The use of Connors’ equation, or variations thereof, to predict the velocity at which fluidelastic instability occurs in cylinder arrays subject to cross-flow has become ubiquitous. The implicit assumption being that this equation accurately models the physics of fluidelastic instability, and all that is required is to find the “correct” value of Connors’ constant. The evidence for and against this assumption is examined in this paper. Other theoretical models of fluidelastic instability are reviewed and compared with Connors’ analysis. In addition, evidence from experimental data is considered. It is concluded that there are many deficiencies associated with Connors’ equation, and that if better “design guides” are to be obtained, more emphasis must be put on examining the physics of fluidelastic instability.

1.
Zdravkovich, M. M., 1993, “Interstitial Flow Fields and Fluid Forces,” Chapt. 2, Part III, Fluid-Structure Interaction, Technology for the 90s, ed., M. K. Au-Yang, ASME, New York, NY, pp. 593–658.
2.
Price
,
S. J.
,
1995
, “
A Review of Theoretical Models for Fluidelastic Instability in Cross-Flow
,”
J. Fluids Struct.
,
9
, pp.
463
518
.
3.
Pai¨doussis
,
M. P.
,
1983
, “
A Review of Flow-Induced Vibrations in Reactors and Reactor Components
,”
Nucl. Eng. Des.
,
74
, pp.
31
60
.
4.
Chen
,
S. S.
,
1984
, “
Guidelines for the Instability Flow Velocity of Tube Arrays in Cross-Flow
,”
J. Sound Vib.
,
93
, pp.
439
455
.
5.
Weaver
,
D. S.
, and
Fitzpatrick
,
J. A.
,
1988
, “
A Review of Flow Induced Vibrations in Heat Exchangers
,”
J. Fluids Struct.
,
2
, pp.
73
93
.
6.
Pettigrew
,
M. J.
, and
Taylor
,
C. E.
,
1991
, “
Fluid-Elastic Instability of Heat Exchanger Tube Bundles: Review and Design Recommendations
,”
ASME J. Pressure Vessel Technol.
,
113
, pp.
242
256
.
7.
Schro¨der
,
K.
, and
Gelbe
,
H.
,
1999
, “
New Design Recommendations for Fluidelastic Instability in Heat Exchanger Tube Bundles
,”
J. Fluids Struct.
,
13
, pp.
361
379
.
8.
Pettigrew
,
M. J.
, and
Taylor
,
C. E.
,
1993
, “
Two-Phase Flow-Induced Vibration: An Overview
,”
ASME J. Pressure Vessel Technol.
,
116
, pp.
233
253
.
9.
Connors, H. J., 1970, “Fluidelastic Vibration of Tube Arrays Excited by Cross Flow,” Flow-Induced Vibration in Heat Exchangers, ed., D. D. Reiff, ASME, New York, NY, pp. 42–56.
10.
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.
11.
Blevins
,
R. D.
,
1974
, “
Fluidelastic Whirling of a Tube Row
,”
ASME J. Pressure Vessel Technol.
,
98
, pp.
263
267
.
12.
Whiston
,
G. S.
, and
Thomas
,
G. D.
,
1982
, “
Whirling Instabilities in Heat Exchanger Tube Arrays
,”
J. Sound Vib.
,
81
, pp.
1
31
.
13.
Fung, Y. C., 1955, An Introduction to the Theory of Aeroelasticity, Wiley, New York, NY.
14.
Zdravkovich
,
M. M.
,
1982
, “
Scruton Number, a Proposal
,”
J. Wind. Eng. Ind. Aerodyn.
,
10
, pp.
263
265
.
15.
Blevins, R. D., 1979, “Fluid Damping and the Whirling Instability of Tube Arrays,” Flow-Induced Vibrations, eds., S. S. Chen and M. D. Bernstein, ASME, New York, NY, pp. 35–39.
16.
Kassera
,
V.
, and
Strohmeier
,
K.
,
1997
, “
Simulation of Tube Bundle Vibrations Induced by Cross-Flow
,”
J. Fluids Struct.
,
11
, pp.
909
928
.
17.
Schro¨der, K., and Gelbe, H., 1999, “Simulation of Flow-Induced Vibration in Tube Arrays,” Flow-Induced Vibration, ASME PVP-Vol. 389, ed., M. J. Pettigrew, pp. 9–16.
18.
Tanaka
,
H.
, and
Takahara
,
S.
,
1981
, “
Fluid Elastic Vibration of Tube Array in Cross Flow
,”
J. Sound Vib.
,
77
, pp.
19
37
.
19.
Tanaka, H., Tanaka, K., and Shimizu, F., 2000, “Characteristics of Tube Bundle Vibrations in Cross Flow,” Flow-Induced Vibration, eds., S. Ziada and T. Staubli, Balkema, Rotterdam, Holland, pp. 473–480.
20.
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
, pp.
51
58
.
21.
Chen
,
S. S.
,
1983
, “
Instability Mechanisms and Stability Criteria of a Group of Circular Cylinders Subject to Cross-Flow. Part II: Numerical Results and Discussion
,”
ASME J. Vib., Acoust., Stress, Reliab. Des.
,
105
, pp.
253
260
.
22.
Lever
,
J. H.
, and
Weaver
,
D. S.
,
1982
, “
A Theoretical Model for the Fluid-Elastic Instability in Heat Exchanger Tube Bundles
,”
ASME J. Pressure Vessel Technol.
,
104
, pp.
147
158
.
23.
Yetisir
,
M.
, and
Weaver
,
D. S.
,
1993
, “
An Unsteady Theory for Fluidelastic Instability in an Array of Flexible Tubes in Cross-Flow. Part I: Theory
,”
J. Fluids Struct.
,
7
, pp.
751
766
.
24.
Yetisir
,
M.
, and
Weaver
,
D. S.
,
1993
, “
An Unsteady Theory for Fluidelastic Instability in an Array of Flexible Tubes in Cross-Flow. Part II: Results and Comparison With Experiments
,”
J. Fluids Struct.
,
7
, pp.
767
782
.
25.
Price
,
S. J.
, and
Pai¨doussis
,
M. P.
,
1984
, “
An Improved Mathematical Model for the Stability of Cylinder Rows Subject to Cross-Flow
,”
J. Sound Vib.
,
97
, pp.
615
640
.
26.
Price
,
S. J.
, and
Pai¨doussis
,
M. P.
,
1986
, “
A Constrained-Mode Analysis of the Fluidelastic Instability of a Double Row of Circular Cylinders Subject to Cross-Flow: A Theoretical Investigation of System Parameters
,”
J. Sound Vib.
,
105
, pp.
121
142
.
27.
Price
,
S. J.
,
Pai¨doussis
,
M. P.
, and
Giannis
,
N.
,
1990
, “
A Generalized Constrained-Mode Analysis for Cylinder Arrays in Cross-Flow
,”
J. Fluids Struct.
,
4
, pp.
171
202
.
28.
Price
,
S. J.
, and
Pai¨doussis
,
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
, pp.
193
199
.
29.
Granger
,
S.
, and
Pai¨doussis
,
M. P.
,
1996
, “
An Improvement to the Quasi-Steady Model With Application to Cross-Flow-Induced Vibration of Tube Arrays
,”
J. Fluid Mech.
,
320
, pp.
163
184
.
30.
Price
,
S. J.
, and
Kuran
,
S.
,
1991
, “
Fluidelastic Stability of a Rotated Square Array With Multiple Flexible Cylinders Subject to Cross-Flow
,”
J. Fluids Struct.
,
5
, pp.
551
572
.
31.
Pai¨doussis
,
M. P.
,
Price
,
S. J.
,
Nakamura
,
T.
,
Mark
,
B.
, and
Mureithi
,
W. N.
,
1989
, “
Flow-Induced Vibrations and Instabilities in a Rotated-Square Cylinder Array in Cross-Flow
,”
J. Fluids Struct.
,
3
, pp.
229
254
.
32.
Andjelic
,
A.
,
Austermann
,
R.
, and
Popp
,
K.
,
1990
, “
Multiple Stability Boundaries of Tubes in a Normal Triangular Cylinder Array
,”
ASME J. Pressure Vessel Technol.
,
114
, pp.
336
343
.
33.
Andjelic
,
A.
, and
Popp
,
K.
,
1999
, “
Stability Effects in a Normal Triangular Cylinder Array
,”
J. Fluids Struct.
,
3
, pp.
165
186
.
34.
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
, pp.
303
322
.
35.
Pai¨doussis
,
M. P.
,
Price
,
S. J.
, and
Mureithi
,
N. W.
,
1996
, “
On the Virtual Nonexistence of Multiple Instability Regions for Some Heat-Exchanger Arrays in Crossflow
,”
ASME J. Fluids Eng.
,
118
, pp.
103
109
.
36.
Nakamura, T., Chen, S. S., Mureithi, N. W., and Kusakabe, T., 1997, “Improved Estimation of Fluidelastic Instability Threshold for Tube Arrays in Two-Phase Flow: A Model Incorporating Temporal Fluid Force Correlation Along the Tube Axis,” 4th Int. Symposium on Fluid-Structure Interactions, Aeroelasticity, Flow-Induced Vibration and Noise, Vol. II, ed., M. P. Pai¨doussis, New York, ASME, NY, pp. 365–372.
37.
Weaver
,
D. S.
, and
Koroyannakis
,
D.
,
1982
, “
The Cross-Flow Response of a Tube Array in Water—A Comparison With the Same Array in Air
,”
ASME J. Pressure Vessel Technol.
,
104
, pp.
139
146
.
38.
Price
,
S. J.
, and
Pai¨doussis
,
M. P.
,
1989
, “
The Flow-Induced Response of a Single Flexible Cylinder in an In-Line Array of Rigid Cylinders
,”
J. Fluids Struct.
,
3
, pp.
61
82
.
39.
Pettigrew, M. J., Rogers, R. J., and Axisa, F., 1986, “Damping of Multispan Heat Exchanger Tubes—Part 2: In Liquids,” Symp. on Special Topics of Structural Vibration, ASME PVP-Vol. 104, pp. 89–98.
40.
Chen
,
S. S.
, and
Zendrejczyk
,
J. A.
,
1981
, “
Flow-Velocity Dependence of Damping in Tube Arrays Subjected to Liquid Cross Flow
,”
ASME J. Pressure Vessel Technol.
,
103
, pp.
130
135
.
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