Code_Aster ®
Version
6.4
Titrate:
FDLV105 - Masse added on axisymmetric piston


Date:
16/07/03
Author (S):
NR. GREFFET Key
:
V8.01.105-B Page:
1/4

Organization (S): EDF-R & D/AMA

Handbook of Validation
V8.01 booklet: Fluid
V8.01.105 document

FDLV105 - Masse 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 modelled
respectively by machine elements and thermal axisymmetric. One validates the calculation thus of
mass added in axisymmetric configuration.

Handbook of Validation
V8.01 booklet: Fluid HT-66/03/008/A

Code_Aster ®
Version
6.4
Titrate:
FDLV105 - Masse added on axisymmetric piston


Date:
16/07/03
Author (S):
NR. GREFFET Key
:
V8.01.105-B Page:
2/4

1
Problem of reference

1.1 Geometry

arises
piston
L = 1 m
Free face
Y
0
E = 0.03 m
X
H = 0.025 m
fluid


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 = 2.1013 Pa
= 0.3
S = 7800 kg/m3
105
The spring has a stiffness by radian of K = 2 NR/m/rad
Fluid: thermal material are equivalent
= 1.


C = 1000 kg/m3
F
p

1.3
Boundary conditions and loadings

Side structure: ddl DX of all the nodes of the structure is blocked: DX: 0.0

Fluid side: one imposes a pressure (i.e temperature) null on the nodes of the free face.
Handbook of Validation
V8.01 booklet: Fluid HT-66/03/008/A

Code_Aster ®
Version
6.4
Titrate:
FDLV105 - Masse added on axisymmetric piston


Date:
16/07/03
Author (S):
NR. GREFFET Key
:
V8.01.105-B Page:
3/4

2
Reference solution

2.1
Method of calculation used for the reference solution

One solves the analytically following coupled problem:



F forces hydrodynamic pressure on the piston
m y & + K y = F


2

p
p pressure hydrodynamic in the fluid

= - 0
with

y
2


m, K

: mass and stiffness of the piston respectively
p


= y


y
F &

by radian



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:

E

e2
F =
p R D R = -
y L
F


N
& 2
0

e2
the mass added by radian is worth: m = L
has
F

2

1
K
the clean mode of the coupled system is worth: F =
=
2
27.25Hz
m + my

2.2
Results of reference

Analytical.

2.3 References
bibliographical

[1]
GIBERT R.J.: Vibrations of the structures, Eyrolles (1988).
Handbook of Validation
V8.01 booklet: Fluid HT-66/03/008/A

Code_Aster ®
Version
6.4
Titrate:
FDLV105 - Masse added on axisymmetric piston


Date:
16/07/03
Author (S):
NR. GREFFET Key
:
V8.01.105-B Page:
4/4

3 Modeling
With

3.1
Characteristics of modeling

· Side structure:

8 machine elements axisymmetric MEAXQU4,

1 specific element of type K_T_N modelling the spring,

· fluid side:

380 thermal elements axisymmetric THAXQU4 modelling the fluid,

8 thermal elements axisymmetric THAXSE2 modelling the fluid interface/structure.

3.2
Characteristics of the grid

Side structure:
8 meshs QUAD4
Fluid side:
8 meshs SEG2
1maille POI1
320 meshs QUAD4
A number of meshs:
337



3.3 Functionalities
tested

Commands


AFFE_MODELE “AXIS”
THERMIQUE

CALC_MATR_AJOU OPTION
“MASS_AJOU”


4
Results of modeling A

4.1 Values
tested

Identification Hz
Hz
% difference
Reference
Aster
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).

Handbook of Validation
V8.01 booklet: Fluid HT-66/03/008/A

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