Multicomponent Reynolds-averaged Navier-Stokes simulations of reshocked Richtmyer-Meshkov instability-induced mixing

摘要

A third-order weighted essentially nonoscillatory (WENO) finite-difference implementation of a two-equation K-ε multicomponent Reynolds-averaged Navier-Stokes (RANS) model is used to simulate reshocked Richtmyer-Meshkov turbulent mixing of air and sulfur hexafluoride at incident shock Mach numbers Ma_s = 1.24, 1.50, 1.98 with Atwood number At = 0.67 and Ma_s = 1.45 with At = -0.67. The predicted mixing layer width evolutions are compared with experimental measurements of the width before and after reshock [M. Vetter, B. Sturtevant, Shock Waves 4 (1995) 247; F. Poggi, M.H. Thorembey, G. Rodriguez, Phys. Fluids 10 (1998) 2698] and with the analytical self-similar power-law solution of the simplified model equations before reshock. A new procedure is introduced for the specification of the initial turbulent kinetic energy and its dissipation rate, in which these quantities are related by the linear instability growth rate. The predicted mixing layer widths before reshock are shown to be sensitive to changes in the initial turbulent kinetic energy and its dissipation rate, while the widths after reshock are sensitive to changes in the model coefficients C_(ε0) and σ_ρ appearing in the buoyancy (shock) production terms in the turbulent kinetic energy and dissipation rate equations. A set of model coefficients and initial conditions is shown to predict mixing layer widths in generally good agreement with the pre-reshock experimental data, and very good agreement with the post-reshock data for all cases. Budgets of the turbulent kinetic energy equation just before and after reshock for the Mas = 1.24 case are used to identify the principal physical mechanisms generating turbulence in reshocked Richtmyer-Meshkov instability: buoyancy production (pressure work) and shear production. Numerical convergence of the mixing layer widths under spatial grid refinement is also demonstrated for each of the Mach numbers considered.