Prediction of fluid-elastic instability onset is a great matter of importance in designing cross-flow heat exchangers from the perspective of vibration. In the present paper, the threshold of fluid-elastic instability has been numerically predicted by the simulation of incompressible, unsteady, and turbulent cross flow through a tube bundle in a normal triangular arrangement. In the tube bundle under study, there were single or multiple flexible cylinders surrounded by rigid tubes. A finite volume solver based on a Cartesian-staggered grid was implemented. In addition, the ghost-cell method in conjunction with the great-source-term technique was employed in order to directly enforce the no-slip condition on the cylinders' boundaries. Interactions between the fluid and the structures were considered in a fully coupled manner by means of intermittence solution of the flow field and structural equations of motion in each time step of the numerical modeling algorithm. The accuracy of the solver was validated by simulation of the flow over both a rigid and a flexible circular cylinder. The results were in good agreement with the experiments reported in the literatures. Eventually, the flow through seven different flexible tube bundles was simulated. The fluid-elastic instability was predicted and analyzed by presenting the structural responses, trajectory of flexible cylinders, and critical reduced velocities.

References

References
1.
Paidoussis
,
M. P.
,
1983
, “
A Review of Flow-Induced Vibrations in Reactor and Reactor Components
,”
Nucl. Eng. Des.
,
74
, pp.
31
60
.10.1016/0029-5493(83)90138-3
2.
Paidoussis
,
M. P.
,
Curling
,
L. I. R.
, and
Gagnon
,
J. O.
,
1982
, “
Experiments on Fluid-Elastic Instability of Cylinder Clusters in Axial Flow
,”
ASME J. Fluids Eng.
,
104
(
3
), pp.
342
347
.10.1115/1.3241846
3.
Pettigrew
,
M. J.
, and
Taylor
,
C. E.
,
2003
, “
Vibration Analysis of Shell-and-Tube Heat Exchangers: An Overview—Part 1: Flow, Damping, Fluid-Elastic Instability
,”
J. Fluid. Struct.
,
18
, pp.
469
483
.10.1016/j.jfluidstructs.2003.08.007
4.
Pettigrew
,
M. J.
, and
Taylor
,
C. E.
,
2003
, “
Vibration Analysis of Shell-and-Tube Heat Exchangers: An Overview—Part 2: Vibration Response, Fretting-Wear, Guidelines
,”
J. Fluid. Struct.
,
18
, pp.
485
500
.10.1016/j.jfluidstructs.2003.08.008
5.
Schroder
,
K.
, and
Gelbe
,
H.
,
1999
, “
New Design Recommendations for Fluid-Elastic Instability in Heat Exchanger Tube Bundles
,”
J. Fluid Struct.
,
13
, pp.
361
379
.10.1006/jfls.1999.0208
6.
Chen
,
S. S.
,
1984
, “
Guidelines for the Instability Flow Velocity of Tube Arrays in Cross-Flow
,”
J. Sound Vib.
,
93
(
3
), pp.
439
455
.10.1016/0022-460X(84)90340-7
7.
Price
,
S. J.
,
1995
, “
A Review of Theoretical Models for Fluid-Elastic Instability of Tubes in Cross-Flow
,”
J. Fluid. Struct.
,
9
, pp.
463
518
.10.1006/jfls.1995.1028
8.
Paidoussis
,
M. P.
,
Price
,
S. J.
, and
Mavriplis
,
D.
,
1985
, “
A Semipotential Flow Theory for the Dynamics of Cylinder Arrays in Cross Flow
,”
ASME J. Fluids Eng.
,
107
(
4
), pp.
500
506
.10.1115/1.3242520
9.
Price
,
S. J.
, and
Paidoussis
,
M. P.
,
1986
, “
A Single-Flexible-Cylinder Analysis for the Fluid-Elastic Instability of an Array of Flexible Cylinders in Cross-Flow
,”
ASME J. Fluids Eng.
,
108
(
2
), pp.
193
199
.10.1115/1.3242562
10.
Paidoussis
,
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
(
1
), pp.
103
109
.10.1115/1.2817486
11.
Kassera
,
V.
, and
Strohmeier
,
K.
,
1997
, “
Simulation of Tube Bundle Vibrations Induced by Cross-Flow
,”
J. Fluid Struct.
,
11
, pp.
909
928
.10.1006/jfls.1997.0114
12.
Schroder
,
K.
, and
Gelbe
,
H.
,
1999
, “
Two- and Three-Dimensional CFD-Simulation of Flow-Induced Vibration Excitation in Tube Bundles
,”
Chem. Eng. Proc.
,
38
, pp.
621
629
.10.1016/S0255-2701(99)00063-X
13.
Longatte
,
E.
,
Bendjeddou
,
Z.
, and
Souli
,
M.
,
2003
, “
Methods for Numerical Study of Tube Bundle Vibrations in Cross-Flows
,”
J. Fluid. Struct.
,
18
, pp.
513
528
.10.1016/j.jfluidstructs.2003.08.010
14.
Lam
,
K.
,
Jiang
,
G. D.
,
Liu
,
Y.
, and
So
,
R. M. C.
,
2006
, “
Simulation of Cross-Flow-Induced Vibration of Cylinder Arrays by Surface Vorticity Method
,”
J. Fluid. Struct.
,
22
, pp.
1113
1131
.10.1016/j.jfluidstructs.2006.03.004
15.
Sweeney
,
C.
, and
Meskell
,
C.
,
2003
, “
Fast Numerical Simulation of Vortex Shedding in Tube Arrays Using a Discrete Vortex Method
,”
J. Fluid. Struct.
,
18
, pp.
501
512
.10.1016/j.jfluidstructs.2003.08.009
16.
Schneider
,
K.
, and
Farge
,
M.
,
2005
, “
Numerical Simulation of the Transient Flow Behavior in Tube Bundles Using a Volume Penalization Method
,”
J. Fluid. Struct.
,
20
, pp.
555
566
.10.1016/j.jfluidstructs.2005.02.006
17.
Kevlahan
,
N. K.
, and
Wadsley
,
J.
,
2005
, “
Suppression of Three-Dimensional Flow Instabilities in Tube Bundles
,”
J. Fluid. Struct.
,
20
, pp.
611
620
.10.1016/j.jfluidstructs.2005.02.010
18.
Dehkordi
,
B. G.
, and
Jafari
,
H. H.
,
2009
, “
Numerical Simulation of Flow Through Tube Bundles in In-Line Square and General Staggered Arrangements
,”
Int. J. Num. Meth. Heat Fluid
,
19
(
8
), pp.
1038
1062
.10.1108/09615530910994487
19.
Dehkordi
,
B. G.
, and
Jafari
,
H. H.
,
2010
, “
On the Suppression of Vortex Shedding From Circular Cylinders Using Detached Short Splitter-Plates
,”
ASME J. Fluids Eng.
,
132
(
4
), p.
044501
.10.1115/1.4001384
20.
Meskell
,
C.
, and
Fitzpatrick
,
J. A.
,
2003
, “
Investigation of the Nonlinear Behavior of Damping Controlled Fluid-Elastic Instability in a Normal Triangular Tube Array
,”
J. Fluid. Struct.
,
18
, pp.
573
593
.10.1016/j.jfluidstructs.2003.08.013
21.
Patankar
,
S. V.
,
1980
,
Numerical Heat Transfer and Fluid Flow
,
Hemisphere Publishing Corporation
,
New York
.
22.
Ye
,
T.
,
Mittal
,
R.
,
Udaykumar
,
H. S.
, and
Shyy
,
W.
,
1999
, “
An Accurate Cartesian Grid Method for Viscous Incompressible Flows With Complex Immersed Boundaries
,”
J. Comput. Phys.
,
156
, pp.
209
240
.10.1006/jcph.1999.6356
23.
Tseng
,
Y. H.
, and
Ferziger
,
J. H.
,
2003
, “
A Ghost-Cell Immersed Boundary Method for Flow in Complex Geometry
,”
J. Comput. Phys.
,
192
, pp.
593
623
.10.1016/j.jcp.2003.07.024
24.
Gopalkrishnan
,
R.
,
1993
, “
Vortex-Induced Forces on Oscillating Bluff Cylinders
,” Ph.D. thesis, Department of Ocean Engineering, MIT, Cambridge, MA.
25.
Zdravkovich
,
M.
,
1997
,
Flow Around Circular Cylinders: Fundamentals
, Vol.
1
,
Oxford University Press
,
Oxford, UK
.
26.
Dong
,
S. G.
, and
Karniadakis
,
E.
,
2005
, “
DNS of Flow Past a Stationary and Oscillating Cylinder at Re=10,000
,”
J. Fluid. Struct.
,
20
, pp.
519
531
.10.1016/j.jfluidstructs.2005.02.004
27.
Liaw
,
K. F.
,
2005
, “
Simulation of Flow Around Bluff Bodies and Bridge Deck Sections Using CFD
,” Ph.D. thesis, School of Civil Engineering, University of Nottingham, Nottingham, UK.
28.
Khalak
,
A.
, and
Williamson
,
C. H. K.
,
1996
, “
Dynamics of a Hydroelastic Cylinder With Very Low Mass and Damping
,”
J. Fluid. Struct.
,
10
, pp.
455
472
.10.1006/jfls.1996.0031
29.
Meneghini
,
J. R.
,
Saltara
,
F.
, and
Bearman
,
P. W.
,
1997
, “
Numerical Simulation of Vortex Shedding From an Oscillating Circular Cylinder
,”
Computational Methods and Experimental Measurements
,
P.
Anangnostopolos
,
G. M.
Carlomagno
and
C. A.
Brebbia
, eds.,
Computational Mechanics Publications
,
Southampton
,
UK
, pp.
409
418
.
30.
Wanderley
,
J. B. V.
, and
Levi
,
C. A.
,
2005
, “
Vortex Induced Loads on Marine Risers
,”
Ocean Eng.
,
32
, pp.
1281
1295
.10.1016/j.oceaneng.2004.12.007
31.
Paidoussis
,
M.
,
1979
, “
Flow-Induced Vibrations in Nuclear Reactors and Heat Exchangers (Practical Experiences and State of Knowledge)
,”
Practical Experiences With Flow-Induced Vibration
,
E.
Naudascher
, and
D.
Rockwell
, eds.,
Springer
,
Berlin
, pp.
1
81
.
32.
Blevines
,
R. D.
,
1990
,
Flow-Induced Vibration
,
2nd ed.
,
Van Nostrand Reinhold
,
New York
.
33.
Lin
,
T. K.
, and
Yu
,
M. H.
,
2005
, “
An Experimental Study on the Cross-Flow Vibration of a Flexible Cylinder in Cylinder Arrays
,”
Exp. Therm. Fluid Sci.
,
29
, pp.
523
536
.10.1016/j.expthermflusci.2004.06.004
34.
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
.10.1016/0022-460X(81)90344-8
35.
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
.10.1016/0022-460X(78)90506-0
36.
Tanaka
,
H.
,
Tanaka
,
K.
,
Shimizu
,
F.
,
Takahara
,
S.
,
2002
, “
Fluid-Elastic Analysis of Tube Bundle Vibration in Cross-Flow
,”
J. Fluid. Struct.
,
16
(
1
), pp.
93
112
.10.1006/jfls.2001.0411
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