Code_Aster
®
Version
6.4
Titrate:
FDLL200 - Piping embedded and free by beam fluid-structure
Date:
08/07/03
Author (S):
F. STIFKENS, G. DEVESA
Key
:
V8.21.200-A
Page:
1/6
Manual of Validation
V8.21 booklet: Accoustics HT-66/03/008/A
Organization (S):
EDF-R & D/AMA
Manual of Validation
V8.21 booklet: Accoustics
Document: V8.21.200
FDLL200 - Piping embedded and free by beam
fluid-structure
Summary:
The objective is to calculate the low frequency behavior of a piping filled with water. Piping has
a circular section; it is embedded at an end and free other side.
One uses the elements of beam élasto-accoustics available in Code_Aster which take into account
the fluid interaction structure (
PHENOMENON = “MECHANICAL”, MODELING = “FLUI_STRU”
).
The boundary conditions are mechanical to simulate the embedding of the structure, and accoustics for
to simulate the condition of tank of the fluid in this point (boundary conditions of null pressure and potential of
fluid displacement no one).
The fluid which one considers is a heavy fluid in order to put forward the phenomenon of coupling enters
the column of fluid and the structure constitutive of piping. Properties of the fluid and material of
structure are selected so that the celerity of a wave being propagated in the fluid is the same one as
celerity of a mechanical wave being propagated in piping. Under these conditions, first mode of
structure resounds at the same frequency as the column of fluid.
An exact analytical solution exists which provides the first Eigen frequency. Its comparison with
results produced by Code_Aster (search for eigenvalues) makes it possible to validate the taking into account of
fluid coupling structure in the longitudinal direction, the transverse effects being non-existent in this model.
One tests thus partially the matrix of stiffness and that of mass.
Code_Aster
®
Version
6.4
Titrate:
FDLL200 - Piping embedded and free by beam fluid-structure
Date:
08/07/03
Author (S):
F. STIFKENS, G. DEVESA
Key
:
V8.21.200-A
Page:
2/6
Manual of Validation
V8.21 booklet: Accoustics HT-66/03/008/A
1
Problem of reference
1.1 Geometry
Piping is a hollow roll with circular section, filled with fluid.
Characteristics of piping:
length: L = 1,0 m
external diameter: D = 0,1 m
thickness: ep = 0,01 m
1.2
Properties of materials
The physical characteristics of material constituting the tube are as follows:
Young modulus:
E
= 1,0·10
10
AP
Poisson's ratio:
= 0,3
density:
S
= 1,0·10
4
kg/m
3
celerity longitudinal wave:
=
=
S
S
C
E
1,0·10
3
m/s
The physical characteristics of fluid material in the tube are as follows:
density:
F
= 1,0·10
3
kg/m
3
speed of sound:
F
C
= 1,0·10
3
m/s
1.3
Boundary conditions and loading
Displacement only according to the x axis.
Embedding of piping in end A.
Free piping in the end B.
For the fluid condition of tank in end A.
Code_Aster
®
Version
6.4
Titrate:
FDLL200 - Piping embedded and free by beam fluid-structure
Date:
08/07/03
Author (S):
F. STIFKENS, G. DEVESA
Key
:
V8.21.200-A
Page:
3/6
Manual of Validation
V8.21 booklet: Accoustics HT-66/03/008/A
2
Reference solution
2.1
Method of calculation used for the reference solution
One studies the vibratory behavior of a piping filled with fluid. Piping is embedded with
one of its ends and free at the other end. The section of piping is circular. One
be interested in the low frequencies of the longitudinal behavior of piping.
One defines:
length of the tube:
L,
Young modulus of the pipe:
E,
diameter external of the pipe:
D,
thickness of the walls:
ep,
surface of the solid section:
S
S
,
surface of the fluid section:
S
F
celerity in the pipe (structure):
C
S
,
celerity in the fluid:
C
F
,
One chose the characteristics of the fluid and the pipe in order to have the following relation:
m/s
1000
C
C
S
S
F
=
=
=
=
C
E
In this particular case of equality of celerities, one shows [bib2] that the first Eigen frequency of
coupled problem is such as:
2
.
tg
C
E
S
S
C
L
F
F
S
S
=
It is worth in this case: F = 157,94 Hz
2.2
Results of reference
Only one modeling is used. The calculation of the modes is in formulation U, p,
.
2.3
Uncertainty of the solution
Analytical solution.
2.4 References
bibliographical
[1]
WAECKEL F., DUVAL C.: Note principle and of use of the pipes
implemented in Code_Aster. Note intern R & D HP-61/92.138
[2]
DUVAL C.: Dynamic response under random excitation in Code_Aster. Note intern
R & D HP-61/92.148
Code_Aster
®
Version
6.4
Titrate:
FDLL200 - Piping embedded and free by beam fluid-structure
Date:
08/07/03
Author (S):
F. STIFKENS, G. DEVESA
Key
:
V8.21.200-A
Page:
4/6
Manual of Validation
V8.21 booklet: Accoustics HT-66/03/008/A
3 Modeling
With
3.1
Characteristics of modeling
The modeling of the beams élasto-acoustics is in formulation U,
, p,
.
It is carried out by the assignment on meshs of the type SEG2 (segments with 2 nodes) of elements
PHENOMENON = “MECHANICAL”, MODELING = “FLUI_STRU”
.
One assigns to the elements the characteristics of circular section:
external radius
R
ext.
= 0,100 m
thickness
ep = 0,010 m
cf [§1.1]
One also assigns to these elements a mixed material of behavior at the same time
ELAS
:
Young modulus
E = 1,0.1010 AP
Poisson's ratio
= 0,3
density
S
= 1000 kg/m
3
and
FLUID
:
celerity
C = 1000 m/s
density
F
= 1000 kg/m
3
cf [§1.2]
Degrees of freedom (DDL) of translation in y and Z (
DY
and
DZ
) and all DDL of rotation (
DRX
,
DRY
and
DRZ
) of all the nodes are locked.
In order to embed end A of piping, one also locks the DDL of translation in X (
DX
) of
node NO1.
For the fluid the condition of tank at end A is imposed by
NEAR: 0.
and
PHI: 0.
with
node NO1.
3.2
Characteristics of the mesh
The total number of nodes used for this mesh is 26.
The meshs are 25 and of type
SEG2
.
The file of mesh is with the format
ASTER
.
3.3 Calculation
One wishes to validate the elements of beam élasto-accoustics.
One carries out the calculation of the frequency of the first axial mode coupled with the operator
MODE_ITER_SIMULT
.
3.4 Functionalities
tested
Controls
MECHANICAL AFFE_MODELE
FLUI_STRU
FLUID DEFI_MATERIAU
ELAS
RHO, CELE_R
AFFE_CHAR_MECA
DDL_IMPO
DX, DY…
NEAR, PHI
MODE_ITER_SIMULT
Code_Aster
®
Version
6.4
Titrate:
FDLL200 - Piping embedded and free by beam fluid-structure
Date:
08/07/03
Author (S):
F. STIFKENS, G. DEVESA
Key
:
V8.21.200-A
Page:
5/6
Manual of Validation
V8.21 booklet: Accoustics HT-66/03/008/A
4
Results of modeling A
4.1 Values
tested
The test relates to the frequency of the first coupled axial mode of piping containing a fluid.
The tolerance of relative variation compared to the analytical value is worth 0,1%.
Number of the mode
Analytical value
Computed value
Relative variation
1 157,93981
Hz
Value not regression
157,94539 Hz
+ 0,004%
Test of nonregression of the code:
the tolerance of relative variation compared to the reference is worth 0,1%
4.2 Notice
The values of reference are at the same time the analytical values and also those obtained by
Code_Aster during the restitution of the case-test, which will thus make it possible to check nonthe regression
later of the code during its evolution.
Code_Aster
®
Version
6.4
Titrate:
FDLL200 - Piping embedded and free by beam fluid-structure
Date:
08/07/03
Author (S):
F. STIFKENS, G. DEVESA
Key
:
V8.21.200-A
Page:
6/6
Manual of Validation
V8.21 booklet: Accoustics HT-66/03/008/A
5
Summary of the results
It is noted that the computed value of the frequency of the first coupled axial mode reproduced very
exactly the analytical value with a relative precision of 0.004%.