Code_Aster
®
Version
6.4
Titrate:
FDLV105 - Mass added on axisymmetric piston
Date:
16/07/03
Author (S):
NR. GREFFET
Key
:
V8.01.105-B
Page:
1/4
Manual of Validation
V8.01 booklet: Fluid HT-66/03/008/A
Organization (S):
EDF-R & D/AMA
Manual of Validation
V8.01 booklet: Fluid
V8.01.105 document
FDLV105 - Mass added on axisymmetric piston
coupled to a column of incompressible fluid
Summary:
This test of the field of the fluids implements a modal analysis on a system coupled fluid structure
incompressible of type piston column of fluid with free face. The piston and the fluid are modelized
respectively by machine elements and thermal axisymmetric. One validates the calculation thus of
mass added in axisymmetric configuration.
Code_Aster
®
Version
6.4
Titrate:
FDLV105 - Mass added on axisymmetric piston
Date:
16/07/03
Author (S):
NR. GREFFET
Key
:
V8.01.105-B
Page:
2/4
Manual of Validation
V8.01 booklet: Fluid HT-66/03/008/A
1
Problem of reference
1.1 Geometry
L = 1 m
E = 0.03 m
Free face
fluid
H = 0.025 m
piston
arises
0
Y
X
The system consists of a circular piston vibrating in contact with an annular column of fluid
finished by a free face:
Length: 1 m
width: 0.03 m
height: 0.025 m
the axis of revolution is axis OY of the reference mark. OX indicates the radial axis.
1.2
Properties of materials
Structure: steel - material elastic
E = 2.10
13
AP
= 0.3
S
= 7800 kg/m
3
The spring has a stiffness by radian of
K
=
10
2
5
NR/m/rad
Fluid: thermal material are equivalent
=
=
1.
1000 kg/m
3
F
p
C
1.3
Boundary conditions and loadings
Side structure: the ddl
DX
of all the nodes of the structure is locked:
DX: 0.0
Fluid side: one imposes a pressure (i.e temperature) null on the nodes of the free face.
Code_Aster
®
Version
6.4
Titrate:
FDLV105 - Mass added on axisymmetric piston
Date:
16/07/03
Author (S):
NR. GREFFET
Key
:
V8.01.105-B
Page:
3/4
Manual of Validation
V8.01 booklet: Fluid HT-66/03/008/A
2
Reference solution
2.1
Method of calculation used for the reference solution
One solves the analytically following coupled problem:
m y K y F
y
p
y
y
p
m K
p
F
&&
&&
+
=
= -
=
2
2
0
,
with
force hydrodynamic pressure on the piston
hydrodynamic pressure in the fluid
: mass and stiffness of the piston respectively
by radian
F
The hydrodynamic field of pressure in the fluid is written:
()
p
y y L
F
= -
-
&&
from where the compressive force being exerted on the piston:
F
p R D R
y L E
F
E
=
= -
N
&&
2
0
2
the mass added by radian is worth:
m
L E
has
F
=
2
2
the clean mode of the coupled system is worth:
F
K
m m
has
=
+
=
1
2
27.25Hz
2.2
Results of reference
Analytical.
2.3 References
bibliographical
[1]
GIBERT R.J.: Vibrations of the structures, Eyrolles (1988).
Code_Aster
®
Version
6.4
Titrate:
FDLV105 - Mass added on axisymmetric piston
Date:
16/07/03
Author (S):
NR. GREFFET
Key
:
V8.01.105-B
Page:
4/4
Manual of Validation
V8.01 booklet: Fluid HT-66/03/008/A
3 Modeling
With
3.1
Characteristics of modeling
·
Side structure:
8 axisymmetric machine elements
MEAXQU4
,
1 specific element of type
K_T_N
modelizing the spring,
·
fluid side:
380 axisymmetric thermal elements
THAXQU4
modelizing the fluid,
8 axisymmetric thermal elements
THAXSE2
modelizing the fluid interface/structure.
3.2
Characteristics of the mesh
Side structure:
8 meshs QUAD4
1maille POI1
Fluid side:
8 meshs SEG2
320 meshs QUAD4
A number of meshs:
337
3.3 Functionalities
tested
Controls
AFFE_MODELE “AXIS”
THERMICS
CALC_MATR_AJOU OPTION
“MASS_AJOU”
4
Results of modeling A
4.1 Values
tested
Identification Hz
Reference
Hz
Aster
% difference
N°1 mode
27.25
27.37
0.469
5
Summary of the results
The calculation of mass added on axisymmetric elements is very well carried out. One will note
however that the calculated quantities are masses added by radian (divided by 2
).