On the Stability of Parallel Bubbly Cavitating Flows

This paper reviews some recent results on the effects of the dynamics of bubbles with various vapor-gas contents on the stability of two-dimensional parallel bubbly flows of low void fraction. The equations of motion for the bubbly mixture are linearized for small perturbations and the parallel flow assumption in used to obtain ODE systems governing the inviscid and viscous stability problems and equivalent to modified Rayleigh and Orr-Sommeifeld equations of single-phase barotropic flows. These systems are then used for the study of the spatial stability of two-dimensional inviscid shear layers and Blasius boundary layers. The effect of compressibility, inertia and energy dissipation due to the viscosity of the liquid and the transfer of heat and mass between the two phases are included in the bubble dynamic model. Numerical solutions of the eigenvalue problem for the stability equations are obtained by means of a shooting method combined, in the viscous case, with the O'Drury-Davey's (1983) orthogonalization algorithm in order to overcome the inherent stiffness of the equations. at higher Reynolds numbers. The present analysis confirms that the presence of the dispersed phase has a stabilizing effect and, depending on the values of the flow parameters, can induce significant departures from the classical results for single phase fluids, especially when the occurrence of resonant bubble oscillations greatly enhances the coupling with the perturbation field. More importantly, the present analysis points out some major differences in the stability characteristics of parallel flows containing vapor-gas bubbles when compared to those containing non-condensable gas. Results are shown to illustrate these effects for some representative flow configurations and conditions.