Quasi-one-dimensional steady-state cavitating nozzle flows

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 in to account bubble/bubble interactions by a local homogeneous mean-held theo ry and the various damping mechanisms by a damping coefficient, lumping the m together in the form of viscous dissipation. The resulting system of quas i-one-dimensional cavitating nozzle flow equations is then uncoupled leadin g to a nonlinear third-order ordinary differential equation for the flow sp eed. This equation is then cast into a nonlinear dynamical system of scaled variables which describe deviations of the flow field from its correspondi ng incompressible single-phase value. The solution of the initial-value pro blem of this dynamical system can be carried out very accurately, leading t o an exact description of the hydrodynamic field for the model considered. A bubbly liquid composed of water vapour-air bubbles in water at 20 degrees C for two different area variations is considered, and the initial cavitati on number is chosen in such a way that cavitation can occur in the nozzle. Results obtained, when bubble/bubble interactions are neglected, show solut ions with flow instabilities, similar to the flashing flow solutions found recently by Wang and Brennen. Stable steady-state cavitating nozzle flow so lutions, either with continuous growth of bubbles or with growth followed b y collapse of bubbles, were obtained when bubble/bubble interactions were c onsidered together with various damping mechanisms.