Code_Aster
®
Version
5.0
Titrate:
TTLP304 Transfer of heat in an orthotropic plate: imposed flows
Date:
20/09/02
Author (S):
C. DURAND,
E. SCREWS, F. LEBOUVIER
Key
:
V4.23.304-A
Page:
1/6
Manual of Validation
V4.23 booklet: Transitory thermics of the plane systems
HT-66/02/001/A
Organization (S):
EDF/AMA, EDF/UTO/LOCATED, Delta CAD
Manual of Validation
V4.23 booklet: Transitory thermics of the plane systems
V4.23.304 document
TTLP304 - Transfer 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.
Code_Aster
®
Version
5.0
Titrate:
TTLP304 Transfer of heat in an orthotropic plate: imposed flows
Date:
20/09/02
Author (S):
C. DURAND,
E. SCREWS, F. LEBOUVIER
Key
:
V4.23.304-A
Page:
3/6
Manual of Validation
V4.23 booklet: Transitory thermics of the plane systems
HT-66/02/001/A
2
Reference solution
2.1
Method of calculation used for the reference solution
T X y T
B
N
X
L
J y
Ly
N
L
J
L
T
N
N
X
J
X
X
y
y
(,)
cos (
)
sin
exp
(
)
=
-
-
-
+
=
=
1
1
2
2
2
2
2
2
2
1
2
2
1
4
where
[
]
B
T
J
N
N
I
N
J
=
-
-
-
-
-
+
8
2
1
1
1
1
3 2 59
2
2
()
(
) (
)
(
)
T
T
I
O
=
+
5
9
32
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.
Code_Aster
®
Version
5.0
Titrate:
TTLP304 Transfer of heat in an orthotropic plate: imposed flows
Date:
20/09/02
Author (S):
C. DURAND,
E. SCREWS, F. LEBOUVIER
Key
:
V4.23.304-A
Page:
4/6
Manual of Validation
V4.23 booklet: Transitory thermics of the plane systems
HT-66/02/001/A
3 Modeling
With
3.1
Characteristics of modeling
PLAN (QUAD4, TRIA3)
y
X
With
B
F
E
Limiting conditions
- dimensioned AB, BH, HE: T=-1.111°C
- dimensioned EFF, FG, GA:
= 0
Cutting:
- AB, GH, FE 9 elements
- AG, BH 5 elements
- GF, HE 4 elements
2.7 m
2.7 m
TRIA3
QUAD4
1.5m
G
H
3.2
Characteristics of the mesh
A number of nodes:
100
A number of meshs and types: 117 (45 QUAD4, 72 TRIA3)
3.3 Functionalities
tested
Controls
AFFE_MODELE
THERMICS
PLAN
ALL
DEFI_MATERIAU
THER_ORTH
AFFE_CHAR_THER_F
TEMP_IMPO
AFFE_CARA_ELEM
SOLID MASS
THER_LINEAIRE
TEMP_INIT
VALE
CARA_ELEM
LIST_INST
RECU_CHAMP
INST
3.4 Remarks
The discretization in pitch of time is as follows:
10 pitches for [0. , 5.00D0] is
T = 0.5
9 pitches for [5.00D0, 5.00D1] are
T = 5.
9 pitches for [5.00D1, 5.00D2] are
T = 50.
38 pitches for [5.00D2, 4.30D3] are
T = 100.
1 pitch for [4.30D3, 4.32D3] is
T = 20.
