Multicomponent Reynolds-Averaged Navier--Stokes Modeling of Reshocked Richtmyer--Meshkov Instability-Induced Turbulent Mixing Using the Weighted Essentially Nonoscillatory Method

Elucidating reshocked Richtmyer--Meshkov instability is important for improving current techniques in predicting turbulence in complex flows and advancing many areas of high-energy-density physics. Shock-driven turbulent mixing induced by reshocked Richtmyer--Meshkov instability is investigated here using a multicomponent Reynolds-averaged Navier--Stokes (RANS) model including mixture molecular transport and thermodynamic coefficients closed with a two-equation K-epsilon turbulence model. The model is implemented in a hydrodynamics code using a third-order weighted essentially nonoscillatory (WENO) finite-difference method for the advection terms and a second-order centered WENO method for the gradients in the source and diffusion terms. Turbulent mixing generated by a shock accelerated perturbed air-sulfur hexafluoride interface is simulated for a variety of experiments with incident shock Mach numbers 1.20 < Mas < 1.98. Parametric studies are conducted to study the model sensitivity to variations in buoyancy production model coefficients, initial conditions, and incident shock Mach number. The time-evolution of the predicted mixing layer widths corresponding to different reshock times by variations in shock tube test section lengths is also considered. The RANS model results are compared with experimental data, previous large-eddy simulation (LES) and turbulence model predictions, and the early-time analytical self-similar mixing layer width. The model is also applied to reshocked Richtmyer--Meshkov instability for positive and negative Atwood numbers of 0.21, 0.67, and 0.87 with Mas=1.50, as experimental and numerical simulation data for Atwood numbers different from 0.67 are sparse. Shock-driven instabilities are also considered with larger incident shock Mach numbers 3.00 and 5.00, as limited turbulent mixing investigations with larger Mas values have been conducted. These studies are considered for cases with negative Atwood numbers, -0.21, -0.67, and -0.87. The budgets of the turbulent kinetic energy and turbulent kinetic energy dissipation rate transport equations are investigated to determine the key mechanisms in turbulent mixing. Results for convergence under grid refinement for mixing layer widths and the mean and turbulent fields are also presented. These investigations are considered for early-time and post-reshock mixing, as well as for changes in the mixing due to secondary expansion, rarefaction, and reshock waves.PHDNuclear Engineering & Radiological SciencesUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/100088/1/timoran_1.pd