17.2448
- 17.1515
- 17.1189
2.7
- 17.7778 - 17.5764 - 17.3948
- 17.2507
- 17.1581
- 17.1262
2.4
- 17.7778 - 17.5832 - 17.4077
- 17.2684
- 17.1790
- 17.1482
2.1
- 17.7778 - 17.5945 - 17.4291
- 17.2979
- 17.2137
- 17.1847
1.8
- 17.7778 - 17.6102 - 17.4590
- 17.3391
- 17.2620
- 17.2355
1.5
- 17.7778 - 17.6302 - 17.4970
- 17.3914
- 17.3235
- 17.3002
1.2
- 17.7778 - 17.6542 - 17.5426
- 17.4541
- 17.3973
- 17.3777
0.9
- 17.7778 - 17.6816 - 17.5949
- 17.5261
- 17.4819
- 17.4667
0.6
- 17.7778 - 17.7120 - 17.6526
- 17.6056
- 17.5753
- 17.5649
0.3
- 17.7778 - 17.7444 - 17.7142
- 17.6903
- 17.6749
- 17.6696
0.0
- 17.7778 - 17.7778 - 17.7778
- 17.7778
- 17.7778
- 17.7778
YÇ
XÆ
0.0
0.3
0.6
0.9
1.2
1.5
The values of reference are obtained with N = J = 1000
2.2
Results of reference
T = 4.320s (1.2hr): temperature at the following points:
· in X = 0.6: for y = 0.6, 1.5, 2.4, 3.0
· in X = 1.5: for y = 0.6, 1.5, 2.4, 3.0
2.3
Uncertainty on the solution
Analytical solution.
2.4 References
bibliographical
[1]
J.C. Bruch Jr., G. Zyroloski, `Transient two-dimensional heat conduction problems solved by
the finite element method', Int. J. num. Meth. Engng, flight 8, n°3, p 481-494, 1974.
Handbook of Validation
V4.23 booklet: Transitory thermics of the plane systems
HI-75/98/040 - Ind A
Code_Aster ®
Version
4.0
Titrate:
TTLP303 Transfert of heat in an orthotropic plate
Date: 01/12/98
Author (S)
:
E. SCREWS, F. LEBOUVIER
Key:
V4.23.303-A Page:
4/10
3 Modeling
With
3.1
Characteristics of modeling
COQUE (TRIA6)
y
1.5 m
G
F
Limiting conditions
- dimensioned EFF, FG: = 0
- dimensioned AE, AG: T =-17.778°C
Cutting:
- 5 elements in X
y
- 10 elements in y
3.0 m
X
With
E
3.2
Characteristics of the grid
A number of nodes:
231
A number of meshs and types: 100 TRIA6
3.3 Functionalities
tested
Commands
Keys
AFFE_MODELE
THERMIQUE
COQUE
TOUT
[U4.22.01]
DEFI_MATERIAU
THER_ORTH
[U4.23.01]
AFFE_CARA_ELEM
COQUE
[U4.24.01]
AFFE_CHAR_THER_F
TEMP_IMPO
[U4.25.02]
THER_LINEAIRE
TEMP_INIT
VALE
[U4.33.01]
CARA_ELEM
LIST_INST
RECU_CHAMP
INST
[U4.62.01]
Handbook of Validation
V4.23 booklet: Transitory thermics of the plane systems
HI-75/98/040 - Ind A
Code_Aster ®
Version
4.0
Titrate:
TTLP303 Transfert of heat in an orthotropic plate
Date: 01/12/98
Author (S)
:
E. SCREWS, F. LEBOUVIER
Key:
V4.23.303-A Page:
5/10
4
Results of modeling A
4.1 Values
tested
Relative variation %
Absolute deviation
Identification
Reference
Aster
difference
tolerance
difference
tolerance
Temperature in °C
X = 0.6
T (y = 0.6)
- 17.6526
1%
0.05
T (y = 1.5)
- 17.4970
1%
0.05
T (y = 2.4)
- 17.4077
1%
0.05
T (y = 3.0)
- 17.3905
1%
0.05
X = 1.5
T (y = 0.6)
- 17.5649
1%
0.05
T (y = 1.5)
- 17.3002
1%
0.05
T (y = 2.4)
- 17.1482
1%
0.06
T (y = 3.0)
- 17.1189
1%
0.05
4.2 Parameters
of execution
Version: 3.06
Machine: CRAY C90
System: 8.04 UNICOS
Obstruction memory:
megawords
Time CPU To use: seconds
Handbook of Validation
V4.23 booklet: Transitory thermics of the plane systems
HI-75/98/040 - Ind A
Code_Aster ®
Version
4.0
Titrate:
TTLP303 Transfert of heat in an orthotropic plate
Date: 01/12/98
Author (S)
:
E. SCREWS, F. LEBOUVIER
Key:
V4.23.303-A Page:
6/10
5 Modeling
B
5.1
Characteristics of modeling
COQUE (TRIA3)
y
1.5 m
G
F
Limiting conditions
- dimensioned EFF, FG: = 0
- dimensioned AE, AG: T = - 17.778°C
Cutting:
- 5 elements in X
y
- 10 elements in y
3.0 m
X
With
E
5.2
Characteristics of the grid
A number of nodes:
66
A number of meshs and types: 100 TRIA3
5.3 Functionalities
tested
Commands
Keys
AFFE_MODELE
THERMIQUE
COQUE
TOUT
[U4.22.01]
DEFI_MATERIAU
THER_ORTH
[U4.23.01]
AFFE_CARA_ELEM
COQUE
[U4.24.01]
AFFE_CHAR_THER_F
TEMP_IMPO
[U4.25.02]
THER_LINEAIRE
TEMP_INIT
VALE
[U4.33.01]
CARA_ELEM
LIST_INST
RECU_CHAMP
INST
[U4.62.01]
Handbook of Validation
V4.23 booklet: Transitory thermics of the plane systems
HI-75/98/040 - Ind A
Code_Aster ®
Version
4.0
Titrate:
TTLP303 Transfert of heat in an orthotropic plate
Date: 01/12/98
Author (S)
:
E. SCREWS, F. LEBOUVIER
Key:
V4.23.303-A Page:
7/10
6
Results of modeling B
6.1 Values
tested
Relative variation %
Absolute deviation
Identification
Reference
Aster
difference
tolerance
difference
tolerance
Temperature in °C
X = 0.6
T (y = 0.6)
- 17.6526
1%
0.05
T (y = 1.5)
- 17.4970
1%
0.05
T (y = 2.4)
- 17.4077
1%
0.05
T (y = 3.0)
- 17.3905
1%
0.05
X = 1.5
T (y = 0.6)
- 17.5649
1%
0.05
T (y = 1.5)
- 17.3002
1%
0.05
T (y = 2.4)
- 17.1482
1%
0.06
T (y = 3.0)
- 17.1189
1%
0.05
6.2 Parameters
of execution
Version: 3.06
Machine: CRAY C90
System: 8.04 UNICOS
Obstruction memory:
megawords
Time CPU To use: seconds
Handbook of Validation
V4.23 booklet: Transitory thermics of the plane systems
HI-75/98/040 - Ind A
Code_Aster ®
Version
4.0
Titrate:
TTLP303 Transfert of heat in an orthotropic plate
Date: 01/12/98
Author (S)
:
E. SCREWS, F. LEBOUVIER
Key:
V4.23.303-A Page:
8/10
7 Modeling
C
7.1
Characteristics of modeling
PLAN (QUAD9)
y
G
Limiting conditions
1.5 m
- dimensioned EFF, FG: = 0
- dimensioned AE, AG: T = - 17.778°C
F
N225
N231
N181
N187
Y
3. m
N115
N121
N49
X
N55
With
=15°
0.5
X
E
7.2
Characteristics of the grid
A number of nodes:
231
A number of meshs and types: 50 QUAD9
7.3 Functionalities
tested
Commands
Keys
AFFE_MODELE
THERMIQUE
PLAN
TOUT
[U4.22.01]
DEFI_MATERIAU
THER_ORTH
[U4.23.01]
AFFE_CHAR_THER_F
TEMP_IMPO
[U4.25.02]
AFFE_CARA_ELEM
MASSIF
ANGL_REP
[U4.24.01]
THER_LINEAIRE
TEMP_INIT
VALE
[U4.33.01]
CARA_ELEM
LIST_INST
RECU_CHAMP
INST
[U4.62.01]
7.4 Remarks
The discretization in step of time is as follows:
240 steps for [0. , 4320.D0] is T = 18.D0
Handbook of Validation
V4.23 booklet: Transitory thermics of the plane systems
HI-75/98/040 - Ind A
Code_Aster ®
Version
4.0
Titrate:
TTLP303 Transfert of heat in an orthotropic plate
Date: 01/12/98
Author (S)
:
E. SCREWS, F. LEBOUVIER
Key:
V4.23.303-A Page:
9/10
8
Results of modeling C
8.1 Values
tested
Relative variation %
Absolute deviation
Identification
Reference
Aster
difference
tolerance
difference
tolerance
Temperature in °C
X = 0.6
N49 (y = 0.6)
- 17.6526
- 17.6515
- 0.006
1%
0.001
0.05
N115 (y = 1.5)
- 17.4970
- 17.4942
- 0.016
1%
0.003
0.05
N181 (y = 2.4)
- 17.4077
- 17.4040
- 0.021
1%
0.004
0.05
N225 (y = 3.0)
- 17.3905
- 17.3867
- 0.022
1%
0.004
0.05
X = 1.5
T (y = 0.6)
- 17.5649
- 17.5627
- 0.012
1%
0.002
0.05
T (y = 1.5)
- 17.3002
- 17.2952
- 0.029
1%
0.005
0.05
T (y = 2.4)
- 17.1482
- 17.1418
- 0.037
1%
0.006
0.06
T (y = 3.0)
- 17.1189
- 17.1123
- 0.039
1%
0.007
0.05
8.2 Parameters
of execution
Version: 4.02
Machine: CRAY C90
System: 8.04 UNICOS
Obstruction memory:
8 megawords
Time CPU To use: 20.6 seconds
Handbook of Validation
V4.23 booklet: Transitory thermics of the plane systems
HI-75/98/040 - Ind A
Code_Aster ®
Version
4.0
Titrate:
TTLP303 Transfert of heat in an orthotropic plate
Date: 01/12/98
Author (S)
:
E. SCREWS, F. LEBOUVIER
Key:
V4.23.303-A Page:
10/10
9
Summary of the results
Two modelings COQUE give results very far away from the reference solution, two
anomalies software were emitted under numbers Al 96-144 et al. 96-178.
The modeling PLAN, carried out with meshs QUAD9, gives satisfactory results, the variation
maximum obtained is 0.039%.
Handbook of Validation
V4.23 booklet: Transitory thermics of the plane systems
HI-75/98/040 - Ind A