Code_Aster ®
Version
4.0
Titrate:
Thermal TTLL100 Choc 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
Organization (S): EDF/IMA/MN
Handbook of Validation
V4.21 booklet: Transitory thermics of the linear structures
Document: V4.21.100
TTLL100 - Thermal Choc 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 the assistance
of a condition limits of exchange. The shock is modelled 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 '').
Handbook of Validation
V4.21 booklet: Transitory thermics of the linear structures
HI-75/98/040 - Ind A
Code_Aster ®
Version
4.0
Titrate:
Thermal TTLL100 Choc 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
1
Problem of reference
1.1 Geometry
y
With
B
C
- L
0
M1
2
M
L
X
AB = BC = L = 0.1 m
X (M1) = 0.02 m
X (m2) = 0.08 m
1.2
Material properties
= 1 W/m °C
C
p = 1000 J/m3 °C
1.3
Boundary conditions and loadings
T
Exchange
= (
-
H T
T (X, T
ext.
))
N x=±L
with
H =
.
100 W/M2 ° C
T
=
ext. (C)
.
100
t=
0
T
- =
ext. (C)
.
0
t=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 = 103 S
9
not for
[1 D2
,
1.D1]
that is to say
T = 102 S
9
not for
[1.D1
,
1.]
that is to say
T = 101 S
5
not for
[1.
,
2.]
that is to say
T = 2.101 S
8
not for
[2.
,
10.]
that is to say
T = 1 S
Handbook of Validation
V4.21 booklet: Transitory thermics of the linear structures
HI-75/98/040 - Ind A
Code_Aster ®
Version
4.0
Titrate:
Thermal TTLL100 Choc 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
2
Reference solution
2.1
Method of calculation used for the reference solution
T (X, T) - T
+
X
ext. =
With exp (
-
T
N
N
) cos (N
)
T
0 - T
C L
L
ext.
n=1
p
X
= X-coordinate
T
= time
T0 =
initial temperature
T
=
ext.
outside temperature
N
=
,
1
,
2
,
3…
with
positive roots of tan = hL =
N
N
N
/
.
10
4 sin
and
WITH = A
N
=
N
N
2 +
N
sin (2 N)
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.
Handbook of Validation
V4.21 booklet: Transitory thermics of the linear structures
HI-75/98/040 - Ind A
Code_Aster ®
Version
4.0
Titrate:
Thermal TTLL100 Choc 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
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.
M'1
M'2
D
C
Limiting conditions
on [AB], [AD] and [CD]: null flow
H
on [BC]: exchange H, Text
Text
With
B
M1
M2
100 °C
0°C
T
0
102 S
Initial conditions
points
nodes
X
y
T = 100 °C
M1 N16
0.02
0.0
M2 N6
0.08
0.0
M'1
N14
0.02
0.1
M'2
N4
0.08
0.1
3.2
Characteristics of the grid
A number of nodes: 18
A number of meshs and types: 5 QUAD4, 10 TRIA3
3.3 Functionalities
tested
Commands
Keys
AFFE_MODELE
MODELISATION
PLAN_DIAG
[U4.22.01]
AFFE_CHAR_THER_F
ECHANGE
[U4.25.02]
THER_LINEAIRE
[U4.62.01]
Handbook of Validation
V4.21 booklet: Transitory thermics of the linear structures
HI-75/98/040 - Ind A
Code_Aster ®
Version
4.0
Titrate:
Thermal TTLL100 Choc 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
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
Obstruction memory:
8 megawords
Time CPU To use: 9.2 seconds
Handbook of Validation
V4.21 booklet: Transitory thermics of the linear structures
HI-75/98/040 - Ind A
Code_Aster ®
Version
4.0
Titrate:
Thermal TTLL100 Choc 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
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.
M'1
M'2
D
C
Limiting conditions
on [AB], [AD] and [CD]: null flow
H
on [BC]: exchange H, Text
Text
With
B
M1
M2
100 °C
0°C
T
0
102 S
Initial conditions
points
nodes
X
y
T = 100 °C
M1 N16
0.02
0.0
M2 N6
0.08
0.0
M'1
N14
0.02
0.1
M'2
N4
0.08
0.1
5.2
Characteristics of the grid
A number of nodes: 55
A number of meshs and types: 5 QUAD9, 10 TRIA6
5.3 Functionalities
tested
Commands
Keys
CREA_MAILLAGE
MODI_MAILLE
OPTION:
“QUAD8_9”
[U4.12.06]
AFFE_MODELE
MODELISATION
PLAN_DIAG
[U4.22.01]
AFFE_CHAR_THER_F
ECHANGE
[U4.25.02]
THER_LINEAIRE
[U4.62.01]
Handbook of Validation
V4.21 booklet: Transitory thermics of the linear structures
HI-75/98/040 - Ind A
Code_Aster ®
Version
4.0
Titrate:
Thermal TTLL100 Choc 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
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
Obstruction memory:
8 megawords
Time CPU To use: 10.0 seconds
Handbook of Validation
V4.21 booklet: Transitory thermics of the linear structures
HI-75/98/040 - Ind A
Code_Aster ®
Version
4.0
Titrate:
Thermal TTLL100 Choc 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
7
Summary of the results
Modeling “PLAN_DIAG” gives rather satisfactory results. Although the grid 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.
Handbook of Validation
V4.21 booklet: Transitory thermics of the linear structures
HI-75/98/040 - Ind A