Quasi-one-dimensional steady-state cavitating nozzle flows

Abstract

Quasi-one-dimensional cavitating nozzle flows are considered by employing a homogeneous bubbly liquid flow model. The nonlinear dynamics of cavitating bubbles is described by a modified Rayleigh–Plesset equation that takes into account bubble/bubble interactions by a local homogeneous mean-field theory and the various damping mechanisms by a damping coefficient, lumping them together in the form of viscous dissipation. The resulting system of quasi-one-dimensional cavitating nozzle flow equations is then uncoupled leading to a nonlinear third-order ordinary differential equation for the flow speed. This equation is then cast into a nonlinear dynamical system of scaled variables which describe deviations of the flow field from its corresponding incompressible single-phase value. The solution of the initial-value problem of this dynamical system can be carried out very accurately, leading to an exact description of the hydrodynamic field for the model considered.

A bubbly liquid composed of water vapour–air bubbles in water at 20 °C for two different area variations is considered, and the initial cavitation number is chosen in such a way that cavitation can occur in the nozzle. Results obtained, when bubble/bubble interactions are neglected, show solutions with flow instabilities, similar to the flashing flow solutions found recently by Wang and Brennen. Stable steady-state cavitating nozzle flow solutions, either with continuous growth of bubbles or with growth followed by collapse of bubbles, were obtained when bubble/bubble interactions were considered together with various damping mechanisms.