Code_Aster
®
Version
4.0
Titrate:
Concentric FDLV103 Spheres separated by a fluid
Date:
12/01/98
Author (S):
G. ROUSSEAU
Key:
V8.01.103-A
Page:
1/6
Manual of Validation
V8.01 booklet: Fluid
HP-51/96/031 - Ind A
Organization (S):
EDF/EP/AMV
Manual of Validation
V8.01 booklet: Fluid
V8.01.103 document
FDLV103 - Separate concentric spheres
by an incompressible fluid
Summary:
This test relates to the field of the fluids in the aspect inertial coupling. One carries out a modal analysis of one
rigid sphere connected to the solid mass by springs and diving in an incompressible volume of fluid of form
spherical.
The test validates the calculation of mass added in 3D as well as modal calculation for a system fluid-structure
coupled in 3D.
Code_Aster
®
Version
4.0
Titrate:
Concentric FDLV103 Spheres separated by a fluid
Date:
12/01/98
Author (S):
G. ROUSSEAU
Key:
V8.01.103-A
Page:
2/6
Manual of Validation
V8.01 booklet: Fluid
HP-51/96/031 - Ind A
1
Problem of reference
1.1 Geometry
P
1
P
2
R
2
R
1
S
1
()
S
2
()
1
2
K
K
Z
X
y
The interior sphere has one
radius = 0.35 Mr.
The external sphere has one
radius = 0.45 Mr.
S
1
()
S
2
()
R
1
R
2
1.2
Material properties
The interior sphere
()
S
1
is out of steel:
S
: 7.800 kg/m
3
E: 2.1 10
11
AP
: 0.3
The fluid filling out volume included/understood enters
()
S
1
and
()
S
2
is water of density
F
: 1.000 kg
(equivalent thermal characteristics:
= 1,
F
C
= 1.000).
One passes to modelize the fluid by a thermal modeling 3D.
1.3
Boundary conditions and loadings
One supposes a null temperature in a point of the fluid mesh.
One embeds the springs on the level of the solid mass at the points
P
1
and
P
2
.
Code_Aster
®
Version
4.0
Titrate:
Concentric FDLV103 Spheres separated by a fluid
Date:
12/01/98
Author (S):
G. ROUSSEAU
Key:
V8.01.103-A
Page:
3/6
Manual of Validation
V8.01 booklet: Fluid
HP-51/96/031 - Ind A
2
Reference solution
2.1
Method of calculation used for the reference solution
One bases oneself on an analytical result [bib1]:
In the case of two concentric spheres immersed in the same fluid, it is shown that the mass
added induced by the fluid confined on the internal sphere
()
S
1
is worth:
m
R
R
R
R
R
has
F
=
+
-
2
3
1 2
1
1
2
3
1
2
3
1
3
If it is supposed that the sphere has one degree of freedom according to OZ, clean mode of translation
sphere
()
S
1
according to OZ is given by:
F
K
m
m
has
=
+
1
2
2
Numerical application
10 NR/m
12,00 kg
329,17 kg
3.8534 Hz
5
:
,
,
K
m
m
F
has
=
=
=
=
2.2 References
bibliographical
[1]
R.D. BLEVINS, “Formulated for natural frequency and mode shape”, ED. KRIEGER
Code_Aster
®
Version
4.0
Titrate:
Concentric FDLV103 Spheres separated by a fluid
Date:
12/01/98
Author (S):
G. ROUSSEAU
Key:
V8.01.103-A
Page:
4/6
Manual of Validation
V8.01 booklet: Fluid
HP-51/96/031 - Ind A
3 Modeling
With
3.1
Characteristics of modeling
Modeling includes/understands:
·
side structure:
2 discrete elements of type
K_TR_L
(mesh SEG2)
1316 elements of hulls of the type
DKT
(mesh TRIA3)
·
fluid side:
1316 thermal elements of face of the type 3D
(mesh TRIA3)
14454 thermal elements of volume of the type 3D
(mesh TETRA4)
The nodes of the hull interns are locked according to all their degrees of freedom of rotation, like
their two D.D.L of translation DX and DY (
GROUP_NO: NOINT
).
The springs are embedded with the solid mass at the points P1 and P2 (
GROUP_NO: ENCAST
).
The hulls are thickness 1 Misters.
3.2
Characteristics of the mesh
A number of meshs and types: 2632 TRIA3, 2 SEG2, 14454 TETRA4.
3.3 Functionalities
tested
Controls
Keys
AFFE_MODELE
“THERMAL”
“3D”
[U4.22.01]
CALC_MATR_AJOU
OPTION “MASS_AJOU”
[U4.55.10]
MODE_MECA
NUME_DDL_GENE
NUME_DDL_GENE
“FULL”
STORAGE
[U4.55.07]
Code_Aster
®
Version
4.0
Titrate:
Concentric FDLV103 Spheres separated by a fluid
Date:
12/01/98
Author (S):
G. ROUSSEAU
Key:
V8.01.103-A
Page:
5/6
Manual of Validation
V8.01 booklet: Fluid
HP-51/96/031 - Ind A
4
Results of modeling A
4.1 Values
tested
Identification
Reference
Aster
% difference
Command of the clean mode: 1
3.8534
3.8983
+1.15%
4.2 Parameters
of execution
Version: 3.05.24
Machine: CRAY C98
Overall dimension memory:
30 MW
Time CPU To use:
212.86 seconds
Code_Aster
®
Version
4.0
Titrate:
FDLV103 concentric Spheres separated by a fluid
Date:
12/01/98
Author (S):
G. ROUSSEAU
Key:
V8.01.103-A
Page:
6/6
Manual of Validation
V8.01 booklet: Fluid
HP-51/96/031 - Ind A
5
Summary of the results
One finds the values of the analytical results well.
The small variation observed on the added mass can come:
·
of a discretization not rather fine of the surface of the sphere,
·
or of a discretization not fine enough of fluid volume.