Code_Aster ®
Version
5.0
Titrate:
TTLP304 Transfert of heat in an orthotropic plate: imposed flows
Date:
20/09/02
Author (S):
C. DURAND, E. SCREW, F. LEBOUVIER Clé
:
V4.23.304-A Page:
1/6
Organization (S): EDF/AMA, EDF/UTO/LOCATED, Delta CAD
Handbook of Validation
V4.23 booklet: Transitory thermics of the plane systems
V4.23.304 document
TTLP304 - Transfert of heat in a plate
orthotropic: imposed flows
Summary:
This test results from the validation independent of version 3 in linear transitory thermics.
It is about a problem plane 2D represented by a modeling (plane).
The functionalities tested are as follows:
· plane thermal element,
· orthotropic material,
· transitory algorithm of thermics,
· limiting conditions: imposed flow.
The interest of the test lies in the taking into account of an orthotropic material.
The results are compared with an analytical solution.
Handbook of Validation
V4.23 booklet: Transitory thermics of the plane systems
HT-66/02/001/A
Code_Aster ®
Version
5.0
Titrate:
TTLP304 Transfert of heat in an orthotropic plate: imposed flows
Date:
20/09/02
Author (S):
C. DURAND, E. SCREW, F. LEBOUVIER Clé
:
V4.23.304-A Page:
2/6
1
Problem of reference
1.1 Geometry
y
Lx = 2.7 m
D
C
L
T
y = 5.4 m
O (X, y, 0) = - 1.111°C
X
With
B
1.2
Properties of material
X = 2.638 W/m °C conductivity thermal along axis X
y = 0.633 W/m °C conductivity thermal along the axis y
C 1899.1
J/voluminal m3 °C heat
1.3
Boundary conditions and loadings
Contour [AB], [BC], [CD]: T = - 17.778°C
Side [AD]: = 0
1.4 Conditions
initial
T (T = 0) = - 1.111°C
Handbook of Validation
V4.23 booklet: Transitory thermics of the plane systems
HT-66/02/001/A
Code_Aster ®
Version
5.0
Titrate:
TTLP304 Transfert of heat in an orthotropic plate: imposed flows
Date:
20/09/02
Author (S):
C. DURAND, E. SCREW, F. LEBOUVIER Clé
:
V4.23.304-A Page:
3/6
2
Reference solution
2.1
Method of calculation used for the reference solution
(2n 1) X
jy
(2n 1) 2 2
j2 2
T (X, y, T) =
-
B
X
y
cos
sin
exp -
-
+
T
N
2
2
2
4
N =1
J 1
L
Ly
=
L
L
X
X
y
8 (T)
5
2
5
where B
I
N +
J
=
(- 1)
(- 1) - 1 - 3 2
=
+ 32
N
2
[
]
T
T
J (2 N - 1)
9
I
O
9
Temperature in °F with T =1.2 hr (4320s)
2.7 15,615115,648015,745515,9049 16,1211 16,3876 16,6964 17,038117,4022 17,7778
2.4 15,646215,678615,774815,9318 16,1449 16,4076 16,7120 17,048717,4076 17,7778
2.1 15,739115,770015,862016,0122 16,2160 16,4673 16,7584 17,080517,4238 17,7778
1.8 15,892115,920816,005816,1447 16,3333 16,5657 16,8349 17,132817,4503 17,7778
1.5 16,102516,127916,203516,3269 16,4944 16,7009 16,9401 17,204817,4869 17,7778
1.2 16,365516,386916,450616,5547 16,6959 16,8700 17,0716 17,294717,5325 17,7778
0.9 16,674416,691116,740916,8222 16,9325 17,0685 17,2261 17,400417,5862 17,7778
0.6 17,020317,031817,066017,1218 17,1975 17,2909 17,3991 17,518717,6462 17,7778
0.3 17,392317,398217,415617,4440 17,4825 17,5300 17,5851 17,645917,7108 17,7778
0.0 17,777817,777817,777817,7778 17,7778 17,7778 17,7778 17,777817,7778 17,7778
Y
X
0.0
0.3
0.6
0.9
1.2
1.5
1.8
2.1
2.4
2.7
The values of reference are obtained with n=j=1000
2.2
Results of reference
T = 1.2hr (4320s): temperature at the following points:
· in X = 0.0: for y = 0.6, 1.5, 2.7,
· in X = 0.9: for y = 0.6, 1.5, 2.7,
· in X = 1.8: for y = 0.6, 1.5, 2.7.
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
HT-66/02/001/A
Code_Aster ®
Version
5.0
Titrate:
TTLP304 Transfert of heat in an orthotropic plate: imposed flows
Date:
20/09/02
Author (S):
C. DURAND, E. SCREW, F. LEBOUVIER Clé
:
V4.23.304-A Page:
4/6
3 Modeling
With
3.1
Characteristics of modeling
PLAN (QUAD4, TRIA3)
y
2.7 m
F
E
Limiting conditions
- dimensioned AB, BH, HE: T=-1.111°C
TRIA3
- dimensioned EFF, FG, GA: = 0
G
H
Cutting:
2.7 m
- AB, GH, FE 9 elements
- AG, BH 5 elements
QUAD4
- GF, HE 4 elements
1.5m
X
With
B
3.2
Characteristics of the grid
A number of nodes:
100
A number of meshs and types: 117 (45 QUAD4, 72 TRIA3)
3.3 Functionalities
tested
Commands
AFFE_MODELE
THERMIQUE
PLAN
TOUT
DEFI_MATERIAU
THER_ORTH
AFFE_CHAR_THER_F
TEMP_IMPO
AFFE_CARA_ELEM
MASSIF
THER_LINEAIRE
TEMP_INIT
VALE
CARA_ELEM
LIST_INST
RECU_CHAMP
INST
3.4 Remarks
The discretization in step of time is as follows:
10 steps for [0. , 5.00D0] is T = 0.5
9 steps for [5.00D0, 5.00D1] are T = 5.
9 steps for [5.00D1, 5.00D2] are T = 50.
38 steps for [5.00D2, 4.30D3] are T = 100.
1 step for [4.30D3, 4.32D3] is T = 20.
Handbook of Validation
V4.23 booklet: Transitory thermics of the plane systems
HT-66/02/001/A
Code_Aster ®
Version
5.0
Titrate:
TTLP304 Transfert of heat in an orthotropic plate: imposed flows
Date:
20/09/02
Author (S):
C. DURAND, E. SCREW, F. LEBOUVIER Clé
:
V4.23.304-A Page:
5/6
4
Results of modeling A
4.1 Values
tested
Relative variation %
Absolute deviation
Identification Référence Aster difference tolerance difference
tolerance
Temperature
in
°F
X
=
0.0
N3 (y = 0.6)
- 17.0203
- 17.0146 - 0.033
1% 0.006 0.05
N6 (y = 1.5)
- 16.1025
- 16.0957 - 0.042
1% 0.007 0.05
N10 (y = 2.7)
- 15.6151
- 15.5784 - 0.235
1% 0.037 0.05
X = 0.9
N33 (y = 0.6)
- 17.1218
- 17.1167 0.029 1%
0.005
0.05
N36 (y = 1.5)
- 16.3269
- 16.3127 - 0.087 1%
0.014
0.05
N40 (y = 2.7)
- 15.9049
- 15.8905 - 0.091
1% 0.014 0.05
X = 1.8
N63 (y = 0.6)
- 17.3991
- 17.3961 - 0.017
1% 0.003 0.05
N66 (y = 1.5)
- 16.9401
- 16.9297 - 0.061
1% 0.010 0.05
N70 (y = 2.7)
- 16.6964
- 16.6930 - 0.020
1% 0.003 0.05
4.2 Parameters
of execution
Version: 5.03
Machine: SGI - ORIGIN 2000 - R12000
Obstruction memory:
8 megawords
Time CPU To use: 4.11 seconds
Handbook of Validation
V4.23 booklet: Transitory thermics of the plane systems
HT-66/02/001/A
Code_Aster ®
Version
5.0
Titrate:
TTLP304 Transfert of heat in an orthotropic plate: imposed flows
Date:
20/09/02
Author (S):
C. DURAND, E. SCREW, F. LEBOUVIER Clé
:
V4.23.304-A Page:
6/6
5
Summary of the results
The results obtained are satisfactory, the maximum change obtained is 0.235%.
For the points of observation selected, the variations are more important with the nodes belonging to
meshs TRIA3.
Handbook of Validation
V4.23 booklet: Transitory thermics of the plane systems
HT-66/02/001/A
Outline document