Code_Aster ®
Version
5.0
Titrate:
TPLV103 - Infinite Cylindre in anisotropic stationary thermics
Date:
23/09/02
Author (S):
C. Key DURAND
:
V4.04.103-B Page:
1/6
Organization (S): EDF/AMA
Handbook of Validation
V4.04 booklet: Stationary thermics of the voluminal structures
Document: V4.04.103
TPLV103 - Infinite Cylindre 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.
Handbook of Validation
V4.04 booklet: Stationary thermics of the voluminal structures
HT-66/02/001/A
Code_Aster ®
Version
5.0
Titrate:
TPLV103 - Infinite Cylindre in anisotropic stationary thermics
Date:
23/09/02
Author (S):
C. Key DURAND
:
V4.04.103-B Page:
2/6
1
Problem of reference
1.1 Geometry
Z0
Y0
C
B
1/4 of cylinder
G
F
E
With
I
0
H
D
X0
In the reference mark (X0, Y0, Z0), 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).
3
R = 1
= 0.5
Z = 3 W/°
m C
C = 2 J/m °C
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 1st member as well as 2nd.
Handbook of Validation
V4.04 booklet: Stationary thermics of the voluminal structures
HT-66/02/001/A
Code_Aster ®
Version
5.0
Titrate:
TPLV103 - Infinite Cylindre in anisotropic stationary thermics
Date:
23/09/02
Author (S):
C. Key DURAND
:
V4.04.103-B Page:
3/6
2
Reference solution
2.1
Method of calculation used for the reference solution
Analytical solution.
Temperature varying linearly in.
in (R, Z)
T () [
= T (C) T (A)] 2
+ T (A)
(A)
1
Y=-
T
1
2
= -
T C - T A.
R
R (A) [()
()]
2.2
Results of reference
Temperatures at points A and B, flow following Y to point A.
100
T ()
To = 100
T ()
B = 50
(A) Y =
15.915
2
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.
Handbook of Validation
V4.04 booklet: Stationary thermics of the voluminal structures
HT-66/02/001/A
Code_Aster ®
Version
5.0
Titrate:
TPLV103 - Infinite Cylindre in anisotropic stationary thermics
Date:
23/09/02
Author (S):
C. Key DURAND
:
V4.04.103-B Page:
4/6
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 grid
Regulated in 250 HEXA8 (5 elements on the edges HD and DM, 10 elements on DF) by IDEAS.
3.3 Functionalities
tested
Commands
Key word factor
Single-ended spanner word
Argument
DEFI_MATERIAU
THER_ORTH
AFFE_CARA_ELEM
MASSIF
ANGL_AXE
(0. , 90.)
MASSIF
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 grid 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.
Handbook of Validation
V4.04 booklet: Stationary thermics of the voluminal structures
HT-66/02/001/A
Code_Aster ®
Version
5.0
Titrate:
TPLV103 - Infinite Cylindre in anisotropic stationary thermics
Date:
23/09/02
Author (S):
C. Key DURAND
:
V4.04.103-B Page:
5/6
5 Modeling
B
5.1
Characteristics of modeling
Similar to the modeling A, but solved in plan HIED.
5.2
Characteristics of the grid
Grid IDEAS with 50 QUAD4 and 66 nodes.
5.3 Functionalities
tested
Commands
Key word factor
Single-ended spanner word
Argument
DEFI_MATERIAU
THER_ORTH
AFFE_CARA_ELEM
MASSIF
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 grid 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.
Handbook of Validation
V4.04 booklet: Stationary thermics of the voluminal structures
HT-66/02/001/A
Code_Aster ®
Version
5.0
Titrate:
TPLV103 - Infinite Cylindre in anisotropic stationary thermics
Date:
23/09/02
Author (S):
C. Key DURAND
:
V4.04.103-B Page:
6/6
7
Summary of the results
Key words ANGL_AXE and ORIG_AXE introduced into command AFFE_CARA_ELEM are tested
in 3D and plane 2D for an anisotropic problem of thermics.
Handbook of Validation
V4.04 booklet: Stationary thermics of the voluminal structures
HT-66/02/001/A
Outline document