Code_Aster
®
Version
5.0
Titrate:
TPLV103 - Infinite cylinder in anisotropic stationary thermics
Date:
23/09/02
Author (S):
C. DURAND
Key
:
V4.04.103-B
Page:
1/6
Manual of Validation
V4.04 booklet: Stationary thermics of the voluminal structures
HT-66/02/001/A
Organization (S):
EDF/AMA
Manual of Validation
V4.04 booklet: Stationary thermics of the voluminal structures
Document: V4.04.103
TPLV103 - Infinite cylinder in stationary thermics
anisotropic
Summary:
This test the purpose of which relates to it thermal linear stationary and transitory be to test the anisotropy
cylindrical.
Two modelings are carried out:
·
a first into voluminal,
·
a second in plane 2D.
The results obtained are in perfect agreement with the analytical values.
Code_Aster
®
Version
5.0
Titrate:
TPLV103 - Infinite cylinder in anisotropic stationary thermics
Date:
23/09/02
Author (S):
C. DURAND
Key
:
V4.04.103-B
Page:
2/6
Manual of Validation
V4.04 booklet: Stationary thermics of the voluminal structures
HT-66/02/001/A
1
Problem of reference
1.1 Geometry
H
D
0
I
G
C
B
With
E F
Z
0
X
0
Y
0
1/4 of cylinder
In the reference mark (X
0
, Y
0
, Z
0
), the points have as co-ordinates:
C (0; 2, 1)
D (2; 0; 0)
E (0; 2; 0)
F (1; 0; 1)
O (0; 0; 0)
To (2; 0; 1)
B
(
)
2
2 1
;
;
G (0; 1; 1)
H (1; 0; 0)
I (0; 1; 0)
1.2
Material properties
Anisotropic material, direction privileged along the axes of the cylindrical reference mark
(
)
U U U
R
Z
,
,
.
R
Z
C
=
=
=
=
°
°
1
0.5
3 W/m C
2 J/m
C
3
1.3
Boundary conditions and loadings
face AFHD:
Temperature imposed on 100 °C
face CGIE:
Temperature with 0 °C
others faces:
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 1
Er
member as well as the 2
ème
.
Code_Aster
®
Version
5.0
Titrate:
TPLV103 - Infinite cylinder in anisotropic stationary thermics
Date:
23/09/02
Author (S):
C. DURAND
Key
:
V4.04.103-B
Page:
3/6
Manual of Validation
V4.04 booklet: Stationary thermics of the voluminal structures
HT-66/02/001/A
2
Reference solution
2.1
Method of calculation used for the reference solution
Analytical solution.
Temperature varying linearly in
.
in
(
)
R
Z
,
() () ()
[
]
()
()
() () ()
[
]
2
.
1
1
2
With
T
C
T
With
R
T
R
Y
With
With
T
With
T
C
T
T
-
-
=
-
=
+
-
=
2.2
Results of reference
Temperatures at points A and B, flow following Y to point A.
()
()
()
T WITH
T B
WITH Y
=
=
=
100
50
100
2
15.915
2.3
Uncertainty on the solution
Analytical solution.
2.4 References
bibliographical
[1]
NR. RICHARD: “Development of the thermal anisotropy in the software Aster”, Note
technique HM-18/94/0011.
Code_Aster
®
Version
5.0
Titrate:
TPLV103 - Infinite cylinder in anisotropic stationary thermics
Date:
23/09/02
Author (S):
C. DURAND
Key
:
V4.04.103-B
Page:
4/6
Manual of Validation
V4.04 booklet: Stationary thermics of the voluminal 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 in transient.
3.2
Characteristics of the mesh
Regulated into 250
HEXA8
(5 elements on the edges HD and DM, 10 elements on DF) by IDEAS.
3.3 Functionalities
tested
Controls
Key word factor
Single-ended spanner word
Argument
DEFI_MATERIAU
THER_ORTH
AFFE_CARA_ELEM
SOLID MASS
ANGL_AXE
(0. , 90.)
SOLID MASS
ORIG_AXE
(0. , 0. , 0. )
THER_LINEAIRE
--
PARM_THETA
0.8
--
CARA_ELEM
CALC_CHAM_ELEM
--
CARA_ELEM
--
OPTION
“FLUX_ELNO_TEMP”
4
Results of modeling A
4.1 Values
tested
Identification Reference
Aster %
difference
T (A) * N1
100
100
0
T (B) N133
50
50
0
()
R
R
WITH Y
15.9155 15.950
0.22
*: imposed temperature
4.2 Remarks
The symmetry of the mesh makes that the solution T with the nodes of the network is exact, but in
elements, the extrapolated solution is not exact.
Flow is calculated by Aster at the points of integration of the elements then deferred to the nodes by
extrapolation. As flow is not uniform, this extrapolation involves a difference enters
calculation and reference.
Code_Aster
®
Version
5.0
Titrate:
TPLV103 - Infinite cylinder in anisotropic stationary thermics
Date:
23/09/02
Author (S):
C. DURAND
Key
:
V4.04.103-B
Page:
5/6
Manual of Validation
V4.04 booklet: Stationary thermics of the voluminal structures
HT-66/02/001/A
5 Modeling
B
5.1
Characteristics of modeling
Similar to the modeling A, but solved in plan HIED.
5.2
Characteristics of the mesh
Mesh IDEAS with 50 QUAD4 and 66 nodes.
5.3 Functionalities
tested
Controls
Key word factor
Single-ended spanner word
Argument
DEFI_MATERIAU
THER_ORTH
AFFE_CARA_ELEM
SOLID MASS
ORIG_AXE
(0. , 0. )
THER_LINEAIRE
--
PARM_THETA
0.8
--
CARA_ELEM
CALC_CHAM_ELEM
--
CARA_ELEM
--
OPTION
“FLUX_ELNO_TEMP”
6
Results of modeling B
6.1 Values
tested
Identification Reference
Aster %
difference
T (A) * N6
100
100
0
T (B) N36
50
50
0
()
R
R
WITH Y
15.9155 15.950
0.22
*: imposed temperature
6.2 Remarks
The symmetry of the mesh makes that the solution T with the nodes of the network is exact. But in
elements, the extrapolated solution is not exact.
Flow is calculated by Aster at the points of integration of the elements then deferred to the nodes by
extrapolation. As flow is not uniform, this extrapolation involves a difference enters
calculation and reference.
Code_Aster
®
Version
5.0
Titrate:
TPLV103 - Infinite cylinder in anisotropic stationary thermics
Date:
23/09/02
Author (S):
C. DURAND
Key
:
V4.04.103-B
Page:
6/6
Manual of Validation
V4.04 booklet: Stationary thermics of the voluminal structures
HT-66/02/001/A
7
Summary of the results
Key words
ANGL_AXE
and
ORIG_AXE
introduced into the control
AFFE_CARA_ELEM
are tested
in 3D and plane 2D for an anisotropic problem of thermics.