Effects of Surface Tension and Viscosity on Immiscible Rayleigh-Taylor Mixing

While considerable advances in numerical simulation of the Rayleigh-Taylor (RT) instability have been achieved for miscible fluids, the immiscible case continues to present a particular challenge due to the large gradients and singularities at the fluid interface, which is a source of numerical instabilities in several methods for multi-component fluids. This work applies a recently developed localized artificial diffusivity (LAD) method for a high-order compact finite difference scheme to stabilize large property discontinuities and study the effects of immiscibility and surface tension on the compressible RT instability. Results of implicit Large Eddy Simulations show that the sharpening methods do not deteriorate the scale resolving properties of the high-order method and properties of interest converge with increasing resolution. Results of Direct Numerical Simulations explore a broader range of initial conditions that vary the viscosity (Reynolds number), density (Atwood number), and surface tension (Weber number). Relevant quantities of interest are assessed, like the growth rate of the mixing layer (α), 'mixedness' (θ), length scales within the mixing layer, velocity and density spectra. Results show that for immiscible RT at various Weber numbers, growth rates are larger than for the miscible case (consistent with experimental findings and an improvement over previous simulations). The relationship between Weber and Reynolds number in the transition to turbulence is discussed.