Shocks in quasi-one-dimensional bubbly cavitating nozzle flows

Abstract

Stationary and propagating shock waves in bubbly cavitating flows through quasi-one-dimensional converging-diverging nozzles are considered by employing a homogeneous bubbly liquid flow model, where the nonlinear dynamics of cavitating bubbles is described by a modified Rayleigh-Plesset equation. The model equations are uncoupled by scale separation leading to two evolution equations, one for the flow speed and the other for the bubble radius. The initial/boundary value problem of the evolution equations is then formulated and a semi-analytical solution is constructed. The solution for the mixture pressure, the mixture density and the void fraction are then explicitly related to the solution of the evolution equations. The steady-state compressible limit of the solution with stationary shocks is obtained and the stability of such shocks are examined. Finally, results obtained using the semi-analytical constructed algorithm for propagating shock waves in bubbly cavitating flows through converging-diverging nozzles, which agree with those of previous numerical investigations, are presented.