Ensemble phase averaged equations for bubbly flows

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The Physics of Fluids

A system of averaged equations describing the motion of a mixture of spherical compressible bubbles in an inviscid liquid is derived by the ensemble?averaging method introduced in an earlier paper [Zhang and Prosperetti, J. Fluid Mech. 267, 185 (1994)]. The averaging procedure introduces new terms in the equations, among which a contribution to the liquid stress tensor is of special interest. An extension of the well?known Rayleigh–Plesset equation to the case of bubbles interacting with the flow is also found. The general system of equations is closed in a rigorous manner in the dilute limit generalizing and correcting earlier averaged equations models. The results are illustrated by considering the problem of linear pressure wave propagation in a nonuniform bubbly liquid. Gradients of the bubble concentration are shown to dampen or amplify the wave strength.

Wave propagation, Bubble dynamics, Bubbly liquids
Copyright 1994 Physics of Fluids. Recommended citation: Zhang, D. Z., and A. Prosperetti. "Ensemble phase?averaged equations for bubbly flows." Physics of Fluids 6, no. 9 (1994): 2956-2970. DOI: 10.1063/1.868122 URL: https://aip.scitation.org/doi/abs/10.1063/1.868122 Reproduced in accordance with the original publisher’s licensing terms and with permission from the author(s).