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Code_Aster
®
Version
6.4
Titrate:
TPLV101 - Stationary thermics with exchange between walls
Date:
03/06/03
Author (S):
J.P. LEFEBVRE
Key
:
V4.04.101-B
Page:
1/8
Manual of Validation
V4.04 booklet: Stationary thermics of the voluminal structures
HT-66/03/008/A
Organization (S):
EDF-R & D/AMA















Manual of Validation
V4.04 booklet: Stationary thermics of the voluminal structures
Document: V4.04.101



TPLV101 - Stationary thermics with condition
of exchange between walls in opposite




Summary:

This elementary test makes it possible to deal with stationary problem in thermics bringing into play two fields
separated by imposing a boundary condition of the type exchanges between walls.

For modelings presented here, the results obtained by Code_Aster are identical to the reference
calculated analytically.
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Code_Aster
®
Version
6.4
Titrate:
TPLV101 - Stationary thermics with exchange between walls
Date:
03/06/03
Author (S):
J.P. LEFEBVRE
Key
:
V4.04.101-B
Page:
2/8
Manual of Validation
V4.04 booklet: Stationary thermics of the voluminal structures
HT-66/03/008/A
1
Problem of reference
1.1 Geometry

L
With
1
B
1
D
1
C
1
E
1
F
1
G
1
H
1
J
1
I
1
L
With
2
B
2
D
2
C
2
E
2
F
2
G
2
H
2
I
2
J
2
L
Height L = 3. m
Width I = 1. m

1.2
Material properties
Voluminal heat
C
p
= 0.
Thermal conductivity K = 1.W/m°C

1.3
Boundary conditions and loadings
Outgoing flow through the plan B
1
F
1
G
1
C
1
identical to flow
entering through plan A
2
E
2
H
2
D
2
Temperature imposed in A
1
Temperature imposed out of B
2
T = 0.°C
T = 4.5°C
Normal flow imposed on the plan B
2
F
2
G
2
C
2
Normal flow imposed on the plans C
1
G
1
H
1
D
1
and C
2
G
2
H
2
D
2
= 3.W/m
2
= 6.W/m
2
Normal flow imposed on the plans E
1
F
1
G
1
H
1
and E
2
F
2
G
2
H
2
= 2.W/m
2
Source imposed in field 1
Source imposed in field 2
S
1
S
2
Z
y
X
background image
Code_Aster
®
Version
6.4
Titrate:
TPLV101 - Stationary thermics with exchange between walls
Date:
03/06/03
Author (S):
J.P. LEFEBVRE
Key
:
V4.04.101-B
Page:
3/8
Manual of Validation
V4.04 booklet: Stationary thermics of the voluminal structures
HT-66/03/008/A
2
Reference solution
2.1
Method of calculation used for the reference solution
One has a simple analytical solution, since it is about exhiber a harmonic function and
to adjust the source associated in each field:
·
in field 1:
()
2
2
2
1
,
,
Z
y
X
With
T
Z
y
X
T
+
+
+
=
)
(
, (in the reference mark of origin A
1
),
·
in field 2:
()
2
2
2
2
2
1
,
,
Z
y
X
With
T
Z
y
X
T
+
+
+
=
)
(
, (in the reference mark of origin A
2
).
One deduces the values from them from S
1
and S
2
, S
1
= ­ 6. , S
2
= ­ 5.W/m
3
.

2.2
Results of reference
Temperatures at the points of the plans B
1
F
1
G
1
C
1
and A
2
E
2
H
2
D
2

2.3
Uncertainty on the solution
Analytical solution.
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Code_Aster
®
Version
6.4
Titrate:
TPLV101 - Stationary thermics with exchange between walls
Date:
03/06/03
Author (S):
J.P. LEFEBVRE
Key
:
V4.04.101-B
Page:
4/8
Manual of Validation
V4.04 booklet: Stationary thermics of the voluminal structures
HT-66/03/008/A
3 Modeling
With
3.1
Characteristics of modeling
Modeling 2D:
N2
N6
N3
N11
N9
N28
N22
N19
N26
N31
N36
N33
N16
N14
3.2
Boundary conditions and loadings
Outgoing flow through the wall B
1
C
1
identical to entering flow
through wall A
2
D
2
Temperature imposed in A
1
Temperature imposed out of B
2
T = 0.°C
T = 4.5°C
Normal flow imposed on the wall B
2
C
2
Normal flow imposed on the plans C
1
D
1
and C
2
D
2
= 3.W/m
2
= 6.W/m
2
Source imposed in field 1
Source imposed in field 2
S
1
S
2
3.3
Characteristics of the mesh
6 QUAD8
36 nodes
3.4
Functionalities tested
Order
Key word factor
Simple key word
Argument
DEFI_MATERIAU THER
LAMBDA
CP
AFFE_CHAR_THER SOURCE
TEMP_IMPO
FLUX_REP
ECHANGE_PAROI
LIAISON_GROUP
STATIONARY THER_LINEAIRE TEMP_INIT
“YES”
INCREMENT
D
2
C
2
B
2
With
2
D
1
C
1
With
1
B
1
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Code_Aster
®
Version
6.4
Titrate:
TPLV101 - Stationary thermics with exchange between walls
Date:
03/06/03
Author (S):
J.P. LEFEBVRE
Key
:
V4.04.101-B
Page:
5/8
Manual of Validation
V4.04 booklet: Stationary thermics of the voluminal structures
HT-66/03/008/A
4
Results of modeling A
4.1 Values
tested

Identification
Temperature
Reference
Aster %
difference
node N2 (B
1
) 1.00
1.00
0.0
N3 node
2.00
2.00
0.0
N6 node
1.25
1.25
0.0
N11 node
3.25
3.25
0.0
N9 node
5.00
5.00
0.0
N16 node
7.25
7.25
0.0
node N14 (C
1
) 10.00
10.00
0.0
node N19 (A
2
) 2.00
2.00
0.0
N22 node
3.00
3.00
0.0
N26 node
2.25
2.25
0.0
N31 node
4.25
4.25
0.0
N28 node
6.00
6.00
0.0
N36 node
8.25
8.25
0.0
node N33 (D
2
) 11.00
11.00
0.0

4.2 Remarks
The functions of form of element QUAD8 being of command 2, it is natural to obtain the solution of
reference which is expressed in the form of a polynomial of command 2.
The command file deposited contains a list of moments and calls the control
THER_LINEAIRE
to carry out a transitory calculation which is not of interest, the coefficient of
voluminal heat being taken equal to 0.
background image
Code_Aster
®
Version
6.4
Titrate:
TPLV101 - Stationary thermics with exchange between walls
Date:
03/06/03
Author (S):
J.P. LEFEBVRE
Key
:
V4.04.101-B
Page:
6/8
Manual of Validation
V4.04 booklet: Stationary thermics of the voluminal structures
HT-66/03/008/A
5 Modeling
B
5.1
Characteristics of modeling

Modeling 3D:


A3
A10
A2
A15
A7
A26
A22
A30
A39
A35
B4
B8
B1
B13 B5
B21
B33
B28
B40
B44


5.2
Characteristics of the mesh
6 HEXA20
88 nodes

5.3
Functionalities tested
Order
Key word factor
Simple key word
Argument
DEFI_MATERIAU
THER LAMBDA
CP
AFFE_CHAR_THER SOURCE
TEMP_IMPO
FLUX_REP
AFFE_CHAR_THER_F ECHANGE_PAROI
LIAISON_GROUP
STATIONARY THER_LINEAIRE TEMP_INIT
“YES”
INCREMENT
background image
Code_Aster
®
Version
6.4
Titrate:
TPLV101 - Stationary thermics with exchange between walls
Date:
03/06/03
Author (S):
J.P. LEFEBVRE
Key
:
V4.04.101-B
Page:
7/8
Manual of Validation
V4.04 booklet: Stationary thermics of the voluminal structures
HT-66/03/008/A
6
Results of modeling B
6.1 Values
tested

Identification
Temperature
Reference
Aster
% difference
node A2 (B
1
) 1.00
1.00
0.0
node A3 (F
1
) 2.00
2.00
0.0
A7 node
3.00
3.00
0.0
A10 node
1.25
1.25
0.0
A15 node
2.25
2.25
0.0
A22 node
5.00
5.00
0.0
A26 node
3.25
3.25
0.0
A30 node
5.25
5.25
0.0
node A35 (G
1
) 11.00
11.00
0.0
A39 node
8.25
8.25
0.0
node B1 (A
2
) 2.00
2.00
0.0
node B4 (E
2
) 3.00
3.00
0.0
B5 node
3.00
3.00
0.0
B8 node
4.00
4.00
0.0
B13 node
2.25
2.25
0.0
B21 node
6.00
6.00
0.0
B28 node
5.25
5.25
0.0
node B33 (D
2
) 11.00
11.00
0.0
B40 node
9.25
9.25
0.0
B44 node
11.25
11.25
0.0

6.2 Remarks
The functions of form of element HEXA20 being of command 2, it is natural to obtain the solution of
reference which is expressed in the form of a polynomial of command 2.
The command file deposited contains a list of moments and calls the control
THER_LINEAIRE
to carry out a transitory calculation which is not of interest, the coefficient of
voluminal heat being taken equal to 0.
background image
Code_Aster
®
Version
6.4
Titrate:
TPLV101 - Stationary thermics with exchange between walls
Date:
03/06/03
Author (S):
J.P. LEFEBVRE
Key
:
V4.04.101-B
Page:
8/8
Manual of Validation
V4.04 booklet: Stationary thermics of the voluminal structures
HT-66/03/008/A
7
Summaries of the results
Two modelings with elements of command 2 lead in an exact way to the solution
analytical and the establishment of the boundary conditions of the type validates
ECHANGE_PAROI
.