Having previously verified the quasi-steady model under two-phase flow laboratory conditions, the present work investigates the feasibility of practical application of the model to a prototypical steam generator (SG) tube subjected to a nonuniform two-phase flow. The SG tube vibration response and normal work-rate induced by tube-support interaction are computed for a range of flow conditions. Similar computations are performed using the Connors model as a reference case. In the quasi-steady model, the fluid forces are expressed in terms of the quasi-static drag and lift force coefficients and their derivatives. These forces have been measured in two-phase flow over a wide range of void fractions making it possible to model the effect of void fraction variation along the tube span. A full steam generator tube subjected to a nonuniform two-phase flow was considered in the simulations. The nonuniform flow distribution corresponds to that along a prototypical steam-generator tube based on thermal-hydraulic computations. Computation results show significant and important differences between the Connors model and the two-phase flow based quasi-steady model. While both models predict the occurrence of fluidelastic instability, the predicted pre-instability and post instability behavior is very different in the two models. The Connors model underestimates the flow-induced negative damping in the pre-instability regime and vastly overestimates it in the post instability velocity range. As a result the Connors model is found to underestimate the work-rate used in the fretting wear assessment at normal operating velocities, rendering the model potentially nonconservative under these practically important conditions. Above the critical velocity, this model largely overestimates the work-rate. The quasi-steady model on the other hand predicts a more moderately increasing work-rate with the flow velocity. The work-rates predicted by the model are found to be within the range of experimental results, giving further confidence to the predictive ability of the model. Finally, the two-phase flow based quasi-steady model shows that fluidelastic forces may reduce the effective tube damping in the pre-instability regime, leading to higher than expected work-rates at prototypical operating velocities.

References

References
1.
Connors
,
H. J. J.
,
1970
, “
Fluidelastic Vibration of a Tube Array Excited by Cross Flow
,”
Proceedings of the Symposium on Flow-Induced Vibration in Heat Exchanger, ASME Winter Annual Meeting
,
NY
, pp.
42
56
.
2.
Connors
,
H. J.
,
J.
,
1978
, “
Fluidelastic Vibration of Heat Exchanger Tube Arrays
,”
Trans. ASME J. Mech. Des.
,
100
(
2
), pp.
347
353
.10.1115/1.3453921
3.
Blevins
,
R. D.
,
1974
, “
Fluidelastic Whirling of a Tube Row
,”
Trans. ASME J. Pressure Vessel Technol.
,
96
, pp.
263
267
.10.1115/1.3454179
4.
Price
,
S. J.
, and
Paidoussis
,
M. P.
,
1983
, “
Fluidelastic Instability of an Infinite Double Row of Circular Cylinders Subject to a Uniform Cross-Flow
,”
ASME J. Vib., Acoust., Stress, Reliab. Des.
,
105
(
1
), pp.
59
66
.10.1115/1.3269067
5.
Price
,
S. J.
, and
Païdoussis
,
M. P.
,
1984
, “
Improved Mathematical Model for the Stability of Cylinder Rows Subject to Cross-Flow
,”
J. Sound Vib.
,
97
, pp.
615
640
.10.1016/0022-460X(84)90512-1
6.
Price
,
S. J.
, and
Païdoussis
,
M. P.
,
1986
, “
A Constrained-Mode Analysis of the Fluidelastic Instability of a Double Row of Flexible Circular Cylinders Subject to Cross-Flow: A Theoretical Investigation of System Parameters
,”
J. Sound Vib.
,
105
, pp.
121
142
.10.1016/0022-460X(86)90225-7
7.
Price
,
S. J.
, and
Païdoussis
,
M. P.
,
1986
, “
A Single Flexible Cylinder Analysis for the Fluidelastic Instability of an Array of Flexible Cylinder in Cross Flow
,”
ASME J. Fluids Eng.
,
108
, pp.
193
199
.10.1115/1.3242562
8.
Price
,
S. J.
,
Païdoussis
,
M. P.
, and
Giannias
,
N.
,
1990
, “
A Generalized Constrained-Mode Analysis for Cylinder Arrays in Cross-Flow
,”
J. Fluids Struct.
,
4
, pp.
171
202
.10.1016/0889-9746(90)90072-D
9.
Tanaka
,
H.
, and
Takahara
,
S.
,
1980
, “
Unsteady Fluid Dynamic Force on Tube Bundle and Its Dynamic Effect on Vibration
,”
American Society of Mechanical Engineers, Pressure Vessels and Piping Division (Publication) PVP
, Vol.
41
, pp.
77
92
.
10.
Tanaka
,
H.
, and
Takahara
,
S.
,
1981
, “
Fluid Elastic Vibration of Tube Array in Cross-Flow
,”
J. Sound Vib.
,
77
, pp.
19
37
.10.1016/S0022-460X(81)80005-3
11.
Chen
,
S. S.
,
1983
, “
Instability Mechanisms and Stability Criteria of a Group of Circular Cylinders Subjected to Cross-Flow. Part 1: Theory
,”
ASME J. Vib., Acoust., Stress, Reliab. Des.
,
105
(
1
), pp.
51
58
.10.1115/1.3269066
12.
Chen
,
S. S.
,
1987
, “
A General Theory for Dynamic Instability of Tube Arrays in Cross-Flow
,”
ASME J. Fluids Eng.
,
1
, pp.
35
53
.10.1016/S0889-9746(87)90170-8
13.
Lever
,
J.
, and
Weaver
,
D. S.
,
1982
, “
A Theoretical Model for Fluid-Elastic Instability in Heat Exchanger Tube Bundles
,”
Trans. ASME J. Pressure Vessel Technol.
,
104
, pp.
147
158
.10.1115/1.3264196
14.
Lever
,
J.
, and
Weaver
,
D. S.
,
1986
, “
On the Stability of Heat Exchanger Tube Bundles Part 1: Modified Theoretical Model
,”
J. Sound Vib.
,
107
, pp.
375
392
.10.1016/S0022-460X(86)80114-6
15.
Lever
,
J.
, and
Weaver
,
D. S.
,
1986
, “
On the Stability of Heat Exchanger Tube Bundles, Part 2: Numerical Results and Comparison With Experiments
,”
J. Sound Vib.
,
107
, pp.
375
392
.10.1016/S0022-460X(86)80114-6
16.
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 Conference Proceedings
,
2007
(
42827
), pp.
245
252
.
17.
Mureithi
,
N. W.
,
2010
, “
On the Feasibility of Modeling Two-Phase Flow-Induced Fluidelastic Instability in Tube Bundles
,”
Proceedings of 7th International Symposium FSI2 & FIV+N 2010 3rd Joint US-European Fluids Engineering Summer Meeting, American Society of Mechanical Engineers, Fluids Engineering Division (Publication) FEDSM, American Society of Mechanical Engineers
, Vol.
3
, pp.
459
468
.
18.
Axisa
,
F.
,
Antunes
,
J.
, and
Villard
,
B.
,
1988
, “
Overview of Numerical Methods for Predicting Flow-Induced Vibration
,”
Trans. ASME J. Pressure Vessel Technol.
,
110
, pp.
6
14
.10.1115/1.3265570
19.
Fricker
,
A. J.
,
1992
, “
Numerical Analysis of the Fluidelastic Vibration of a Steam Generator Tube With Loose Supports
,”
J. Fluids Struct.
,
6
, pp.
85
107
.10.1016/0889-9746(92)90057-A
20.
Sauve
,
R. G.
,
1996
, “
Computational Time Domain Approach to Fluidelastic Instability for Nonlinear Tube Dynamics
,”
American Society of Mechanical Engineers, Pressure Vessels and Piping Division (Publication) PVP
, Vol.
328
, pp.
327
335
.
21.
Au-Yang
,
M. K.
,
2001
,
Flow-Induced Vibration of Power and Process Plant Components: A Practical Workbook, ASME Press
,
New York
.
22.
Price
,
S. J.
,
2001
, “
An Investigation on the Use of Connors' Equation to Predict Fluidelastic Instability in Cylinder Arrays
,”
Trans. ASME J. Pressure Vessel Technol.
,
123
(
4
), pp.
448
553
.10.1115/1.1403445
23.
Eisinger
,
F. L.
,
Rao
,
M. S. M.
,
Steininger
,
D. A.
, and
Haslinger
,
K. H.
,
1995
, “
Numerical Simulation of Cross-Flow-Induced Fluidelastic Vibration of Tube Arrays and Comparison With Experimental Results
,”
Trans. ASME J. Pressure Vessel Technol.
,
117
(
1
), pp.
31
39
.10.1115/1.2842087
24.
Mureithi
,
N. W.
,
Nakamura
,
T.
,
Hirota
,
K.
,
Murata
,
M.
,
Utsumi
,
S.
,
Kusakabe
,
T.
, and
Takamatsu
,
H.
,
2002
, “
Dynamics of an Inline Tube Array Subjected to Steam-Water Cross-Flow. Part 2: Unsteady Fluid Forces
,”
J. Fluids Struct.
,
16
(
2
), pp.
137
152
.10.1006/jfls.2001.0407
25.
Rao
,
S. S.
,
2007
,
Vibration of Continuous Systems
,
John Wiley & Sons, Inc.
, Hoboken, NJ.
26.
Pettigrew
,
M. J.
,
Taylor
,
C. E.
, and
Kim
,
B. S.
,
1989
, “
Vibration of Tube Bundles in Two-Phase Cross-Flow: Part 1—Hydrodynamic Mass and Damping
,”
Trans. ASME J. Pressure Vessel Technol.
,
111
, pp.
466
477
.10.1115/1.3265705
27.
Pettigrew
,
M. J.
, and
Taylor
,
C. E.
,
1991
, “
Fluidelastic Instability of Heat Exchanger Tube Bundles. Review and Design Recommendations
,”
Trans. ASME J. Pressure Vessel Technol.
,
113
(
2
), pp.
242
256
.10.1115/1.2928752
28.
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. Fluids Struct.
,
18
, pp.
485
500
.10.1016/j.jfluidstructs.2003.08.008
29.
De
Langre
,
E.
, and
Villard
,
B.
,
1998
, “
An Upper Bound on Random Buffeting Forces Caused by Two-Phase Flows Across Tubes
,”
J. Fluids Struct.
,
12
(
8
), pp.
1005
1023
.10.1006/jfls.1998.0180
30.
Granger
,
S.
, and
Paidoussis
,
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
.10.1017/S0022112096007495
31.
Meskell
,
C.
,
2009
, “
A New Model for Damping Controlled Fluidelastic Instability in Heat Exchanger Tube Arrays
,”
Proc. Inst. Mech. Eng., Part A
,
223
(
4
), pp.
361
368
.10.1243/09576509JPE700
32.
Roshko
,
A.
,
1961
, “
Experiments on Flow Past Circular Cylinder at Very High Reynolds Number
,”
J. Fluid Mech.
,
10
(
3
), pp.
345
356
.10.1017/S0022112061000950
33.
Jayaweera
,
K. O. L. F.
, and
Mason
,
B. J.
,
1965
, “
The Behaviour of Freely Falling Cylinders and Cones in a Viscous Fluid
,”
J. Fluid Mech.
,
22
, pp.
709
720
.10.1017/S002211206500109X
34.
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
,”
Trans. ASME J. Pressure Vessel Technol.
,
128
(
1
), pp.
148
159
.10.1115/1.2138064
35.
Sawadogo
,
T. P.
,
Mureithi
,
N. W.
,
Azizian
,
R.
, and
Pettigrew
,
M. J.
,
2009
, “
Modeling of Fluidelastic Instability in Tube Bundle Subjected to Two-Phase Cross-Flow
,”
Proceedings of the 6th CNS International Steam Generator Conference
,
Toronto
,
Ontario
,
Canada
,
Nov. 8–11
.
36.
Yetisir
,
M.
,
McKerrow
,
E.
, and
Pettigrew
,
M. J.
,
1998
, “
Fretting Wear Damage of Heat Exchanger Tubes: A Proposed Damage Criterion Based on Tube Vibration Response
,”
Trans. ASME J. Pressure Vessel Technol.
,
120
, pp.
297
305
.10.1115/1.2842061
37.
Janzen
,
V. P.
,
Hagberg
,
E. G.
,
Patrick
,
J. N. F.
,
Pettigrew
,
M. J.
,
Taylor
,
C. E.
, and
Whan
,
T. G.
,
2002
, “
Vibration Work-Rate Measurements of Steam-Generator U-Tubes in Air-Water Cross-Flow
,”
Proceedings of ASME International Mechanical Engineering Congress and Exposition
,
New Orleans, LA
, pp.
1019
1032
.
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