Code_Aster
®
Version
4.0
Titrate:
FDLV104 Masses added on model generalized 3D
Date:
12/01/98
Author (S):
G. ROUSSEAU
Key:
V8.01.104-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
V8.01.104 document
FDLV104 - Calculation of mass added on model
generalized 3D
Summary:
This test of the field of the fluids (fluid coupling/structure) validates the calculation of mass added on a model
generalized of type 3D, namely two spheres coupled by an incompressible fluid.
By a modal analysis carried out by dynamic under-structuring, one obtains the coupled modes of both
spheres because of the presence of the fluid. The Eigen frequencies are compared with those determined by one
direct calculation.
One obtains the Eigen frequencies with a margin of less than 3%.
Code_Aster
®
Version
4.0
Titrate:
FDLV104 Masses added on model generalized 3D
Date:
12/01/98
Author (S):
G. ROUSSEAU
Key:
V8.01.104-A
Page:
2/6
Manual of Validation
V8.01 booklet: Fluid
HP-51/96/031 - Ind A
1
Problem of reference
1.1 Geometry
Sphere 1
H
L
R
K2
K2
0
K1
K3
K3
K3
K1
K1
K1
K3
K2
Sphere 2
L
Y
X
Z
Length:
L = 4 m
width:
L = 2 m
height:
H = 2 m
Thickness of the hulls:
E = 10
3
m
Radius of the spheres:
R = 0.5 m
1.2
Properties of materials
Structure: steel - material elastic
E = 2.10
11
AP
= 0.3
S
= 7800 kg/m
3
The springs have as respective stiffnesses:
K1 = 10
6
NR/m
K2 = 10
5
NR/m
K3 = 10
7
NR/m
Fluid: water - thermal material are equivalent
= 1.
the specific heat plays the part of density of the fluid:
F
= 1000 kg/m
3
1.3
Boundary conditions and loadings
Side structure: ddl of rotation
DRX
,
DRY
,
DRZ
sphere 1 are locked:
DRX: 0.0
DRY: 0.0
DRZ: 0.0
Fluid side: one imposes a pressure (i.e temperature) null in a node of the fluid mesh.
Code_Aster
®
Version
4.0
Titrate:
FDLV104 Masses added on model generalized 3D
Date:
12/01/98
Author (S):
G. ROUSSEAU
Key:
V8.01.104-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 uses a direct modal calculation to obtain the Eigen frequencies modified by the fluid around
spheres.
The two spheres result by a translation from vector from components (2, 0., 0.) and for one
rotation of nautical analyzes (90., 0., 90.) what makes it possible to plan to build a model
generalized on the 1ère sphere. One will be able to carry out same modal calculation with coupling
fluid/structure by using the dynamic under-structuring. Direct calculation with taking into account of
mass added leads to the Eigen frequencies of the immersed system following:
F
1
=
3.1172 Hz
F
2
=
3.1183 Hz
F
3
=
9.2727 Hz
F
4
=
9.8267 Hz
F
5
=
22.4400 Hz
F
6
=
30.3295 Hz
2.2
Results of reference
Direct modal calculation by
Code_Aster
.
2.3
Uncertainty on the solution
Uncertainties on the solution are related to the discretization of the fluid interface/structure and on
the invariance of the mesh by rotation of nautical angles (90°, 0°, 90°).
Code_Aster
®
Version
4.0
Titrate:
FDLV104 Masses added on model generalized 3D
Date:
12/01/98
Author (S):
G. ROUSSEAU
Key:
V8.01.104-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:
336 elements of hulls
DKT
modelizing sphere 1,
6 discrete elements of type
K_TR_L
(modeling
DIS_TR
) modelizing the six springs connecting
sphere 1 with the solid mass,
·
fluid side:
672
THER_FACE3
thermal elements modelizing the fluid interface/structure,
39 445
THER_TETRA4
thermal elements modelizing the fluid.
3.2
Characteristics of the mesh
A number of meshs and types: 672 meshs
TRIA3
, 39 445
TETRA4
, 6
SEG2
3.3 Functionalities
tested
Controls
Keys
CALC_MATR_AJOU
MODELE_GENE
[U4.55.10]
OPTION
“MASS_AJOU”
Code_Aster
®
Version
4.0
Titrate:
FDLV104 Masses added on model generalized 3D
Date:
12/01/98
Author (S):
G. ROUSSEAU
Key:
V8.01.104-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
Hz
Reference
Hz
Aster
% difference
N°1 mode
3.1172
3.1189
+0.056%
N°2 mode
3.1183
3.1321
+0.44%
N°3 mode
9.2727
9.3144
+0.45%
N°4 mode
9.8267
9.8533
+0.27%
N°5 mode
22.4400
23.1291
+3.1%
N°6 mode
30.3295
31.1779
+2.8%
4.2 Remarks
The variation on the two last Eigen frequencies is explained by a not-symmetry of the mesh of
the fluid interface/structure (thermal) compared to that of the first. Mesh of the interface
fluid/structure (thermal elements) of the second sphere does not result exactly from that from
the first by rotation of nautical angles of 90°, 0°, 90°.
4.3 Parameters
of execution
Version: NEW 3.5.24
Machine: CRAY C90
Overall dimension memory:
30 MW
Time CPU to use:
161.3 seconds
Code_Aster
®
Version
4.0
Titrate:
FDLV104 Masses added on model generalized 3D
Date:
12/01/98
Author (S):
G. ROUSSEAU
Key:
V8.01.104-A
Page:
6/6
Manual of Validation
V8.01 booklet: Fluid
HP-51/96/031 - Ind A
5
Summary of the results
The results obtained by calculation by dynamic under-structuring show perfect
agreement with direct calculation. Nevertheless, to have this agreement, it should be taken care that them
mesh of the interfaces fluid/structure (thermal elements) of the substructures which are repeated with
the interior of the fluid mesh result perfectly by rotations of nautical angle defined in
DEFI_MODELE_GENE
.