Code_Aster ®
Version
7.2
Titrate:
FDLV108 - Calcul of damping added in annular flow
Date:
01/03/04
Author (S):
NR. GREFFET, G. Key ROUSSEAU
:
V8.01.108-A Page:
1/6

Organization (S): EDF-R & D/AMA, EDF-DPN/UTO
Handbook of Validation
V8.01 booklet: Fluid
Document: V8.01.108

FDLV108 - Calcul of damping added in
annular flow (variable density)

Summary:

This test of the fluid-structure field implements the calculation of mass and damping added on one
cylindrical structure subjected to an annular flow which one supposes potential. One calculates mass and
damping added by the flow on the structure for a speed upstream of 4 Mr. s1, on a model 3D
for the fluid and hull for the structure. The structure has a displacement of rotation around a pivot located at
the downstream end of the cylinder compared to the flow. The interest of the test lies in the taking into account of one
fluid field of nonhomogeneous density.

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

Code_Aster ®
Version
7.2
Titrate:
FDLV108 - Calcul of damping added in annular flow
Date:
01/03/04
Author (S):
NR. GREFFET, G. Key ROUSSEAU
:
V8.01.108-A Page:
2/6

1
Problem of reference

1.1 Geometry

L
V 0
Z
nentrée
R I
1
2
nso rtie
y
R E
O
C
X
roll fixed intern
fluid
external cylinder
mobile in rotation compared to axis Cx


L = 50 m

R = 1 m
I

R = 1.1 m
E

C: not pivot of the external structure (swivelling around Cx)

1.2
Properties of materials

fluid: density 1 = 1000 kg.m3; 2 = 750 kg.m3;

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

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 model the variation of density, one forces a condition of continuity of
flow with the interface;
· 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.

Structure:

L

· one imposes on the external cylinder a displacement of the type X =
- y Z
I



with the nodes of
2
grid of this cylinder.
Handbook of Validation
V8.01 booklet: Fluid
HT-66/04/005/A

Code_Aster ®
Version
7.2
Titrate:
FDLV108 - Calcul of damping added in annular flow
Date:
01/03/04
Author (S):
NR. GREFFET, G. Key ROUSSEAU
:
V8.01.108-A Page:
3/6

2
Reference solution

2.1
Method of calculation used for the reference solution

For the calculation of the added coefficients:

one shows [bib1] that the coefficients of mass and added depreciation depend, in
each area where is constant, of the permanent potential fluid speeds as well as
two fluctuating potentials and: these potentials are written the movement in the case of of
1
2
rotation of the external cylinder around the pivot C [bib1]:



= V y

0
R2

R2

E
I

L
L

For the area relative to

R

1
=
+
y
sin
:
with X
y
1
Z
2
2
I

R - R
2
2
E
I
R
+




=
-





R2 V

R2


=
E
0
R + I sin
2
R2 - R2
E
I
R




V
= 1 0 y



2
2
R

2
R

E
I

L
L

For the area relative to

R

2
=
+
y
sin
:
1
with X
y
I
Z

2
R - 2
R
E
I
R
+


2
=
-

2

1
2
R V

2
R

=
E
0
R + I sin
2

2
2
2 R - R
E
I
R


However the added modal coefficients projected on this mode of rotation are written:

M =
X. N dS
has

1 I
external cylinder

Ca =
(+.
2
1) (Xi. N) dS
external cylinder

maybe by separating the integral on two half-cylinders:

V R2
C
0
E
2
2
2
has = -
+
1
E
2 (R
R
E
I) L
R - R
2
I

R2
L
3
M
E
2
2
has = (7 +
1
2)
+
E
2 (R
R
E
I)
R - R
3
2
I

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

Code_Aster ®
Version
7.2
Titrate:
FDLV108 - Calcul of damping added in annular flow
Date:
01/03/04
Author (S):
NR. GREFFET, G. Key ROUSSEAU
:
V8.01.108-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 =
- 2 m
L =
m
R = m
R =
m
With =
8 NR m rad -
2 10
50
1
11
4 24 10
1
.
,
.
.
S
I
2


The added mass brought by the flow is worth:

M
kg m
has = 1.614.109
2
.
(independent of the value rate of flow)

Added damping is worth with V0 = 4 Mr. s1 (it is independent of the change of mass
voluminal):

C
NR m rad S
has = -
-
0.399.109
1
.
.


Knowing that the damping of the mechanical system is worth A =
NR m rad -
4 24 108
1
.
.
S,
the total damping of the fluid system/structure is written:

· with V =
m S
8
= -
NR m rad 1
4
15 10
-
/
:
.
.
S
0


The flow does not amplify the vibrations. Structural damping interns is
sufficient important to dissipate the energy brought by the flow to the structure.
The system is still deadened.

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

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

Code_Aster ®
Version
7.2
Titrate:
FDLV108 - Calcul of damping added in annular flow
Date:
01/03/04
Author (S):
NR. GREFFET, G. Key ROUSSEAU
:
V8.01.108-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:
240 meshs QUAD4
elements of hulls MEDKQU4


For the fluid:
240 meshs QUAD4

thermal elements THER_FACE4

on cylindrical surfaces



540 meshs QUAD4

thermal elements THER_FACE4

on the faces of input, of output and interface
fluid volume



720 meshs HEXA8

thermal elements THER_HEXA8

in fluid annular volume

3.2 Functionalities
tested

Commands


CALC_MATR_AJOU OPTION
“MASS_AJOU”



“AMOR_AJOU”

4
Results of modeling A

4.1 Values
tested

Identification Reference
Aster error
(%)
Added coefficients



mass:
1.614 109
1.608 109
0.3
damping
­ 0.399 109
­ 0.393 109
0.15

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

Code_Aster ®
Version
7.2
Titrate:
FDLV108 - Calcul of damping added in annular flow
Date:
01/03/04
Author (S):
NR. GREFFET, G. Key ROUSSEAU
:
V8.01.108-A Page:
6/6

5
Summary of the results

The computational tool of damping under flow (potential assumption) was validated on the mode of
rotation of a cylindrical structure subjected to an annular flow with density
variable. It should however be noted [bib1] that the very good agreement enters the semi-analytical model
proposed for comparison and numerical calculation is obtained only if the cylinder is sufficiently
length, the semi-analytical model being makes of it only one approximate solution of the problem arising.

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

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