Reynolds-Averaged Navier-Stokes Modeling of Turbulent Rayleigh-Taylor, Richtmyer-Meshkov, and Kelvin-Helmholtz Mixing Using a Higher-Order Shock-Capturing Method

Abstract

A numerical implementation of a large number of Reynolds-averaged Navier–Stokes (RANS) models based on two-, three-, four-equation, and Reynolds stress turbulence models (using either the turbulent kinetic energy dissipation rate or the turbulent lengthscale) in an Eulerian, finite-difference shock-capturing code is described. The code uses third-order weighted essentially nonoscillatory (WENO) reconstruction of the advective fluxes, and second- or fourth-order central difference derivatives for the computation of spatial gradients. A third-order TVD Runge–Kutta time-evolution scheme is used to evolve the fields in time. Improved closures for the turbulence production terms, compressibility corrections, mixture transport coefficients, and a consistent initialization methodology for the turbulent fields are briefly summarized. The code framework allows for systematic comparisons of detailed predictions from a variety of turbulence models of increasing complexity. Applications of the code with selected K–ε based models are illustrated for each of the three instabilities. Simulations of Rayleigh–Taylor unstable flows for Atwood numbers 0.1–0.9 are shown to be consistent with previous implicit LES (ILES) results and with the expectation of increased asymmetry in the mixing layer characteristics with increasing stratification. Simulations of reshocked Richtmyer–Meshkov turbulent mixing corresponding to experiments with light-to-heavy transition in air/sulfur hexafluoride and incident shock Mach number Mas = 1.50, and heavy-to-light transition in sulfur hexafluoride/air with Mas = 1.45 are shown to be in generally good agreement with both pre- and post-reshock mixing layer widths. Finally, simulations of the seven Brown–Roshko Kelvin–Helmholtz experiments with various velocity and density ratios using nitrogen, helium, and air are shown to give mixing layer predictions in good agreement with data. The results indicate that the numerical algorithms and turbulence models are suitable for simulating these classes of inhomogeneous turbulent flows.