Late-time turbulent mixing induced by multimode Richtmyer–Meshkov instability in cylindrical geometry

Abstract

Turbulent mixing induced by Richtmyer–Meshkov instability (RMI) in convergent geometry widely exists in natural phenomena and in engineering applications. In the present work, high-resolution numerical simulations of RMI at a complete cylindrical interface, with the imploding shock wave initially passing from the heavy fluid to the light fluid, are presented. Two different initial perturbations are applied. The mixing zone finally reaches a convergence ratio Cr ≈ 1.6 in both cases. Compared to classical RM instability, the more complex wave system, as well as the geometrical effect induced by the radial movement of mixing fluid, modifies the evolution of the mixing zone. The growth rate of the mixing width is analyzed in terms of the stretching or compression effect and species-penetration effect. In a cylindrical geometry, the stretching or compression effect is mainly induced by the wave system and the nonplanar geometric environment. The late-time turbulent mixing width induced by the penetration effect scales as (t−t0)θ, as with the evolution of planar RMI. For both cases, the mass-fraction profiles are collapsed at the late time if the radial coordinate is first shifted with the spike-front position and then scaled by the mixing width. By analyzing the distribution of the bubble (spike) contour, the dominant bubble (spike) diameter [D¯b(s)] is obtained. The ratios [βb(s)] between the dominant bubble (spike) diameter and the bubble (spike) amplitude [Wb(s)] are calculated, and a stable ratio of spike βs is observed during the late stage. Meanwhile, the ratio of the bubble βb is greater than 1 at late time.