Code_Aster ®
Version
7.2
Titrate:
FDLV109 - Calcul of coefficients added in plane flow
Date:
01/03/04
Author (S):
NR. GREFFET, G. Key ROUSSEAU
:
V8.01.109-A Page:
1/6

Organization (S): EDF-R & D/AMA, EDF-DPN/UTO
Handbook of Validation
V8.01 booklet: Fluid
Document: V8.01.109

FDLV109 - Calcul of coefficients added in
plane flow

Summary:

This test of the fluid field/structure implements the calculation of mass, rigidity and damping added on
a plane structure subjected to a confined flow which one supposes potential. These added coefficients are
calculated for a speed upstream of 4 Mr. s1, on a model 3D for the fluid and hull for the structure.
structure is subjected to an imposed displacement of inflection.

Handbook of Validation
V8.01 booklet: Fluid
HT-66/04/005/A

Code_Aster ®
Version
7.2
Titrate:
FDLV109 - Calcul of coefficients added in plane flow
Date:
01/03/04
Author (S):
NR. GREFFET, G. Key ROUSSEAU
:
V8.01.109-A Page:
2/6

1
Problem of reference

1.1 Geometry

L
V0
X
Z
y
N
nsortie
input
O
L
E
fluid


L = 50 m

I = 5 m

thickness of fluid E = 0.5 m

thickness of the plate H = 0.5 m

E
the Oxyz reference mark is at a distance from
plate
2

1.2
Properties of materials

Fluid: density = 1000 kg.m3 (water).

Structure: = 7800 kg/m3; E = 2.1 1011 Pa; = 0.3 (steel).
S

1.3
Boundary conditions and loadings

Fluid:

· to simulate the permanent flow, one forces on the face of input of the fluid a speed
normal of ­ 4 m/s (by thermal analysis, one imposes a normal heat flow equivalent
of ­ 4),
· to calculate the fluid disturbance brought by the movement of the external cylinder one forces
a boundary condition of Dirichlet in a node of the fluid.
E
· one imposes in X =
the condition = = which corresponds to a null flow through
2
1
2
0
higher fluid wall.

Structure:

· the plate is subjected to a displacement corresponding to its the first two modes of
inflection [bib2]:

y
2y
X = sin
; X
1
= sin

L
2
L
Handbook of Validation
V8.01 booklet: Fluid
HT-66/04/005/A

Code_Aster ®
Version
7.2
Titrate:
FDLV109 - Calcul of coefficients added in plane flow
Date:
01/03/04
Author (S):
NR. GREFFET, G. Key ROUSSEAU
:
V8.01.109-A Page:
3/6

2
Reference solution

2.1
Method of calculation used for the reference solution

For the calculation of the added coefficients:

it is shown [bib1] that the coefficients of mass and added depreciation depend on
permanent potential fluid speeds as well as two fluctuating potentials and
1
2: these
potentials are in the case of written the movement of inflection of the plate [bib1]:


()
1 =

V y
0
() 1
E
y
For the first mode:

= X -
sin

1


2

L
() V
E
y
1
0


2 =
X -
cos
L
2

L


(2)

=

V y
0
(2)
E
2y
For the second mode:

= X -

sin

1


2

L
(2)
V
2
E
2 y


0


2 =
X -
cos
L
2

L

However the added modal coefficients projected on these modes of inflection are written:

has
(I)
M =
X. N dS
ij

1
J
external cylinder
has
(I)
(I)
(I)
Cij =

.
.

external cylinder (
+

2
1) (X J N) dS
has
(I)
(I)
Kij =

.
.
external cylinder (
2) (X J N) dS


that is to say:

L
M has = M has = el
; M has
11
22
12 = 0
2
8
Ca = Ca = 0; Ca = Ca = - elV
11
22
12
21
0

3
2
L
2
2 L
K has = - eV 2
; K has = - eV 2
; K has
11
0
= 0
2L
22
0
L
12
Handbook of Validation
V8.01 booklet: Fluid
HT-66/04/005/A

Code_Aster ®
Version
7.2
Titrate:
FDLV109 - Calcul of coefficients added in plane flow
Date:
01/03/04
Author (S):
NR. GREFFET, G. Key ROUSSEAU
:
V8.01.109-A Page:
4/6

· Numerical applications:

One made a calculation of added damping which corresponds for the speed given to one
deadened vibratory behavior of the structure:

V0 speed to 4 Mr. s1

The values of the mechanical system are:

E = H =
-
510 1
.
m
L = 50m
L = 5 m

The added mass brought by the flow is worth:

M has
5
= 0 625
.
10

kg
11
M has
5
= 0 625
.
10

kg
22

M a12 = 0

Added damping is worth with V0 = 4 Mr. s1:

Ca11 = 0
Ca22 = 0

Ca
5
= 0 266
.
10 N.m 1
-
12

The added stiffness is worth with V0 = 4 Mr. s1:

K has
4
= 0
- 3943
.
10 N.m 1
- rad 2
11
K has
5
= - 01577
.
10 N.m 1
- rad 2
22

K a12 = 0

2.2
Results of reference

Analytical result.

2.3 References
bibliographical

[1]
ROUSSEAU G., LUU H.T.: Mass, damping and stiffness added for a structure
vibrating placed in a potential flow - Bibliographie and establishment in
Code_Aster - HP-61/95/064
[2]
BLEVINS R.D: Formulated for natural frequency and shape mode. ED. Krieger 1984

Handbook of Validation
V8.01 booklet: Fluid
HT-66/04/005/A

Code_Aster ®
Version
7.2
Titrate:
FDLV109 - Calcul of coefficients added in plane flow
Date:
01/03/04
Author (S):
NR. GREFFET, G. Key ROUSSEAU
:
V8.01.109-A Page:
5/6

3 Modeling
With

3.1
Characteristics of modeling

For the system 3D on which one calculates the added coefficients:

For the solid:
160 meshs QUAD4
elements of hulls MEDKQU4


For the fluid:
160 meshs QUAD4

elements thermics THER_FACE4

on the plane surface



184 meshs QUAD4

thermal elements THER_FACE4

on the faces of input and output of fluid volume



480 meshs HEXA8

thermal elements THER_HEXA8

in fluid volume

3.2 Functionalities
tested

Commands


CALC_MATR_AJOU OPTION
“MASS_AJOU”

MACRO_MATR_AJOU OPTION
MATR_AMOR_AJOU



MATR_RIGI_AJOU


MODE_ITER_SIMULT OPTION
“BANDE”



4
Results of modeling A

4.1 Values
tested

Identification Reference
Aster %
difference
M has
0.625 105 0.624
105 0.1
11
M has
0.625 105 0.621
105 0.6
22
M has
0 0.6
10­6 -
12
Ca
0 ­ 0.81
10­6 -
11
Ca
0 ­ 0.68
10­6 -
22
Ca
0.266 105 0.265
105 0.3
12
K has
­ 0.394 104 ­ 0.394
104 0.0
11
K has
­ 0.157 105 ­ 0.157
105 0.0
22
K has
0 ­ 0.134
10­5 -
12
Handbook of Validation
V8.01 booklet: Fluid
HT-66/04/005/A

Code_Aster ®
Version
7.2
Titrate:
FDLV109 - Calcul of coefficients added in plane flow
Date:
01/03/04
Author (S):
NR. GREFFET, G. Key ROUSSEAU
:
V8.01.109-A Page:
6/6

5
Summary of the results

The computational tool of coefficients added under flow (potential assumption) was validated on
the first two modes of inflection of a plane structure. It should however be noted [bib1] that the very maid
agreement between the semi-analytical model suggested for comparison and numerical calculation is not
obtained that if the plate is sufficiently long, the semi-analytical model being does only one of them
approximate solution of the problem arising.

Handbook of Validation
V8.01 booklet: Fluid
HT-66/04/005/A

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