Shock propagation in polydisperse bubbly flows

Abstract

The effect of distributed bubble nuclei sizes on shock propagation in dilute bubbly liquids is computed using a continuum two-phase model. An ensemble-averaging technique is employed to derive the statistically averaged equations and a finitevolume 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. The numerical model is verified by computing linear wave propagation and comparing to the acoustic theory of dilute bubbly liquids. It is known that for the case of monodisperse mixtures, relaxation oscillations occur behind the shock due to the bubble dynamics. The present computations show that bubble size distributions lead to additional damping of the average shock dynamics. If the distribution is sufficiently broad, the effect of polydispersity dominates over the singlebubble-dynamic damping and the shock profile is smoothed out. The size distribution effect on bubble screen problems is also discussed.