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

[+] Author and Article Information
A. Crespo, J. Garcı́a, J. Jiménez-Fernández

Universidad Politécnica de Madrid, Departamento de Ingenierı́a Energética y Fluidomecánica, José Gutiérrez Abascal, 2, 28006 Madrid, Spain

J. Fluids Eng 123(4), 836-840 (Aug 08, 2001) (5 pages) doi:10.1115/1.1412564 History: Received October 04, 2000; Revised August 08, 2001
Copyright © 2001 by ASME
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van Wijngaarden,  L., 1972, “One-dimensional flow of liquids containing small gas bubbles,” Annu. Rev. Fluid Mech., 4, pp. 369–396.
Wang,  Y., and Brennen,  C. E., 1998, “One-dimensional bubbly cavitating flows through a converging-diverging nozzle,” ASME J. Fluids Eng., 120, pp. 166–170.
Wang,  Y., 2000, “Stability analysis of one-dimensional steady cavitating nozzle flows with bubble size distribution,” ASME J. Fluids Eng., 122, pp. 425–430.
Delale,  C. F., Schnerr,  G. H., and Sauer,  J., 2001, “Quasi-one-dimensional steady-state cavitating nozzle flows,” J. Fluid Mech., 427, pp. 167–204.
Crespo, A., Garcı́a, J., and Jiménez-Fernández, J., 1999, “One dimensional waves in a liquids containing bubbles flowing along a tube with an elastic wall,” IUTAM Symposium on Nonlinear Waves in Multiphase Flow. University of Notre Dame. July Proceedings pp. 251–260. Fluid Mechanics and its Applications, Vol. 57, Kluwer.
Watanabe,  M., and Prosperetti,  A., 1994, “Shock waves in dilute bubbly liquids,” J. Fluid Mech., 274, pp. 349–381.


Grahic Jump Location
Comparison of the bifurcation parameter for the two nozzle shapes
Grahic Jump Location
Variation of the bifurcation parameter as function of σ/|cp min|, and |cp min|. Comparison of the solutions obtained with Eq. (30), the system of equations (3), (4), (5′), (6′), and the original system of equations of Wang and Brennen 2.
Grahic Jump Location
Schematic showing the evolution of the bubble radius for γ above and below its critical value




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