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Numerical simulation of shock and detonation waves in bubbly liquids

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Abstract

A well-posed mathematical model of nonisothermal, two-phase, two-velocity flow of a bubbly medium with chemically inert liquid and chemically inert or active gas bubbles is proposed. The model is based on the two-phase Euler equations with the introduction of an additional pressure at the gas-bubble surface, which ensures the well-posedness of the Cauchy problem for a system of governing equations, and the Rayleigh–Plesset equation for radial pulsation of gas bubbles allowing solutions of the soliton type that are realized in experiments to be obtained. The model is validated by comparing calculations of detonation wave propagation with experimental data in water or an aqueous solution of glycerin with bubbles of acetylene–oxygen mixture or with bubbles of argon–hydrogen–oxygen mixture for a volume gas content of 1–6%. The model is shown to provide satisfactory results for the detonation propagation velocity and detonation pressure profiles.

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Acknowledgements

This work was supported by the subsidy given to the N.N. Semenov Federal Research Center for Chemical Physics of the Russian Academy of Sciences to implement the state assignment on the topic No. 0082-2016-0011 “Fundamental studies of conversion processes of energetic materials and development of scientific grounds of controlling these processes” (Registration No. AAAA-A17-117040610346-5) and to the Federal State Institution “Scientific Research Institute for System Analysis of the Russian Academy of Sciences” to implement the state assignment on the topic No. 0065-2019-0005 “Mathematical modeling of dynamic processes in deformed and reactive media using multiprocessor computational systems” (Registration No. AAAA-A19-119011 590092-6), and partially supported by the Russian Foundation for Basic Research (Project 16-29-01065ofi-m).

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  1. N.N. Semenov Federal Research Center for Chemical Physics, Russian Academy of Sciences, Moscow, Russia

    R. R. Tukhvatullina & S. M. Frolov

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  1. R. R. Tukhvatullina
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Correspondence to R. R. Tukhvatullina.

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Tukhvatullina, R.R., Frolov, S.M. Numerical simulation of shock and detonation waves in bubbly liquids. Shock Waves 30, 263–271 (2020). https://doi.org/10.1007/s00193-019-00914-2

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