Two-phase flow exists in many shell-and-tube heat exchangers such as condensers, evaporators, and nuclear steam generators. Some knowledge on tube damping mechanisms is required to avoid flow-induced vibration problems. This paper outlines the development of a semi-empirical model to formulate damping of heat exchanger tube bundles in two-phase cross flow. The formulation is based on information available in the literature and on the results of recently completed experiments. The compilation of a database and the formulation of a design guideline are outlined in this paper. The effects of several parameters such as flow velocity, void fraction, confinement, flow regime and fluid properties are discussed. These parameters are taken into consideration in the formulation of a practical design guideline.

1.
Carlucci
,
L. N.
,
1980
, “
Damping and Hydrodynamic Mass of a Cylinder in Simulated Two-Phase Flow
,”
ASME J. Mech. Des.
,
102
, pp.
597
602
.
2.
Carlucci
,
L. N.
, and
Brown
,
J. D.
,
1983
, “
Experimental Studies of Damping and Hydrodynamic Mass of a Cylinder in Confined Two-Phase Flow
,”
ASME J. Vibr. Acoust., Stress, Reliab. Des.
105
, pp.
83
89
.
3.
Gorman, D. J., 1975, “Experimental and Analytical Study of Liquid and Two-Phase Flow-Induced Vibration in Reactor Fuel Bundles,” ASME Paper 75-PVP-52.
4.
Hara, F., and Kohgo, O., 1982, “Added Mass and Damping of a Vibrating Rod in a Two-Phase Air-Water Mixed Fluid,” ASME PVP Publication, 63, ASME, New York, pp. 1–8.
5.
Pettigrew, M. J., and Knowles, G. D., 1992, “Some Aspects of Heat Exchanger Tube Damping in Two-Phase Mixtures,” ASME Int. Symposium on Flow-Induced Vibration and Noise, 1, ASME, New York, pp. 141–160.
6.
Pettigrew, M. J., and Gorman, D. J., 1977, “Experimental Studies on Flow-Induced Vibration to Support Steam Generator Design, Part III: Vibration of Small Tube Bundles in Liquid and Two-Phase Cross Flow,” AECL Report, AECL-5804.
7.
Heilker
,
W. J.
, and
Vincent
,
R. Q.
,
1981
, “
Vibration in Nuclear Heat Exchangers Due to Liquid and Two-Phase Flow
,”
ASME J. Eng. Power
,
103
, pp.
358
365
.
8.
Remy, F. N., 1982, “Flow Induced Vibration of Tube Bundles in Two-Phase Cross Flow,” Proceedings of 3rd International Conference on Vibration in Nuclear Plants, 1, Paper No. 1.9, Keswick, UK, pp. 135–160.
9.
Axisa, F., Villard, B., Gibert, R. J., Hetsroni, G., and Sundheimer, P., 1984, “Vibration of Tube Bundles Subjected to Air-Water and Steam-Water Cross Flow: Preliminary Results on Fluidelastic Instability,” Proceedings of ASME Symposium on Flow-Induced Vibrations, 2, ASME, New York, pp. 269–284.
10.
Axisa, F., Boheas, M. A., and Villard, B., 1985, “Vibration of Tube Bundles Subjected to Steam-Water Cross Flow: A Comparative Study of Square and Triangular Arrays,” 8th International Conference on Structural Mechanics in Reactor Technology, Paper No. B1/2, Brussels.
11.
Nakamura
,
T.
,
Fujita
,
K.
,
Kawanishi
,
K.
, and
Saito
,
I.
,
1986
, “
A Study on the Flow Induced Vibration of a Tube Array by a Two-Phase Flow (2nd Report: Large Amplitude Vibration of Steam-Water Flow)
,”
Trans. Jpn. Soc. Mech. Eng., Ser. C
,
52
, No. 483, pp.
2790
2795
.
12.
Nakamura
,
T.
,
Yamaguchi
,
N.
,
Tsuge
,
A.
,
Fujita
,
K.
,
Sakata
,
K.
, and
Saito
,
I.
,
1986
, “
Study on Flow-Induced Vibration of a Tube Array by a Two-Phase Flow (1st Report: Large Amplitude Vibration by Air-Water Flow)
,”
Trans. Jpn. Soc. Mech. Eng., Ser. C
,
52
, No.
473
, pp.
252
257
.
13.
Taylor, C. E., Pettigrew, M. J., Axisa, F., and Villard, B., 1987, “Damping Measurements in Two-Phase Cross Flow,” Proceedings of 11th CANCAM Conference, Edmonton, Canada, pp. B148–B149.
14.
Axisa, F., Wullschleger, M., Villard, B., and Taylor, C., 1988, “Two-Phase Cross Flow Damping in Tube Arrays,” Proceedings of ASME Pressure Vessel and Piping Conference, PVP Vol. 133, ASME, New York, pp. 9–15.
15.
Pettigrew
,
M. J.
,
Tromp
,
J. H.
, and
Mastorakos
,
J.
,
1985
, “
Vibration of Tube Bundles Subjected to Two-Phase Cross Flow
,”
ASME J. Pressure Vessel Technol.
,
107
, pp.
335
343
.
16.
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
,”
ASME J. Pressure Vessel Technol.
,
111
, pp.
466
477
.
17.
Pettigrew
,
M. J.
,
Kim
,
B. S.
,
Taylor
,
C. E.
, and
Tromp
,
J. H.
,
1989
, “
Vibration of Tube Bundles in Two-Phase Cross Flow—Part 2: Fluidelastic Instability
,”
ASME J. Pressure Vessel Technol.
,
111
, pp.
478
487
.
18.
Taylor
,
C. E.
,
Pettigrew
,
M. J.
,
Currie
,
I. G.
, and
Kim
,
B. S.
,
1989
, “
Vibration of Tube Bundles in Two-Phase Cross Flow—Part 3: Turbulence Induced Excitation
,”
ASME J. Pressure Vessel Technol.
,
111
, pp.
488
500
.
19.
Pettigrew
,
M. J.
,
Taylor
,
C. E.
,
Jong
,
J. H.
, and
Currie
,
I. G.
,
1995
, “
Vibration of a Tube Bundle in Two-Phase Freon Cross Flow
,”
ASME J. Pressure Vessel Technol.
,
117
, pp.
321
329
.
20.
Pettigrew
,
M. J.
,
Taylor
,
C. E.
,
Janzen
,
V. P.
, and
Whan
,
T.
,
2002
, “
Vibration Behavior of Rotated Triangular Tube Bundles in Two-Phase Cross Flows
,”
ASME J. Pressure Vessel Technol.
,
124
(
2
), pp.
144
153
.
21.
Feenstra, P. A., Weaver, D. S., and Judd, R. L., 1996, “Damping and Fluidelastic Instability of a Tube Array in Two-Phase R-11 Cross Flow,” Proceedings of Symposium on Flow-Induced Vibration-1996, Vol. 328, ASME, New York, pp. 89–102.
22.
Grant, I. D. R., 1975, “Flow and Pressure Drop With Single Phase and Two-Phase Flow in the Shell-Side of Segmentally Baffled Shell-and-Tube Heat Exchangers,” NEL Report No. 590, National Engineering Laboratory, Glasgow, pp. 1–22.
23.
McNaught, J. M., 1982, “Two-Phase Forced Convection Heat Transfer During Condensation on Horizontal Tube Bundles,” 7th International Heat Transfer Conference, 5, Hemisphere Publishing Corporation, Washington, DC, pp. 125–131.
24.
Collier, J. G., 1979, “Two-Phase Gas-Liquid Flows Within Rod Bundles,” Turbulent Forced Convection in Channels and Bundles: Theory and Applications to Heat Exchangers and Nuclear Reactors, 2, Hemisphere Publishing Corporation, Washington, DC., pp. 1041–1055.
25.
Pettigrew
,
M. J.
,
Rogers
,
R. J.
, and
Axisa
,
F.
,
1986
, “
Damping of Multispan Heat Exchanger Tubes—Part 2: In Liquids
,”
ASME Pressure Vessels Symposium on Special Topics of Structural Vibration, and Piping Conference, Chicago
,
104
, pp.
89
98
.
26.
Chen
,
S. S.
,
Wambsganss
,
M. W.
, and
Jendrzyczyk
,
J. A.
,
1976
, “
Added Mass and Damping of a Vibrating Rod in Confined Viscous Fluids
,”
ASME J. Appl. Mech.
,
43
, pp.
325
329
.
27.
McAdams
,
W. H.
et al.
,
1942
, “
Vaporization Inside Horizontal Tubes: II—Benzene-Oil Mixtures
,”
Trans. ASME
,
64
, p.
193
193
.
28.
Rogers, R. G., Taylor, C. E., and Pettigrew, M. J., 1984, “Fluid Effects on Multi-Span Heat Exchanger Tube Vibration,” Proceedings of ASME PVP Conference, ASME, New York, pp. 17–26.
29.
Axisa, F., Villard, B., and Sundheimer, P., 1986, “Flow-Induced Vibration of Steam Generator Tubes,” Electric Power Research Institute Report EPRI-NP4559.
30.
Pettigrew
,
M. J.
,
Taylor
,
C. E.
, and
Kim
,
B. S.
,
2001
, “
The Effects of Tube Bundle Geometry on Vibration in Two-Phase Cross Flow
,”
ASME J. Pressure Vessel Technol.
,
123
(
4
), pp.
414
420
.
31.
Taylor
,
C. E.
,
Pettigrew
,
M. J.
,
Axisa
,
F.
, and
Villard
,
B.
,
1988
, “
Experimental Determination of Single and Two-Phase Cross Flow-Induced Forces on Tube Rows
,”
ASME J. Pressure Vessel Technol.
,
110
, pp.
22
28
.
32.
Pettigrew, M. J., Taylor, C. E., and Yasuo, A., 1994, “Vibration Damping of Heat Exchanger Tube Bundles in Two-Phase Flow,” Pressure Vessel Research Council Bulletin WRC 389, pp. 1–41.
33.
Hara, F., and Kohgo, O., 1986, “Numerical Approach to Added Mass and Damping of a Vibrating Circular Cylinder in a Two-Phase Bubble Fluid,” Proceedings of Int. Conf. on Computational Mechanics, Tokyo, VII, pp. 255–260.
You do not currently have access to this content.