Code_Aster
®
Version
5.0
Titrate:
FDLV111 Absorption of a wave of pressure in a fluid column
Date:
09/10/01
Author (S):
G. DEVESA, V. TO MOW
Key
:
V8.01.111-A
Page:
1/10
Manual of Validation
V8.01 booklet: Fluid HT-62/01/012/A
Organization (S):
EDF/RNE/AMV
Manual of Validation
V8.01 booklet: Fluid
Document: V8.01.111
FDLV111 - Absorption of a wave of pressure in
a fluid column
Summary:
One tests the fluid paraxial elements of command 1 intended to apply conditions absorbing to the border
of a mesh finite elements to simulate the infinite one in direct transitory calculations.
Are used they to modelize an infinite fluid column, in 3D or 2D, in which one creates a wave of
pressure using a piston. One is interested in nonthe reflection of the wave at the “infinite” end of the column.
One tests successively the two direct transitory operators of Code_Aster, namely DYNA_LINE_TRAN and
DYNA_NON_LINE.
Code_Aster
®
Version
5.0
Titrate:
FDLV111 Absorption of a wave of pressure in a fluid column
Date:
09/10/01
Author (S):
G. DEVESA, V. TO MOW
Key
:
V8.01.111-A
Page:
2/10
Manual of Validation
V8.01 booklet: Fluid HT-62/01/012/A
1
Problem of reference
1.1 Geometry
The system considered in the case 3D is that of a column of fluid with square section and of a piston
of the same section animated of a rigid movement of body according to the axis of the column. Side surface
column consists of a motionless rigid guide. One places the elements absorbents on the face
opposed to the piston to simulate the infinite character of the column in this direction. In the case 2D,
the principle is identical with a very broad supposed column and a piston which one does not modelize
that a vertical section (see diagram).
Section case 3D:
Section case 2D:
1.2
Properties of materials
Piston: concrete
Acoustic fluid: water
Density:
2400 kg.m
3
Density:
1000 kg.m
3
Young modulus:
3,6.10
10
AP
Celerity:
1500 Mr. S
1
Poisson's ratio: 0,48
Piston
Acoustic fluid
Surface absorbing
X
Z
y
Z
Code_Aster
®
Version
5.0
Titrate:
FDLV111 Absorption of a wave of pressure in a fluid column
Date:
09/10/01
Author (S):
G. DEVESA, V. TO MOW
Key
:
V8.01.111-A
Page:
3/10
Manual of Validation
V8.01 booklet: Fluid HT-62/01/012/A
1.3
Boundary conditions and loadings
One has on side surface of the column the elements fluid-structure which one locks the ddl
displacements with zero to reproduce the condition of rigid wall.
One imposes on all the nodes of the face of the piston in contact with the fluid a displacement according to X
with the function of following temporal excitation:
Displacement of the piston according to X
0,00E+00
1,00E-01
2,00E-01
3,00E-01
4,00E-01
5,00E-01
6,00E-01
7,00E-01
8,00E-01
9,00E-01
1,00E+00
- 0,1
0,1
0,3
0,5
0,7
0,9
1,1
1,3
1,5
Time (S)
Displacement (
m
)
1.4 Conditions
initial
The displacement of the piston is null at the initial moment and the fluid is at rest.
2
Reference solution
The solution must show the absorption of an acoustic wave by absorbing surface. The movement
piston is a uniform translation according to the x axis. Taking into account the symmetry of the problem
around this axis, one will obtain an identical field of pressure in all the plans X = Cte. Moreover,
the absorbing border is orthogonal with this axis. One thus studies the absorption of waves of pressure
plane under normal angle of attack. The theory [bib1] known as that with a fluid paraxial border of command 1,
this absorption is perfect. It is what one must check with this reference solution.
One thus goes, by observing the evolution of the pressure in a given point of the mesh, to stick to
to find in the signal obtained the duration of excitation and the return at rest after the passage of the wave,
characteristic of its absorption.
Code_Aster
®
Version
5.0
Titrate:
FDLV111 Absorption of a wave of pressure in a fluid column
Date:
09/10/01
Author (S):
G. DEVESA, V. TO MOW
Key
:
V8.01.111-A
Page:
4/10
Manual of Validation
V8.01 booklet: Fluid HT-62/01/012/A
2.1
Results of reference
One gives in this paragraph the results obtained with Code_Aster in this configuration. One
check that they are satisfactory and one takes them as reference for the future.
They concern, for the case 3D, the evolution of pressure in a point of the fluid located at 150 m of the piston
in direction X and in the center of the section in the yz plan. For the case 2D, the point is located at 40 m
piston according to X and in the middle of the section in the direction y (in 2D, one takes a shorter mesh
and refined).
Pressure in the fluid - case 3D
- 8,00E+03
- 6,00E+03
- 4,00E+03
- 2,00E+03
0,00E+00
2,00E+03
4,00E+03
6,00E+03
8,00E+03
0,00E+00
5,00E-01
1,00E+00
1,50E+00
2,00E+00
2,50E+00
Time (S)
Pressure (AP)
Pressure in the fluid - case 2D
- 5,00E+03
- 4,00E+03
- 3,00E+03
- 2,00E+03
- 1,00E+03
0,00E+00
1,00E+03
2,00E+03
3,00E+03
4,00E+03
5,00E+03
0,00E+00
5,00E-01
1,00E+00
1,50E+00
2,00E+00
2,50E+00
Time (S)
Pressure (AP)
As envisaged, the width of the signal measured in both cases is identical to that of the function
of excitation. Physically, one observes well compression due to advanced piston, then
depression corresponding to its retreat to return to its initial position. One notes also clearly
the return at rest immediately after the passage of the wave and the absence of signal thought of
the end of the mesh.
Code_Aster
®
Version
5.0
Titrate:
FDLV111 Absorption of a wave of pressure in a fluid column
Date:
09/10/01
Author (S):
G. DEVESA, V. TO MOW
Key
:
V8.01.111-A
Page:
5/10
Manual of Validation
V8.01 booklet: Fluid HT-62/01/012/A
2.2 Uncertainties
It is about a numerical result of the study. The qualitative forecasts are found. Values
numerical are related to the precision of calculation. Only the return at rest is clearly given by
analysis.
2.3 References
bibliographical
[1]
B. ENGQUIST, A. MAJDA “Absorbing boundary conditions for the numerical simulation off
waves. “ Mathematics off Computation (1977).
Code_Aster
®
Version
5.0
Titrate:
FDLV111 Absorption of a wave of pressure in a fluid column
Date:
09/10/01
Author (S):
G. DEVESA, V. TO MOW
Key
:
V8.01.111-A
Page:
6/10
Manual of Validation
V8.01 booklet: Fluid HT-62/01/012/A
3
Modeling a: case 3D
3.1
Characteristics of modeling
Piston: PHENOMENON: “MECHANICAL”
MODELING: “3D”
Fluid: PHENOMENON: “MECHANICAL”
MODELING: “3d_FLUIDE”
3.2
Characteristics of the mesh
3.3 Functionalities
tested
Controls
AFFE_MODELE AFFE
MODELING
3d_FLUI_ABSO
DYNA_LINE_TRAN
DYNA_NON_LINE
201 m
50 m
A number of nodes: 54
A number of meshs and types: 20 HEXA8
40 QUA4 (faces of HEXA8)
Node 16
Node 18
Node 47
Code_Aster
®
Version
5.0
Titrate:
FDLV111 Absorption of a wave of pressure in a fluid column
Date:
09/10/01
Author (S):
G. DEVESA, V. TO MOW
Key
:
V8.01.111-A
Page:
7/10
Manual of Validation
V8.01 booklet: Fluid HT-62/01/012/A
3.4 Values
tested
One tests the values of the pressure to nodes 16, 18 and 47 (see mesh). For node 16, one tests
the two maximum ones (compression and depression) and the return at rest. For nodes 18 and 47, one tests
the maximum in compression.
·
DYNA_LINE_TRAN:
Node
Moment (S)
Calculation with
Code_Aster
(AP Pressure)
Results of
reference
(AP Pressure
Variations reference -
calculation with
Code_Aster (%)
N16 4.71250D01 7.13737D+03
NON_REGRESSION
NON_REGRESSION
7.27500D01
7.08305D+03
NON_REGRESSION
NON_REGRESSION
1.27375D+00 0.182
0.
0.182
ABSOLUTE
N18 4.71250D01 7.13737D+03
NON_REGRESSION
NON_REGRESSION
N47 3.72500E01 7.09321E+03
NON_REGRESSION NON_REGRESSION
·
DYNA_NON_LINE:
Node
Moment (S)
Calculation with
Code_Aster
(AP Pressure)
Results of
reference
(AP Pressure
Variations reference -
calculation with
Code_Aster (%)
N16 4.71000E01 7.11473E+03
NON_REGRESSION NON_REGRESSION
7.26000E01
7.00022E+03
NON_REGRESSION NON_REGRESSION
1.20000E+00 37.5
0.
37.5
ABSOLUTE
N18 4.71000E01 7.11473E+03
NON_REGRESSION NON_REGRESSION
N47 3.72000E01 7.08110E+03
NON_REGRESSION NON_REGRESSION
3.5 Parameters
of execution
Version: 5.2.16
Machine: SGI ORIGIN 2000 (claster)
Time CPU: 300
Memory: 64 Mo
Code_Aster
®
Version
5.0
Titrate:
FDLV111 Absorption of a wave of pressure in a fluid column
Date:
09/10/01
Author (S):
G. DEVESA, V. TO MOW
Key
:
V8.01.111-A
Page:
8/10
Manual of Validation
V8.01 booklet: Fluid HT-62/01/012/A
4
Modeling b: case 2D
4.1
Characteristics of modeling
Piston: PHENOMENON: “MECHANICAL”
MODELING: “D_PLAN”
Fluid: PHENOMENON: “MECHANICAL”
MODELING: “2d_FLUIDE”
4.2
Characteristics of the mesh
A number of nodes: 35
A number of meshs and types: 24 QUA4
18 SEG2 (faces of QUA4)
4.3 Functionalities
tested
Controls
AFFE_MODELE AFFE
MODELING
2d_FLUI_ABSO
DYNA_LINE_TRAN
DYNA_NON_LINE
25 m
51 m
Node 10
Node 7
Code_Aster
®
Version
5.0
Titrate:
FDLV111 Absorption of a wave of pressure in a fluid column
Date:
09/10/01
Author (S):
G. DEVESA, V. TO MOW
Key
:
V8.01.111-A
Page:
9/10
Manual of Validation
V8.01 booklet: Fluid HT-62/01/012/A
4.4 Values
tested
One tests the values of the pressure to nodes 7 and 10 (see mesh). For node 10, one tests them
two maximum (compression and depression) and the return at rest. For node 7, one tests the maximum
in compression.
·
DYNA_LINE_TRAN:
Node
Moment (S)
Calculation with
Code_Aster
(AP Pressure)
Results of
reference
(AP Pressure
Variations reference -
calculation with
Code_Aster (%)
N10 3.86000E01 4.88962E+03
NON_REGRESSION NON_REGRESSION
6.37000E01
4.93961E+03
NON_REGRESSION NON_REGRESSION
1.15600E+00 0.434
0.
0.434
ABSOLUTE
N7 3.86000E01
4.89074E+03
NON_REGRESSION NON_REGRESSION
·
DYNA_NON_LINE:
Node
Moment (S)
Calculation with
Code_Aster
(AP Pressure)
Results of
reference
(AP Pressure
Variations reference -
calculation with
Code_Aster (%)
N10 3.84000E01 4.87451E+03
NON_REGRESSION NON_REGRESSION
6.44000E01
4.88583E+03
NON_REGRESSION NON_REGRESSION
1.09400E+00
3.1
0.
3.1
ABSOLUTE
N7 3.84000E01 4.88877E+03
NON_REGRESSION NON_REGRESSION
4.5 Parameters
of execution
Version: 5.2.16
Machine: SGI ORIGIN 2000
Time CPU: 500
Memory: 64 Mo
Code_Aster
®
Version
5.0
Titrate:
FDLV111 Absorption of a wave of pressure in a fluid column
Date:
09/10/01
Author (S):
G. DEVESA, V. TO MOW
Key
:
V8.01.111-A
Page:
10/10
Manual of Validation
V8.01 booklet: Fluid HT-62/01/012/A
5
Summary of the results
One finds by calculation with two modelings qualitatively, the maximum ones of pressure with
good moments and the return at rest after the passage of the wave.
The results obtained with operators DYNA_LINE_TRAN and DYNA_NON_LINE are very close.
The difference comes from obtaining to each pitch in time from the state from balance from the efforts from the second
member with operator DYNA_NON_LINE. This difference remains however tiny because the pitch of
time used with DYNA_LINE_TRAN is sufficiently small.