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.
Stability Criteria of the Steady Flow of a Liquid Containing Bubbles Along a Nozzle
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.
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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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