The development of a theoretical model for fluidelastic instability (FEI) in tube arrays is presented. Based on the simple model of Lever and Weaver, it considers a group of seven tubes which move in both the streamwise and transverse directions. The analysis does not constrain either tube frequency or relative mode shape so that the tubes' behavior evolves from a perturbation naturally. No additional empirical input is required. A particular case is used to evaluate the model's performance and the ratio of streamwise-to-transverse natural frequency is varied. Both streamwise and transverse directions of FEI are predicted and the results agree well with experimental observations.

References

References
1.
Païdoussis
,
M.
,
1983
, “
A Review of Flow-Induced Vibrations in Reactors and Reactor Components
,”
Nucl. Eng. Des.
,
74
(
1
), pp.
31
60
.
2.
Weaver
,
D.
, and
Fitzpatrick
,
J.
,
1988
, “
A Review of Crossflow Induced Vibrations in Heat Exchanger Tube Arrays
,”
J. Fluids Struct.
,
2
(
1
), pp.
73
93
.
3.
Pettigrew
,
M. J.
, and
Taylor
,
C. E.
,
1991
, “
Fluidelastic Instability of Heat Exchanger Tube Bundles: Review and Design Recommendations
,”
ASME J. Pressure Vessel Technol.
,
113
(
2
), pp.
242
256
.
4.
Schröder
,
K.
, and
Gelbe
,
H.
,
1999
, “
New Design Recommendations for Fluidelastic Instability in Heat Exchanger Tube Bundles
,”
J. Fluids Struct.
,
13
(
3
), pp.
361
379
.
5.
Price
,
S. J.
,
1995
, “
A Review of Theoretical Models for Fluidelastic Instability of Cylinder Arrays in Cross-Flow
,”
J. Fluids Struct.
,
9
(
5
), pp.
463
518
.
6.
Pettigrew
,
M.
, and
Taylor
,
C.
,
2003
, “
Vibration Analysis of Shell-and-Tube Heat Exchangers: An Overview–Part 1: Flow, Damping, Fluidelastic Instability
,”
J. Fluids Struct.
,
18
(
5
), pp.
469
483
.
7.
Pettigrew
,
M.
, and
Taylor
,
C.
,
2003
, “
Vibration Analysis of Steam Generators and Heat Exchangers: An Overview: Part 2: Vibration Response, Fretting-Wear, Guidelines
,”
J. Fluids Struct.
,
18
(
5
), pp.
485
500
.
8.
Weaver
,
D. S.
,
2008
, “
Some Thoughts on the Elusive Mechanism of Fluidelastic Instability in Heat Exchanger Tube Arrays
,”
9th International Conference on Flow-Induced Vibrations
(FIV-2008), Prague, Czech Republic, June 30–July 3,
I.
Zolotarev
, and
J.
Horacek
, eds.,
Institute of Thermomechanics, Academy of Sciences of the Czech Republic
,
Prague, Czech Republic
, pp.
21
28
.
9.
Weaver
,
D.
, and
Schneider
,
W.
,
1983
, “
The Effect of Flat Bar Supports on the Crossflow Induced Response of Heat Exchanger U-Tubes
,”
ASME J. Pressure Vessel Technol.
,
105
(4), pp.
775
781
.
10.
Yetisir
,
M.
, and
Weaver
,
D.
,
1986
, “
The Dynamics of Heat Exchanger U-Bend Tubes With Flat-Bar Supports
,”
ASME J. Pressure Vessel Technol.
,
108
(
4
), pp.
406
412
.
11.
Au-Yang
,
M. K.
,
2001
,
Flow-Induced Vibration of Power and Process Plant Components: A Practical Workbook
,
ASME Press
,
New York
.
12.
Hassan
,
M.
, and
Weaver
,
D.
,
2014
, “
The Effect of Flat Bar Supports on Streamwise Fluidelastic Instability in Heat Exchanger Tube Arrays
,”
ASME
Paper No. PVP2014-29038.
13.
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 Crossflow
,”
ASME J. Pressure Vessel Technol.
,
127
(
1
), pp.
84
91
.
14.
Mureithi
,
N.
,
Zhang
,
C.
,
Ruel
,
M.
, and
Pettigrew
,
M.
,
2005
, “
Fluidelastic Instability Tests on an Array of Tubes Preferentially Flexible in the Flow Direction
,”
J. Fluids Struct.
,
21
(
1
), pp.
75
87
.
15.
Violette
,
R.
,
Pettigrew
,
M. J.
, and
Mureithi
,
N. W.
,
2005
, “
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
.
16.
Feenstra
,
P.
,
Nakamura
,
T.
, and
Weaver
,
D. S.
,
2009
, “
Two Phase Flow-Induced Vibration of Parallel Triangular Tube Arrays With Asymmetric Support Stiffness
,”
ASME J. Pressure Vessel Technol.
,
131
(
3
), p.
031301
.
17.
Hirota
,
K.
,
Morita
,
H.
,
Hirai
,
J.
,
Iwasaki
,
A.
,
Utsumi
,
S.
,
Shimamura
,
K.
, and
Kawakami
,
R.
,
2013
, “
Investigation on In-Flow Fluidelastic Instability of an Array of Tubes
,”
ASME
Paper No. PVP2013-97163.
18.
Nakamura
,
T.
,
2012
, “
Study on In-Flow Fluid-Elastic Instability of Circular Cylinder Arrays
,” 10th International Conference on Flow-Induced Vibration & Flow-Induced Noise (FIV2012), Dublin, Ireland, July 3–6, pp. 99–106.
19.
Nakamura
,
T.
,
Nishimura
,
K.
,
Fujita
,
Y.
, and
Kohara
,
C.
,
2011
, “
Study on In-Flow Vibration of Cylinder Arrays Caused by Cross Flow
,”
ASME
Paper No. PVP2011-57068.
20.
Nakamura
,
T.
,
Fujita
,
Y.
, and
Sumitani
,
T.
,
2011
, “
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.
Nakamura
,
T.
,
2014
, “
An Analysis of In-Flow Fluidelastic Instability Based on a Physical Insight
,”
ASME
Paper No. PVP2014-28231.
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
(
3
), pp.
147
158
.
23.
Lever
,
J. H.
, and
Weaver
,
D. S.
,
1986
, “
On the Stability of Heat Exchanger Tube Bundles, Part I: Modified Theoretical Model
,”
J. Sound Vib.
,
107
(
3
), pp.
375
392
.
24.
Lever
,
J. H.
, and
Weaver
,
D. S.
,
1986
, “
On the Stability of Heat Exchanger Tube Bundles, Part II: Numerical Results and Comparison With Experiments
,”
J. Sound Vib.
,
107
(
3
), pp.
393
410
.
25.
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
(
7
), pp.
751
766
.
26.
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
(
7
), pp.
767
782
.
27.
Païdoussis
,
M.
,
Price
,
S.
, and
de Langre
,
E.
,
2011
,
Fluid-Structure Interactions: Cross-Flow-Induced Instabilities
,
Cambridge University Press
, New York.
28.
Chen
,
S. S.
,
1983
, “
Instability Mechanisms and Stability Criteria of a Group of Circular Cylinders Subjected to Cross Flow. I. Theory
,”
J. Vib., Acoust., Stress Reliab. Des.
,
105
(
1
), pp.
51
58
.
29.
Mahmoud
,
F.
, and
Hassan
,
M.
,
2007
, “
Modeling of Fluidelastic Instability Forces in Fully Flexible Tube Arrays
,”
ASME
Paper No. PVP2007-26653.
30.
El Bouzidi
,
S.
, and
Hassan
,
M.
,
2015
, “
An Investigation of Time Lag Causing Fluidelastic Instability in Tube Arrays
,”
J. Fluids Struct.
,
57
, pp.
264
276
.
31.
Khalifa
,
A.
,
Weaver
,
D. S.
, and
Ziada
,
S.
,
2013
, “
An Experimental Study of the Interaction Between Tube Vibration and the Associated Flow Perturbation in Tube Arrays
,”
ASME J. Pressure Vessel Technol.
,
135
(
3
), p.
030904
.
32.
El Bouzidi
,
S.
, and
Hassan
,
M.
,
2015
, “
The Effect of Streamwise Unsteady Fluid Forces on the Stability of a Vibrating Tube Subjected to Flow
,”
ASME
Paper No. PVP2015-45600.
33.
Hassan
,
M. A.
,
Rogers
,
R. J.
, and
Gerber
,
A. G.
,
2011
, “
Damping-Controlled Fluidelastic Instability Forces in Multi-Span Tubes With Loose Supports
,”
Nucl. Eng. Des.
,
241
(
8
), pp.
2666
2673
.
34.
Hassan
,
M.
, and
Mohany
,
A.
,
2013
, “
Fluidelastic Instability Modeling of Loosely Supported Multispan U-Tubes in Nuclear Steam Generators
,”
ASME J. Pressure Vessel Technol.
,
135
(
1
), p.
011306
.
35.
Hassan
,
M.
,
Weaver
,
D. S.
, and
Dokainish
,
M.
,
2003
, “
The Effects of Support Geometry on the Turbulence Response of Loosely Supported Heat Exchanger Tubes
,”
J. Fluids Struct.
,
18
(
5
), pp.
529
554
.
36.
Antunes
,
J.
,
Delaune
,
X.
,
Piteau
,
P.
, and
Borsoi
,
L.
,
2008
, “
A Simple Consistent Method for the Time-Domain Simulation of Turbulence Excitations Applied to Tube/Support Dynamical Analysis Under Non-Uniform Flows
,”
9th International Conference on Flow Induced Vibrations (FIV-2008)
,
Prague
,
Czech Republic
, June 30–July 3.
37.
Khalifa
,
A.
,
Weaver
,
D. S.
, and
Ziada
,
S.
,
2012
, “
A Single Flexible Tube in a Rigid Array as a Model for Fluidelastic Instability in Tube Arrays
,”
J. Fluids Struct.
,
34
, pp.
14
32
.
38.
Soper
,
B. M.
,
1980
, “
The Effect of Tube Layout on the Fluidelastic Instability of Tube Bundles in Cross Flow
,”
Flow-Induced Heat Exchanger Tube Vibration—1980
,
J. M.
Chenoweth
, and
J. R.
Stenner
, eds.,
ASME
,
New York
, pp.
1
9
.
39.
Weaver
,
D. S.
, and
Grover
,
L. K.
,
1978
, “
Cross-Flow Induced Vibrations in a Tube Bank-Turbulent Buffeting and Fluid Elastic Instability
,”
J. Sound Vib.
,
59
(
2
), pp.
277
294
.
40.
Pettigrew
,
M. J.
,
Sylvestre
,
Y.
, and
Campagna
,
A. O.
,
1978
, “
Vibration Analysis of Heat Exchanger and Steam Generator Designs
,”
Nucl. Eng. Des.
,
48
(
1
), pp.
97
115
.
41.
Heilker
,
W. J.
, and
Vincent
,
R. Q.
,
1980
, “
Vibration in Nuclear Heat Exchangers Due to Liquid and Two-Phase Flow
,”
ASME J. Eng. Power
,
103
(
2
), pp.
358
366
.
42.
Hartlen
,
R. T.
,
1974
, “
Wind Tunnel Determination of Fluidelastic Vibration Thresholds for Typical Heat Exchanger Tube Patterns
,” Ontario Hydra, Toronto, ON, Canada, Report No. 74-309-K.
43.
Scott
,
P.
,
1987
, “
Flow Visualization of Cross-Flow-Induced Vibrations in Tube Arrays
,” M.S. thesis, McMaster University, Hamilton, ON, Canada.
44.
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
(
3
), pp.
139
146
.
45.
Pettigrew
,
M. J.
, and
Gorman
,
D. J.
,
1978
, “
Vibration of Heat Exchange Components in Liquid and Two-Phase Cross-Flow
,” Atomic Energy of Canada, Ltd., Chalk River, ON, Canada,
Report No. AECL-6184
.
46.
Yeung
,
H.
, and
Weaver
,
D. S.
,
1983
, “
The Effect of Approach Flow Direction on the Flow Induced Vibrations of a Triangular Tube Array
,”
ASME J. Mech. Des.
,
105
(7), pp.
76
82
.
47.
Gorman
,
D. J.
,
1976
, “
Experimental Development of Design Criteria to Limit Liquid Cross-Flow-Induced Vibration in Nuclear Reactor Heat Exchange Equipment
,”
Nucl. Sci. Eng.
,
61
(3), pp.
324
336
.
48.
Weaver
,
D. S.
, and
El-Kashlan
,
M.
,
1981
, “
On the Number of Tube Rows Required to Study Cross-Flow Induced Vibrations in Tube Banks
,”
J. Sound Vib.
,
75
(
2
), pp.
265
273
.
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