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
Outline document