The steady cavitating flow through a converging-diverging nozzle is considered. A continuum model is assumed with the Rayleigh-Plesset equation to account for the bubble dynamics. A similar problem has been studied previously by Wang and Brennen, and they found that if the upstream gas volume fraction of the bubbles exceeds a critical value there is flashing flow instability. In the present work, a perturbation analysis is made introducing a small parameter, ε, that is the ratio of the initial bubble diameter to the length scale of the nozzle. As a result of this analysis, the critical value of the upstream void fraction is calculated as a function of the several parameters appearing in the problem, and turns out to be very small and proportional to A correlation is proposed giving explicitly the functional dependence of this critical value.
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December 2001
Technical Papers
Stability Criteria of the Steady Flow of a Liquid Containing Bubbles Along a Nozzle
A. Crespo,
A. Crespo
Universidad Polite´cnica de Madrid, Departamento de Ingenierı´a Energe´tica y Fluidomeca´nica, Jose´ Gutie´rrez Abascal, 2, 28006 Madrid, Spain
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J. Garcı´a,
J. Garcı´a
Universidad Polite´cnica de Madrid, Departamento de Ingenierı´a Energe´tica y Fluidomeca´nica, Jose´ Gutie´rrez Abascal, 2, 28006 Madrid, Spain
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J. Jime´nez-Ferna´ndez
J. Jime´nez-Ferna´ndez
Universidad Polite´cnica de Madrid, Departamento de Ingenierı´a Energe´tica y Fluidomeca´nica, Jose´ Gutie´rrez Abascal, 2, 28006 Madrid, Spain
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A. Crespo
Universidad Polite´cnica de Madrid, Departamento de Ingenierı´a Energe´tica y Fluidomeca´nica, Jose´ Gutie´rrez Abascal, 2, 28006 Madrid, Spain
J. Garcı´a
Universidad Polite´cnica de Madrid, Departamento de Ingenierı´a Energe´tica y Fluidomeca´nica, Jose´ Gutie´rrez Abascal, 2, 28006 Madrid, Spain
J. Jime´nez-Ferna´ndez
Universidad Polite´cnica de Madrid, Departamento de Ingenierı´a Energe´tica y Fluidomeca´nica, Jose´ Gutie´rrez Abascal, 2, 28006 Madrid, Spain
Contributed by the Fluids Engineering Division for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received by the Fluids Engineering Division October 4, 2000; revised manuscript received August 8, 2001. Associate Editor: Y. Matsumoto.
J. Fluids Eng. Dec 2001, 123(4): 836-840 (5 pages)
Published Online: August 8, 2001
Article history
Received:
October 4, 2000
Revised:
August 8, 2001
Citation
Crespo , A., Garcı´a , J., and Jime´nez-Ferna´ndez, J. (August 8, 2001). "Stability Criteria of the Steady Flow of a Liquid Containing Bubbles Along a Nozzle ." ASME. J. Fluids Eng. December 2001; 123(4): 836–840. https://doi.org/10.1115/1.1412564
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