Code_Aster ®
Version
4.0
Titrate:
AHLV101 Guide of wave at anechoic exit
Date:
12/01/98
Author (S):
F. STIFKENS, G. ROUSSEAU
Key:
V8.22.101-A Page:
1/12
Organization (S): EDF/EP/AMV
Handbook of Validation
V8.22 booklet: Harmonic accoustics
V8.22.101 document
AHLV101 - Guide of wave at anechoic exit
Summary:
A rectilinear guide of wave at anechoic exit, with rigid walls, whose propagation medium is air
“normal”, is excited by a harmonic incidental wave, normal with the face of input. One calculates the field of
acoustic pressure of the harmonic response by using the élasto-accoustics formulation in
pressure-displacement-potential of displacements.
The tests relate to 3 different modelings (finite elements élasto-acoustics three-dimensional,
two-dimensional and axisymmetric), they make it possible to validate the matrices of rigidity, mass, impedance and
vector source for 3 modelings.
The result of reference comes from an analytical calculation.
Handbook of Validation
V8.22 booklet: Harmonic accoustics
HP-51/96/094 - Ind A
Code_Aster ®
Version
4.0
Titrate:
AHLV101 Guide of wave at anechoic exit
Date:
12/01/98
Author (S):
F. STIFKENS, G. ROUSSEAU
Key:
V8.22.101-A Page:
2/12
1
Problem of reference
1.1 Geometry
y
wave
plane
B
output
D
anechoic
O
X
.
With
C
rigid side surfaces
Z
Tube with rectangular section:
length:
L = lx = 1.0 m
height:
H = ly = 0.1 m
width:
L = lz = 0.2 m
Co-ordinates of the points (in m):
With
B
C
D
X
0.
0.
1.00
1.00
y
0.
0.05
0.
0.05
Z
0.20
0.10
0.20
0.10
1.2
Properties of materials
Air:
= 1.3 kg. m3
C = 343. Mr. s1
1.3
Boundary conditions and loading
Pressure of normal incidental wave at the entry
P = P
0 * exp
0 =
I
(I T) vec P 10 has. Pa
Frequency
F = 500 Hz
2
1
Impedance at the end CD
Z = .c =
- -
445 9
. Kg.m
S
Handbook of Validation
V8.22 booklet: Harmonic accoustics
HP-51/96/094 - Ind A
Code_Aster ®
Version
4.0
Titrate:
AHLV101 Guide of wave at anechoic exit
Date:
12/01/98
Author (S):
F. STIFKENS, G. ROUSSEAU
Key:
V8.22.101-A Page:
3/12
2
Reference solution
2.1
Method of calculation used for the reference solution
The frequencies of the excitation are rather low and jointly the guide of wave is sufficiently
length compared to its side dimensions so that one limits oneself to the plane waves: the phenomenon is
then identical in all points of a plan of wave, i.e. does not depend on the co-ordinates describing
points of this plan, y and Z for example.
One gives on this assumption the well-known general solution of the equations of accoustics for
the two sizes pressure p and acoustic speed v:
X
X
v = F T -
G
T
éq 2.1-1
C +
+
C
X
X
p = C F T -
G
T
éq 2.1-2
C -
+
C
The guide is supposed to be closed at the end of X-coordinate L on an impedance ZL; there is one
reflection on the level of this impedance, which gives a wave of return G.
In each point of the guide, there is then superposition of the two functions F and G; by definition even
final impedance ZL imposes on the point of X-coordinate L, between p and the v relation.
pL = Z
v
L
L
In the harmonic case F and G are written:
X
X
I T
F T -
I E
C
C =
X
X
I t+
G T +
R E
C
C =
where I and R are determined by the boundary conditions.
p
In the calculation of the impedance Z =
in any item X the variable time this time is eliminated,
v
in accordance with the calculation even of the impedances and is written:
X
X
- I
I
(
I E
C - R E C
Z X) = Z0
X
X
- I
I
I E
C + R E C
Handbook of Validation
V8.22 booklet: Harmonic accoustics
HP-51/96/094 - Ind A
Code_Aster ®
Version
4.0
Titrate:
AHLV101 Guide of wave at anechoic exit
Date:
12/01/98
Author (S):
F. STIFKENS, G. ROUSSEAU
Key:
V8.22.101-A Page:
4/12
The final impedance becomes:
L
L
- I
I
I E
C - R E C
Z = Z
L
0
L
L
- I
I
I E
C + R E C
One calls Z = C
0
iterative impedance.
On the fluid border at the entry of the guide the condition limits of incidental wave type imposed on
P
P I.E.(internal excitation) T
=
I
0
, is obtained by writing at the border the following linear relation:
p - C v = P
N
I
éq 2.1-3
where v =
N
v. N is the speed according to unit normal N outgoing of the fluid.
One imposes moreover on the output of the guide a value of final impedance Z = Z
L
0 which does one of them
anechoic end.
The final impedance is equal to the iterative impedance Z0 when R = 0, i.e. when there is not
no the wave of return; one then has a pure travelling wave in the direction of the incidental wave, that is to say:
X
I T
C
v = I E
X
I T
C
p = C IE
thus the relation of imposed incidental wave [éq 2.1-3] is written:
p v = (
p
=)
0 + (=)
0 = 2
I
C
X
cv X
C IE
T
N
I T
from where 2 are identified
C IE
= pi; one deduces the expression from it from the travelling wave of pressure in
guide when one imposes pi on the input of the guide:
X
X
P -
P
I T
I
I
0
C
p =
E
C =
E
2
2
Handbook of Validation
V8.22 booklet: Harmonic accoustics
HP-51/96/094 - Ind A
Code_Aster ®
Version
4.0
Titrate:
AHLV101 Guide of wave at anechoic exit
Date:
12/01/98
Author (S):
F. STIFKENS, G. ROUSSEAU
Key:
V8.22.101-A Page:
5/12
2.2
Results of reference
Pressure at the points A, B, C, D (for modelings A, B, C).
2.3
Uncertainty on the solution
Analytical solution.
2.4 References
bibliographical
[1]
F. STIFKENS “Introduction in Code_Aster of condition limits of incidental wave type in
vibroacoustic - Rapport HP-61/95/026/
Handbook of Validation
V8.22 booklet: Harmonic accoustics
HP-51/96/094 - Ind A
Code_Aster ®
Version
4.0
Titrate:
AHLV101 Guide of wave at anechoic exit
Date:
12/01/98
Author (S):
F. STIFKENS, G. ROUSSEAU
Key:
V8.22.101-A Page:
6/12
3 Modeling
With
3.1
Characteristics of modeling
Pressure-potential formulation of elements displacements “3d_FLUIDE” (MEFL_HEXA20 and
MEFL_FACE8)
y
vis-a-vis impedance
imposed
B
D
X
vis-a-vis wave
incidental imposed
C
With
Z
Cutting =
15
meshs HEXA20 according to the x axis
2
meshs HEXA20 according to the y axis
2
meshs HEXA20 according to the axis of Z
Limiting conditions:
ONDE_FLUI:
(GROUP_MA: Input
PRES: 1.0)
IMPE_FACE:
(GROUP_MA: Output
IMPE: 445.9)
Name of the nodes
With = No1
B = No780
C = No751
D = No763
3.2
Characteristics of the grid
A number of nodes:
471
A number of meshs and types:
60 HEXA20 8 QUAD8
3.3 Functionalities
tested
Commands
Keys
AFFE_MODELE
“MECANIQUE”
“3D”
GROUP_MA
[U4.22.01]
DEFI_MATERIAU
FLUIDE
RHO
[U4.23.01]
CELE_R
AFFE_CHAR_MECA
ONDE_FLUI
PRES
GROUP_MA
[U4.25.01]
IMPE_FACE
IMPE
CALC_MATR_ELEM
“RIGI_MECA”
MODELE
[U4.41.01]
“MASS_MECA”
CHAM_MATER
“IMPE_MECA”
CHARGE
“ONDE_FLUI”
CALC_VECT_ELEM
“CHAR_MECA”
MODELE
[U4.41.02]
CHAM_MATER
CHARGE
DYNA_LINE_HARM
[U4.54.02]
Handbook of Validation
V8.22 booklet: Harmonic accoustics
HP-51/96/094 - Ind A
Code_Aster ®
Version
4.0
Titrate:
AHLV101 Guide of wave at anechoic exit
Date:
12/01/98
Author (S):
F. STIFKENS, G. ROUSSEAU
Key:
V8.22.101-A Page:
7/12
4
Results of modeling A
4.1 Values
tested
Localization
Sizes
Reference
Aster
% difference
With
p (real)
0.5
0.499997
6 104
p (imag)
0.0
1.2 105
-
B
p (real)
0.5
0.499997
6 104
p (imag)
0.0
1.2 105
-
C
p (real)
0.482466
0.482352
2.4 102
p (imag)
0.131252
0.131670
3.2 101
D
p (real)
0.482466
0.482352
2.4 102
p (imag)
0.131252
0.131670
3.2 101
4.2 Parameters
of execution
Version: 3.05.10
Machine: CRAY C90
System:
UNICOS 8.0
Obstruction memory:
8 megawords
Time CPU To use:
64.08 seconds
Handbook of Validation
V8.22 booklet: Harmonic accoustics
HP-51/96/094 - Ind A
Code_Aster ®
Version
4.0
Titrate:
AHLV101 Guide of wave at anechoic exit
Date:
12/01/98
Author (S):
F. STIFKENS, G. ROUSSEAU
Key:
V8.22.101-A Page:
8/12
5 Modeling
B
5.1
Characteristics of modeling
Formulation pressure potential of elements displacements “2d_FLUIDE” (MEFLSE3 and MEFLQU8)
y
vis-a-vis
impedance
imposed
B
D
X
vis-a-vis wave
With
C
incidental imposed
Cutting =
15
meshs QUAD8 according to the x axis
2
meshs QUAD8 according to the y axis
Limiting conditions:
ONDE_FLUI:
(GROUP_MA: Input
PRES: 1.0)
IMPE_FACE:
(GROUP_MA: Output
IMPE: 445.9)
Name of the nodes
With = No1
B = NO3
C = No751
D = No153
5.2
Characteristics of the grid
A number of nodes:
125
A number of meshs and types:
30 QUAD8 4 SEG3
5.3 Functionalities
tested
Commands
Keys
AFFE_MODELE
“MECANIQUE”
“2d_FLUIDE”
GROUP_MA
[U4.22.01]
DEFI_MATERIAU
FLUIDE
RHO
[U4.23.01]
CELE_R
AFFE_CHAR_MECA
ONDE_FLUI
PRES
GROUP_MA
[U4.25.01]
IMPE_FACE
IMPE
CALC_MATR_ELEM
“RIGI_MECA”
MODELE
[U4.41.01]
“MASS_MECA”
CHAM_MATER
“IMPE_MECA”
CHARGE
“ONDE_FLUI”
CALC_VECT_ELEM
“CHAR_MECA”
MODELE
[U4.41.02]
CHAM_MATER
CHARGE
DYNA_LINE_HARM
[U4.54.02]
Handbook of Validation
V8.22 booklet: Harmonic accoustics
HP-51/96/094 - Ind A
Code_Aster ®
Version
4.0
Titrate:
AHLV101 Guide of wave at anechoic exit
Date:
12/01/98
Author (S):
F. STIFKENS, G. ROUSSEAU
Key:
V8.22.101-A Page:
9/12
6
Results of modeling B
6.1 Values
tested
Localization
Sizes
Reference
Aster
% difference
With
p (real)
0.5
0.499997
6 104
p (imag)
0.0
1.2 105
-
B
p (real)
0.5
0.499997
6 104
p (imag)
0.0
1.2 105
-
C
p (real)
0.482466
0.482352
2.4 102
p (imag)
0.131252
0.131670
3.2 101
D
p (real)
0.482466
0.482352
2.4 102
p (imag)
0.131252
0.131670
3.2 101
6.2 Parameters
of execution
Version: 3.05.10
Machine: CRAY C90
System:
UNICOS 8.0
Obstruction memory:
8 megawords
Time CPU To use:
62.57 seconds
Handbook of Validation
V8.22 booklet: Harmonic accoustics
HP-51/96/094 - Ind A
Code_Aster ®
Version
4.0
Titrate:
AHLV101 Guide of wave at anechoic exit
Date:
12/01/98
Author (S):
F. STIFKENS, G. ROUSSEAU
Key:
V8.22.101-A Page:
10/12
7 Modeling
C
7.1
Characteristics of modeling
Pressure-potential formulation of displacements elements “AXIS_FLUIDE” (MEAXFLS3 and
MEAXFLQ8)
vis-a-vis impedance
vis-a-vis wave
imposed
incidental imposed
With
C
y
B
D
X
Cutting =
15
meshs QUAD8 according to the y axis
2
meshs QUAD8 according to the x axis
Limiting conditions:
ONDE_FLUI:
(GROUP_MA: Input
PRES: 1.0)
IMPE_FACE:
(GROUP_MA: Output
IMPE: 445.9)
Name of the nodes
With = No1
B = NO3
C = No151
D = No153
7.2
Characteristics of the grid
A number of nodes:
125
A number of meshs and types:
30 QUAD8 4 SEG3
7.3 Functionalities
tested
Commands
Keys
AFFE_MODELE
“MECANIQUE”
“AXIS_FLUIDE”
GROUP_MA
[U4.22.01]
DEFI_MATERIAU
FLUIDE
RHO
[U4.23.01]
CELE_R
AFFE_CHAR_MECA
ONDE_FLUI
PRES
GROUP_MA
[U4.25.01]
IMPE_FACE
IMPE
CALC_MATR_ELEM
“RIGI_MECA”
MODELE
[U4.41.01]
“MASS_MECA”
CHAM_MATER
“IMPE_MECA”
CHARGE
“ONDE_FLUI”
CALC_VECT_ELEM
“CHAR_MECA”
MODELE
[U4.41.02]
CHAM_MATER
CHARGE
DYNA_LINE_HARM
[U4.54.02]
Handbook of Validation
V8.22 booklet: Harmonic accoustics
HP-51/96/094 - Ind A
Code_Aster ®
Version
4.0
Titrate:
AHLV101 Guide of wave at anechoic exit
Date:
12/01/98
Author (S):
F. STIFKENS, G. ROUSSEAU
Key:
V8.22.101-A Page:
11/12
8
Results of modeling C
8.1 Values
tested
Localization
Sizes
Reference
Aster
% difference
With
p (real)
0.5
0.499997
6 104
p (imag)
0.0
1.2 105
-
B
p (real)
0.5
0.499997
6 104
p (imag)
0.0
1.2 105
-
C
p (real)
0.482466
0.482352
2.4 102
p (imag)
0.131252
0.131670
3.2 101
D
p (real)
0.482466
0.482352
2.4 102
p (imag)
0.131252
0.131670
3.2 101
8.2 Parameters
of execution
Version: 3.05.12
Machine: CRAY C98
System:
UNICOS 8.0
Obstruction memory:
8 megawords
Time CPU To use:
62.77 seconds
Handbook of Validation
V8.22 booklet: Harmonic accoustics
HP-51/96/094 - Ind A
Code_Aster ®
Version
4.0
Titrate:
AHLV101 Guide of wave at anechoic exit
Date:
12/01/98
Author (S):
F. STIFKENS, G. ROUSSEAU
Key:
V8.22.101-A Page:
12/12
9
Summary of the results
The discretization is strong since it is approximately 45 nodes by wavelength. This is why us
let us obtain results of a high precision: pressure calculated by Code_Aster at the point it
less favorable differs from the theoretical value from less than 1%.
It should be also noted that all modelings used give identical results.
Handbook of Validation
V8.22 booklet: Harmonic accoustics
HP-51/96/094 - Ind A