Code_Aster ®
Version
5.0
Titrate:
Thermal TTLP302 Transfert in a Plan field with singularity
Date:
20/09/02
Author (S):
C. DURAND, E. SCREW, F. LEBOUVIER Clé
:
V4.23.302-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
V4.23.302 document

TTLP302 - Thermal Transfert 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.

Handbook of Validation
V4.23 booklet: Transitory thermics of the plane systems
HT-66/02/001/A

Code_Aster ®
Version
5.0
Titrate:
Thermal TTLP302 Transfert in a Plan field with singularity
Date:
20/09/02
Author (S):
C. DURAND, E. SCREW, F. LEBOUVIER Clé
:
V4.23.302-A Page:
2/6

1
Problem of reference

1.1 Geometry

Y
T= 0°
J
I
H
G
T=1000°
C
D
0.5
0.2
X
With
B
E
F
0.3
0.4
0.3


1.2
Properties of material


=
1. W/m°C
Thermal conductivity
CP = 1. J/m3 °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

X
T (X, y,)
0 = erfc (
) for T = 0.0005 S
2 T

Handbook of Validation
V4.23 booklet: Transitory thermics of the plane systems
HT-66/02/001/A

Code_Aster ®
Version
5.0
Titrate:
Thermal TTLP302 Transfert in a Plan field with singularity
Date:
20/09/02
Author (S):
C. DURAND, E. SCREW, F. LEBOUVIER Clé
:
V4.23.302-A Page:
3/6

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 steps 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.

Handbook of Validation
V4.23 booklet: Transitory thermics of the plane systems
HT-66/02/001/A

Code_Aster ®
Version
5.0
Titrate:
Thermal TTLP302 Transfert in a Plan field with singularity
Date:
20/09/02
Author (S):
C. DURAND, E. SCREW, F. LEBOUVIER Clé
:
V4.23.302-A Page:
4/6

3 Modeling
With

3.1
Characteristics of modeling

PLAN (QUAD4)

y
J
I
H
G
Limiting conditions:
N42
N64
- dimensioned AJ: T = 1000°C
- dimensioned FG: T = 0°C
- dimensioned AB, BC, CD,
OF, EFF, GJ = 0
N39
N61
C
D
N37
N59
X
With
B
E
F


3.2
Characteristics of the grid

A number of nodes:
82
A number of meshs and types: 60 QUAD4

3.3 Functionalities
tested


Commands




AFFE_MODELE
THERMIQUE
PLAN
TOUT
AFFE_CHAR_THER_F
TEMP_IMPO

AFFE_CHAM_NO
GRANDEUR
“TEMP_R”

THER_LINEAIRE
AFFE
NOEUD

TEMP_INIT
CHAM_NO

RECU_CHAMP
LIST_INST

INST


3.4 Remarks

The discretization in step of time is as follows:

10 steps for [0. , 1.D-4] is T = 1.D-5
9 steps for [1.D-4, 1.D-3] are T = 1.D-4
9 steps for [1.D-3, 1.D-2] are T = 1.D-3
9 steps for [1.D-2, 1.D-1] are T = 1.D-2
Handbook of Validation
V4.23 booklet: Transitory thermics of the plane systems
HT-66/02/001/A

Code_Aster ®
Version
5.0
Titrate:
Thermal TTLP302 Transfert in a Plan field with singularity
Date:
20/09/02
Author (S):
C. DURAND, E. SCREW, F. LEBOUVIER Clé
:
V4.23.302-A Page:
5/6

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

Obstruction memory:
8 megawords
Time CPU To use: 3.28 seconds
Handbook of Validation
V4.23 booklet: Transitory thermics of the plane systems
HT-66/02/001/A

Code_Aster ®
Version
5.0
Titrate:
Thermal TTLP302 Transfert in a Plan field with singularity
Date:
20/09/02
Author (S):
C. DURAND, E. SCREW, F. LEBOUVIER Clé
:
V4.23.302-A Page:
6/6

5
Summary of the results

Modeling carried out (PLAN 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 type erfc (X/(2t) was carried out correctly. It has
need the use of command AFFE_CHAM_NO allowing to define a field of temperature
initial of each node of the model.

Handbook of Validation
V4.23 booklet: Transitory thermics of the plane systems
HT-66/02/001/A

Outline document