This study investigates unsteady flow in tube bundles and fluid forces, which can lead to large tube vibration amplitudes, in particular, amplitudes associated with fluidelastic instability (FEI). The fluidelastic forces are approximated by the coupling of the unsteady flow model (UFM) with computational fluid dynamics (CFD). The CFD model employed solves the Reynolds averaged Navier–Stokes equations for unsteady turbulent flow and is cast in an arbitrary Lagrangian–Eulerian form to handle any motion associated with tubes. The CFD solution provides time domain forces that are used to calculate added damping and stiffness coefficients employed with the UFM. The investigation demonstrates that the UFM utilized in conjunction with CFD is a viable approach for calculating the stability map for a given tube array. The FEI was predicted for in-line square and normal triangle tube arrays over a mass damping parameter range of 0.1– 100. The effect of the P/d ratio and the Reynolds number on the FEI threshold was also investigated.

1.
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.
0889-9746,
18
(
5
), pp.
469
483
.
2.
Weaver
,
D.
,
Ziada
,
S.
,
Au-Yang
,
M.
,
Chen
,
S.
,
Païdoussis
,
M. P.
, and
Pettigrew
,
M.
, 2000, “
Flow-Induced Vibrations in Power and Process Plant Components—Progress and Prospects
,”
ASME J. Pressure Vessel Technol.
0094-9930,
122
, pp.
339
348
.
3.
Païdoussis
,
M.
, 1983, “
A Review of Flow-Induced Vibrations in Reactors and Reactor Components
,”
Nucl. Eng. Des.
0029-5493,
74
, pp.
31
60
.
4.
Païdoussis
,
M.
, 1980, “
Flow-Induced Vibrations in Nuclear Reactors and Heat Exchangers. Practical Experiences and State of Knowledge
,”
Practical Experiences With Flow-Induced Vibrations
,
E.
Naudascher
and
D.
Rockwell
, eds.,
Springer
,
Berlin
, pp.
1
81
.
5.
Connors
,
H. J.
, 1970, “
Fluidelastic Vibration of Tube Arrays Excited by Cross Flow
,”
Flow-Induced Vibration in Heat Exchangers
,
D. D.
Reiff
, ed.,
ASME
,
New York
, pp.
42
57
.
6.
Chen
,
S. S.
, 1984, “
Guidelines for the Instability Flow Velocity of Tube Arrays in Cross-Flow
,”
J. Sound Vib.
0022-460X,
93
, pp.
439
455
.
7.
Weaver
,
D.
, and
Fitzpatrick
,
J.
, 1988, “
A Review of Cross-Flow Induced Vibrations in Heat Exchanger Tube Arrays
,”
J. Fluids Struct.
0889-9746,
2
, pp.
73
93
.
8.
Pettigrew
,
M.
, and
Taylor
,
C.
, 1991, “
Fluidelastic Instability of Heat Exchanger Tube Bundles: Review and Design Recommendations
,”
ASME J. Pressure Vessel Technol.
0094-9930,
113
(
2
), pp.
242
256
.
9.
Schröder
,
K.
, and
Gelbe
,
H.
, 1999, “
New Design Recommendations for Fluidelastic Instability in Heat Exchanger Tube Bundles
,”
J. Fluids Struct.
0889-9746,
13
, pp.
361
379
.
10.
Connors
,
H.
, 1981, “
Flow-Induced Vibration and Wear of Steam Generator Tubes
,”
Nucl. Technol.
0029-5450,
55
, pp.
311
331
.
11.
Tanaka
,
H.
, and
Takahara
,
S.
, 1981, “
Fluid Elastic Vibration of Tube Array in Cross-Flow
,”
J. Sound Vib.
0022-460X,
77
, pp.
19
37
.
12.
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.
0094-9930,
104
, pp.
104
147
.
13.
Price
,
S. J.
, and
Païdoussis
,
M.
, 1983, “
Fluidelastic Instability of an Infinite Double Row of Circular Cylinders Subject to a Uniform Cross-Flow
,”
ASME J. Vib., Acoust., Stress, Reliab. Des.
0739-3717,
105
, pp.
59
66
.
14.
Chen
,
S. S.
, 1983, “
Instability Mechanisms and Stability Criteria of a Group of Cylinders Subjected to Cross-Flow. Part 1: Theory
,”
ASME J. Vib., Acoust., Stress, Reliab. Des.
0739-3717,
105
, pp.
51
58
.
15.
Granger
,
S.
, and
Païdoussis
,
M. P.
, 1996, “
An Improvement to the Quasi-Steady Model With Application to Cross-Flow-Induced Vibration of Tube Array
,”
J. Fluid Mech.
0022-1120,
320
, pp.
163
184
.
16.
Yetisir
,
M.
, and
Weaver
,
D.
, 1993, “
An Unsteady Theory for Fluidelastic Instability in an Array of Flexible Tubes in Cross-Flow. Part 1: Theory
,”
J. Fluids Struct.
0889-9746,
7
, pp.
751
766
.
17.
Hassan
,
M.
, and
Hayder
,
M.
, 2008, “
Modelling of Fluidelastic Vibrations of Heat Exchanger Tubes With Loose Supports
,”
Nucl. Eng. Des.
0029-5493,
238
(
10
), pp.
2507
2520
.
18.
Romberg
,
O.
, and
Popp
,
K.
, 1998, “
Fluid-Damping Controlled Instability in Tube Bundles Subjected to Air Cross-Flow
,”
Flow, Turbul. Combust.
1386-6184,
61
, pp.
285
300
.
19.
So
,
R.
,
Liu
,
Y.
,
Chan
,
S.
, and
Lam
,
K.
, 2001, “
Numerical Studies of a Freely Vibrating Cylinder in Cross-Flow
,”
J. Fluids Struct.
0889-9746,
15
, pp.
845
866
.
20.
Evangelinos
,
C.
, and
Karniadakis
,
G.
, 1999, “
Dynamics and Flow Structures in the Turbulent Wake of Rigid and Flexible Cylinders Subject to Vortex-Induced Vibrations
,”
J. Fluid Mech.
0022-1120,
400
, pp.
91
124
.
21.
Reichel
,
C.
, 2006, “
Numerical Simulation of Flow Induced Tube Bundle Oscillations
,” Ph.D. thesis, Technical University of Munich, Munich, Germany.
22.
Nakamura
,
A.
, and
Okajima
,
A.
, 2001, “
A Numerical Simulation and Vortex Structures of In-Line Oscillation of an Elastically Supported Circular Cylinder
,”
ASME PVP Flow-Induced Vibration
,
M. J.
Pettigrew
, ed.,
ASME
,
New York
, Vol.
420
, pp.
177
184
.
23.
Meneghini
,
J. R.
,
Saltara
,
F.
,
Siqueira
,
C. L.
, and
Ferrari
,
J. A.
, Jr.
, 2001, “
Numerical Simulation of Flow Interference Between Two Circular Cylinders in Tandem and Side-by-Side Arrangements
,”
J. Fluids Struct.
0889-9746,
15
, pp.
327
350
.
24.
Liu
,
Y.
,
So
,
R.
,
Lau
,
Y.
, and
Zhou
,
Y.
, 2001, “
Numerical Studies of Two Side-by-Side Elastic Cylinders in a Cross-Flow
,”
J. Fluids Struct.
0889-9746,
15
, pp.
1009
1030
.
25.
Hassan
,
Y. A.
, and
Barsamian
,
H. R.
, 2004, “
Tube Bundle Flows With Large Eddy Simulation Technique in Curvilinear Coordinates
,”
Int. J. Heat Mass Transfer
0017-9310,
47
, pp.
3057
3071
.
26.
Kevlahan
,
N. R.
, and
Wadsley
,
J.
, 2005, “
Suppression of Three-Dimensional Flow Instabilities in Tube Bundles
,”
J. Fluids Struct.
0889-9746,
20
(
4
), pp.
611
620
.
27.
Liang
,
C.
, and
Papadakis
,
G.
, 2007, “
Large Eddy Simulation of Cross-Flow Through a Staggered Tube Bundle at Subcritical Reynolds Number
,”
J. Fluids Struct.
0889-9746,
23
(
8
), pp.
1215
1230
.
28.
Schröder
,
K.
, and
Gelbe
,
H.
, 1999, “
Two- and Three-Dimensional CFD Simulation of Flow-Induced Vibration Excitation in Tube Bundles
,”
Chem. Eng. Process.
0255-2701,
38
, pp.
621
629
.
29.
Kassera
,
V.
, and
Strohmeier
,
K.
, 1997, “
Simulation of Tube Bundle Vibrations Induced by Cross-Flow
,”
J. Fluids Struct.
0889-9746,
11
, pp.
909
928
.
30.
Longatte
,
E.
,
Bendjeddou
,
Z.
, and
Souli
,
M.
, 2003, “
Methods for Numerical Study of Tube Bundle Vibrations in Cross-Flows
,”
J. Fluids Struct.
0889-9746,
18
, pp.
513
528
.
31.
Meskell
,
C.
, and
Fitzpatrick
,
J.
, 2003, “
Investigation of the Nonlinear Behaviour of Damping Controlled Fluidelastic Instability in a Normal Triangular Tube Array
,”
J. Fluids Struct.
0889-9746,
18
(
5
), pp.
573
593
.
32.
Gillen
,
S.
, and
Meskell
,
C.
, 2008, “
Variation of Fluidelastic Critical Velocity With Mass Ratio and Reynolds Number in a Densely Packed Normal Triangular Tube Array
,”
Flow-Induced Vibrations
,
I.
Zolotarev
and
J.
Horáêek
, eds.,
Institute of Thermomechanics
,
Prague, Czech Republic
, pp.
193
198
.
33.
Weber
,
D. P.
,
Brewster
,
R.
,
Chen
,
S.
, and
Wei
,
T. Y.
, 2001, “
Numerical Method for Fluidelastic Instability Evaluation in Nuclear Reactor System and Plant Components
,”
SMIRT 16 Transactions
, Paper No. 1194.
34.
Schneider
,
G. E.
, and
Raw
,
M. J.
, 1987, “
Control Volume Finite-Element Method for Heat Transfer and Fluid Flow Using Collocated Variables—1 Computational Procedure
,”
Numer. Heat Transfer
0149-5720,
11
, pp.
363
390
.
35.
Menter
,
F. R.
, 1994, “
Two-Equation Eddy Viscosity Turbulence Models for Engineering Applications
,”
AIAA J.
0001-1452,
32
(
8
), pp.
1598
1605
.
36.
Raw
,
M. J.
, 1996, “
Robustness of Coupled Algebraic Multi-Grid for the Navier–Stokes Equation
,”
Proceedings of the 34th Aerospace and Sciences Meeting and Exhibit
.
37.
Chen
,
S. S.
, and
Srikantiah
,
G. S.
, 2001, “
Motion-Dependent Fluid Force Coefficients for Tube Arrays in Crossflow
,”
J. Pressure Vessel Technol.
0094-9930,
123
, pp.
429
436
.
38.
Chen
,
S.
,
Jendrzjczyk
,
J.
, and
Wambsganss
,
M.
, 1985, “
Dynamics of Tubes in Fluid With Tube-Baffle Interaction
,”
J. Pressure Vessel Technol.
0094-9930,
107
, pp.
7
17
.
39.
Williams
,
E.
, 2004, “
A Computational Fluid Dynamics Study of Unsteady Flow Theory Coefficients for Tube Array Fluidelastic Instability
,” MS thesis, University of New Brunswick, New Brunswick, Canada.
40.
Alonzo
,
C.
, and
Macagno
,
E.
, 1973, “
Numerical Integration of the Time-Dependent Equations of Motion for Taylor Vortex Flow
,”
Comput. Fluids
0045-7930,
1
, pp.
301
315
.
41.
Lam
,
K.
,
Jiangb
,
G. D.
,
Liua
,
Y.
, and
Soa
,
R.
, 2006, “
Simulation of Cross-Flow-Induced Vibration of Cylinder Arrays by Surface Vorticity Method
,”
J. Fluids Struct.
0889-9746,
22
, pp.
1113
1131
.
42.
Chen
,
S. -S.
, 1975, “
Vibration of Nuclear Fuel Bundles
,”
Nucl. Eng. Des.
0029-5493,
35
(
3
), pp.
399
422
.
43.
Tanaka
,
H.
,
Tanaka
,
K.
, and
Shimizu
,
F.
, 2002, “
Fluidelastic Analysis of Tube Bundle Vibration in Cross-Flow
,”
J. Fluids Struct.
0889-9746,
16
(
1
), pp.
93
112
.
44.
Austermann
,
R.
, and
Popp
,
K.
, 1995, “
Stability Behaviour of a Single Flexible Cylinder in Rigid Tube Arrays of Different Geometry Subjected to Cross-Flow
,”
J. Fluids Struct.
0889-9746,
9
(
3
), pp.
303
322
.
45.
Price
,
S. J.
, 1995, “
A Review of Theoretical Models for Fluidelastic Instability of Cylinder Arrays in Cross-Flow
,”
J. Fluids Struct.
0889-9746,
9
, pp.
463
518
.
46.
Connors
,
H. J.
, 1980, “
Fluidelastic Vibration of Tube Arrays Excited by Nonuniform Cross Flow
,”
Flow-Induced Vibration of Power Plant Components
,
ASME
,
New York
, Vol.
41
, pp.
93
107
.
47.
Elkashlan
,
M.
, 1983, “
Array Geometry Effects on Vortex Shedding and Instability in Heat Exchanger Tube Array
,” Ph.D. thesis, McMaster University, ON, Canada.
48.
Chen
,
S. S.
, and
Jendrzjczyk
,
J. A.
, 1981, “
Experiments on Fluid Instability in Tube Banks Subjected to Liquid Cross Flow
,”
J. Sound Vib.
0022-460X,
78
, pp.
355
381
.
49.
Gross
,
H.
, 1975, “
Untersuchung Aeroelastischer Schwingungsmechanismen und Deren Berucksichtigung bei der Auslegung von Rohrbundelwarmetauschern
,” Ph.D. thesis, Technical University of Hannover, Hannover, Germany.
50.
Hartlen
,
R. T.
, 1974, “
Wind Tunnel Determination of Fluidelastic Vibration Thresholds for Typical Heat-Exchanger Tube Patterns
,” Ontario Hydro Research Division, Report No. 74-309-K.
51.
Pettigrew
,
M.
, and
Gorman
,
D.
, 1978, “
Vibration of Heat Exchanger Components in Liquid and Two-Phase Cross-Flow
,”
Proceedings of the BNES International Conference on Vibration in Nuclear Plant
, Keswick, UK.
52.
Soper
,
B. M.
, 1983, “
The Effect of Tube Layout on the Fluid Elastic Instability of Tube Bundles in Cross Flow
,”
ASME J. Heat Transfer
0022-1481,
105
, pp.
744
750
.
53.
Price
,
S. J.
, and
Païdoussis
,
M. P.
, 1989, “
The Flow-Induced Response of a Single Flexible Cylinder in an In-Line Array of Rigid Cylinders
,”
J. Fluids Struct.
0889-9746,
3
, pp.
61
82
.
54.
Blevins
,
R.
,
Gibert
,
R.
, and
Villard
,
B.
, 1981, “
Experiment on Vibration of Heat Exchanger Tube Arrays in Cross Flow
,”
Proceedings of the Sixth International Conference on Structural Mechanics in Reactor Technology
, Paris.
55.
Andjelíc
,
M.
, and
Popp
,
K.
, 1989, “
Stability Effects in a Normal Triangular Cylinder Array
,”
J. Fluids Struct.
0889-9746,
3
(
2
), pp.
165
185
.
56.
Price
,
S. J.
, and
Zahn
,
M. L.
, 1991, “
Fluidelastic Behaviour of a Normal Triangular Array Subject to Cross-Flow
,”
J. Fluids Struct.
0889-9746,
5
, pp.
259
278
.
57.
Teh
,
C. E.
, and
Goyder
,
H. G. D.
, 1988, “
Data for the Fluidelastic Instability of Heat Exchanger Tube Bundles
,”
Symposium on Flow Induced Vibration and Noise
,
M. P.
Païdoussis
,
S. S.
Chen
, and
M. D.
Bernstein
, eds.,
ASME
,
New York
, Vol.
3
, pp.
77
94
.
58.
Weaver
,
D. S.
, and
Yeung
,
H. C.
, 1984, “
The Effect of Tube Mass on the Flow Induced Response of Various Tube Arrays in Water
,”
J. Sound Vib.
0022-460X,
93
, pp.
409
425
.
59.
Scott
,
P.
, 1987, “
Flow Visualization of Cross-Flow-Induced Vibrations in Tube Arrays
,” MS thesis, McMaster University, Hamilton, ON, Canada.
60.
Gorman
,
D.
, 1976, “
Experimental Development of Design Criteria to Limit Liquid Cross-Flow Induced Vibration in Nuclear Reactor Heat Exchanger Equipment
,”
Nucl. Sci. Eng.
0029-5639,
61
, pp.
324
336
.
61.
Zukauskas
,
A.
, and
Katinas
,
V.
, 1980, “
Flow-Induced Vibration in Heat-Exchanger Tube Banks
.
Practical Experiences With Flow-Induced Vibrations
,
E.
Naudascher
and
D.
Rockwell
, eds.,
Springer
,
New York
, pp.
188
196
.
You do not currently have access to this content.