Ensemble phase-averaged equations for bubbly flows

Journal Article · Thu Sep 01 04:00:00 EDT 1994 · Physics of Fluids; (United States)

DOI:https://doi.org/10.1063/1.868122· OSTI ID:7242030

Zhang, D Z; Prosperetti, A ^[1]

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1. Department of Mechanical Engineering, The Johns Hopkins University, Baltimore, Maryland 21218 (United States)

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. [bold 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.

• DOE Contract Number: FG02-89ER14043
• OSTI ID: 7242030
• Journal Information: Physics of Fluids; (United States), Journal Name: Physics of Fluids; (United States) Vol. 6:9; ISSN 1070-6631; ISSN PHFLE6
• Country of Publication: United States
• Language: English

Related Subjects

661300* -- Other Aspects of Physical Science-- (1992-)
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
BUBBLES
CONCENTRATION RATIO
DISPERSIONS
FLUID FLOW
FLUIDS
LIQUIDS
MIXTURES
MULTIPHASE FLOW
POTENTIAL FLOW
SPHERES
SUSPENSIONS
WAVE PROPAGATION