Code_Aster ®
Version
7.3
Titrate:
FDNV100 Ballottement of a water tank with deformable wall elastic Date:
04/10/04
Author (S):
NR. GREFFET Key
:
V8.03.100-A Page:
1/8
Organization (S): EDF-R & D/AMA
Handbook of Validation
V8.03 booklet: Nonlinear fluid
Document: V8.03.100
FDNV100 - Ballottement of a water tank with
elastic deformable wall
Summary:
This test, of the fluid-structure field, proposes the implementation of a transitory dynamic calculation (operator
DYNA_NON_LINE) with taking into account of a free face. Being given the absence of values of reference
adapted, it is about a case-test of nonregression.
Handbook of Validation
V8.03 booklet: Nonlinear fluid
HT-66/04/005/A
Code_Aster ®
Version
7.3
Titrate:
FDNV100 Ballottement of a water tank with deformable wall elastic Date:
04/10/04
Author (S):
NR. GREFFET Key
:
V8.03.100-A Page:
2/8
1
Problem of reference
This case-test, based on the model of the article [bib1], aims to test the correct taking into account
of a free face in a calculation fluid-structure coupled with operator DYNA_NON_LINE.
1.1 Geometry
One considers a parallelepipedic tank, filled with water, whose external walls are
indeformable. This rigid tank comprises a deformable internal plate, named. It is
embedded at its base at the bottom of the tank, its sides vertical being free. This flexible wall exceeds
free face a 12,9 cm height:
Deformable plate
Q
Z
free face
12,9cm
free face
N3119
N145
fluid field
FONDP
: segment of straight line
intersection of bottom (FONDS) and of
z=18,2cm
the vertical deformable plate
y
x=19,1cm
X
FONDS: bottom of
r=23,1cm
fluid field
y=10cm
X
1.2
Properties of materials
The fluid (water) contents in the tank has as characteristics:
density:
F = 1000 kg/m3
speed of sound:
C = 1500 m/s
The deformable wall is elastic linear (duralumin):
density:
S = 2787 kg/m3
Young modulus:
E = 62,43 Gpa
Poisson's ratio:
= 0,35
Handbook of Validation
V8.03 booklet: Nonlinear fluid
HT-66/04/005/A
Code_Aster ®
Version
7.3
Titrate:
FDNV100 Ballottement of a water tank with deformable wall elastic Date:
04/10/04
Author (S):
NR. GREFFET Key
:
V8.03.100-A Page:
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1.3
Boundary conditions and loading
1.3.1 Conditions of Dirichlet
The loading defined here is of the displacement type imposed on a surface. More precisely, one
consider that the bottom of the tank can move only according to direction X.
According to this direction X, one will request the system by imposing on the bottom of the tank a displacement
sinusoidal in time, of frequency 1,7704 Hz and amplitude 0,001 Mr.
This imposed displacement can be compared to a stress of the mono-support type applied by
base tank (seismic application).
1.3.2 Conditions of Neumann
In superposition in the surface condition of Dirichlet previously defined, one subjects also it
model with the field of gravity (imposed voluminal effort).
Lastly, the upper surface of the fluid field is seen characterized by conditions of the type surfaces
free.
Handbook of Validation
V8.03 booklet: Nonlinear fluid
HT-66/04/005/A
Code_Aster ®
Version
7.3
Titrate:
FDNV100 Ballottement of a water tank with deformable wall elastic Date:
04/10/04
Author (S):
NR. GREFFET Key
:
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2
Reference solution
2.1
Method of calculation used for the reference solution
The only results of the literature [bib1] are modal types: Eigen frequencies and paces of
certain modes.
Being given the need for testing operator DYNA_NON_LINE, and being given relative complexity
model which is 3D, it is not possible to find the Eigen frequencies by transitory analysis
in a reasonable time CPU.
For information, this type of analysis carried out with a random loading corresponding to a noise
white requires, for reasons of probabilistic convergence, a calculation for a physical time of
loading of 250 S, which corresponds to a time CPU of a few hours.
In order to have a calculating time about a few minutes, it is obligatory to calculate the evolution
over a time runs (a few seconds). This restrictive framework does not make it possible to find precisely
and in a way compatible with a postprocessing automated the results of modal analysis.
The validation brought by this test can thus be only of the type not regression of the solution
numerical.
As the functionalities of calculation coupled fluid-structure are the subject already of a certain number of
tests of validation in addition, this limitation with nonthe regression for this particular case-test is not
crippling.
As complementary validation, complete calculation with signal of 250 S.A. carried out.
spectra at the points of observations indeed showed a good agreement with the results
of modal analysis of [bib1].
2.2
Results of reference
One tests values of displacements at various moments, according to direction X, for two points of
grid: N145 and N3119. These points are on the free face, on both sides of the wall
deformable, as one can see it on the diagram of the paragraph [§1.1].
2.3
Uncertainty on the solution
Numerical solution (calculated with version 7.03.06 of the code).
2.4 Reference
bibliographical
[1]
BERMUDEZ A., RODRIGUEZ R., SANTAMARINA D.: “Finite element computation off
sloshing modes in containers with elastic baffle punts ", Int. J. Numer. Meth. In Engrg., Flight.
56, 447-467, 2003
Handbook of Validation
V8.03 booklet: Nonlinear fluid
HT-66/04/005/A
Code_Aster ®
Version
7.3
Titrate:
FDNV100 Ballottement of a water tank with deformable wall elastic Date:
04/10/04
Author (S):
NR. GREFFET Key
:
V8.03.100-A Page:
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3 Modeling
With
3.1
Characteristics of modeling
Modeling 2d_FLUI_PESA
Modeling
DIST_TR
Q
Modeling
solid 3D
On each immersed side
deformable plate:
modeling FLUI_STRU
Modeling
3d_FLUIDE
GRID CASE TEST 2D_FLUI_PESA
· The total grid comprises 8163 nodes, that is to say approximately 125000 ddls,
· The specific element Q (modeling DIS_TR) makes it possible to represent one simply
accelerometer present in the model of the article [bib1],
· The deformable plate is modelled by 5120 elements of massive solid (modeling 3D)
pentaedric with 6 nodes (10 layers in the thickness for a good approximation of
behavior in inflection in spite of the linearity of the elements),
· the free face is modelled by 512 elements MEFP_FACE3 (modeling 2d_FLUI_PESA)
triangles with 3 nodes,
· fluid volume is modelled by 24576 elements of fluid (modeling 3d_FLUIDE)
tetrahedral with 4 nodes.
Handbook of Validation
V8.03 booklet: Nonlinear fluid
HT-66/04/005/A
Code_Aster ®
Version
7.3
Titrate:
FDNV100 Ballottement of a water tank with deformable wall elastic Date:
04/10/04
Author (S):
NR. GREFFET Key
:
V8.03.100-A Page:
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3.2
Writing of the boundary conditions
The bottom of the tank can move only according to direction X:
CONDLIM=AFFE_CHAR_MECA (
MODELE=MODELE,
DDL_IMPO= (_F (
GROUP_NO= (“FUNDS”, “FONDP”,),
DY=0.0,
DZ=0.0,),),);
According to this direction X, one imposes on the bottom of the tank a sinusoidal displacement in time, of
frequency 1,7704 Hz and of amplitude 0,001 m:
FREQ
=
1.7704;
LFONC=DEFI_LIST_REEL (DEBUT=0.0,
INTERVALLE=_F (
JUSQU_A=10.0,
PAS=0.01,),);
FONC = FORMULA (REAL = ''' (REAL:INST) =
(0.001) * SIN (2 * PI * FREQ * INST) ''');
DEPLX=CALC_FONC_INTERP (
FONCTION=FONC,
NOM_PARA=' INST',
LIST_PARA=LFONC,);
CHARG_SE=AFFE_CHAR_MECA_F (
MODELE=MODELE,
DDL_IMPO=_F (
GROUP_NO= (“FUNDS”, “FONDP”,), DX=DEPLX,),);
The voluminal loading of gravity is defined as follows:
PESA=AFFE_CHAR_MECA (
MODELE=MODELE,
PESANTEUR
:
(9.81,
0.,
0.,
1.));
3.3
Characteristics of the grid
The grid contains:
24575 TETRA4
5120
PENTA6
4096
TRIA3
3.4 Functionalities
tested
Commands
AFFE_MODELE MODELING
“FLUI_STRU”
AFFE_MODELE MODELING
“2d_FLUI_PESA”
AFFE_CHAR_MECA GRAVITY
DYNA_NON_LINE
Handbook of Validation
V8.03 booklet: Nonlinear fluid
HT-66/04/005/A
Code_Aster ®
Version
7.3
Titrate:
FDNV100 Ballottement of a water tank with deformable wall elastic Date:
04/10/04
Author (S):
NR. GREFFET Key
:
V8.03.100-A Page:
7/8
4
Results of modeling A
4.1 Values
tested
The tests are done on the value of displacement following X (noted DX) for various moments and for
nodes N145 and N3119.
Identification Reference
Aster %
difference
DX (N145, t=0,8 S)
5.1624169321991e-04
5.1624169321991e-04
2.10e-14
DX (N145, t=1,4 S)
1.4970110314375e-04
1.4970110314375e-04
- 2.63e-12
DX (N145, t=2,0 S)
- 2.3927413131721e-04
- 2.3927413131721e-04
- 2.32e-12
DX (N3119, t=1,0 S)
- 9.9736272860105e-04
- 9.9736285773823e-04
- 1.74e-13
DX (N3119, t=1,6 S)
- 8.7855056121762e-04
- 8.7855056121762e-04
1.73e-13
DX (N3119, t=2,0 S)
- 2.3929161952584e-04
- 2.3929161952584e-04
4.98e-13
Handbook of Validation
V8.03 booklet: Nonlinear fluid
HT-66/04/005/A
Code_Aster ®
Version
7.3
Titrate:
FDNV100 Ballottement of a water tank with deformable wall elastic Date:
04/10/04
Author (S):
NR. GREFFET Key
:
V8.03.100-A Page:
8/8
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Handbook of Validation
V8.03 booklet: Nonlinear fluid
HT-66/04/005/A
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