Code_Aster
®
Version
4.0
Titrate:
TTLP303 Transfer of heat in an orthotropic plate
Date:
01/12/98
Author (S)
:
E. SCREWS, F. LEBOUVIER
Key:
V4.23.303-A
Page:
1/10
Manual of Validation
V4.23 booklet: Transitory thermics of the plane systems
HI-75/98/040 - Ind A
Organization (S)
: EDF/IMA/MN, Delta CAD
Manual of Validation
V4.23 booklet: Transitory thermics of the plane systems
Document: V4.23.303
TTLP303 - Transfer 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
Code_Aster
®
Version
4.0
Titrate:
TTLP303 Transfer of heat in an orthotropic plate
Date:
01/12/98
Author (S)
:
E. SCREWS, F. LEBOUVIER
Key:
V4.23.303-A
Page:
2/10
Manual of Validation
V4.23 booklet: Transitory thermics of the plane systems
HI-75/98/040 - Ind A
1
Problem of reference
1.1 Geometry
y
X
L
y
= 6 m
With
B
D
C
T
O
(X, y, 0) = - 1.111°C
L
X
= 3 m
1.2
Properties of material
X
=
1.319 W/m °C
thermal conductivity along axis X
y
=
0.659 W/m °C
thermal conductivity along the axis y
C
1899.1 J/m
3
°C
voluminal heat
1.3
Boundary conditions and loadings
Contour ABCD: T =
-
17.778°C
1.4 Conditions
initial
T
O
(T = 0) =
-
1.111°C
Code_Aster
®
Version
4.0
Titrate:
TTLP303 Transfer of heat in an orthotropic plate
Date:
01/12/98
Author (S)
:
E. SCREWS, F. LEBOUVIER
Key:
V4.23.303-A
Page:
3/10
Manual of Validation
V4.23 booklet: Transitory thermics of the plane systems
HI-75/98/040 - Ind A
2
Reference solution
2.1
Method of calculation used for the reference solution
()
()
[
]
()
[
]
T X y T
With
N X
L
J y
L
N
L
J
L
T
C
With
T
nj
T
T
N
N
X
J
X
X
y
y
N
I
N
J
I
O
y
(,)
sin
sin
exp
/
.
=
-
+
=
-
-
-
- -
=
+
=
=
1
1
2
2
2
2
2
2
2
4
1
1
1
1
32 5
9
5
9
32
where
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
Y
C
X
Æ
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.
Code_Aster
®
Version
4.0
Titrate:
TTLP303 Transfer of heat in an orthotropic plate
Date:
01/12/98
Author (S)
:
E. SCREWS, F. LEBOUVIER
Key:
V4.23.303-A
Page:
4/10
Manual of Validation
V4.23 booklet: Transitory thermics of the plane systems
HI-75/98/040 - Ind A
3 Modeling
With
3.1
Characteristics of modeling
HULL (TRIA6)
Limiting conditions
- dimensioned EFF, FG:
= 0
- dimensioned AE, AG: T =-17.778°C
Cutting:
- 5 elements in X
- 10 elements in y
y
X
With
E
G
F
1.5 m
3.0 m
y
3.2
Characteristics of the mesh
A number of nodes:
231
A number of meshs and types: 100 TRIA6
3.3 Functionalities
tested
Controls
Keys
AFFE_MODELE
THERMICS
HULL
ALL
[U4.22.01]
DEFI_MATERIAU
THER_ORTH
[U4.23.01]
AFFE_CARA_ELEM
HULL
[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]
Code_Aster
®
Version
4.0
Titrate:
TTLP303 Transfer of heat in an orthotropic plate
Date:
01/12/98
Author (S)
:
E. SCREWS, F. LEBOUVIER
Key:
V4.23.303-A
Page:
5/10
Manual of Validation
V4.23 booklet: Transitory thermics of the plane systems
HI-75/98/040 - Ind A
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
Overall dimension memory:
megawords
Time CPU To use: seconds
Code_Aster
®
Version
4.0
Titrate:
TTLP303 Transfer of heat in an orthotropic plate
Date:
01/12/98
Author (S)
:
E. SCREWS, F. LEBOUVIER
Key:
V4.23.303-A
Page:
6/10
Manual of Validation
V4.23 booklet: Transitory thermics of the plane systems
HI-75/98/040 - Ind A
5 Modeling
B
5.1
Characteristics of modeling
HULL (TRIA3)
Limiting conditions
- dimensioned EFF, FG:
= 0
- dimensioned AE, AG: T = - 17.778°C
Cutting:
- 5 elements in X
- 10 elements in y
y
X
With
E
G
F
1.5 m
3.0 m
y
5.2
Characteristics of the mesh
A number of nodes:
66
A number of meshs and types: 100 TRIA3
5.3 Functionalities
tested
Controls
Keys
AFFE_MODELE
THERMICS
HULL
ALL
[U4.22.01]
DEFI_MATERIAU
THER_ORTH
[U4.23.01]
AFFE_CARA_ELEM
HULL
[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]
Code_Aster
®
Version
4.0
Titrate:
TTLP303 Transfer of heat in an orthotropic plate
Date:
01/12/98
Author (S)
:
E. SCREWS, F. LEBOUVIER
Key:
V4.23.303-A
Page:
7/10
Manual of Validation
V4.23 booklet: Transitory thermics of the plane systems
HI-75/98/040 - Ind A
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
Overall dimension memory:
megawords
Time CPU To use: seconds
Code_Aster
®
Version
4.0
Titrate:
TTLP303 Transfer of heat in an orthotropic plate
Date:
01/12/98
Author (S)
:
E. SCREWS, F. LEBOUVIER
Key:
V4.23.303-A
Page:
8/10
Manual of Validation
V4.23 booklet: Transitory thermics of the plane systems
HI-75/98/040 - Ind A
7 Modeling
C
7.1
Characteristics of modeling
PLAN (QUAD9)
Limiting conditions
- dimensioned EFF, FG:
= 0
- dimensioned AE, AG: T = - 17.778°C
Y
X
With
E
G
F
1.5 m
y
0.5
3. m
=15°
X
N49
N115
N181
N225
N55
N121
N187
N231
7.2
Characteristics of the mesh
A number of nodes:
231
A number of meshs and types: 50 QUAD9
7.3 Functionalities
tested
Controls
Keys
AFFE_MODELE
THERMICS
PLAN
ALL
[U4.22.01]
DEFI_MATERIAU
THER_ORTH
[U4.23.01]
AFFE_CHAR_THER_F
TEMP_IMPO
[U4.25.02]
AFFE_CARA_ELEM
SOLID MASS
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 pitch of time is as follows:
240 pitches for [0. , 4320.D0] is
T = 18.D0
Code_Aster
®
Version
4.0
Titrate:
TTLP303 Transfer of heat in an orthotropic plate
Date:
01/12/98
Author (S)
:
E. SCREWS, F. LEBOUVIER
Key:
V4.23.303-A
Page:
9/10
Manual of Validation
V4.23 booklet: Transitory thermics of the plane systems
HI-75/98/040 - Ind A
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
Overall dimension memory:
8 megawords
Time CPU To use: 20.6 seconds
Code_Aster
®
Version
4.0
Titrate:
TTLP303 Transfer of heat in an orthotropic plate
Date:
01/12/98
Author (S)
:
E. SCREWS, F. LEBOUVIER
Key:
V4.23.303-A
Page:
10/10
Manual of Validation
V4.23 booklet: Transitory thermics of the plane systems
HI-75/98/040 - Ind A
9
Summary of the results
Two modelings HULL give results very far away from the reference solution, two
faults software were emitted under numbers Al 96-144 et al. 96-178.
Modeling PLAN, carried out with meshs QUAD9, gives satisfactory results, the variation
maximum obtained is 0.039%.