Two-equation and multi-fluid turbulence models for Rayleigh-Taylor mixing

This paper presents a new, improved version of the K-L model, as well as a detailed investigation of K-L and multi-fluid models with reference to high-resolution implicit large eddy simulations of compressible Rayleigh-Taylor mixing. The accuracy of the models is examined for different interface pressures and specific heat ratios for Rayleigh-Taylor flows at initial density ratios 3:1 and 20:1. It is shown that the original version of the K-L model requires modifications in order to provide comparable results to the multi-fluid model. The modifications concern the addition of an enthalpy diffusion term to the energy equation; the formulation of the turbulent kinetic energy (source) term in the K equation; and the calculation of the local Atwood number. The proposed modifications significantly improve the results of the K-L model, which are found in good agreement with the multi-fluid model and implicit large eddy simulations with respect to the self-similar mixing width; peak turbulent kinetic energy growth rate, as well as volume fraction and turbulent kinetic energy profiles. However, a key advantage of the two-fluid model is that it can represent the degree of molecular mixing in a direct way, by transferring mass between the two phases. The limitations of the single-fluid K-L model as well as the merits of more advanced Reynolds-averaged Navier-Stokes models are also discussed throughout the paper.