Modeling of turbulent mixing with an improved K–L model

Abstract

Turbulent mixing, induced by Rayleigh–Taylor (RT), Richtmyer–Meshkov (RM), and Kelvin–Helmholtz (KH) instabilities, broadly occurs in both natural phenomena, such as supernova explosions, and engineering applications, such as inertial confinement fusion (ICF). These three instabilities usually simultaneously exist and are highly coupled to drive and affect turbulent mixing, which raises a great challenge for turbulence modeling. In this study, an improved version of the K–L model is proposed. The modifications include that: (i) the deviatoric shear stress is considered to describe the KH instability; (ii) the concept of characteristic acceleration is introduced to better distinguish RT and RM instabilities; and (iii) an enthalpy diffusion is directly derived from the internal energy equation to model the turbulent diffusion term. Then, a unified set of model coefficients is systematically derived based on the self-similar analysis and physical observations. This model is validated by canonical RT, RM, and KH mixings and further investigated for more complex cases, including the RM mixing with multiple reshocks, the two-dimensional RT mixing called “tilted-rig,” and the simple spherical implosion, a much simplified version of an ICF implosion. Good agreement with the corresponding experimental and numerical data is achieved, revealing the ability of the present model to describe combined buoyancy, shock, and shear effects, which will contribute to a further application in real problems.