This paper investigates the linearized dynamics of three-dimensional bubbly cavitating flows in helical inducers. The purpose is to understand the impact of the bubble response on the radial and tangential rotordynamic forces exerted by the fluid on the rotor and stator stages of whirling turbomachines under cavitating conditions. The flow in the inducer annulus is modeled as a homogeneous inviscid mixture, containing vapor bubbles with a small amount of noncondensable gas. The effects of several contributions to the damping of the bubble dynamics are included in the model. The governing equations of the inducer flow are written in “body-fitted” orthonormal helical Lagrangian coordinates, linearized for small-amplitude perturbations about the mean flow, and solved by modal decomposition. The whirl excitation generates finite-speed propagation and resonance phenomena in the two-phase flow within the inducer. These, in turn, lead to a complex dependence of the lateral rotordynamic fluid forces on the excitation frequency, the void fraction, the average size of the cavitation bubbles, and the turbopump operating conditions (including, rotational speed, geometry, flow coefficient and cavitation number). Under cavitating conditions the dynamic response of the bubbles induces major deviations from the noncavitating flow solutions, especially when the noncondensable gas content of the bubbles is small and thermal effects on the bubble dynamics are negligible. Then, the quadratic dependence of rotordynamic fluid forces on the whirl speed, typical of cavitation-free operation, is replaced by a more complex behavior characterized by the presence of different regimes where, depending on the whirl frequency, the fluid forces have either a stabilizing or a destabilizing effect on the inducer motion. Results are presented to illustrate the influence of the relevant flow parameters.

1.
Bhattacharyya, A., 1994, “Internal Flows and Force Matrices in Axial Flow Inducers,” Ph.D. thesis, Division of Engineering and Applied Science, California Institute of Technology, Pasadena, CA.
2.
Brennen, C. E., 1994, Hydrodynamics of Pumps, Concepts ETI, Inc. and Oxford University Press.
3.
Brennen, C. E., 1995, Cavitation and Bubble Dynamics, Oxford University Press.
4.
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
, Vol.
94
, pp.
172
183
.
5.
d’Agostino
L.
, and
Brennen
C. E.
,
1988
, “
Acoustical Absorption and Scattering Cross-Sections of Spherical Bubble Clouds
,”
Journal of the Acoustical Society of America
, Vol.
84
(
6
), pp.
2126
2134
.
6.
d’Agostino
L.
, and
Brennen
C. E.
,
1989
, “
Linearized Dynamics of Spherical Bubble Clouds
,”
Journal of Fluid Mechanics
, Vol.
199
, pp.
155
176
.
7.
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
.
8.
d’Auria, F., d’Agostino L. and Brennen C. E., 1994, “Linearized Dynamics of Bubbly and Cavitating Flows in Cylindrical Ducts,” ASME FED Vol. 194, pp. 59–66.
9.
d’Auria F., d’Agostino L. and Brennen C. E., 1995, “Bubble Dynamic Effects on the Rotordynamic Forces in Cavitating Inducers,” ASME FED Vol. 201, pp. 47–54.
10.
d’Auria
F.
,
d’Agostino
L.
, and
Brennen
C. E.
,
1996
, “
Dynamic Response of Ducted Bubbly Flows to Turbomachinery-Induced Perturbations
,”
ASME JOURNAL OF FLUIDS ENGINEERING
, Vol.
118
, pp.
595
601
.
11.
d’Auria, F., d’Agostino, L., and Burzagli, F., 1997, “Linear Stability of Parallel Two-Dimensional Shear Layers Containing Vapor-gas Bubbles,” ASME FEDSM, Vancouver, BC, June 22–26.
12.
Franz
R.
,
Acosta
A. J.
,
Brennen
C. E.
, and
Caughey
T. K.
,
1990
, “
The Rotordynamic Forces on a Centrifugal Pump Impeller in the Presence of Cavitation
,”
ASME JOURNAL OF FLUIDS ENGINEERING
, Vol.
112
, pp.
264
271
.
13.
Jery, B., Brennen, C. E., Caughey, T. K., and Acosta, A. J., 1985, “Forces on Centrifugal Pump Impellers,” Second International Pump Symposium, Houston, Texas, April 29-May 2.
14.
Lebedev, N. N., 1965, Special Functions and Their Applications, Prentice Hall.
15.
Nigmatulin
R. I.
,
Khabeev
N. S.
, and
Nagiev
F. B.
,
1981
, “
Dynamics, Heat and Mass Transfer of Vapor-Gas Bubbles in a Liquid
,”
International Journal of Mass Transfer
, Vol.
24
(
6
), pp.
1033
1044
.
16.
Prosperetti, A., 1984, “Bubble Phenomena in Sound Fields: Part One,” Ultrasonics, Mar., pp. 69–78.
17.
Prosperetti
A.
,
1991
, “
The Thermal Behavior of Oscillating Gas Bubbles
,”
Journal of Fluid Mechanics
, Vol.
222
, pp.
587
616
.
18.
Rosenmann, W., 1965, “Experimental Investigations of Hydrodynamically Induced Shaft Forces with a Three Bladed Inducer,” Proceedings of the ASME Symposium on Cavitation in Fluid Machinery, pp. 172–195.
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