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Ensemble phase-averaged equations for bubbly flows
Abstract
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.
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Citations
Cited by
Averaged equations for inviscid disperse two-phase flow
Zhang, D. Z., & Prosperetti, A. (1994) · Journal of Fluid Mechanics · doi:10.1017/s0022112094001151 · Cited by 296
Self-citationNumerical analysis of the effects of air on light distribution in a bubble column photobioreactor
McHardy, C., Luzi, G., Lindenberger, C., Agudo, J. R., Delgado, A., & Rauh, C. (2018) · Algal Research · doi:10.1016/j.algal.2018.02.016 · Cited by 25
Metadata
- Authors
- Zhang, D. Z., & Prosperetti, A.
- Venue
- Physics of Fluids
- Publisher
- AIP Publishing
- Published
- 1994-09-01
- Volume
- 6
- Issue
- 9
- Pages
- 2956-2970
- ISSN
- 1070-6631 (ISSN-L)
- 1089-7666
- OpenAlex
- W2063980927
- Cited by
- 174
- References
- 0
- FWCI
- 9.82
- Type
- journal article
- Language
- en
- Open access
- closed
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