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.