On the Stability of Parallel Bubbly Cavitating Flows

This paper illustrates the effects of the dynamics of bubbles with arbitrary vapor-gas contents on the inviscid and viscous stability of two-dimensional parallel bubbly flows of low void fraction. The linear penurbation equations derived for the stability analysis include the effects of bubble compressibility, inertia, and energy dissipation due to the viscosity of the liquid and the transfer of heat and mass as a consequence of compression/ expansion of the noncondensable gas and evaporation/condensation of the vapor contained in the bubbles. Numerical solution of the spatial stability problem for twodimensional inviscid shear layers and Blasius boundary layers confirms that the presence of the dispersed phase is generally in favor of stability. Significant deviations from the classical results for compressible and incompressible single phase fluids are observed, especially when the occurrence of large compliant and/or resonant oscillations of the bubbles greatly enhances their dynamic coupling with the perturbation field. More imponantly, the present analysis points out some major differences in the stability of parallel flows with noncondensable gas bubbles with respect to cavitating flows containing bubbles with a dominant content of vapor. Unconditional stability is predicted in the travelling bubble cavitation limit for low pressures and high vapor mass fraction of the bubble contents. Results are shown to illustrate these effects for some representative flow configurations and conditions.