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Statistical equilibrium of bubble oscillations in dilute bubbly flows

Colonius, Tim and Hagmeijer, Rob and Ando, Keita and Brennen, Christopher E. (2008) Statistical equilibrium of bubble oscillations in dilute bubbly flows. Physics of Fluids, 20 (4). Art. No. 040902. ISSN 1070-6631.

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The problem of predicting the moments of the distribution of bubble radius in bubbly flows is considered. The particular case where bubble oscillations occur due to a rapid (impulsive or step change) change in pressure is analyzed, and it is mathematically shown that in this case, inviscid bubble oscillations reach a stationary statistical equilibrium, whereby phase cancellations among bubbles with different sizes lead to time-invariant values of the statistics. It is also shown that at statistical equilibrium, moments of the bubble radius may be computed using the period-averaged bubble radius in place of the instantaneous one. For sufficiently broad distributions of bubble equilibrium (or initial) radius, it is demonstrated that bubble statistics reach equilibrium on a time scale that is fast compared to physical damping of bubble oscillations due to viscosity, heat transfer, and liquid compressibility. The period-averaged bubble radius may then be used to predict the slow changes in the moments caused by the damping. A benefit is that period averaging gives a much smoother integrand, and accurate statistics can be obtained by tracking as few as five bubbles from the broad distribution. The period-averaged formula may therefore prove useful in reducing computational effort in models of dilute bubbly flow wherein bubbles are forced by shock waves or other rapid pressure changes, for which, at present, the strong effects caused by a distribution in bubble size can only be accurately predicted by tracking thousands of bubbles. Some challenges associated with extending the results to more general (nonimpulsive) forcing and strong two-way coupled bubbly flows are briefly discussed.

Item Type:Article
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Colonius, Tim0000-0003-0326-3909
Additional Information:© 2008 American Institute of Physics. Received 12 October 2007; accepted 18 January 2008; published 30 April 2008. The authors would like to express their thanks to Dr. Rutger IJzermans for his observations about Eq. (18). T.E.C. gratefully acknowledges support by NIH Grant No. PO1 DK43881 and ONR Grant No. N00014-06-1-0730. R.H. worked on this paper while visiting Caltech. He gratefully acknowledges support by Caltech and the University of Twente.
Funding AgencyGrant Number
NIHPO1 DK43881
Office of Naval Research (ONR)N00014-06-1-0730
Subject Keywords:bubbles, compressibility, heat transfer, two-phase flow, viscosity
Issue or Number:4
Record Number:CaltechAUTHORS:COLpof08
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:10399
Deposited By: Archive Administrator
Deposited On:02 May 2008
Last Modified:03 Oct 2019 00:09

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