Stability Analysis of One-Dimensional Steady Cavitating Nozzle Flows With Bubble Size Distribution

[+] Author and Article Information
Yi-Chun Wang

Department of Mechanical Engineering, National Cheng Kung University, Tainan 701, Taiwan

J. Fluids Eng 122(2), 425-430 (Dec 20, 1999) (6 pages) doi:10.1115/1.483273 History: Received April 12, 1999; Revised December 20, 1999
Copyright © 2000 by ASME
Your Session has timed out. Please sign back in to continue.


Wang,  Y.-C., and Brennen,  C. E., 1998, “One-Dimensional Bubbly Cavitating Flows Through a Converging-Diverging Nozzle,” ASME J. Fluids Eng., 120, pp. 166–170.
Ceccio,  S. L., and Brennen,  C. E., 1991, “Observations of the Dynamics and Acoustics of Travelling Bubble Cavitation,” J. Fluid Mech., 233, pp. 633–660.
Tanger, H., Streckwall, H., Weitendorf, E.-A., and Mills, L., 1992, “Recent Investigations of the Free Air Content and its Influence on Cavitation and Propeller-Excited Pressure Fluctuations,” Proceedings of the International Symposium on Propulsors and Cavitation, Hamburg.
Gindroz, B., Henry, P., and Avellan, F., 1992, “Francis Cavitation Tests with Nuclei Injection: A New Test Procedure,” Proceedings of the 16th IAHR, Sao Paulo.
Peterson, F. B., Danel, F., Keller, A. P., and Lecoffre, Y., 1975, “Comparative Measurements of Bubble and Particulate Spectra by Three Optical Methods,” Proceedings of the 14th International Towing Tank Conference, Vol. 2, Ottawa, Canada, pp. 27–52.
Gates,  E. M., and Bacon,  J., 1978, “Determination of Cavitation Nuclei Distribution by Holography,” J. Ship Res., 22, No. 1, pp. 29–31.
Katz, J., 1978, “Determination of Solid Nuclei and Bubble Distributions in Water by Holography,” Report No. 183-3, Division of Engineering and Applied Science, California Institute of Technology, Pasadena, CA.
O’Hern, T. J., Katz, J., and Acosta, A. J., 1985, “Holographic Measurements of Cavitation Nuclei in the Sea,” Proceedings of ASME Cavitation and Multiphase Flow Forum, pp. 39–42.
van Wijngaarden,  L., 1972, “One-Dimensional Flow of Liquids Containing Small Gas Bubbles,” Annu. Rev. Fluid Mech., 4, pp. 369–396.
Biesheuvel,  A., and van Wijngaarden,  L., 1984, “Two-Phase Flow Equations for a Dilute Dispersion of Gas Bubbles in Liquid,” J. Fluid Mech., 148, pp. 301–318.
Muir, J. F., and Eichhorn, R., 1963, “Compressible Flow of an Air-Water Mixture through a Vertical Two-Dimensional Converging-Diverging Nozzle,” Proceedings of the 1963 Heat Transfer and Fluid Mechanics Institute, Stanford University Press, pp. 183–204.
Brennen, C. E., 1995, Cavitation and Bubble Dynamics, Oxford University Press, New York.
Zhang,  D. Z., and Prosperetti,  A., 1994, “Ensemble Phase-Averaged Equations for Bubbly Flows,” Phys. Fluids, 6, No. 9, pp. 2956–2970.
Ishii, M., and Mishima, K., 1983, “Flow Regime Transition Criteria Consistent with a Two-Fluid Model for Vertical Two-Phase Flow,” Reports NUREG/CR-3338 & ANL-83-42.
Plesset,  M. S., and Prosperetti,  A., 1977, “Bubble Dynamics and Cavitation,” Annu. Rev. Fluid Mech., 9, pp. 145–185.
Chapman,  R. B., and Plesset,  M. S., 1971, “Thermal Effects in the Free Oscillation of Gas Bubbles,” ASME J. Basic Eng., 93, pp. 373–376.
Colonius, T., Brennen, C. E., and d’Auria, F., 1998, “Computation of Shock Waves in Cavitating Flows,” ASME 3rd International Symposium on Numerical Methods for Multiphase Flow, FEDSM98-5027.
d’Agostino,  L., and Brennen,  C. E., 1988, “Linearized Dynamics of Two-Dimensional Bubbly and Cavitating Flows over Slender Surfaces,” J. Fluid Mech., 192, pp. 485–509.
Dennis, J. E., and Schnabel, R. B., 1983, Numerical Methods for Unconstrained Optimization and Nonlinear Equations, Prentice-Hall, Englewood Cliffs, NJ.


Grahic Jump Location
Notation for bubbly liquid flow in a converging-diverging nozzle
Grahic Jump Location
The fluid velocity distribution as a function of the normalized position in the flow for four different upstream void fractions. Equilibrium sizes of the upstream nuclei are in the range of [Rs MIN*,Rs MAX*]=[10,200] μm and Rs*=10 μm for the case of single bubble size. Labels of αsb and αsb+ correspond to αs just below and above the value of αb≈17.86×10−6. The various parameters are L=900, σ=0.85, CP MIN=−1.0. The critical fluid velocity which activates the flashing instability is labeled as uc.
Grahic Jump Location
The fluid pressure coefficient corresponding to Fig. 2
Grahic Jump Location
The void fraction distribution corresponding to Fig. 2
Grahic Jump Location
The fluid energy density distribution corresponding to Fig. 2
Grahic Jump Location
Schematic of f(x)=(1−αs)/(1−α(x)), for 0≤x≤xc
Grahic Jump Location
Schematic of bubble growth through a low-pressure region
Grahic Jump Location
Stable and unstable radius distributions for bubbles of three selected equilibrium sizes. Same parameters as Fig. 2 with αsb (solid line) and αsb+ (dashed line).
Grahic Jump Location
Comparison of three numerically calculated f(x) and that given by Eq. (13). Same parameters as Fig. 2.



Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In