Multi-component Reynolds-averaged Navier–Stokes simulations of Richtmyer–Meshkov instability and mixing induced by reshock at different times

Abstract

Turbulent mixing generated by shock-driven acceleration of a perturbed interface is simulated using a new multi-component Reynolds-averaged Navier–Stokes (RANS) model closed with a two-equation \(K\)–\(\epsilon \) model. The model is implemented in a hydrodynamics code using a third-order weighted essentially non-oscillatory finite-difference method for the advection terms and a second-order central difference method for the gradients in the source and diffusion terms. In the present reshocked Richtmyer–Meshkov instability and mixing study, an incident shock with Mach number \(M\!a_{\mathrm{s}}=1.20\) is generated in air and progresses into a sulfur hexafluoride test section. The time evolution of the predicted mixing layer widths corresponding to six shock tube test section lengths are compared with experimental measurements and three-dimensional multi-mode numerical simulations. The mixing layer widths are also compared with the analytical self-similar power-law solution of the simplified model equations prior to reshock. A set of model coefficients and initial conditions specific to these six experiments is established, for which the widths before and after reshock agree very well with experimental and numerical simulation data. A second set of general coefficients that accommodates a broader range of incident shock Mach numbers, Atwood numbers, and test section lengths is also established by incorporating additional experimental data for \(M\!a_{\mathrm{s}}=1.24\), \(1.50\), and \(1.98\) with \(At=0.67\) and \(M\!a_{\mathrm{s}}=1.45\) with \(At=-0.67\) and previous RANS modeling. Terms in the budgets of the turbulent kinetic energy and dissipation rate equations are examined to evaluate the relative importance of turbulence production, dissipation and diffusion mechanisms during mixing. Convergence results for the mixing layer widths, mean fields, and turbulent fields under grid refinement are presented for each of the \(M\!a_{\mathrm{s}}=1.20\) cases.