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Code_Aster

Version

4.0

Titrate:

FDLV100 Piston coupled to a column of incompressible fluid

Date:

12/01/98

Author (S):

G. ROUSSEAU

Key:

V8.01.100-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
V8.01.100 document

FDLV100 - Piston coupled to a column of fluid
incompressible

Summary:

This test of the field of the fluids (coupling fluid-structure) validates the calculation of mass added on modal basis and
carry out, within the framework of a modal analysis, the calculation of the Eigen frequency of a system piston-arises
coupled to a column of incompressible fluid. To modelize the fluid, thermal elements are used
plans; to modelize the piston, one uses machine elements 2D in plane deformation and an element
discrete to modelize a spring. Lastly, the fluid interface/structure is modelized by linear elements
thermics modified to introduce a boundary condition of the type “acceleration” into the fluid. The case-test
comprise only one modeling, two-dimensional. The Eigen frequency of the coupled system is found
to 0.01% of the analytical result.

Code_Aster

Version

4.0

Titrate:

FDLV100 Piston coupled to a column of incompressible fluid

Date:

12/01/98

Author (S):

G. ROUSSEAU

Key:

V8.01.100-A

Page:

2/6

Manual of Validation

V8.01 booklet: Fluid

HP-51/96/031 - Ind A

Problem of reference

1.1 Geometry

Comes out from stiffness K

With

Piston

Fluid

Steel piston connected to the solid mass by a spring and coupled to a column of incompressible fluid:

length:

L = 1.0 m

width:

D = 0.25 m

width AB of the piston:

0.05 m

X-coordinates of the points (in m):

With

0.05

1.2

Material properties

Fluid:

Water:

1000.0 Kg.m

Solid:

Steel:

7800.0 Kg.m

; E = 2.E11 AP;

= 0.3

Arises connecting the piston to the solid mass:

Discrete element of the type

K_T_D_L

: K = (1.E5, 1.E5, 1.E5) NR/m

1.3

Boundary conditions and loading

One imposes a pressure (IE by analogy thermal a null temperature [R4.07.03]) in all them
nodes of the end of the fluid column.

One imposes the embedding of the spring on the solid mass and one imposes a displacement of the null piston according to
OY.

Code_Aster

Version

4.0

Titrate:

FDLV100 Piston coupled to a column of incompressible fluid

Date:

12/01/98

Author (S):

G. ROUSSEAU

Key:

V8.01.100-A

Page:

3/6

Manual of Validation

V8.01 booklet: Fluid

HP-51/96/031 - Ind A

Reference solution

2.1

Method of calculation used for the reference solution

Analytical calculation:

When the structure vibrates in the fluid, it modifies the field of pressure which obeys an equation of
Laplace with boundary conditions of Von Neuman [R4.07.03].
In our case, taking into account symmetries of the problem, the field of pressure depends only on
variable

and checks:

X 0

= -

One notes as well as the field of pressure is a function closely connected of the X-coordinate

. Both

boundary conditions on the pressure imply:

= -

(

)

The compressive force which is exerted on the structure writes:

N N

p (0)

(

)

As the problem is unidimensional, this force can be expressed in an algebraic way according to
component of acceleration according to OX of the structure:

L D

L D X

m X

L D

has

= -

with

It is the linear mass added of the fluid on the structure: it is noticed that it corresponds to the mass
of fluid in the column, i.e. to the mass of fluid moved by the piston.
The equation of the movement of the piston projected on OX is written (free vibration not damped out taking into account
the presence of the fluid):

m X

K X

m X

K X

has

(

)

= -

The Eigen frequency of this immersed system is thus written:

has

The effect of the fluid is thus to lower the Eigen frequency of the system in air.
Practically, in Aster, the matrix of added mass is given on the basis of modal
structure in the vacuum: To calculate the added mass given above, one restricts oneself with the calculation of
clean mode of the system piston-arises which corresponds to a translatory movement normalized with the unit
: one truncates consequently the modal base of the structure to only one mode in air (operator

MODE_ITER_SIMULT

option

PLUS_PETITE).

One determines thanks to this mode the mass added on

the piston.

has

10 NR/m

200 kg/m

78 kg/m

The Eigen frequency of the system piston-arises immersed is thus

3.018 Hz

2.2

Results of reference

Analytical

2.3 References

bibliographical

[1]

R.J GIBERT - Vibrations of the Structures - Interactions with fluids. Eyrolles (1988).

Code_Aster

Version

4.0

Titrate:

FDLV100 Piston coupled to a column of incompressible fluid

Date:

12/01/98

Author (S):

G. ROUSSEAU

Key:

V8.01.100-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

Thermal formulation planes for fluid (QUAD4 and SEG2)
Plane deformation formulation and discrete for solid (QUAD4 and SEG2)

Fluid

Piston

Comes out from stiffness K

· · ·

80 elements THPLQU4

4 elements of interface THPLSE2

4 elements MEDPQU4

1 element

MECA_DIS_T_L

With

Cutting =

21 meshs QUAD4 according to the x axis
4 meshs QUAD4 according to the y axis
4 meshs SEG2 on the fluid interface/piston
1 mesh SEG2 representing the spring binding the piston to the solid mass

Boundary conditions:

DDL_IMPO: (GROUP_NO: noeupist DY: 0. )
DDL_IMPO: (GROUP_NO: embed DX: 0. DY: 0. DZ: 0.)

Name of the nodes:

GROUP_NO NOEUPIST

is consisted of the ten nodes A, B, C, D, E, F,

G, H, I, J

GROUP_NO EMBEDS

is consisted of the node K

3.2

Characteristics of the mesh

A number of nodes: 111 nodes
A number of meshs and types: 84 QUAD4, 5 SEG2

3.3 Functionalities

tested

Controls

Keys

AFFE_MODELE

“THERMAL”

“PLANE”

[U4.22.01]

CALC_MASS_AJOU

MODE_MECA

[U4.??.??]

NUME_DDL_GENE

“FULL”

STORAGE

U4.55.07]

MODE_MECA

MODE_ITER_SIMULT

“TAPE”

FREQ

U4.52.01]

concept

“matr_asse_gene_r”

COMB_MATR_ASSE

COMB_R

[U4.53.01]

concept

“matr_asse_gene_r”

Code_Aster

Version

4.0

Titrate:

FDLV100 Piston coupled to a column of incompressible fluid

Date:

12/01/98

Author (S):

G. ROUSSEAU

Key:

V8.01.100-A

Page:

5/6

Manual of Validation

V8.01 booklet: Fluid

HP-51/96/031 - Ind A

Results of modeling A

4.1 Values

tested

Identification

Reference

(Hz)

Aster

(Hz)

% difference

Command of the clean mode I: 1

3.018

3.01854

+0.018

4.2 Remarks

Calculations of modes carried out by:

MODE_ITER_SIMULT OPTION: “PLUS_PETITE” NMAX_FREQ: 1.

4.3 Parameters

of execution

Version: 3.05.24

Machine: CRAY C98

System:

UNICOS 8.0

Overall dimension memory:

8 megawords

Time CPU To use:

7.09 seconds