Three-Dimensional Numerical Simulations of Shock-Induced Turbulent Mixing in Spherical Implosions

Compressible turbulent mixing evolving from Richtmyer–Meshkov and Rayleigh–Taylor instabilities and Bell–Plesset effects has been investigated using carefully designed high-resolution spherical algorithms and implicit large eddy (ILES) simulations of fundamental spherical implosion problems. Multimode narrowband and broadband initial perturbations consisting of spherical harmonics and multimode cosine perturbations are investigated considering a high Atwood number (At = 0.9) setup and a moderate convergence ratio Cr = 3.6. Several integral quantities, mixedness parameters and turbulence statistics are presented to provide a detailed understanding of the mixing process and the effect of the initial spectrum of perturbations on the subsequent mixing. Furthermore, this research is one of the few efforts to examine turbulent transport and budgets of turbulent kinetic energy, turbulent mass flux and density self-correlation, considering high-Atwood implosion configurations and different initial perturbations spectra. The budgets are investigated while also quantifying the contribution from numerical dissipation and diffusion to the transport equations. Different analytical mix models have been developed for the prediction of mixing layer growth and amount of mixing that occurs. The first model, denoted as the Bell-Plesset model, is an extension of a single mode perturbation growth model, that is based on small-amplitude and linear growth assumptions, to multimode perturbations and reshocks. Bubble and spike growth is also modelled using a Buoyancy-Drag (BD) approach to which modifications were applied to introduce an effective length scale in the drag term to consider the initial conditions and early stages of the mixing process. The BD model was adapted to the spherical implosion case considered here and the effect of geometric convergence was also added to the model