Code_Aster
®
Version
5.0
Titrate:
Thermal TTLP302 Transfer in a Plane field with singularity
Date:
20/09/02
Author (S):
C. DURAND,
E. SCREWS, F. LEBOUVIER
Key
:
V4.23.302-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
V4.23.302 document
TTLP302 - Thermal transfer in a field
Plan with geometrical singularity
Summary:
This test results from the validation independent of version 3 in linear transitory thermics.
It is about a problem plane 2D represented by two modelings, one planes, the other voluminal one.
The functionalities tested are as follows:
·
plane thermal element,
·
voluminal thermal element,
·
transitory algorithm of thermics,
·
geometrical singularity,
·
limiting conditions: imposed temperature.
The interest of the test, in addition to the fact that it is an industrial case, lies in the taking into account of a singularity
geometrical in transitory thermal analysis.
Code_Aster
®
Version
5.0
Titrate:
Thermal TTLP302 Transfer in a Plane field with singularity
Date:
20/09/02
Author (S):
C. DURAND,
E. SCREWS, F. LEBOUVIER
Key
:
V4.23.302-A
Page:
2/6
Manual of Validation
V4.23 booklet: Transitory thermics of the plane systems
HT-66/02/001/A
1
Problem of reference
1.1 Geometry
Y
X
T= 0°
0.3
0.4
0.2
0.5
T=1000°
With
With
F
E
B
J
G
H
I
D
C
0.3
1.2
Properties of material
=
1. W/m°C
Thermal conductivity
C
p
=
1. J/m
3
°C
Voluminal heat
1.3
Boundary conditions and loadings
·
[AJ] imposed temperature T = 1000°C,
·
[FG] imposed temperature T = 0°C,
·
others with dimensions
= 0.
1.4 Conditions
initial
T X y
erfc X T
(,)
(
)
0
2
=
for T = 0.0005 S
Code_Aster
®
Version
5.0
Titrate:
Thermal TTLP302 Transfer in a Plane field with singularity
Date:
20/09/02
Author (S):
C. DURAND,
E. SCREWS, F. LEBOUVIER
Key
:
V4.23.302-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
The reference solution is a numerical solution obtained by the finite element method [bib2]
quoted in the reference [bib1]. This solution is based on a network of 168 square elements of
0.05m. of dimensioned, with 200 pitches of time (
T = 0.0005 S).
2.2
Results of reference
Temperature at the points B C D E H and I at the moment T = 0.1s
2.3
Uncertainty on the solution
Unknown factor.
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.
[2]
G.E. Beautiful, “A method for treating boundary singularities in time-dependant problems” TR/8,
Dept. off Maths., Brunel Univ. Uxbridge, Middlesex, 19 pp., 1972.
Code_Aster
®
Version
5.0
Titrate:
Thermal TTLP302 Transfer in a Plane field with singularity
Date:
20/09/02
Author (S):
C. DURAND,
E. SCREWS, F. LEBOUVIER
Key
:
V4.23.302-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)
Limiting conditions:
- dimensioned AJ: T = 1000°C
- dimensioned FG: T = 0°C
- dimensioned AB, BC, CD,
OF, EFF, GJ
= 0
F
E
B
With
G
H
I
J
C
y
X
D
N42
N37
N39
N64
N59
N61
3.2
Characteristics of the mesh
A number of nodes:
82
A number of meshs and types: 60 QUAD4
3.3 Functionalities
tested
Controls
AFFE_MODELE
THERMICS
PLAN
ALL
AFFE_CHAR_THER_F
TEMP_IMPO
AFFE_CHAM_NO
SIZE
“TEMP_R”
THER_LINEAIRE
AFFE
NODE
TEMP_INIT
CHAM_NO
RECU_CHAMP
LIST_INST
INST
3.4 Remarks
The discretization in pitch of time is as follows:
10 pitches for [0. , 1.D-4] is
T = 1.D-5
9 pitches for [1.D-4, 1.D-3] are
T = 1.D-4
9 pitches for [1.D-3, 1.D-2] are
T = 1.D-3
9 pitches for [1.D-2, 1.D-1] are
T = 1.D-2
Code_Aster
®
Version
5.0
Titrate:
Thermal TTLP302 Transfer in a Plane field with singularity
Date:
20/09/02
Author (S):
C. DURAND,
E. SCREWS, F. LEBOUVIER
Key
:
V4.23.302-A
Page:
5/6
Manual of Validation
V4.23 booklet: Transitory thermics of the plane systems
HT-66/02/001/A
4
Results of modeling A
4.1 Values
tested
Identification Reference
Aster
% difference
Tolerance
Temperature (°C)
T = 0.1 S
Points
B (N37)
787.
785.35
-
0.210
2%
C (N39)
634.
631.74
-
0.357
2%
D (N61)
86.
85.40
-
0.696
2%
E (N59)
28.
27.80
-
0.730
2%
H (N64)
119.
118.84
-
0.136
2%
I
(N42) 538.
536.97
-
0.192
2%
4.2 Parameters
of execution
Version: 5.03
Machine: SGI - ORIGIN 2000 - R12000
Overall dimension memory:
8 megawords
Time CPU To use: 3.28 seconds
Code_Aster
®
Version
5.0
Titrate:
Thermal TTLP302 Transfer in a Plane field with singularity
Date:
20/09/02
Author (S):
C. DURAND,
E. SCREWS, F. LEBOUVIER
Key
:
V4.23.302-A
Page:
6/6
Manual of Validation
V4.23 booklet: Transitory thermics of the plane systems
HT-66/02/001/A
5
Summary of the results
Modeling carried out (PLANE with meshs QUAD4) gives satisfactory results. The variation
maximum is of
-
0.73%, and it is located on the smallest value of reference.
The taking into account of the initial condition of erfc type (X/(2
T) was carried out correctly. It has
need the use of the control
AFFE_CHAM_NO
allowing to define a field of temperature
initial of each node of the model.