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Calculation of small deformations of a radially convergent shock wave inside a cavitation bubble. (English) Zbl 1472.76057

Summary: The possibility of increasing the efficiency of calculation of small axisymmetric non-sphericity of a radially convergent shock wave in a collapsing cavitation bubble by the Godunov method of increased order of accuracy is shown in the case the surfaces of the bubble and the shock wave are presented as a combination of the spherical component and its small perturbation in the form of a spherical harmonic of some degree \(n\). The dynamics of the vapor in the bubble and the surrounding liquid in the final high-speed stage of collapse is governed by the equations of gas dynamics closed by wide-range equations of state. Non-uniform moving radially-divergent grids are applied, condensing to the bubble surface. An increase in the calculation efficiency is achieved by decreasing the apex angle of the computational domain from (normally accepted) \( \pi/2\) to a value that is the minimum among nonzero angles \(\theta\) corresponding to the local extrema of the Legendre polynomial of degree \(n\) in \(\cos{\theta} \). This way of increasing the calculation efficiency was used to study the growth of small axisymmetric non-sphericity of a radially convergent shock wave in a collapsing cavitation bubble in acetone with a temperature of 273.15 K and a pressure of 15 bar in the case of the initial non-sphericity of the bubble in the form of even harmonics of degree \(n=6-18\). It was found that in the initial stage of convergence of the shock wave, where it turns into a strong one, its non-sphericity increases more slowly than during the subsequent convergence. In the initial stage, the growth rate of non-sphericity decreases with increasing \(n\). During the subsequent convergence, the non-sphericity of the shock wave grows, independently of \(n\), proportionally to its radius to the power of \(-1.12\).

MSC:

76L05 Shock waves and blast waves in fluid mechanics
76T10 Liquid-gas two-phase flows, bubbly flows
76M20 Finite difference methods applied to problems in fluid mechanics
76M12 Finite volume methods applied to problems in fluid mechanics
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