Code_Aster
®
Version
5.0
Titrate:
TPLL100 - Anisotropic plane wall in stationary thermics
Date:
23/09/02
Author (S):
C. DURAND
Key
:
V4.02.100-B
Page:
1/6
Manual of Validation
V4.02 booklet: Stationary thermics of the linear structures
HT-66/02/001/A
Organization (S):
EDF/AMA
Manual of Validation
V4.02 booklet: Stationary thermics of the linear structures
Document: V4.02.100
TPLL100 - Anisotropic plane wall in thermics
stationary
Summary:
This test the purpose of which relates to it thermal linear stationary and transitory be to validate the anisotropy
Cartesian.
Two modelings are carried out:
·
a first into voluminal,
·
a second in plan.
The results obtained are in perfect agreement with the analytical values.
Code_Aster
®
Version
5.0
Titrate:
TPLL100 - Anisotropic plane wall in stationary thermics
Date:
23/09/02
Author (S):
C. DURAND
Key
:
V4.02.100-B
Page:
2/6
Manual of Validation
V4.02 booklet: Stationary thermics of the linear structures
HT-66/02/001/A
1
Problem of reference
1.1 Geometry
Y
0
K
F
Z
0
J
E
B
I
D
With
G
C
X
0
Y
1
Z
1
X
1
H
In the reference mark (X
0
, Y
0
, Z
0
), the points have as co-ordinates:
C (0.03; 0; 0)
D (0.07; 0.03; 0)
E (0.04; 0.07; 0)
F (0; 0.04; 0)
To (0.015; 0.02; 0)
B (0.055; 0.05; 0)
G (0.035; 0.035; 0)
(
)
1
0
1
0
//
rad
4
,
0,05.
Z
Z
X
CD
Z
EJ
DI
CH
FK
=
=
=
=
=
1.2
Material properties
Anisotropic material, direction privileged along the axes of the reference mark (X
1
, Y
1
, Z
1
):
X
Y
Z
=
=
=
=
°
°
°
°
1 W/m C
0.5 W/m C
2 W/m C
C
2 J/m
C
p
3
1.3
Boundary conditions and loadings
face FEJK: Outgoing flow of 400 W/m
2
.
face CDIH: Entering flow of 400 W/m
2
.
face EDIJ: Outgoing flow of 1.200 W/m
2
.
face FCHK: Imposed temperature 100°C.
Others faces: condition of Neumann.
1.4 Conditions
initial
To make this stationary calculation, a transitory calculation is made for which the boundary conditions are
constants in time. This makes it possible to test elementary calculations of mass and rigidity
intervening in the first member as well as the second member.
Code_Aster
®
Version
5.0
Titrate:
TPLL100 - Anisotropic plane wall in stationary thermics
Date:
23/09/02
Author (S):
C. DURAND
Key
:
V4.02.100-B
Page:
3/6
Manual of Validation
V4.02 booklet: Stationary thermics of the linear structures
HT-66/02/001/A
2
Reference solution
2.1
Method of calculation used for the reference solution
Analytical solution.
Temperature varying linearly according to
CD
.
Isotherms parallel with faces CHKF and DIJE.
(
)
(
)
(
)
()
()
()
(
)
720
that is to say
720
that is to say
if
:
that is to say
:
with
:
has
one
,
:
identify
In
Z
X
Y
y
X
X
O
Y
X
X
y
X
Y
X
Z
y
X
O
O
X
X
T
With
T
X
X
T
X
T X
T
CH
cos
sin
.
sin
cos
.
,
20
1600
sin
cos
,
400
1200
0
sin
cos
sin
cos
,
,
2
2
1
2
2
1
+
=
-
=
=
+
-
=
+
+
-
=
=
=
=
-
-
+
-
=
X
CD
CD
X
CF
CF
CH
CD
CD
2.2
Results of reference
Temperature at the points A, B, G.
Flow following directions X
O
and Y
O
.
()
()
()
T WITH
100
T B
20
T G
60
=
=
=
=
=
X
Y
O
O
720
1040
2.3 References
bibliographical
[1]
NR. RICHARD: Note technical HM-18/94/0011, “Development of the thermal anisotropy
in the software Aster ".
Code_Aster
®
Version
5.0
Titrate:
TPLL100 - Anisotropic plane wall in stationary thermics
Date:
23/09/02
Author (S):
C. DURAND
Key
:
V4.02.100-B
Page:
4/6
Manual of Validation
V4.02 booklet: Stationary thermics of the linear structures
HT-66/02/001/A
3 Modeling
With
3.1
Characteristics of modeling
diagram in time, forced on 1 to test the calculation of the second member.
4 elements 3D,
HEXA8
.
3.2
Characteristics of the mesh
4 Hexa 8.
3.3 Functionalities
tested
Controls
Key word factor
Single-ended spanner word
Argument
DEFI_MATERIAU
THER_ORTH
AFFE_CARA_ELEM
--
ANGL_REP
--
NET
AFFE_MODELE
AFFE
MODELING
“3D”
THER_LINEAIRE
TEMP_INIT
STATIONARY
“YES”
INCREMENT
LIST_INST
--
PARM_THETA
1.
--
CARA_ELEM
CALC_NO
--
OPTION
“FLUX_ELNO_TEMP”
CALC_CHAM_ELEM
--
CARA_ELEM
--
OPTION
“FLUX_ELNO_TEMP”
--
OPTION
“FLUX_ELGA_TEMP”
4
Results of modeling A
4.1 Values
tested
Identification Reference
Aster %
difference
T (A) N7 *
100°
100°
0.
T (B) N2
20°C
20°C
0.
T (G) N13
60°C
60°C
0.
X
O
720.720 0.
Y
O
1040 1040
0.
*: imposed temperature
4.2 Remarks
The analytical solution being of command 1 and the field represented by the discretization, the code finds,
with the round-off errors close, this solution.
Code_Aster
®
Version
5.0
Titrate:
TPLL100 - Anisotropic plane wall in stationary thermics
Date:
23/09/02
Author (S):
C. DURAND
Key
:
V4.02.100-B
Page:
5/6
Manual of Validation
V4.02 booklet: Stationary thermics of the linear structures
HT-66/02/001/A
5 Modeling
B
5.1
Characteristics of modeling
Similar to the modeling A, but solved in 2D in plan CDEF.
5.2
Characteristics of the mesh
4 QUAD 4.
5.3 Functionalities
tested
Controls
Key word factor
Single-ended spanner word
Argument
DEFI_MATERIAU
THER_ORTH
AFFE_CARA_ELEM
--
ANGL_REP
--
NET
AFFE_MODELE
AFFE
MODELING
“PLANE”
THER_LINEAIRE
TEMP_INIT
STATIONARY
“YES”
INCREMENT
LIST_INST
--
PARM_THETA
1.
--
CARA_ELEM
CALC_NO
--
OPTION
“FLUX_ELNO_TEMP”
CALC_CHAM_ELEM
--
CARA_ELEM
--
OPTION
“FLUX_ELNO_TEMP”
--
OPTION
“FLUX_ELGA_TEMP”
6
Results of modeling B
6.1 Values
tested
Identification Reference
ASTER %
difference
T (A) N5 *
100°
100°
0.
T (B) N2
20°C
20°C
0.
T (G) N8
60°C
60°C
0.
X
O
720.720 0.
Y
O
1040 1040
0.
*: imposed temperature
6.2 Remarks
The analytical solution being of command 1 and the field represented by the discretization, the code finds,
with the round-off errors close, this solution.
Code_Aster
®
Version
5.0
Titrate:
TPLL100 - Anisotropic plane wall in stationary thermics
Date:
23/09/02
Author (S):
C. DURAND
Key
:
V4.02.100-B
Page:
6/6
Manual of Validation
V4.02 booklet: Stationary thermics of the linear structures
HT-66/02/001/A
7
Summary of the results
The key word
ANGL_REP
introduced into the control
AFFE_CARA_ELEM
is thus tested in 3D and plane 2D
on an anisotropic problem of thermics.