Shock propagation in polydisperse bubbly flows

Abstract

The effect of distributed bubble size on shock propagation in homogeneous bubbly liquids is computed using a continuum two-phase model. An ensemble-averaging technique is employed to derive the statistically averaged equations and a finite-volume method is used to solve the model equations. The bubble dynamics are incorporated using a Rayleigh-Plesset-type equation which includes the effects of heat transfer, liquid viscosity and compressibility. For the case of monodisperse bubbles, it is known that relaxation oscillations occur behind the shock due to the bubble dynamics. The present computations for the case of polydisperse bubbles show that bubble size distributions lead to additional damping of the shock dynamics. If the distribution is sufficiently broad, the statistical effect dominates over the physical damping associated with the single bubble dynamics. This smooths out the oscillatory shock structure.