Code_Aster ®
Version
8.0
Titrate:
SDLL134 - Méthode de 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

Organization (S): EDF-R & D/MFTT, CS IF

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

SDLL134 - Méthode de 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.

Handbook of Validation
V2.02 booklet: Linear dynamics of the beams
HT-66/05/005/A

Code_Aster ®
Version
8.0
Titrate:
SDLL134 - Méthode de 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


1
Problem of reference

1.1 Geometry

C

B
D

M1
M2

L1
L2

K1
K2

J1
J2

I1
I2

H1
H2

G1
G2
y

F1
F2

X

With
E
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/m3

The tube is hollow. Its external radius is worth 9.525 mm and its thickness 1.09 Misters.
Handbook of Validation
V2.02 booklet: Linear dynamics of the beams
HT-66/05/005/A

Code_Aster ®
Version
8.0
Titrate:
SDLL134 - Méthode de 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


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 step of step 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%.

Handbook of Validation
V2.02 booklet: Linear dynamics of the beams
HT-66/05/005/A

Code_Aster ®
Version
8.0
Titrate:
SDLL134 - Méthode de 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


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 assistance 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 the critical engine failure speed Cn
V. Their values are given by the equations
(see nomenclature of the variables in [R4.07.04]):

2
2
S (S) V (S) N (S)

ds
Cn
V

=
tube
m N
Nex
F
2
N
E
D
1
2
2
D
S (S) V (S) N (S)
2
S
E
ds
i=1 Ki Lexi

S (S) V 2 (S) 2
N (S)

ds

V = tube
S
in
m (S) 2
N (S)

ds
m
tube

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].
Handbook of Validation
V2.02 booklet: Linear dynamics of the beams
HT-66/05/005/A

Code_Aster ®
Version
8.0
Titrate:
SDLL134 - Méthode de 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


3 Modeling
With

3.1
Characteristics of modeling

Elements 1D POU_D_T (SEG2)

B
D

With
E

3.2
Characteristics of the grid

A number of nodes: 311
A number of meshs and types: 310 SEG2

3.3 Functionalities
tested

Commands




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 of in
V
3.0039489978201 3.0039544634875 1.82E-04
Handbook of Validation
V2.02 booklet: Linear dynamics of the beams
HT-66/05/005/A

Code_Aster ®
Version
8.0
Titrate:
SDLL134 - Méthode de 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


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.
Handbook of Validation
V2.02 booklet: Linear dynamics of the beams
HT-66/05/005/A

Outline document