Code_Aster
®
Version
4.0
Titrate:
TTLP100 Exchange-wall in transitory thermics
Date:
28/01/98
Author (S):
I. VAUTIER
Key:
V4.23.100-A
Page:
1/6
Manual of Validation
V4.23 booklet: Transitory thermics of the plane systems
HI-75/96/029 - Ind A
Organization (S):
EDF/IMA/MN
Manual of Validation
V4.23 booklet: Transitory thermics of the plane systems
Document: V4.23.100
TTLP100 - Exchange-wall in transitory thermics
Summary
One calculates the linear transitory response thermal or not linear of two plates separated by a play in
which is carried out a transfer of heat. The problem is 2D but the boundary conditions make that
temperature depends only on the X-coordinate and time. The stationary state is quickly reached, which is
calculable analytically.
The test makes it possible to check the good taking into account of the terms related to the heat transfer between 2 walls.
Code_Aster
®
Version
4.0
Titrate:
TTLP100 Exchange-wall in transitory thermics
Date:
28/01/98
Author (S):
I. VAUTIER
Key:
V4.23.100-A
Page:
2/6
Manual of Validation
V4.23 booklet: Transitory thermics of the plane systems
HI-75/96/029 - Ind A
1
Problem of reference
1.1 Geometry
0.495 0.505
0
1
X
y
L
1
L
2
0
1
L
1
= L
2
= 0.495 m
L = 1 m
1.2
Material properties
=
°
=
°
=
°
°
-
-
40
7 3 10
0
0
220 10
300
4
3
3
3
W m C
C
J m
C
C
J m
C
p
/
.
/
/
or
with
with
To deal with the same problem in nonlinear thermics, a enthalpy is defined
refine of which
slope is equal to the specific heat
C
p
.
1.3
Boundary conditions and loadings
T (X = 0) = 100°C = T
O
T (X = L) = 300°C = T
L
Heat transfer enters the walls located in X = 0.495 and X = 0.505, with a coefficient of exchange
from 80 W/m
2
°C.
1.4 Conditions
initial
T (T = 0) =
T
O
in the plate of left
T
L
in the plate of straight line
Code_Aster
®
Version
4.0
Titrate:
TTLP100 Exchange-wall in transitory thermics
Date:
28/01/98
Author (S):
I. VAUTIER
Key:
V4.23.100-A
Page:
3/6
Manual of Validation
V4.23 booklet: Transitory thermics of the plane systems
HI-75/96/029 - Ind A
2
Reference solution
2.1
Method of calculation used for the reference solution
The stationary analytical solution is obtained by solving a null Laplacian on each of both
plates of the form T (X) = ax + B, the 4 coefficients (2 per plate) are obtained by clarifying them
boundary conditions:
(
)
(
)
(
)
(
)
(
)
From where:
0
0 495
0 505
1
1
2
1
2
.
.
:
.
. :
=
+
-
+
+
=
-
-
+
+
-
X
T
T
H T
T
H L
L
X
X
T
T
H T
T
H L
L
L
X
O
L
O
L
L
O
2.2
Results of reference
Temperatures on the line y = 0
2.3
Uncertainty on the solution
Analytical solution.
Code_Aster
®
Version
4.0
Titrate:
TTLP100 Exchange-wall in transitory thermics
Date:
28/01/98
Author (S):
I. VAUTIER
Key:
V4.23.100-A
Page:
4/6
Manual of Validation
V4.23 booklet: Transitory thermics of the plane systems
HI-75/96/029 - Ind A
3 Modeling
With
3.1
Characteristics of modeling
N2
N24
N4
N46
N6
N12
N34
N56
N5
N35
N3
N13
N1
N102
N124 N104 N146
N106
N112
N34
N156
N105
N135
N103
N113
N101
The mesh is carried out with elements of the type QUAD8.
Calculation is made in linear thermics, with
= 0.57.
One takes 50 pitches of time from 0 to 5 10
2
S. The results are examined in T = 5 10
2
S.
3.2
Characteristics of the mesh
4 QUAD8, 4 SEG3, 26 nodes
3.3 Functionalities
tested
Order
Keys
AFFE_CHAR_THER
ECHANGE_PAROI
[U4.25.02]
THER_LINEAIRE
PARM_THETA
[U4.33.01]
4
Results of modeling A
4.1 Values
tested
Identification
Reference
Aster
% difference
TEMP
N3 node
133.557026
133.557047
+1.6 10
5
TEMP
N5 node
166.442953
166.442907
2.8 10
5
TEMP
N101 node
233.557047
233.557093
+2. 10
5
TEMP
N103 node
266.442953
266.442973
+7.5 10
6
4.2 Remarks
The solution
Aster
the stationary state starting from T reached = 4.7 10
2
S.
4.3 Parameters
of execution
Version: 3.6.0
Machine: CRAY C90
Overall dimension memory: 8MW
Time CPU To use: 14 seconds
Code_Aster
®
Version
4.0
Titrate:
TTLP100 Exchange-wall in transitory thermics
Date:
28/01/98
Author (S):
I. VAUTIER
Key:
V4.23.100-A
Page:
5/6
Manual of Validation
V4.23 booklet: Transitory thermics of the plane systems
HI-75/96/029 - Ind A
5 Modeling
B
5.1
Characteristics of modeling
Calculation is made in nonlinear thermics, with
= 0.57.
One makes 1 pitch of time from 0 to 10
9
S and 300 pitches of time of 10
9
S with 1.5 10
5
S.
The results are examined in T = 1.5 10
5
S.
5.2
Characteristics of the mesh
4 QUAD8, 4 SEG3, 26 nodes
5.3 Functionalities
tested
Order
Keys
AFFE_CHAR_THER
ECHANGE_PAROI
[U4.25.02]
THER_NON_LINE
PARM_THETA
[U4.33.02]
6
Results of modeling B
6.1 Values
tested
Identification
Reference
Aster
% difference
TEMP
N3 node
133.557026
133.500054
0.043
TEMP
N5 node
166.442953
166.399598
0.026
TEMP
N101 node
233.557047
233.619046
0.027
TEMP
N103 node
266.442953
266.513231
0.026
6.2 Remarks
The precision required on the results is only 10
3
(instead of 10
6
into linear) because one does not have
still, with T = 1.5 10
5
S, rigorously reached the stationary state.
6.3 Parameters
of execution
Version: 3.6.0
Machine: CRAY C90
Overall dimension memory: 50 MW
Time CPU To use: 1700 seconds
Code_Aster
®
Version
4.0
Titrate:
TTLP100 Exchange-wall in transitory thermics
Date:
28/01/98
Author (S):
I. VAUTIER
Key:
V4.23.100-A
Page:
6/6
Manual of Validation
V4.23 booklet: Transitory thermics of the plane systems
HI-75/96/029 - Ind A
7
Summaries of the results
The enormous difference in calculating time enters
THER_LINEAIRE
and
THER_NON_LINE
be explained in
part by the fact that one had to much more finely discretize the pitches of time into nonlinear (3000
between 0 and 1.5 10
5
S instead of 50 between 0 and 5. 10
2
S) to ensure the convergence of
THER_NON_LINE
.
In addition, the algorithm of Lagrangian increased used in
THER_NON_LINE
is much more
expensive that the simple one
- method used in
THER_LINEAIRE
.
A request for improvement of the performances was deposited.