A K-L model with improved realizability for turbulent mixing

Turbulent mixing, induced by Rayleigh-Taylor (RT), Richtmyer-Meshkov (RM), and Kelvin-Helmholtz (KH) instabilities, broadly occurs in both practical astrophysics and inertial confined fusion problems. The Reynolds-averaged Navier-Stokes models remain the most viable approach for the solution of these practical flows. The commonly used mixing models based on the standard eddy viscosity formulation are shown to be capable of accurately predicting the global mixing zone width. However, we find that this approach will become non-realizable for local flow characteristics in the case of a large mean strain rate, including yielding the negative normal stress and the unphysically large turbulence kinetic energy (TKE) in the presence of shocks. This can affect the numerical robustness in calculating turbulent statistics and give rise to highly inaccurate predictions for complex mixings. To overcome this problem, a realizable K-L mixing model is developed, extended from the standard K-L model given by our recent works. A new eddy viscosity formulation is used and modified from the work by Shih et al. to reproduce the growth rate of the KH mixing. This new model yields similar results as the standard model for canonical RT, RM, and KH mixings. However, for complex mixing problems, the present model gives a significant improvement in physically capturing the turbulence characteristics, e.g., predicting the non-negative normal stress for RT mixing with the initial tilted interface and the appropriate TKE when shock interacts with the mixing zone for spherical implosion.