Code_Aster ®
Version
4.0
Titrate:
Concentric FDLV103 Sphères separated by a fluid
Date:
12/01/98
Author (S):
G. ROUSSEAU
Key:
V8.01.103-A Page:
1/6
Organization (S): EDF/EP/AMV
Handbook of Validation
V8.01 booklet: Fluid
V8.01.103 document
FDLV103 - Sphères concentric separate
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.
Handbook of Validation
V8.01 booklet: Fluid
HP-51/96/031 - Ind A

Code_Aster ®
Version
4.0
Titrate:
Concentric FDLV103 Sphères separated by a fluid
Date:
12/01/98
Author (S):
G. ROUSSEAU
Key:
V8.01.103-A Page:
2/6
1
Problem of reference
1.1 Geometry
P1
K
The interior sphere has one
()
Z
S1
radius = 0.35 Mr.
R1
R

1
()
X
The external sphere has one
()
S1
S2
radius = 0.45 Mr.
y
R2
R2

1

2
K
()
S2
P2
1.2
Material properties
The interior sphere (S1) is out of steel:
S: 7.800 kg/m3
E: 2.1 1011 Pa
: 0.3
The fluid filling out the volume ranging between (S1) and (S2) is water of density F: 1.000 kg
(equivalent thermal characteristics: = 1, F

C = 1.000).
One passes to model the fluid by a thermal modeling 3D.
1.3
Boundary conditions and loadings
One supposes a null temperature in a point of the fluid grid.
One embeds the springs on the level of the solid mass at the points P1 and P2.
Handbook of Validation
V8.01 booklet: Fluid
HP-51/96/031 - Ind A

Code_Aster ®
Version
4.0
Titrate:
Concentric FDLV103 Sphères separated by a fluid
Date:
12/01/98
Author (S):
G. ROUSSEAU
Key:
V8.01.103-A Page:
3/6
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 (S1) is worth:


3
R
1+ 2 1
2

R2
m
=
R3

has
F

3

3 1
R
1 - 1

R2



If it is supposed that the sphere has one degree of freedom according to OZ, clean mode of translation
sphere (S1) according to OZ is given by:
1
2K
F
= 2 m+ma
5
Numerical application:
K = 10 NR/m, m = 12,00 kg, m = 329,17 kg
has
F = 3.8534 Hz
2.2 References
bibliographical
[1]
R.D. BLEVINS, “Formulas for natural frequency and shape mode”, ED. KRIEGER
Handbook of Validation
V8.01 booklet: Fluid
HP-51/96/031 - Ind A

Code_Aster ®
Version
4.0
Titrate:
Concentric FDLV103 Sphères separated by a fluid
Date:
12/01/98
Author (S):
G. ROUSSEAU
Key:
V8.01.103-A Page:
4/6
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 blocked 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 grid
A number of meshs and types: 2632 TRIA3, 2 SEG2, 14454 TETRA4.
3.3 Functionalities
tested
Commands
Keys
AFFE_MODELE
“THERMIQUE”
“3D”
[U4.22.01]
CALC_MATR_AJOU
OPTION “MASS_AJOU”
[U4.55.10]
MODE_MECA
NUME_DDL_GENE
NUME_DDL_GENE
“PLEIN”
STOCKAGE
[U4.55.07]
Handbook of Validation
V8.01 booklet: Fluid
HP-51/96/031 - Ind A

Code_Aster ®
Version
4.0
Titrate:
Concentric FDLV103 Sphères separated by a fluid
Date:
12/01/98
Author (S):
G. ROUSSEAU
Key:
V8.01.103-A Page:
5/6
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
Obstruction memory:
30 MW
Time CPU To use:
212.86 seconds
Handbook of Validation
V8.01 booklet: Fluid
HP-51/96/031 - Ind A

Code_Aster ®
Version
4.0
Titrate:
Concentric FDLV103 Sphères separated by a fluid
Date:
12/01/98
Author (S):
G. ROUSSEAU
Key:
V8.01.103-A Page:
6/6
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.
Handbook of Validation
V8.01 booklet: Fluid
HP-51/96/031 - Ind A