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

Abstract

A continuum bubbly mixture model coupled to the Rayleigh-Plesset equation for the bubble dynamics is employed to study one-dimensional steady bubbly cavitating flows through a converging-diverging nozzle. A distribution of nuclei sizes is specified upstream of the nozzle, and the upstream cavitation number and nozzle contraction are chosen so that cavitation occurs in the flow. The computational results show very strong interactions between cavitating bubbles and the flow. The bubble size distribution may have significant effects on the flow; it is shown that it reduces the level of fluctuations and therefore reduces the “cavitation loss” compared to a monodisperse distribution. Another interesting interaction effect is that flashing instability occurs as the flow reaches a critical state downstream of the nozzle. A stability analysis is proposed to predict the critical flow variables. Excellent agreement is obtained between the analytical and numerical results for flows of both equal bubble size and multiple bubble sizes. [S0098-2202(00)00702-1]