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