One-dimensional Bubbly Cavitating Flows through a Converging-diverging Nozzle

A non-barotropic continuum bubbly mixture model is used to study the one-dimensional cavitating ow 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 e ects on this con ned ow eld. One clear interaction e ect is the Bernoulli e ect caused by the growing and collapsing bubbles in the nozzle. It is found that the characteristics of the ow change dramatically even when the upstream void fraction is very small. Two di erent ow regimes are found from the steady state solutions and are termed: quasi-steady and quasi-unsteady. The former is characterized by large spatial uctuations downstream of the throat which are induced by the pulsations of the cavitation bubbles. The quasi-unsteady solutions correspond to ashing ow. Bifurcation occurs as the ow 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.