Analysis of Rayleigh–Taylor instability at high Atwood numbers using fully implicit, non-dissipative, energy-conserving large eddy simulation algorithm

Abstract

Large eddy simulation of three-dimensional, multi-mode Rayleigh–Taylor instability at high Atwood numbers is performed using a recently developed, kinetic energy-conserving, non-dissipative, fully implicit, finite volume algorithm. The algorithm was especially designed for simulating low-Mach number, variable density/viscosity, transitional, and turbulent flows. No interface capturing mechanism is required. Buoyancy and heat transfer effects can be handled without relying on the Boussinesq assumption. Because of this feature, unlike the pure incompressible ones, it does not suffer from the loss of physical accuracy at high Atwood and Rayleigh numbers. In this study, the mixing phenomenon in Rayleigh–Taylor instability and the effects of high Atwood numbers on the development of the flow are investigated using various diagnostics such as local mole fractions, bubble and spike penetration lengths and growth rates, mixing efficiencies, Taylor micro-scales, and corresponding Reynolds numbers and energy ratios. Additionally, some important terms of the Reynolds stress transport equation are also introduced, such as Reynolds stresses (and their anisotropies) and turbulent production. Results show that Rayleigh–Taylor instability at high Atwood numbers is characterized by rapid development of instability due to the increasing growth rates and higher velocities of spike fronts, larger asymmetry in the mixing region, denser interactions in the non-linear phase, and changes in bubble and spike morphologies. It is also found that interactions of spike-fronts with their surroundings are the primary mechanisms of turbulent production and transition to turbulence. However, late time mean flow measures such as energy ratio and mixedness are not significantly affected. A scaling relation between the spike to bubble penetration ratio and the heavy to light density ratio is also provided.