Code_Aster
®
Version
7.2
Titrate:
FDLV108 - Calculation of damping added in annular flow
Date:
01/03/04
Author (S):
NR. GREFFET, G. ROUSSEAU
Key
:
V8.01.108-A
Page:
1/6
Manual of Validation
V8.01 booklet: Fluid
HT-66/04/005/A
Organization (S):
EDF-R & D/AMA, EDF-DPN/UTO
Manual of Validation
V8.01 booklet: Fluid
Document: V8.01.108
FDLV108 - Calculation 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. S
1
, 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.
Code_Aster
®
Version
7.2
Titrate:
FDLV108 - Calculation of damping added in annular flow
Date:
01/03/04
Author (S):
NR. GREFFET, G. ROUSSEAU
Key
:
V8.01.108-A
Page:
2/6
Manual of Validation
V8.01 booklet: Fluid
HT-66/04/005/A
1
Problem of reference
1.1 Geometry
Z
y
X
V
0
fluid
L
roll fixed intern
external cylinder
mobile in rotation compared to axis Cx
R
I
R
E
N
input
N
exit
1
2
C
O
L
= 50 m
R
I
= 1 m
R
E
= 1.1 m
C
: not pivot of the external structure (swivelling around Cx)
1.2
Properties of materials
fluid: density
1
= 1000 kg.m
3
;
2
= 750 kg.m
3
;
Structure:
S
= 7800 kg/m
3
;
E
= 2.1 10
11
AP;
= 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 transfer rate equivalent
of 4);
· to modelize 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:
· one imposes on the external cylinder a displacement of the type
X
Z
I
L
y
=
-
2
with the nodes of
mesh of this cylinder.
Code_Aster
®
Version
7.2
Titrate:
FDLV108 - Calculation of damping added in annular flow
Date:
01/03/04
Author (S):
NR. GREFFET, G. ROUSSEAU
Key
:
V8.01.108-A
Page:
3/6
Manual of Validation
V8.01 booklet: Fluid
HT-66/04/005/A
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, permanent potential fluid speeds
as well as
two fluctuating potentials
1
2
and
: these potentials are written the movement in the case of of
rotation of the external cylinder around the pivot C [bib1]:
For the area relative to
1
:
=
=
-
+
+
=
-
=
-
+
V y
R
R
R
R
R
R
y
L
L
y
R V
R
R
R
R
R
E
E
I
I
I
E
E
I
I
0
1
2
2
2
2
2
2 0
2
2
2
2
2
sin
sin
with
X
Z
For the area relative to
2
:
=
=
-
+
+
=
-
=
-
+
1 0
2
1
2
2
2
2
2
1
2
2 0
2
2
2
2
2
V y
R
R
R
R
R
R
y
L
L
y
R V
R
R
R
R
R
E
E
I
I
I
E
E
I
I
sin
sin
with
X
Z
However the added modal coefficients projected on this mode of rotation are written:
(
) (
)
M
dS
C
dS
has
I
has
I
=
=
+
1
2
1
X
N
X
N
external cylinder
external cylinder
.
.
.
maybe by separating the integral on two half-cylinders:
(
)
(
)
(
)
C
V R
R
R
R
R
L
M
R
R
R
R
R
L
has
E
E
I
E
I
has
E
E
I
E
I
= -
-
+
=
+
-
+
1
0
2
2
2
2
2
2
1
2
2
2
2
2
2
3
7
3
Code_Aster
®
Version
7.2
Titrate:
FDLV108 - Calculation of damping added in annular flow
Date:
01/03/04
Author (S):
NR. GREFFET, G. ROUSSEAU
Key
:
V8.01.108-A
Page:
4/6
Manual of Validation
V8.01 booklet: Fluid
HT-66/04/005/A
· Numerical applications:
One made a calculation of added damping which corresponds for the speed given to one
deadened vibratory behavior of the structure:
speed
V
0
to 4 Mr. S
1
The values of the mechanical system are:
E
m
L
m
R
m
R
m
With
NR m rad S
I
=
=
=
=
=
-
-
2 10
50
1
11
4 24 10
2
2
8
1
.
,
.
.
The added mass brought by the flow is worth:
M
kg m
has
= 1614 10
9
2
.
(independent of the value rate of flow)
Added damping is worth with
V
0
= 4 Mr. S
1
(it is independent of the change of mass
voluminal):
C
NR m rad S
has
= -
-
0.399 10
9
1
.
.
Knowing that the damping of the mechanical system is worth
With
NR m rad S
=
-
4 24 10
8
1
.
.
,
the total damping of the fluid system/structure is written:
· with
V
m S
NR m rad S
0
8
1
4
15 10
=
= -
-
/
:
.
.
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 - Bibliography and establishment in
Code_Aster - HP-61/95/064
Code_Aster
®
Version
7.2
Titrate:
FDLV108 - Calculation of damping added in annular flow
Date:
01/03/04
Author (S):
NR. GREFFET, G. ROUSSEAU
Key
:
V8.01.108-A
Page:
5/6
Manual of Validation
V8.01 booklet: Fluid
HT-66/04/005/A
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 exit and interface
fluid volume
720 meshs HEXA8
thermal elements THER_HEXA8
in fluid annular volume
3.2 Functionalities
tested
Controls
CALC_MATR_AJOU OPTION
“MASS_AJOU”
“AMOR_AJOU”
4
Results of modeling A
4.1 Values
tested
Identification Reference
Aster error
(%)
Added coefficients
mass:
damping
1.614 10
9
0.399 10
9
1.608 10
9
0.393 10
9
0.3
0.15
Code_Aster
®
Version
7.2
Titrate:
FDLV108 - Calculation of damping added in annular flow
Date:
01/03/04
Author (S):
NR. GREFFET, G. ROUSSEAU
Key
:
V8.01.108-A
Page:
6/6
Manual of Validation
V8.01 booklet: Fluid
HT-66/04/005/A
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.