Code_Aster
®
Version
4.0
Titrate:
ADLV101 Modes of shaking of a tank filled with water
Date:
17/05/99
Author (S):
G. ROUSSEAU, Fe WAECKEL
Key:
V8.21.101-A
Page:
1/10
Manual of Validation
V8.21 booklet: Modal accoustics
HP-51/99/011 - Ind A
Organization (S):
EDF/EP/AMV
Manual of Validation
V8.21 booklet: Modal accoustics
Document: V8.21.101
ADLV101 - Modes of shaking of a tank
filled of water
Summary:
This test, of the acoustic and fluid field, relates to the search of the Eigen frequencies of a tank
rectangular filled of a fluid including/understanding a free face. The modal analysis determines the first thus
modes of shaking of the surface of the fluid filling the tank. The first three Eigen frequencies are
found with less than 1% of the analytically calculated frequencies.
Code_Aster
®
Version
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Titrate:
ADLV101 Modes of shaking of a tank filled with water
Date:
17/05/99
Author (S):
G. ROUSSEAU, Fe WAECKEL
Key:
V8.21.101-A
Page:
2/10
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V8.21 booklet: Modal accoustics
HP-51/99/011 - Ind A
1
Problem of reference
1.1 Geometry
free face
H
L
L
dimensions of the tank:
height: H = 0.3 m
length: L = 0.8 m
width: L = 0.1 m
1.2
Properties of materials
The modelized material is the fluid contained in the tank:
density:
C
= 1000 kg/m
3
speed of sound:
C
= 1400 m/s
1.3
Boundary conditions and loading
One imposes the field of gravity on the whole of the fluid model
charge = AFFE_CHAR_MECA
(
…
GRAVITY: (9.81, 0., 0., 1.));
Code_Aster
®
Version
4.0
Titrate:
ADLV101 Modes of shaking of a tank filled with water
Date:
17/05/99
Author (S):
G. ROUSSEAU, Fe WAECKEL
Key:
V8.21.101-A
Page:
3/10
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V8.21 booklet: Modal accoustics
HP-51/99/011 - Ind A
2
Reference solution
2.1
Method of calculation used for the reference solution
The reference [bib3] provides the general formula of the modes of shaking in a tank
parallelepipedic:
F
G it jl HT H it jl
ij
=
+
+
1
2
2
2
2
2
2
2
2
2
where
I
and
J
are the commands of the longitudinal and transverse modes (a number of nodal lines in
each direction).
In the particular case or
-
L
L
is large, the formula is simplified for the longitudinal modes [bib1],
[bib2].
2.2
Results of reference
For
L
L
H
=
=
8
0 3
.
.
and
the first four modes are at frequencies 0.898, 1.384, 1.709 and 1.975.
2.3 References
bibliographical
[1]
WAECKEL F., LEPOUTERE C. Note internal EDF/DER “Effect of gravity on surface
free of a fluid coupled to a structure ", HP-61/93/139.
[2]
MUTO, KASA, NAKAHARA, Experimental ISHIDA “tests one sloshing response off has toilets pool
with submerged blocks " - ASME, flight PVP 98, (1985).
[3]
BLEVINS R.D. Formulas for natural frequency and shape mode. ED Krieger
Code_Aster
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Version
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Titrate:
ADLV101 Modes of shaking of a tank filled with water
Date:
17/05/99
Author (S):
G. ROUSSEAU, Fe WAECKEL
Key:
V8.21.101-A
Page:
4/10
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V8.21 booklet: Modal accoustics
HP-51/99/011 - Ind A
3 Modeling
With
3.1
Characteristics of modeling
MEFL_QUAD4
H
L
MEFP_FACE4
L
·
the free face is modelized by 57 elements
MEFP_FACE4
(modeling
2d_FLUI_PESA
)
quadrangle with 4 nodes,
·
fluid volume is modelized by 513 elements of fluid (modeling
3d_FLUIDE
) cubic
with 8 nodes.
3.2
Characteristics of the mesh
The mesh contains:
513
HEXA8
57
QUAD4
3.3 Functionalities
tested
Controls
Keys
AFFE_CHAR_MECA
GRAVITY
[U4.25.01]
AFFE_MODELE
MODELING
“2d_FLUI_PESA”
[U4.22.01]
Code_Aster
®
Version
4.0
Titrate:
ADLV101 Modes of shaking of a tank filled with water
Date:
17/05/99
Author (S):
G. ROUSSEAU, Fe WAECKEL
Key:
V8.21.101-A
Page:
5/10
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V8.21 booklet: Modal accoustics
HP-51/99/011 - Ind A
4
Results of modeling A
4.1 Values
tested
Identification
Reference
Aster
% difference
mode1
8.98250e-01
8.99460e-01
0.135
mode 2
1.38452e+00
1.39010e+00
0.403
mode 3
1.70952e+00
1.72406e+00
0.851
mode 4
1.97551e+00
2.00526e+00
1.506
4.2 Parameters
of execution
Version: 5.02
Machine: Origin 2000
Overall dimension memory:
8 MW
Time CPU to use:
5.13 seconds
Code_Aster
®
Version
4.0
Titrate:
ADLV101 Modes of shaking of a tank filled with water
Date:
17/05/99
Author (S):
G. ROUSSEAU, Fe WAECKEL
Key:
V8.21.101-A
Page:
6/10
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HP-51/99/011 - Ind A
5 Modeling
B
5.1
Characteristics of modeling
This modeling differs from modeling A only by the type of free element of face and by
type of element of fluid:
·
the free face is modelized by 57 elements MEFP_FACE8 (modeling 2d_FLUI_PESA)
quadrangle with 8 nodes,
·
fluid volume is modelized by 513 elements of fluid (modeling 3d_FLUIDE) cubic
with 20 nodes.
5.2
Characteristics of the mesh
the mesh contains:
513 HEXA20
57 QUAD8
5.3 Functionalities
tested
Controls
Key word factor
Key word
Argument
Keys
AFFE_CHAR_MECA
GRAVITY
[U4.25.01]
AFFE_MODELE
AFFE
MODELING
“2d_FLUI_PESA”
[U4.22.01]
AFFE
MODELING
“3d_FLUIDE”
MODE_ITER_INV
CALC_FREQ
OPTION
“NEAR”
[U4.52.01]
6
Results of modeling B
6.1 Values
tested
Identification
Reference
Aster
% difference
mode1
8.98250e-01
8.98252e-01
0.000
mode 2
1.38452e+00
1.38452e+00
0.000
mode 3
1.70952e+00
1.70958e+00
0.003
mode 4
1.97551e+00
1.97569e+00
0.009
6.2 Parameters
of execution
Version: 5.02
Machine: Origin 2000
Overall dimension memory:
8 MW
Time CPU to use:
34. seconds
Code_Aster
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Version
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Titrate:
ADLV101 Modes of shaking of a tank filled with water
Date:
17/05/99
Author (S):
G. ROUSSEAU, Fe WAECKEL
Key:
V8.21.101-A
Page:
7/10
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V8.21 booklet: Modal accoustics
HP-51/99/011 - Ind A
7 Modeling
C
7.1
Characteristics of modeling
This modeling differs from modeling A only by the type of free element of face and by
type of element of fluid:
·
the free face is modelized by 57 elements MEFP_FACE9 (modeling 2d_FLUI_PESA)
quadrangle with 9 nodes,
·
fluid volume is modelized by 513 elements of fluid (modeling 3d_FLUIDE) cubic
with 27 nodes.
7.2
Characteristics of the mesh
the mesh contains:
513 HEXA27
57 QUAD9
7.3 Functionalities
tested
Controls
Key word factor
Key word
Argument
Keys
AFFE_CHAR_MECA
GRAVITY
[U4.25.01]
AFFE_MODELE
AFFE
MODELING
“2d_FLUI_PESA”
[U4.22.01]
AFFE
MODELING
“3d_FLUIDE”
MODE_ITER_INV
CALC_FREQ
OPTION
“NEAR”
[U4.52.01]
8
Results of modeling C
8.1 Values
tested
Identification
Reference
Aster
% difference
mode1
8.98250e-01
8.98252e-01
0.000
mode 2
1.38452e+00
1.38452e+00
0.000
mode 3
1.70952e+00
1.70957e+00
0.003
mode 4
1.97551e+00
1.97569e+00
0.009
8.2 Parameters
of execution
Version: 5.02
Machine: Origin 2000
Overall dimension memory:
8 MW
Time CPU to use:
64.85 seconds
Code_Aster
®
Version
4.0
Titrate:
ADLV101 Modes of shaking of a tank filled with water
Date:
17/05/99
Author (S):
G. ROUSSEAU, Fe WAECKEL
Key:
V8.21.101-A
Page:
8/10
Manual of Validation
V8.21 booklet: Modal accoustics
HP-51/99/011 - Ind A
9 Modeling
D
9.1
Characteristics of modeling
This modeling differs from modeling A by the type of element used. Each mesh of
modeling A is cut into two by a vertical plane.
·
the free face is modelized by 114 elements MEFP_FACE3 (modeling
2d_FLUI_PESA) triangle with 3 nodes,
·
fluid volume is modelized by 1026 elements of fluid (modeling 3d_FLUIDE)
pentaedric with 6 nodes.
9.2
Characteristics of the mesh
the mesh contains:
1026 PENTA6
114 TRIA3
9.3 Functionalities
tested
Controls
Key word factor
Key word
Argument
Keys
AFFE_CHAR_MECA
GRAVITY
[U4.25.01]
AFFE_MODELE
AFFE
MODELING
“2d_FLUI_PESA”
[U4.22.01]
AFFE
MODELING
“3d_FLUIDE”
MODE_ITER_INV
CALC_FREQ
OPTION
“NEAR”
[U4.52.01]
10
Results of modeling D
10.1 Values
tested
Identification
Reference
Aster
% difference
mode 1
8.98250e-01
8.99450e-01
0.134
mode 2
1.38452e+00
1.39004e+00
0.399
mode 3
1.70952e+00
1.72387e+00
0.839
mode 4
1.97551e+00
2.00473e+00
1.479
10.2 Parameters
of execution
Version: 5.02
Machine: Origin 2000
Overall dimension memory:
8 MW
Time CPU to use:
5.52 seconds
Code_Aster
®
Version
4.0
Titrate:
ADLV101 Modes of shaking of a tank filled with water
Date:
17/05/99
Author (S):
G. ROUSSEAU, Fe WAECKEL
Key:
V8.21.101-A
Page:
9/10
Manual of Validation
V8.21 booklet: Modal accoustics
HP-51/99/011 - Ind A
11 Modeling
E
11.1 Characteristics of modeling
This modeling differs from modeling B by the type of element used. Each mesh of
modeling B is cut by a vertical plane.
·
the free face is modelized by 114 elements MEFP_FACE6 (modeling
2d_FLUI_PESA) triangle with 6 nodes,
·
fluid volume is modelized by 1026 elements of fluid (modeling 3d_FLUIDE)
pentaedric with 15 nodes.
11.2 Characteristics of the mesh
the mesh contains:
1026 PENTA15
114 TRIA6
11.3 Functionalities
tested
Controls
Key word factor
Key word
Argument
Keys
AFFE_CHAR_MECA
GRAVITY
[U4.25.01]
AFFE_MODELE
AFFE
MODELING
“2d_FLUI_PESA”
[U4.22.01]
AFFE
MODELING
“3d_FLUIDE”
MODE_ITER_INV
CALC_FREQ
OPTION
“NEAR”
[U4.52.01]
12
Results of modeling E
12.1 Values
tested
Identification
Reference
Aster
% difference
mode 1
8.98250e-01
8.98252e-01
0.000
mode 2
1.38452e+00
1.38452e+00
0.000
mode 3
1.70952e+00
1.70957e+00
0.003
mode 4
1.97551e+00
1.97569e+00
0.009
12.2 Parameters
of execution
Version: 5.02
Machine: Origin 2000
Overall dimension memory:
8 MW
Time CPU to use:
44.17 seconds
Code_Aster
®
Version
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Titrate:
ADLV101 Modes of shaking of a tank filled with water
Date:
17/05/99
Author (S):
G. ROUSSEAU, Fe WAECKEL
Key:
V8.21.101-A
Page:
10/10
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V8.21 booklet: Modal accoustics
HP-51/99/011 - Ind A
13
Summary of the results
Modeling A implements elements of fluid of the type HEXA8 and elements of surface
free of type QUAD4. The result obtained reveals a maximum error of 1.52% compared to
analytical solution.
Modeling B utilizes elements of fluid of the type HEXA20 and elements of surface
free of type QUAD8. The results correlate perfectly with the analytical solution.
Elements fluid of the type HEXA27 and fluid weighing of type QUAD9 are used for
modeling C. the results obtained are identical to the reference solution.
Modeling D makes it possible to validate elements fluid of the type PENTA6 and elements of surface
free of type TRIA3. The results obtained reveal a relative error of 1.479% compared to
the reference solution.
Modeling E makes it possible to validate the elements of free face of type TRIA6. They are connected to
elements of fluid of the type PENTA15. There is perfect coincidence of the results with the solution
analytical.
Generally, it is observed that the results obtained by elements with interpolation
quadratic (HEXA20, HEXA27) are in excellent agreement with the analytical results. Nevertheless
the elements with linear interpolation have an acceptable precision on the results.