Numerical study and buoyancy–drag modeling of bubble and spike distances in three-dimensional spherical implosions

Abstract

High-resolution three-dimensional implicit large eddy simulations of implosion in spherical geometries are presented. The growth of perturbations is due to Rayleigh–Taylor (RT) and Richtmyer–Meshkov (RM) instabilities and also to geometric convergence and compression effects. RM and RT instabilities have been studied extensively in planar configurations, but there are comparatively few studies on spherical geometries. Planar geometries lack the effect of convergence that changes the morphology and growth of perturbations in spherical geometries. This paper presents a study of turbulent mixing in spherical geometries considering different narrowband (NB) and broadband multimode initial perturbations and examines several quantities including the evolution of the integral mixing layer width and integral bubble and spike heights using novel integral definitions. The growth of the bubble and spike is modeled using a Buoyancy–Drag (BD) approach that is based on simple ordinary differential equations to model the growth of the turbulent mixing layer. In a recent study, Youngs and Thornber [“Buoyancy-drag modelling of bubble and spike distances for single-shock Richtmyer-Meshkov mixing,” Physica D 410, 132517 (2020)] constructed modifications to the BD equations to take into account the early stages of the mixing process that are dependent on the initial conditions. Those modifications are shown to be important to obtain correct results. The current study adopted the same modifications and adapted the BD equations to the spherical implosion case. The results of the BD model are compared with those of different initial NB cases that include different initial amplitudes and wavelengths of the perturbations, for validation purposes. The predictions from the new BD model are in very good agreement with the numerical results; however, there exist some limitations in the accuracy of the model, in particular the use of the interface position and fluid velocity from one-dimensional data.