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
Organization (S): EDF/RNE/AMV
Handbook 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 grid finite elements to simulate the infinite one in direct transitory calculations.
Are used they to model 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.
Handbook of Validation
V8.01 booklet: Fluid HT-62/01/012/A
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
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 model
that a vertical section (see diagram).
Z
X
Piston
Acoustic fluid
Surface absorbing
Section case 3D:
Section case 2D:
Z
y
1.2
Properties of materials
Piston: concrete
Acoustic fluid: water
Density:
2400 kg.m3
Density:
1000 kg.m3
Young modulus:
3,6.1010 Pa
Celerity:
1500 Mr. s1
Poisson's ratio: 0,48
Handbook of Validation
V8.01 booklet: Fluid HT-62/01/012/A
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
1.3
Boundary conditions and loadings
One has on side surface of the column the elements fluid-structure which one blocks 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
1,00E+00
9,00E-01
8,00E-01
)
m 7,00E-01
6,00E-01
5,00E-01
4,00E-01
3,00E-01
Displacement (2,00E-01
1,00E-01
0,00E+00
- 0,1
0,1
0,3
0,5
0,7
0,9
1,1
1,3
1,5
Time (S)
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 incidence. 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 grid, 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.
Handbook of Validation
V8.01 booklet: Fluid HT-62/01/012/A
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
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 grid
and refined).
Pressure in the fluid - case 3D
8,00E+03
6,00E+03
4,00E+03
2,00E+03
0,00E+00
0,00E+00
5,00E-01
1,00E+00
1,50E+00
2,00E+00
2,50E+00
- 2,00E+03
Pressure (Pa)
- 4,00E+03
- 6,00E+03
- 8,00E+03
Time (S)
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
0,00E+00
5,00E-01
1,00E+00
1,50E+00
2,00E+00
2,50E+00
Pressure (Pa) - 2,00E+03
- 3,00E+03
- 4,00E+03
- 5,00E+03
Time (S)
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 grid.
Handbook of Validation
V8.01 booklet: Fluid HT-62/01/012/A
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
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).
Handbook of Validation
V8.01 booklet: Fluid HT-62/01/012/A
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
3
Modeling a: case 3D
3.1
Characteristics of modeling
Piston: PHENOMENE: “MECANIQUE”
MODELISATION: “3D”
Fluid: PHENOMENE: “MECANIQUE”
MODELISATION: “3d_FLUIDE”
3.2
Characteristics of the grid
A number of nodes: 54
A number of meshs and types: 20 HEXA8
40 QUA4 (faces of HEXA8)
Node 47
201 m
Node 16
50 m
Node 18
3.3 Functionalities
tested
Commands
AFFE_MODELE AFFE
MODELISATION
3d_FLUI_ABSO
DYNA_LINE_TRAN
DYNA_NON_LINE
Handbook of Validation
V8.01 booklet: Fluid HT-62/01/012/A
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
3.4 Values
tested
One tests the values of the pressure to nodes 16, 18 and 47 (see grid). 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
Results of
Variations reference -
Code_Aster
reference
calculation with
(Pa Pressure)
(Pa Pressure
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
ABSOLU
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
Results of
Variations reference -
Code_Aster
reference
calculation with
(Pa Pressure)
(Pa Pressure
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
ABSOLU
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
Handbook of Validation
V8.01 booklet: Fluid HT-62/01/012/A
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
4
Modeling b: case 2D
4.1
Characteristics of modeling
Piston: PHENOMENE: “MECANIQUE”
MODELISATION: “D_PLAN”
Fluid: PHENOMENE: “MECANIQUE”
MODELISATION: “2d_FLUIDE”
4.2
Characteristics of the grid
25 m
51 m
Node 7
Node 10
A number of nodes: 35
A number of meshs and types: 24 QUA4
18 SEG2 (faces of QUA4)
4.3 Functionalities
tested
Commands
AFFE_MODELE AFFE
MODELISATION
2d_FLUI_ABSO
DYNA_LINE_TRAN
DYNA_NON_LINE
Handbook of Validation
V8.01 booklet: Fluid HT-62/01/012/A
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
4.4 Values
tested
One tests the values of the pressure to nodes 7 and 10 (see grid). 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
Results of
Variations reference -
Code_Aster
reference
calculation with
(Pa Pressure)
(Pa Pressure
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
ABSOLU
N7 3.86000E01
4.89074E+03
NON_REGRESSION NON_REGRESSION
·
DYNA_NON_LINE:
Node
Moment (S)
Calculation with
Results of
Variations reference -
Code_Aster
reference
calculation with
(Pa Pressure)
(Pa Pressure
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
ABSOLU
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
Handbook of Validation
V8.01 booklet: Fluid HT-62/01/012/A
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
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 step 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 step of
time used with DYNA_LINE_TRAN is sufficiently small.
Handbook of Validation
V8.01 booklet: Fluid HT-62/01/012/A
Outline document