Numerical simulation of shock and detonation waves in bubbly liquids

摘要

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.