Code_Aster ®
Version
4.0
Titrate:
Stationary TPLV106 nonlinear Thermique in pointer
Date:
07/12/98
Author (S):
F. WAECKEL, B. NEDJAR
Key:
V4.04.106-A Page:
1/6
Organization (S): EDF/IMA/MN
Handbook of Validation
V4.04 booklet: Stationary thermics of the voluminal structures
Document: V4.04.106
TPLV106 - Stationary nonlinear Thermique
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-diffusion).
It also makes it possible to check the taking into account of a solid phase shift/liquid 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 modelled in the plane case.
Handbook of Validation
V4.04 booklet: Stationary thermics of the voluminal structures
HI-75/98/040 - Ind A

Code_Aster ®
Version
4.0
Titrate:
Stationary TPLV106 nonlinear Thermique in pointer
Date:
07/12/98
Author (S):
F. WAECKEL, B. NEDJAR
Key:
V4.04.106-A Page:
2/6
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).
TL = 1000°C
T T

1 = 585° C
T
T = 615°C
2
T0 = 200 °C
liquid phase
solid phase
X = L = 1 m
X = 0
V
1.2 Properties

materials
· thermal conductivity is constant: K = 150 W/m°C
· the function enthalpy is such as:
C
T
;
T T
S

1
(T) = C
T1 + C
-
;
1
1

S
SSL (T
T)
T
T
T

2
C T1 + C
2 - 1 +
-
;
2

S
SSL (T
T) Cl (T T)
T
T2
with the following values:
C = C = 1
7 J/m3°C
S
L
3 10
C = 8 333
.
107 J/M3° C
SSL
T1 =
°
585 C
T2 =
°
615 C
Handbook of Validation
V4.04 booklet: Stationary thermics of the voluminal structures
HI-75/98/040 - Ind A

Code_Aster ®
Version
4.0
Titrate:
Stationary TPLV106 nonlinear Thermique in pointer
Date:
07/12/98
Author (S):
F. WAECKEL, B. NEDJAR
Key:
V4.04.106-A Page:
3/6
(T) 8
J/m3
7
6
5
Cl = Cs
4
3
Csl
2
1
Cs
0 0
200
400
600
800
1000
1200
1400
1600
T°C
585
615
1.3
Boundary conditions and loadings
Temperatures imposed at the ends
T =
°C
for
X =
0
200
0
T = 1000° C for
X = L = 1m
L
Rate of travel of the solid: V = 10­4 m/s
Handbook of Validation
V4.04 booklet: Stationary thermics of the voluminal structures
HI-75/98/040 - Ind A

Code_Aster ®
Version
4.0
Titrate:
Stationary TPLV106 nonlinear Thermique in pointer
Date:
07/12/98
Author (S):
F. WAECKEL, B. NEDJAR
Key:
V4.04.106-A Page:
4/6
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), - KT
=
X
, xx
0

éq 2.1-1

with (T
= 0
=
x=0)
T and (
T x=L)
TL
by integrating the equation [éq 2.1-1] one obtains:
V (
dT
T) -
= A
éq 2.1-2
K
dx
V
where A is a constant depending on the boundary conditions, of the report/ratio
and of the function
K
enthalpy (T).
This constant will be analytically given.
The equation [éq 2.1-2] led to:
(
T X)

dT
X =

éq 2.1-3
V

With +
(T)
T0
K
who must check:
TL

dT
L =

éq 2.1-4
V
WITH + (T)
T0
K
Knowing T T, L V
, T and (T)
0, L
, the equation [éq 2.1-4] must give the value of the constant
of integration A.
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 A.
With the facts of the case (T, T, T, T, C = C, C
0
L
1
2
S
L
SSL
), we obtained the solution
(physics) of A which takes the value A = ­ 294,9117.
From this constant, the analytical solution of the problem [éq 2.1-1] is analytical.
Handbook of Validation
V4.04 booklet: Stationary thermics of the voluminal structures
HI-75/98/040 - Ind A

Code_Aster ®
Version
4.0
Titrate:
Stationary TPLV106 nonlinear Thermique in pointer
Date:
07/12/98
Author (S):
F. WAECKEL, B. NEDJAR
Key:
V4.04.106-A Page:
5/6
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 grid
80 QUAD8
3.3 Functionalities
tested
Commands
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
MODELE
CHAM_MATER
EXCIT
CHARGE
Handbook of Validation
V4.04 booklet: Stationary thermics of the voluminal structures
HI-75/98/040 - Ind A

Code_Aster ®
Version
4.0
Titrate:
Stationary TPLV106 nonlinear Thermique in pointer
Date:
07/12/98
Author (S):
F. WAECKEL, B. NEDJAR
Key:
V4.04.106-A Page:
6/6
4
Results of modeling A
4.1 Values
tested
Identification
Reference
Aster
% difference
Temperature
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
Obstruction 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%.
Handbook of Validation
V4.04 booklet: Stationary thermics of the voluminal structures
HI-75/98/040 - Ind A