One-Dimensional Bubbly Cavitating Flows Through a Converging-Diverging Nozzle

Abstract

A nonbarotropic continuum bubbly mixture model is used to study the one-dimensional cavitating flow through a converging-diverging nozzle. The nonlinear dynamics of the cavitation bubbles are modeled by the Rayleigh-Plesset equation. Analytical results show that the bubble/bubble interaction through the hydrodynamics of the surrounding liquid has important effects on this confined flow field. One clear interaction effect is the Bernoulli effect caused by the growing and collapsing bubbles in the nozzle. It is found that the characteristics of the flow change dramatically even when the upstream void fraction is very small. Two different flow regimes are found from the steady state solutions and are termed: quasi-steady and quasi-unsteady. The former is characterized by large spatial fluctuations downstream of the throat which are induced by the pulsations of the cavitation bubbles. The quasi-unsteady solutions correspond to flashing flow. Bifurcation occurs as the flow transitions from one regime to the other. An analytical expression for the critical bubble size at the bifurcation is obtained. Physical reasons for this quasi-static instability are also discussed.