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Small Non-Sphericity of a Convergent Shock Wave in a Collapsing Cavitation Bubble in Tetradecane

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Abstract

The paper is devoted to studying the growth of small deformations of the radially-convergent shock wave in a collapsing bubble with a radius of 500 \(\mu\)m in tetradecane at its temperature and pressure of 663.15 K and 70 bar. The initial bubble non-sphericity is taken in the form of single spherical harmonics with even numbers in the range 2–8. The vapor and liquid flow is governed by gas dynamic equations with allowing for the heat conduction in both fluids, the heat and mass exchange at the interface, with applying wide-range equations of state of vapor and liquid. It is shown that before transformation of the shock wave into a strong one, the variation of the amplitude of its small non-sphericity quite strongly depends on the number of the harmonic determining the small initial non-sphericity of the bubble. After this transformation, the amplitude of small non-sphericity of the shock wave until it remains small is increased with decreasing the shock wave radius according to the power law with an exponent of about \(-\)1.14. The only exception is a small interval in which the non-sphericity of the shock wave abruptly grows due to its interaction with a compression wave catching up with it.

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Authors and Affiliations

  1. Institute of Mechanics and Engineering, Federal Research Center Kazan Scientific Center, Russian Academy of Sciences, 420111, Kazan, Tatarstan, Russia

    A. A. Aganin & T. F. Khalitova

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  1. A. A. Aganin
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  2. T. F. Khalitova
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Correspondence to A. A. Aganin or T. F. Khalitova.

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Aganin, A.A., Khalitova, T.F. Small Non-Sphericity of a Convergent Shock Wave in a Collapsing Cavitation Bubble in Tetradecane. Lobachevskii J Math 41, 1137–1142 (2020). https://doi.org/10.1134/S1995080220070057

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  • DOI: https://doi.org/10.1134/S1995080220070057

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