FDNV100 - Shaking dun tank deau with elastic deformable wall

Code_Aster

Version

7.3

Titrate:

FDNV100 Shaking of a water tank with elastic deformable wall

Date:

04/10/04

Author (S):

NR. GREFFET

Key

V8.03.100-A

Page:

1/8

Manual of Validation

V8.03 booklet: Nonlinear fluid

HT-66/04/005/A

Organization (S):

EDF-R & D/AMA

Manual of Validation
V8.03 booklet: Nonlinear fluid
Document: V8.03.100

FDNV100 - Shaking 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.

Code_Aster

Version

7.3

Titrate:

FDNV100 Shaking of a water tank with elastic deformable wall

Date:

04/10/04

Author (S):

NR. GREFFET

Key

V8.03.100-A

Page:

2/8

Manual of Validation

V8.03 booklet: Nonlinear fluid

HT-66/04/005/A

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 the 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:

1.2

Properties of materials

The fluid (water) contents in the tank has as characteristics:

density:

= 1000 kg/m

speed of sound:

C = 1500 m/s

The deformable wall is elastic linear (duralumin):

density:

= 2787 kg/m

Young modulus:

E = 62,43 Gpa

Poisson's ratio:

= 0,35

y=10cm

=23,1cm

x=19,1cm

z=18,2cm

12,9cm

fluid field

free face

Deformable plate

N3119

N145

free face

MELT

: bottom of

fluid field

FONDP

: segment of straight line

intersection of the bottom (

MELT

) and of

the vertical deformable plate

Code_Aster

Version

7.3

Titrate:

FDNV100 Shaking of a water tank with elastic deformable wall

Date:

04/10/04

Author (S):

NR. GREFFET

Key

V8.03.100-A

Page:

3/8

Manual of Validation

V8.03 booklet: Nonlinear fluid

HT-66/04/005/A

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.

Code_Aster

Version

7.3

Titrate:

FDNV100 Shaking of a water tank with elastic deformable wall

Date:

04/10/04

Author (S):

NR. GREFFET

Key

V8.03.100-A

Page:

4/8

Manual of Validation

V8.03 booklet: Nonlinear fluid

HT-66/04/005/A

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 the 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
mesh: 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

Code_Aster

Version

7.3

Titrate:

FDNV100 Shaking of a water tank with elastic deformable wall

Date:

04/10/04

Author (S):

NR. GREFFET

Key

V8.03.100-A

Page:

5/8

Manual of Validation

V8.03 booklet: Nonlinear fluid

HT-66/04/005/A

3 Modeling

With

3.1

Characteristics of modeling

MESH CASE TEST 2D_FLUI_PESA

The total mesh comprises 8163 nodes, that is to say approximately 125000 ddls,

The specific element Q (modeling

DIS_TR

) allows to represent one simply

accelerometer present in the model of the article [bib1],

The deformable plate is modelized by 5120 elements of massive solid (modeling

)

pentaedric with 6 nodes (10 layers in the thickness for a good approximation of
behavior in bending in spite of the linearity of the elements),

the free face is modelized by 512 elements

MEFP_FACE3

(modeling

2d_FLUI_PESA

)

triangles with 3 nodes,

fluid volume is modelized by 24576 elements of fluid (modeling

3d_FLUIDE

)

tetrahedral with 4 nodes.

Modeling

solid

Modeling

2d_FLUI_PESA

Modeling

3d_FLUIDE

On each immersed side
deformable plate:
modeling

FLUI_STRU

Modeling

DIST_TR

Code_Aster

Version

7.3

Titrate:

FDNV100 Shaking of a water tank with elastic deformable wall

Date:

04/10/04

Author (S):

NR. GREFFET

Key

V8.03.100-A

Page:

6/8

Manual of Validation

V8.03 booklet: Nonlinear fluid

HT-66/04/005/A

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,

GRAVITY

(9.81,

0.,

1.));

3.3

Characteristics of the mesh

The mesh contains:

24575

TETRA4

5120

PENTA6

4096

TRIA3

3.4 Functionalities

tested

Controls

AFFE_MODELE MODELING

“FLUI_STRU”

AFFE_MODELE MODELING

“2d_FLUI_PESA”

AFFE_CHAR_MECA GRAVITY

DYNA_NON_LINE

Code_Aster

Version

7.3

Titrate:

FDNV100 Shaking of a water tank with elastic deformable wall

Date:

04/10/04

Author (S):

NR. GREFFET

Key

V8.03.100-A

Page:

7/8

Manual of Validation

V8.03 booklet: Nonlinear fluid

HT-66/04/005/A

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

2.10e-14

DX (N145, t=1,4 S)

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