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A multiphase buoyancy-drag model for the study of Rayleigh-Taylor and Richtmyer-Meshkov instabilities in dusty gases

Published online by Cambridge University Press:  22 March 2011

Kaushik Balakrishnan  and
Suresh Menon
Kaushik Balakrishnan*
Affiliation:
Computing Sciences, Lawrence Berkeley National Laboratory, Berkeley, California
Suresh Menon
Affiliation:
School of Aerospace Engineering, Georgia Institute of Technology, Atlanta, Georgia
*
Address correspondence and reprint requests to: Kaushik Balakrishnan, Computing Sciences Department, Lawrence Berkeley National Laboratory, 1 Cyclotron Road, Berkeley, CA 94720. E-mail: kaushikb@lbl.gov
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Abstract

A new multiphase buoyancy-drag model is developed for the study of Rayleigh-Taylor and Richtmyer-Meshkov instabilities in dusty gases, extending on a counterpart single-phase model developed in the past by Srebro et al. (2003). This model is applied to single- and multi-mode perturbations in dusty gases and both Rayleigh-Taylor and Richtmyer-Meshkov instabilities are investigated. The amplitude for Rayleigh-Taylor growth is observed to be contained within a band, which lies within limits identified by a multiphase Atwood number that is a function of the fluid densities, particle size, and a Stokes number. The amplitude growth is subdued with (1) an increase in particle size for a fixed particle number density and with (2) an increase in particle number density for a fixed particle size. The power law index for Richtmyer-Meshkov growth under multi-mode conditions also shows dependence to the multiphase Atwood number, with the index for the bubble front linearly decreasing and then remaining constant, and increasing non-linearly for the spike front. Four new classes of problems are identified and are investigated for Rayleigh-Taylor growth under multi-mode conditions for a hybrid version of the model: (1) bubbles in a pure gas rising into a region of particles; (2) spikes in a pure gas falling into a region of particles; (3) bubbles in a region of particles rising into a pure gas; and (4) spikes in a region of particles falling into a pure gas. Whereas the bubbles accelerate for class (1) and the spikes for class (4), for classes (2) and (3), the spikes and bubbles, respectively, oscillate in a gravity wave-like phenomenon due to the buoyancy term changing sign alternatively. The spike or bubble front, as the case may be, penetrates different amounts into the dusty or pure gas for every subsequent penetration, due to drag effects. Finally, some extensions to the presently developed multiphase buoyancy-drag model are proposed for future research.

Keywords

Buoyancy-Drag modelDusty gasHydrodynamic instabilityRayleigh-TaylorRichtmyer-Meshkov
Type
Research Article
Information
Laser and Particle Beams , Volume 29 , Issue 2 , June 2011 , pp. 201 - 217
Copyright
Copyright © Cambridge University Press 2011

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