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Interaction of a shock with elliptical gas bubbles

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Abstract

The interaction of a shock with spherical and elliptical bubbles of light or heavy gas is numerically studied using the axisymmetric Euler equations. A model with a single heat capacity ratio \(\gamma \) is implemented, where bubbles are modeled by areas of the same gas with lower or higher density. Details of the general shock refraction patterns—diverging and converging—are described. The formation and development of secondary, focusing shocks are discussed. A computational parameter study for different Atwood numbers \(\mathrm{At}\, (\hbox {range } -0.54 \le \mathrm{At} \le 0.5)\), shock strengths \(M\, (\hbox {range }1.2 \le M \le 3)\), where \(M\) is the Mach number, and bubble geometries is performed. A basic classification for the shock focusing (cumulation) regimes is suggested, with the division of the internal, external and transitional focusing regimes determined by the position of the shock focusing point relative to the bubble. It is shown that the focusing pattern is governed not only by the Atwood number but also heavily by the Mach number and bubble shape. The qualitative dependence of cumulative intensity on bubble geometry is determined. The theoretical possibility of realizing an extremely intense shock collapse with a relatively small variation in bubble shape is demonstrated for the heavy-bubble scenario.

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Acknowledgments

The present study is financially supported by the Russian Science Foundation (Grant No. 14-11-00773) and Russian Foundation for Basic Research (Grant No. 14-01-00891).

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Authors and Affiliations

  1. Institute of Mechanics, Moscow State University, Michurinskiy pr. 1, Moscow, 119192, Russia

    P. Yu. Georgievskiy , V. A. Levin & O. G. Sutyrin

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  1. P. Yu. Georgievskiy
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  2. V. A. Levin
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  3. O. G. Sutyrin
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Correspondence to O. G. Sutyrin.

Additional information

Communicated by R. Bonazza.

This paper is based on work that was presented at the 29th International Symposium on Shock Waves, Madison, Wisconsin, USA, July 14–19, 2013.

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Georgievskiy , P.Y., Levin, V.A. & Sutyrin, O.G. Interaction of a shock with elliptical gas bubbles. Shock Waves 25, 357–369 (2015). https://doi.org/10.1007/s00193-015-0557-4

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  • DOI: https://doi.org/10.1007/s00193-015-0557-4

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