The present work investigates the dynamics of the three-dimensional, unsteady flow of a bubbly mixture in a cylindrical duct subject to a periodic pressure excitation at one end. One of the purposes is to investigate the bubbly or cavitating flow at inlet to or discharge from a pump whose blade motions would provide such excitation. The flow displays various regimes with radically different wave propagation characteristics. The dynamics effects due to the bubble response may radically alter the fluid behavior depending on the void fraction of the bubbly mixture, the mean bubble size, the pipe diameter, the angular speed of the turbomachine and the mean flow Mach number. This simple linearized analysis illustrates the importance of the complex interactions of the dynamics of the bubbles with the average flow, and provides information on the propagation and growth of the turbopump-induced disturbances in the feed lines operating with bubbly or cavitating liquids. Examples are presented to illustrate the influence of the relevant flow parameters. Finally, the limitations of the theory are outlined.

1.
Brennen, C. E., 1994, “Hydrodynamics of Pumps,” Concepts ETI Inc. and Oxford University Press.
2.
Benzakein
M. J.
,
1972
, “
Research on Fan Noise Generation
,”
Journal of the Acoustical Society of America
, Vol.
51
, No.
5
, Part I, pp.
1427
1438
.
3.
Chahine, G. L., 1982a, “Pressure Field Generated by the Collective Collapse of Cavitation Bubbles,” IAHR Symposium on Operating Problems of Pump Stations and Power Plants, Amsterdam, Netherlands, Vol. 1, Paper No. 2.
4.
Chahine, G. L., 1982b, “Cloud Cavitation Theory,” 14th Symposium on Naval Hydrodynamics, Session I, p. 51.
5.
Chahine, G. L., Duraiswami, R., and Lakshminarasimha, A. N., 1991, “Dynamical Interactions in a Bubble Cloud,” ASME Cavitation and Multiphase Flow Forum, Portland, OR, pp. 49–54.
6.
Chapman, R. B., and Plesset, M. S., 1972, “Nonlinear Effects in the Collapse of a Nearly Spherical Cavity in a Liquid,” ASME Journal of Basic Engineering, pp. 172–183.
7.
d’Agostino, L., and Brennen, C. E., 1983, “On the Acoustical Dynamics of Bubble Clouds,” ASME Cavitation and Multiphase Flow Forum, Houston, TX.
8.
d’Agostino, L., and Brennen, C. E., 1988, “Acoustical Absorption and Scattering Cross-Sections of Spherical Bubble Clouds,” J. Acoust. Soc. Am., No. 84 (6), pp. 2126–2134.
9.
d’Agostino
L.
, and
Brennen
C. E.
,
1989
, “
Linearized Dynamics of Spherical Bubble Clouds
,”
Journal of Fluid Mechanics
, Vol.
199
, pp.
155
176
.
10.
d’Agostino
L.
,
Brennen
C. E.
, and
Acosta
A. J.
,
1988
, “
Linearized Dynamics of Two-Dimensional Bubbly and Cavitating Flows over Slender Surfaces
,”
Journal of Fluid Mechanics
, Vol.
192
, pp.
485
509
.
11.
d’Auria, F., d’Agostino, L., and Brennen, C. E., 1994, “Linearized Dynamics of Bubbly and Cavitating Flows in Cylindrical Ducts,” ASME Cavitation and Multiphase Flow Forum, Lake Tahoe, NV, pp. 59–66.
12.
Hansson
I.
,
Kedriniskii
V.
, and
Mo̸rch
K. A.
,
1981
, “
On the Dynamics of Cavity Clusters
,”
Journal of Applied Physics
, Vol.
15
, pp.
1725
1734
.
13.
Knapp, R. T., Daily, J. W., and Hammit, F. G., 1970, Cavitation, McGraw Hill, New York.
14.
Kumar, S., and Brennen, C. E., 1990, “Nonlinear Effects in Cavitation Cloud Dynamics,” ASME Cavitation and Multiphase Flow Forum, Toronto, Ontario, Canada, pp. 107–113.
15.
Lebedev, N. N., 1965, Special Functions and Their Applications, Prentice Hall.
16.
Mo̸rch, K. A., 1980, “On the Collapse of Cavity Cluster in Flow Cavitation,” Proceedings of the 1st International Conference on Cavitation and Inhomogeneities in Underwater Acoustics, Springer Series in Electrophysics, Vol. 4, pp. 95–100.
17.
Mo̸rch, K. A., 1981, “Cavity Cluster Dynamics and Cavitation Erosion,” ASME Cavitation and Polyphase Flow Forum, 1981, pp. 1–10.
18.
Mo̸rch
K. A.
,
1982
, “
Energy Considerations on the Collapse of Cavity Cluster
,”
Applied Scientific Research
, Vol.
38
, p.
313
313
.
19.
Omta
R.
,
1987
, “
Oscillations of a Cloud of Bubbles of Small and Not So Small Amplitude
,”
Journal of the Acoustical Society of America
, Vol.
82
(
3
), pp.
1018
1033
.
20.
Plesset
M. S.
, and
Prosperetti
A.
,
1977
, “
Bubble Dynamics and Cavitation
,”
Annual Review of Fluid Mechanics
, Vol.
9
, pp.
145
185
.
21.
Pylkka¨nen, J. V., 1986, “Characteristics of Spherical Cloud Cavity,” Advancements in Aerodynamics, Fluid Mechanics and Hydraulics, Amdt et al., eds., ASCE Conference, Minneapolis, MN, pp. 96–103.
22.
Prosperetti, A., 1984, “Bubble Phenomena in Sound Fields: Part One,” Ultrasonics, Mar. pp. 69–78.
23.
Prosperetti
A.
,
1977
, “
Thermal Effects and Damping Mechanisms in the Forced Radial Oscillations of Gas Bubbles in Liquids
,”
Journal of the Acoustical Society of America
, Vol.
61
, No.
1 (6)
, pp.
17
27
.
24.
Stewart
H. B.
, and
Wendroff
B.
,
1984
, “
Two-Phase Flows: Models and Methods
,”
Journal of Computational Physics
, Vol.
56
, pp.
363
409
.
25.
Tyler
J. M.
, and
Sofrin
T. G.
,
1962
, “
Axial Flow Compressor Noise Studies
,”
SAE Transactions
, Vol.
70
, pp.
309
332
.
26.
van Wijngaarden, L., 1964, “On the Collective Collapse of a Large Number of Gas Bubbles in Water,” Proceedings of the 11th International Congress on Applied Mechanics, Springer-Verlag, Berlin, pp. 854–861.
27.
van Wijngaarden
L.
,
1968
, “
On the Equations of Motion of Mixtures of Liquid and Gas Bubbles
,”
Journal of Fluid Mechanics
, Vol.
33
, part 3, pp.
465
474
.
28.
van Wijngaarden
L.
,
1972
, “
One-Dimensional Flow of Liquids Containing Small Gas Bubbles
,”
Annual Review of Fluid Mechanics
, Vol.
4
, pp.
369
396
.
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