Experimental measurements of the steady forces on a central cluster of tubes in a rotated triangular array (P/D=1.5) subjected to two-phase air–water cross-flow have been conducted. The tests were done for a series of void fractions and a Reynolds number (based on the pitch velocity), Re=7.2×104. The forces obtained and their derivatives with respect to the static streamwise displacement of the central tube in the cluster were then used to perform a quasi-steady fluidelastic instability analysis. The predicted instability velocities were found to be in good agreement with the dynamic stability tests. Since the effect of the time delay was ignored, the analysis confirmed the predominance of the stiffness-controlled mechanism in causing streamwise fluidelastic instability. The effect of frequency detuning on the streamwise fluidelastic instability threshold was also explored. It was found that frequency detuning has, in general, a stabilizing effect. However, for a large initial variance in a population of frequencies (e.g., σ2=7.84), a smaller sample drawn from the larger population may have lower or higher variance resulting in a large scatter in possible values of the stability constant, K, some even lower than the average (tuned) case. Frequency detuning clearly has important implications for streamwise fluidelastic instability in the steam generator U-bend region where in-plane boundary conditions, due to preload and contact friction variance, are poorly defined. The present analysis has, in particular, demonstrated the potential of the quasi-steady model in predicting streamwise fluidelastic instability threshold in tube arrays subjected to two-phase cross-flows.

References

References
1.
Weaver
,
D. S.
, and
Fitzpatrick
,
J. A.
,
1988
, “
A Review of Cross-Flow Induced Vibrations in Heat Exchanger Tube Arrays
,”
J. Fluids Struct.
,
2
(
1
), pp.
73
93
.
2.
Chen
,
S. S.
, and
Srikantiah
,
G. S.
,
2001
, “
Motion-Dependent Fluid Force Coefficients for Tube Arrays in Crossflow
,”
ASME J. Pressure Vessel Technol.
,
123
(
4
), pp.
429
436
.
3.
Roberts
,
B. W.
,
1962
, “
Low Frequency, Self-Excited Vibration in a Row of Circular Cylinders Mounted in an Airstream
,” Ph.D. thesis, University of Cambridge, Cambridge, UK.
4.
Roberts
,
B. W.
,
1966
, “
Low Frequency, Aeroelastic Vibrations in a Cascade of Circular Cylinders
,” Mechanical Engineering Science Monograph, No.4, Institution of Mechanical Engineers, London.
5.
Connors
,
H. J.
,
1970
, “
Fluidelastic Vibration of Tube Arrays Excited by Cross Flow
,”
Flow-Induced Vibrations in Heat Exchangers
,
D. D.
Reiff
, ed.,
ASME
,
New York
, pp.
42
56
.
6.
Price
,
S. J.
, and
Paidoussis
,
M. P.
,
1982
, “
A Theoretical Investigation of the Parameters Affecting the Fluidelastic Instability of a Double Row of Cylinders Subject to Cross-Flow
,”
3rd International Conference on Vibrations in Nuclear Plant
, pp.
107
119
.
7.
Price
,
S. J.
, and
Paidoussis
,
M. P.
,
1983
, “
Fluidelastic Instability of a Double Row of Circular Cylinders Subject to Cross-Flow
,”
ASME J. Vib. Acoust. Stress Reliab. Des.
,
105
(
1
), pp.
59
66
.
8.
Price
,
S. J.
, and
Paidoussis
,
M. P.
,
1984
, “
An Improved Mathematical Model for the Stability of Cylinder Rows Subject to Cross-Flow
,”
J. Sound Vib.
,
97
(
4
), pp.
615
640
.
9.
Tanaka
,
H.
, and
Takahara
,
S.
,
1980
, “
Unsteady Fluid Dynamic Force on Tube Bundle and Its Dynamic Effect on Vibration
,”
Flow-Induced Vibration of Power Plant Components
,
M. K.
Au-Yang
, ed.,
ASME
,
New York, NY
, pp.
77
92
.
10.
Tanaka
,
H.
, and
Takahara
,
S.
,
1981
, “
Fluid Elastic Vibration of Tube Array in Cross Flow
,”
J. Sound Vib.
,
77
(
1
), pp.
19
37
.
11.
Lever
,
J. H.
, and
Weaver
,
D. S.
,
1982
, “
A Theoretical Model for the Fluidelastic Instability in Heat Exchanger Tube Bundles
,”
ASME J. Pressure Vessel Technol.
,
104
(
3
), pp.
147
158
.
12.
Lever
,
J. H.
, and
Weaver
,
D. S.
,
1986
, “
On the Stability Behaviour of Heat Exchanger Tube Bundles. Part 2—Numerical Results and Comparison With Experiments
,”
J. Sound Vib.
,
107
(
3
), pp.
393
410
.
13.
Pettigrew
,
M. J.
, and
Taylor
,
C. E.
,
1994
, “
Two-Phase Flow-Induced Vibration: An Overview
,”
ASME J. Pressure Vessel Technol.
,
116
(
3
), pp.
233
253
.
14.
Chen
,
S. S.
,
1983
, “
Instability Mechanisms and Stability Criteria of a Group of Circular Cylinders Subjected to Cross-Flow. Part I: Theory
,”
ASME J. Vib. Acoust. Stress Reliab. Des.
,
105
(
1
), pp.
51
58
.
15.
Chen
,
S. S.
,
1983
, “
Instability Mechanisms and Stability Criteria of a Group of Circular Cylinders Subjected to Cross-Flow. Part II: Numerical Results and Discussion
,”
ASME J. Vib. Acoust. Stress Reliab. Des.
,
105
(
2
), pp.
253
260
.
16.
Austermann
,
R.
, and
Popp
,
K.
,
1995
, “
Stability Behavior of a Single Flexible Cylinder in Rigid Tube Arrays of Different Geometry Subjected to Cross-Flow
,”
J. Fluids Struct.
,
9
(
3
), pp.
303
322
.
17.
Mureithi
,
N. W.
,
Zhang
,
C.
,
Ruel
,
M.
, and
Pettigrew
,
M. J.
,
2005
, “
Fluidelastic Instability Tests on an Array of Tubes Preferentially Flexible in the Flow Direction
,”
J. Fluids Struct.
,
21
(
1
), pp.
75
87
.
18.
Violette
,
R.
,
Pettigrew
,
M. J.
, and
Mureithi
,
N. W.
,
2006
, “
Fluidelastic Instability of an Array of Tubes Preferentially Flexible in the Flow Direction Subjected to Two-Phase Cross Flow
,”
ASME J. Pressure Vessel Technol.
,
128
(
1
), pp.
148
159
.
19.
Janzen
,
V. P.
,
Hagberg
,
E. G.
,
Pettigrew
,
M. J.
, and
Taylor
,
C. E.
,
2005
, “
Fluidelastic Instability and Work-Rate Measurements of Steam-Generator U-Tubes in Air–Water Cross-Flow
,”
ASME J. Pressure Vessel Technol.
,
127
(
1
), pp.
84
91
.
20.
Nakamura
,
T.
,
Fujita
,
Y.
, and
Sumitani
,
T.
,
2014
, “
Study on In-Flow Fluidelastic Instability of Triangular Tube Arrays Subjected to Air Cross Flow
,”
ASME J. Pressure Vessel Technol.
,
136
(
5
), p.
051302
.
21.
Granger
,
S.
,
Campistron
,
R.
, and
Lebret
,
J.
,
1993
, “
Motion-Dependent Excitation Mechanisms in a Square in-Line Tube Bundle Subject to Water Cross-Flow—An Experimental Modal-Analysis
,”
J. Fluids Struct.
,
7
(
5
), pp.
521
550
.
22.
Weaver
,
D. S.
, and
Koroyannakis
,
D.
,
1983
, “
Flow-Induced Vibrations of Heat Exchanger U-Tubes: A Simulation to Study the Effects of a Symmetric Stiffness
,”
ASME J. Vib. Acoust.
,
105
(
1
), pp.
67
75
.
23.
Weaver
,
D. S.
, and
Schneider
,
W.
,
1983
, “
The Effect of Flat Bar Supports on the Crossflow Induced Response of Heat Exchanger U-Tubes
,”
ASME J. Eng. Gas Turbines Power
,
105
(
4
), pp.
775
781
.
24.
Feenstra
,
P. A.
,
Janzen
,
V. P.
, and
Smith
,
T.
,
2014
, “
In-Plane Vibration Damping of a U-Tube With Wet and Dry Flat-Bar Supports
,”
ASME
Paper No. PVP2014-28429.
25.
Hassan
,
M.
, and
Weaver
,
D. S.
,
2015
, “
The Effect of Flat Bar Supports on Streamwise Fluidelastic Instability in Heat Exchanger Tube Arrays
,”
ASME J. Pressure Vessel Technol.
,
137
(
6
), p.
061302
.
26.
S. C. E.
,
2013
, “
San Onofre Nuclear Generating Station Unit 2 Return to Service Report
,” Southern California Edison, Rosemead, CA, Technical
Docket No. 50-361
.
27.
Sawadogo
,
T.
, and
Mureithi
,
N.
,
2014
, “
Fluidelastic Instability in a Rotated Triangular Tube Array Subjected to Two-Phase Cross-Flow. Part II: Experimental Tests and Comparison With Theoretical Results
,”
J. Fluids Struct.
,
49
, pp.
16
28
.
28.
Olala
,
S.
,
Mureithi
,
N.
,
Sawadogo
,
T.
, and
Pettigrew
,
M. J.
,
2014
, “
Streamwise Fluidelastic Forces in Tube Arrays Subjected to Two-Phase Flows
,”
ASME
Paper No. PVP2014-28153.
29.
Price
,
S. J.
, and
Paidoussis
,
M. P.
,
1986
, “
A Single Flexible Cylinder Analysis for the Fluidelastic Instability of an Array of Flexible Cylinders in Cross Flow
,”
ASME J. Fluids Eng.
,
108
(
2
), pp.
193
199
.
30.
Pettigrew
,
M. J.
,
Taylor
,
C. E.
, and
Kim
,
B. S.
,
1989
, “
Vibration of Tube Bundles in Two-Phase Cross-Flow: Part I—Hydrodynamic Mass and Damping
,”
ASME J. Pressure Vessel Technol.
,
111
(4), pp.
446
477
.
31.
Paidoussis
,
M. P.
, and
Price
,
S. J.
,
1988
, “
Mechanisms Underlying Flow-Induced Instabilities of Cylinder Arrays in Cross-Flow
,”
J. Fluid Mech.
,
187
(1), pp.
45
59
.
32.
Shahriary
,
S.
,
Mureithi
,
N. W.
, and
Pettigrew
,
M. J.
,
2007
, “
Quasi-Static Forces and Stability Analysis in a Triangular Tube Bundle Subjected to Two-Phase Cross-Flow
,”
ASME
Paper No. PVP2007-26017.
33.
Inman
,
D. J.
,
2001
,
Engineering Vibration
,
Prentice-Hall
,
Upper Saddle River, NJ
.
34.
Pettigrew
,
M. J.
,
Tromp
,
J. H.
,
Taylor
,
C. E.
, and
Kim
,
B. S.
,
1989
, “
Vibration of Tube Bundles in Two-Phase Cross-Flow: Part 2—Fluidelastic Instability
,”
ASME J. Pressure Vessel Technol.
,
111
(
4
), pp.
478
487
.
35.
Blevins
,
R. D.
,
1979
,
Formulas for Natural Frequency and Mode Shape
,
Van Nostrand Reinhold
,
New York
.
36.
Cheng
,
B.
,
1994
, “
The Mechanisms Underlying Flow-Induced Instability of Cylinder Arrays in Cross-Flow: An Investigation of System Parameters
,”
Ph.D. thesis
, McGill University, Montréal, QC, Canada.
You do not currently have access to this content.