Code_Aster
®
Version
4.0
Titrate:
Thermal TTLL100 Shock on a plane wall with condition of exchange
Date:
01/12/98
Author (S)
:
J.M. PROIX, Mr. A. REDON
Key:
V4.21.100-A
Page:
1/8
Manual of Validation
V4.21 booklet: Transitory thermics of the linear structures
HI-75/98/040 - Ind A
Organization (S)
: EDF/IMA/MN
Manual of Validation
V4.21 booklet: Transitory thermics of the linear structures
Document: V4.21.100
TTLL100 - Thermal shock on a plane wall with
condition of exchange
Summary:
This test of transitory linear thermics consists in imposing a cold thermal shock on an infinite plane wall on aid
of a condition limits of exchange. The shock is modelized by a linear slope
T = 100 °C in 102 S.
The problem is dealt with in plan.
The reference solution is analytical.
The test is carried out on 2 modelings: (TRIA3, QUAD4) and (TRIA6, QUAD9).
One tests the algorithm of linear thermics transitory when the matrix of mass is diagonalisée
(modeling
PLAN_DIAG
with `'farmhouse lumping '').
Code_Aster
®
Version
4.0
Titrate:
Thermal TTLL100 Shock on a plane wall with condition of exchange
Date:
01/12/98
Author (S)
:
J.M. PROIX, Mr. A. REDON
Key:
V4.21.100-A
Page:
2/8
Manual of Validation
V4.21 booklet: Transitory thermics of the linear structures
HI-75/98/040 - Ind A
1
Problem of reference
1.1 Geometry
With
C
L
B
- L
0
2
M
M
1
X
y
AB
=
BC
= L = 0.1 m
X (M1) = 0.02 m
X (m2) = 0.08 m
1.2
Material properties
= 1 W/m °C
CP
= 1000 J/m
3
°C
1.3
Boundary conditions and loadings
()
()
Exchange
with
T
N
H T
T X T
H
W m
C
T
C
T
C
X
L
ext.
ext.
T
ext.
T
=±
=
=
=
-
=
°
=
=
-
(
(,))
.
/
.
.
100
100
0
2
0
10
2
1.4 Conditions
initial
T (X, 0) = 100°C for any X
Discretization in time (T):
10
not for
[0.
,
1.D2]
that is to say
T = 10
3
S
9
not for
[1 D2
,
1.D1]
that is to say
T = 10
2
S
9
not for
[1.D1
,
1.]
that is to say
T = 10
1
S
5
not for
[1.
,
2.]
that is to say
T = 2.10
1
S
8
not for
[2.
,
10.]
that is to say
T = 1
S
Code_Aster
®
Version
4.0
Titrate:
Thermal TTLL100 Shock on a plane wall with condition of exchange
Date:
01/12/98
Author (S)
:
J.M. PROIX, Mr. A. REDON
Key:
V4.21.100-A
Page:
3/8
Manual of Validation
V4.21 booklet: Transitory thermics of the linear structures
HI-75/98/040 - Ind A
2
Reference solution
2.1
Method of calculation used for the reference solution
()
()
T X T
T
T
T
With
C L T
X
L
X
T
T
T
N
hL
With
With
ext.
ext.
N
N
N
p
N
ext.
N
N
N
N
N
N
N
N
,
exp (
) cos (
)
,
tan
/
.
sin
sin
-
-
=
-
=
=
=
=
=
…
=
=
=
=
+
=
+
0
1
0
1 2 3
10
4
2
2
X-coordinate
time
initial temperature
outside air temperature
with
positive roots of
and
2.2
Results of reference
Temperatures at the points M1 (X = 0.02) and m2 (X = 0.08),
and at various moments (T = 0.1, 0.5, 2.0 and 10.0).
The values of reference are obtained by calculating the first 30 terms of the series (Mathematica).
2.3
Uncertainty on the solution
Analytical solution.
2.4 References
bibliographical
[1]
INCROPERA F.P., OF WITT D.P., Fundamentals off heat and farmhouse transfer. Third Edition.
1990.
Code_Aster
®
Version
4.0
Titrate:
Thermal TTLL100 Shock on a plane wall with condition of exchange
Date:
01/12/98
Author (S)
:
J.M. PROIX, Mr. A. REDON
Key:
V4.21.100-A
Page:
4/8
Manual of Validation
V4.21 booklet: Transitory thermics of the linear structures
HI-75/98/040 - Ind A
3 Modeling
With
3.1
Characteristics of modeling
TRIA3, QUAD4
By reason of symmetry, one nets only one half the thickness of the wall. Modeling is made on
a height H = 0.1 m with 2 layers of elements.
With
B
D
C
H
M
1
Me
2
Me
1
M
2
T
0
10
2
S
100 °C
T
ext.
Limiting conditions
on [AB], [AD] and [CD]:
null flow
on [BC]: exchange H, T
ext.
Initial conditions
T = 100 °C
points
M1
M2
nodes
N16
N6
M'2
M'1
N4
N14
y
0.0
0.0
0.1
0.1
X
0.02
0.08
0.02
0.08
0°C
3.2
Characteristics of the mesh
A number of nodes: 18
A number of meshs and types: 5
QUAD4, 10 TRIA3
3.3 Functionalities
tested
Controls
Keys
AFFE_MODELE
MODELING
PLAN_DIAG
[U4.22.01]
AFFE_CHAR_THER_F
EXCHANGE
[U4.25.02]
THER_LINEAIRE
[U4.62.01]
Code_Aster
®
Version
4.0
Titrate:
Thermal TTLL100 Shock on a plane wall with condition of exchange
Date:
01/12/98
Author (S)
:
J.M. PROIX, Mr. A. REDON
Key:
V4.21.100-A
Page:
5/8
Manual of Validation
V4.21 booklet: Transitory thermics of the linear structures
HI-75/98/040 - Ind A
4
Results of modeling A
4.1 Values
tested
Identification
Reference
Aster
% difference
M1 (X = 0.02) N16
T = 0.1
100.00
99.998
+0.00
T = 0.5
99.408
99.042
0.37
T = 2.0
79.859
79.794
0.08
T = 10.0
15.717
16.138
+2.68
M2 (X = 0.08) N6
T = 0.1
93.666
93.380
0.31
T = 0.5
63.500
63.813
+0.49
T = 2.0
35.717
35.667
0.14
T = 10.0
6.7948
6.9326
+2.03
M'1 (X = 0.02) N14
T = 0.1
100.00
99.998
+0.00
T = 0.5
99.408
99.077
0.33
T = 2.0
79.859
80.002
+0.18
T = 10.0
15.717
16.211
+3.14
M'2 (X = 0.08) N4
T = 0.1
93.666
92.895
0.82
T = 0.5
63.500
61.882
2.55
T = 2.0
35.717
35.331
1.08
T = 10.0
6.7948
6.8885
+1.38
4.2 Parameters
of execution
Version: 4.01.12
Machine: CRAY C98
System: UNICOS
Overall dimension memory:
8 megawords
Time CPU To use: 9.2 seconds
Code_Aster
®
Version
4.0
Titrate:
Thermal TTLL100 Shock on a plane wall with condition of exchange
Date:
01/12/98
Author (S)
:
J.M. PROIX, Mr. A. REDON
Key:
V4.21.100-A
Page:
6/8
Manual of Validation
V4.21 booklet: Transitory thermics of the linear structures
HI-75/98/040 - Ind A
5 Modeling
B
5.1
Characteristics of modeling
TRIA6, QUAD9
By reason of symmetry, one nets only one half the thickness of the wall. Modeling is made on
a height H = 0.1 m with 2 layers of elements.
With
B
D
C
H
M
1
Me
2
Me
1
M
2
T
0
10
2
S
100 °C
T
ext.
Limiting conditions
on [AB], [AD] and [CD]:
null flow
on [BC]: exchange H, T
ext.
Initial conditions
T = 100 °C
points
M1
M2
nodes
N16
N6
M'2
M'1
N4
N14
y
0.0
0.0
0.1
0.1
X
0.02
0.08
0.02
0.08
0°C
5.2
Characteristics of the mesh
A number of nodes: 55
A number of meshs and types: 5
QUAD9, 10 TRIA6
5.3 Functionalities
tested
Controls
Keys
CREA_MAILLAGE
MODI_MAILLE
OPTION:
“QUAD8_9”
[U4.12.06]
AFFE_MODELE
MODELING
PLAN_DIAG
[U4.22.01]
AFFE_CHAR_THER_F
EXCHANGE
[U4.25.02]
THER_LINEAIRE
[U4.62.01]
Code_Aster
®
Version
4.0
Titrate:
Thermal TTLL100 Shock on a plane wall with condition of exchange
Date:
01/12/98
Author (S)
:
J.M. PROIX, Mr. A. REDON
Key:
V4.21.100-A
Page:
7/8
Manual of Validation
V4.21 booklet: Transitory thermics of the linear structures
HI-75/98/040 - Ind A
6
Results of modeling B
6.1 Values
tested
Identification
Reference
Aster
% difference
M1 (X = 0.02) N18
T = 0.1
100.00
100.00
+0.00
T = 0.5
99.408
99.278
0.13
T = 2.0
79.859
79.898
+0.05
T = 10.0
15.717
16.043
+2.07
M2 (X = 0.08) N49
T = 0.1
93.666
94.077
+0.44
T = 0.5
63.500
63.979
+0.75
T = 2.0
35.717
35.825
+0.30
T = 10.0
6.7948
6.9321
+2.02
M'1 (X = 0.02) N12
T = 0.1
100.00
100.00
+0.00
T = 0.5
99.408
99.311
0.10
T = 2.0
79.859
80.101
+0.30
T = 10.0
15.717
16.093
+2.39
M'2 (X = 0.08) N30
T = 0.1
93.666
93.469
0.21
T = 0.5
63.500
62.860
1.01
T = 2.0
35.717
35.641
0.21
T = 10.0
6.7948
6.9068
+1.65
6.2 Parameters
of execution
Version: 4.01.12
Machine: CRAY C98
System: UNICOS
Overall dimension memory:
8 megawords
Time CPU To use: 10.0 seconds
Code_Aster
®
Version
4.0
Titrate:
Thermal TTLL100 Shock on a plane wall with condition of exchange
Date:
01/12/98
Author (S)
:
J.M. PROIX, Mr. A. REDON
Key:
V4.21.100-A
Page:
8/8
Manual of Validation
V4.21 booklet: Transitory thermics of the linear structures
HI-75/98/040 - Ind A
7
Summary of the results
Modeling “PLAN_DIAG” gives rather satisfactory results. Although the mesh comprises
few elements in the thickness, the variation on the temperatures remain lower than 3.2%.
Although the thermal shock is brutal, the diagonalisation of the matrix of mass makes it possible to obtain one
solution in temperature which does not oscillate during the transient.