background image
Code_Aster
®
Version
8.0
Titrate:
SDLL134 - Method of Connors for the analysis of the behavior
Date:
06/10/05
Author (S):
A. ADOBES, L. SALMONA
Key
:
V2.02.134-A
Page:
1/6
Manual of Validation
V2.02 booklet: Linear dynamics of the beams
HT-66/05/005/A
Organization (S):
EDF-R & D/MFTT, CS IF















Manual of Validation
V2.02 booklet: Linear dynamics of the beams
V2.02.134 document



SDLL134 - Method of Connors for the analysis of
vibratory behavior of the tubes of Steam Generator



Summary:

This case test aims at the validation of the establishment in Code_Aster of the method of Connors, in so much
that method of analysis of the vibratory behavior of the tubes of Steam Generator.
background image
Code_Aster
®
Version
8.0
Titrate:
SDLL134 - Method of Connors for the analysis of the behavior
Date:
06/10/05
Author (S):
A. ADOBES, L. SALMONA
Key
:
V2.02.134-A
Page:
2/6
Manual of Validation
V2.02 booklet: Linear dynamics of the beams
HT-66/05/005/A
1
Problem of reference
1.1 Geometry






















Co-ordinates of the points:
WITH B C
D
E
X - 0.2944
- 0.2944
0. 0.2944
0.2944
y 0.
9.693
9.9874 9.693 0.
F1 G1 H1
I1
J1
X - 0.2944
- 0.2944
- 0.2944
- 0.2944
- 0.2944
y 1.068 2.136
3.204 4.272 5.34
K1 L1 M1
X - 0.2944
- 0.2944
- 0.2944
y 6.408 7.476
8.544
F2 G2 H2
I2
J2
X 0.2944
0.2944
0.2944
0.2944
0.2944
y 1.068 2.136
3.204 4.272 5.34
K2 L2 m2
X 0.2944
0.2944
0.2944
y 6.408 7.476
8.544
1.2
Properties of materials and characteristic of the tube
Elastic properties
E = 202000 MPa
= 0.3
= 8330 kg/m
3
The tube is hollow. Its external radius is worth 9.525 mm and its thickness 1.09 Misters.
With
B
C
D
E
F1
G1
H1
I1
J1
K1
L1
M1
F2
G2
H2
I2
J2
K2
L2
M2
X
y
background image
Code_Aster
®
Version
8.0
Titrate:
SDLL134 - Method of Connors for the analysis of the behavior
Date:
06/10/05
Author (S):
A. ADOBES, L. SALMONA
Key
:
V2.02.134-A
Page:
3/6
Manual of Validation
V2.02 booklet: Linear dynamics of the beams
HT-66/05/005/A
1.3
Boundary conditions
Boundary conditions:
· on points A, B, D and E: embedding (DX=DY=DZ=RX=RY=RZ=0).
· on the F1 points, G1, H1, I1, J1, K1, L1, M1, F2, G2, H2, I2, J2, K2, L2 and m2: support
(DX=DY=DZ=0).
Fluid loading:
The internal fluid and the external fluid are distinguished. Each one has a dependant density
curvilinear X-coordinate along the tube. Moreover, for the external fluid, the profile speed inter-tubes
transverse with the tube in the plan of the tube is provided.
1.4
Type of network and characteristic of the model of Connors
The network is a square pitch of pitch reduces 1.439895. The constant of Connors is supposed to be
ranging between 3.0 and 5.0 with 3 values équiréparties in this interval, that is to say 3.0, 4.0 and 5.0.
Damping necessary to the application of the method of Connors is damping in fluid
at rest. It is taken equal to 0.64%.
background image
Code_Aster
®
Version
8.0
Titrate:
SDLL134 - Method of Connors for the analysis of the behavior
Date:
06/10/05
Author (S):
A. ADOBES, L. SALMONA
Key
:
V2.02.134-A
Page:
4/6
Manual of Validation
V2.02 booklet: Linear dynamics of the beams
HT-66/05/005/A
2
Reference solution
2.1
Method of calculation used for the reference solution
One is interested in the mode 21 which is more penalizing on the vibratory level. Its frequency
(estimated with aid MODE_ITER_SIMULT with 61.53761 Hz) is regarded as a data of
problem. The values of interest for the case-test are, on the one hand effective speed
in
V
, and
in addition critical engine failure speed
Cn
V
. Their values are given by the equations
(see nomenclature of the variables in [R4.07.04]):

() () ()
() () ()
() () ()
() ()
=
=
=
tube
N
tube
N
S
S
in
E
S
N
Nex
I
Lex
N
S
I
tube
N
S
E
N
Cn
ds
S
m
S
m
ds
S
S
V
S
V
D
m
ds
S
S
V
S
K
ds
S
S
V
S
D
F
V
I
2
2
2
2
1
2
2
2
2
2
1

By using the Excel spreadsheet, it is possible to calculate these values for the different ones
constants of Connors requested.

2.2
Results of reference
The value of reference is the sum of the various values for each constant of
Connors. One thus has for effective speed and the critical engine failure speed of the respective values of
3.0039 and 6.9156.

2.3
Uncertainty on the solution
It is about an semi-analytical solution. Only uncertainty relates to the frequency of mode 21.

2.4 References
bibliographical
[1]
T. KESTENS, Mr. LAINET: Coupling fluid-structure for the tubular structures and them
coaxial hulls, document [R7.07.04].
background image
Code_Aster
®
Version
8.0
Titrate:
SDLL134 - Method of Connors for the analysis of the behavior
Date:
06/10/05
Author (S):
A. ADOBES, L. SALMONA
Key
:
V2.02.134-A
Page:
5/6
Manual of Validation
V2.02 booklet: Linear dynamics of the beams
HT-66/05/005/A
3 Modeling
With
3.1
Characteristics of modeling
Elements 1D POU_D_T (SEG2)























3.2
Characteristics of the mesh
A number of nodes: 311
A number of meshs and types: 310 SEG2

3.3 Functionalities
tested
Controls
DEFI_FLUI_STRU CSTE_CONNORS
NB_CONNORS
CALC_FLUI_STRU AMOR_REDUIT_CONN


4
Results of modeling A
4.1 Values
tested
Size Reference
Aster %
difference
Summon
Cn
V
6.9156037078201 6.9156037078201 1.03E-13
Summon
in
V
3.0039489978201 3.0039544634875 1.82E-04
With
B
D
E
background image
Code_Aster
®
Version
8.0
Titrate:
SDLL134 - Method of Connors for the analysis of the behavior
Date:
06/10/05
Author (S):
A. ADOBES, L. SALMONA
Key
:
V2.02.134-A
Page:
6/6
Manual of Validation
V2.02 booklet: Linear dynamics of the beams
HT-66/05/005/A
5
Summary of the results
The error made by Code_Aster on speeds (critical and effective) is with more than 1.82 10
- 4
% it
who is acceptable and valid the establishment of the method of Connors in the software.