Code_Aster
®
Version
4.0
Titrate:
Stationary nonlinear Thermal TPLV106 in pointer
Date:
07/12/98
Author (S):
F. WAECKEL, B. NEDJAR
Key:
V4.04.106-A
Page:
1/6
Manual of Validation
V4.04 booklet: Stationary thermics of the voluminal structures
HI-75/98/040 - Ind A
Organization (S):
EDF/IMA/MN
Manual of Validation
V4.04 booklet: Stationary thermics of the voluminal structures
Document: V4.04.106
TPLV106 - Stationary nonlinear thermics
in pointer
Summary:
This elementary test makes it possible to treat a reducible three-dimensional example with a problem a variable
of space in stationary nonlinear thermics in pointer (problem of convection-dissemination).
It also makes it possible to check the taking into account of a solid phase shift/fluid by
Code_Aster
.
The reference solution is analytical and the variations with the results obtained by
Code_Aster
are lower
to 1%. The problem is modelized in the plane case.
Code_Aster
®
Version
4.0
Titrate:
Stationary nonlinear Thermal TPLV106 in pointer
Date:
07/12/98
Author (S):
F. WAECKEL, B. NEDJAR
Key:
V4.04.106-A
Page:
2/6
Manual of Validation
V4.04 booklet: Stationary thermics of the voluminal structures
HI-75/98/040 - Ind A
1
Problem of reference
1.1 Geometry
That is to say a bar moving, at the speed V, the right of conditions of temperatures imposed in X = 0
and X = L expressed in a fixed reference frame (compared to the bar moving).
liquid phase
X = L = 1 m
solid phase
T
0
= 200 °C
X = 0
=
615°C
V
T
L
= 1000°C
T
T
=
°
1
585 C
T
T
2
1.2 Properties
materials
·
thermal conductivity is constant: K = 150 W/m°C
·
the function enthalpy is such as:
()
(
)
(
) (
)
T
C T
T
T
C T
C
T
T
T
T
T
C T
C
T
T
C T
T
T
T
S
S
SSL
S
SSL
L
=
+
-
+
-
+
-
;
;
;
1
1
1
1
2
1
2
1
2
2
with the following values:
C
C
J m
C
C
J m
C
T
C
T
C
S
L
SSL
=
=
°
=
°
=
°
=
°
13 10
8.333 10
585
615
7
3
7
3
1
2
/
.
/
Code_Aster
®
Version
4.0
Titrate:
Stationary nonlinear Thermal TPLV106 in pointer
Date:
07/12/98
Author (S):
F. WAECKEL, B. NEDJAR
Key:
V4.04.106-A
Page:
3/6
Manual of Validation
V4.04 booklet: Stationary thermics of the voluminal structures
HI-75/98/040 - Ind A
8
0
7
6
5
4
3
2
1
T
()
0
200
400
600
800
1000
1200
1400
1600
T
°C
C
L
= C
S
615
C
SSL
585
C
S
J/m
3
1.3
Boundary conditions and loadings
Temperatures imposed at the ends
T
C
X
T
C
X
L
m
L
0
200
0
1000
1
=
°
=
=
°
= =
for
for
Rate of travel of the solid:
V
m S
=
10
4
/
Code_Aster
®
Version
4.0
Titrate:
Stationary nonlinear Thermal TPLV106 in pointer
Date:
07/12/98
Author (S):
F. WAECKEL, B. NEDJAR
Key:
V4.04.106-A
Page:
4/6
Manual of Validation
V4.04 booklet: Stationary thermics of the voluminal structures
HI-75/98/040 - Ind A
2
Reference solution
2.1
Method of calculation used for the reference solution
The result of reference is of the semi-analytical type. The equation 1D to be solved is as follows:
()
(
)
(
)
V
T
T
T
T and T
T
X
xx
X
X L
L
,
K,
-
=
=
=
=
=
0
0
0
with
éq 2.1-1
by integrating the equation [éq 2.1-1] one obtains:
()
V
T
dT
dx
With
K
-
=
éq 2.1-2
where
With
is a constant depending on the boundary conditions, the report/ratio
V
K
and of the function
enthalpy
()
T
.
This constant will be analytically given.
The equation [éq 2.1-2] led to:
()
()
X
dT
With
V
K
T
T
T
X
=
+
0
éq 2.1-3
who must check:
()
L
dT
With
V
K
T
T
T
L
=
+
0
éq 2.1-4
Knowing
()
T T
L V T
T
L
0
,
,
and
, the equation [éq 2.1-4] must give the value of the constant
of integration
With
.
However, it is difficult (even impossible) to determine this constant analytically, from where
resort to a numerical resolution of the equation [éq 2.1-4] to determine
With
.
With the facts of the case
(
)
T T T T C
C C
L
S
L
SSL
0
1
2
,
,
,
,
,
=
…
, we obtained the solution
(physics) of
With
who takes the value
With
= 294,9117.
From this constant, the analytical solution of the problem [éq 2.1-1] is analytical.
Code_Aster
®
Version
4.0
Titrate:
Stationary nonlinear Thermal TPLV106 in pointer
Date:
07/12/98
Author (S):
F. WAECKEL, B. NEDJAR
Key:
V4.04.106-A
Page:
5/6
Manual of Validation
V4.04 booklet: Stationary thermics of the voluminal structures
HI-75/98/040 - Ind A
2.2
Results of reference
X-coordinate
Temperature
0.6
387.98514
0.7
451.51001
0.725
469.72232
0.750
488.97505
0.775
509.32766
0.80
530.84296
0.825
553.58738
0.85
577.63114
0.9
683.71269
0.9125
719.51615
0.925
756.32221
0.9375
794.16795
0.95
833.07971
0.9625
873.08751
0.9750
914.22222
0.9875
956.51557
3 Modeling
With
3.1
Characteristics of modeling
Modeling 2D
3.2
Characteristics of the mesh
80 QUAD8
3.3 Functionalities
tested
Controls
Key word factor
Single-ended spanner word
Argument
Keys
DEFI_MATERIAU
THER_NL
LAMBDA
[U4.23.01]
BETA
THER_NON_LINE_MO
CONVERGENCE
CRIT_TEMP_RELA:
1.E-4
[U4.33.04]
CRIT_ENTH_RELA:
1.E-4
ITER_GLOB_MAXI:
130
MODEL
CHAM_MATER
EXCIT
CHARGE
Code_Aster
®
Version
4.0
Titrate:
Stationary nonlinear Thermal TPLV106 in pointer
Date:
07/12/98
Author (S):
F. WAECKEL, B. NEDJAR
Key:
V4.04.106-A
Page:
6/6
Manual of Validation
V4.04 booklet: Stationary thermics of the voluminal structures
HI-75/98/040 - Ind A
4
Results of modeling A
4.1 Values
tested
Identification
Temperature
Reference
Aster
% difference
N80 (X = 0.9875)
956.515
956.884
+0.039
N79 (X = 0.9750)
914.222
914.888
+0.073
N78 (X = 0.9625)
873.087
873.982
+0.103
N77 (X = 0.9500)
833.079
834.137
+0.127
N76 (X = 0.9375)
794.167
795.326
+0.146
N75 (X = 0.9250)
756.322
757.235
+0.159
N74 (X = 0.9125)
719.516
720.701
+0.165
N73 (X = 0.9000)
683.712
684.834
+0.164
N69 (X = 0.8500)
577.631
576.682
0.164
N67 (X = 0.8250)
553.587
553.507
0.014
N65 (X = 0.8000)
530.842
531.519
+0.128
N63 (X = 0.7750)
509.327
510.657
+0.261
N61 (X = 0.7500)
488.975
490.865
+0.387
N59 (X = 0.7250)
469.722
472.086
+0.503
N57 (X = 0.7000)
451.510
454.270
+0.611
N44 (X = 0.6000)
387.985
391.676
+0.951
4.2 Parameters
of execution
Version: 4.0.5
Machine: CRAY C90
Overall dimension memory:
8 MW
Time CPU To use:
59 seconds
5
Summary of the results
The results are very satisfactory with variations with the reference solution lower than 1%.