Code_Aster
®
Version
7.2
Titrate:
FDLV109 - Calculation of coefficients added in plane flow
Date:
01/03/04
Author (S):
NR. GREFFET, G. ROUSSEAU
Key
:
V8.01.109-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: V8.01.109
FDLV109 - Calculation 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. S
1
, on a model 3D for the fluid and hull for the structure.
structure is subjected to an imposed displacement of bending.
Code_Aster
®
Version
7.2
Titrate:
FDLV109 - Calculation of coefficients added in plane flow
Date:
01/03/04
Author (S):
NR. GREFFET, G. ROUSSEAU
Key
:
V8.01.109-A
Page:
2/6
Manual of Validation
V8.01 booklet: Fluid
HT-66/04/005/A
1
Problem of reference
1.1 Geometry
fluid
y
X
Z
N
input
N
exit
L
V
0
L
E
O
L
= 50 m
I
= 5 m
thickness of fluid E = 0.5 m
thickness of the plate H = 0.5 m
the Oxyz reference mark is at a distance from
E
2
plate
1.2
Properties of materials
Fluid: density
= 1000 kg.m
3
(water).
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 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.
· one imposes in
X
E
= 2
the condition
1
2
0
=
=
who corresponds to a null flow through
higher fluid wall.
Structure:
· the plate is subjected to a displacement corresponding to its the first two modes of
bending
[bib2]:
X
y
L
X
y
L
1
2
2
=
=
sin
sin
;
Code_Aster
®
Version
7.2
Titrate:
FDLV109 - Calculation of coefficients added in plane flow
Date:
01/03/04
Author (S):
NR. GREFFET, G. ROUSSEAU
Key
:
V8.01.109-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:
it is shown [bib1] that the coefficients of mass and added depreciation depend on
permanent potential fluid speeds
as well as two fluctuating potentials
1
2
and
: these
potentials are in the case of written the movement of bending of the plate [bib1]:
For the first mode:
()
()
()
1
1
21
=
=
-
=
-
V y
X E
y
L
V
L
X E
y
L
0
0
1
2
2
sin
cos
For the second mode:
()
()
()
2
2
22
=
=
-
=
-
V y
X E
y
L
V
L
X E
y
L
0
0
1
2
2
2
2
2
sin
cos
However the added modal coefficients projected on these modes of bending are written:
()
()
()
()
(
)
(
)
()
()
(
)
(
)
M
dS
C
dS
K
dS
ija
I
J
ija
I
I
I
J
ija
I
I
J
=
=
+
=
1
2
X
N
X
N
X
N
external cylinder
external cylinder
external cylinder
.
.
.
.
.
1
2
that is to say:
M
M
el L
M
C
C
C
C
elV
K
eV
L
L
K
eV
L
L
K
has
has
has
has
has
has
has
has
has
has
11
22
12
11
22
12
21
0
11
02
2
22
02
2
12
2
0
0
8
3
2
2
0
=
=
=
=
=
=
= -
= -
= -
=
;
;
;
;
Code_Aster
®
Version
7.2
Titrate:
FDLV109 - Calculation of coefficients added in plane flow
Date:
01/03/04
Author (S):
NR. GREFFET, G. ROUSSEAU
Key
:
V8.01.109-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 H
m
L
m
L
m
= =
=
=
-
510
50
5
1
.
The added mass brought by the flow is worth:
M
kg
M
kg
M
has
has
has
11
5
22
5
12
0.625 10
0.625 10
0
=
=
=
.
.
Added damping is worth with
V
0
= 4 Mr. S
1
:
C
C
C
NR m
has
has
has
11
22
12
5
1
0
0
0.266 10
=
=
=
-
.
.
The added stiffness is worth with
V
0
= 4 Mr. S
1
:
K
NR m
rad
K
NR m
rad
K
has
has
has
11
4
1
2
22
5
1
2
12
0 3943 10
01577 10
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 - Bibliography and establishment in
Code_Aster - HP-61/95/064
[2]
BLEVINS R.D: Formulated for natural frequency and shape mode. ED. Krieger 1984
Code_Aster
®
Version
7.2
Titrate:
FDLV109 - Calculation of coefficients added in plane flow
Date:
01/03/04
Author (S):
NR. GREFFET, G. ROUSSEAU
Key
:
V8.01.109-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:
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 exit of fluid volume
480 meshs HEXA8
thermal elements THER_HEXA8
in fluid volume
3.2 Functionalities
tested
Controls
CALC_MATR_AJOU OPTION
“MASS_AJOU”
MACRO_MATR_AJOU OPTION
MATR_AMOR_AJOU
MATR_RIGI_AJOU
MODE_ITER_SIMULT OPTION
“TAPE”
4
Results of modeling A
4.1 Values
tested
Identification Reference
Aster %
difference
M
has
11
0.625 10
5
0.624
10
5
0.1
M
has
22
0.625 10
5
0.621
10
5
0.6
M
has
12
0 0.6
10
6
-
C
has
11
0 0.81
10
6
-
C
has
22
0 0.68
10
6
-
C
has
12
0.266 10
5
0.265
10
5
0.3
K
has
11
0.394 10
4
0.394
10
4
0.0
K
has
22
0.157 10
5
0.157
10
5
0.0
K
has
12
0 0.134
10
5
-
Code_Aster
®
Version
7.2
Titrate:
FDLV109 - Calculation of coefficients added in plane flow
Date:
01/03/04
Author (S):
NR. GREFFET, G. ROUSSEAU
Key
:
V8.01.109-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 coefficients added under flow (potential assumption) was validated on
the first two modes of bending 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.