Unified prediction of reshocked Richtmyer–Meshkov mixing with K-L model

Abstract

Hydrodynamic instabilities, including Rayleigh–Taylor, Richtmyer–Meshkov (RM), and Kelvin–Helmholtz, induced turbulent mixing broadly occur in both natural phenomena, such as supernova explosions, and high-energy-density applications, such as inertial confinement fusion. Reshocked RM mixing is the most fundamental physical process that is closely related to practical problems, as it involves three classical instabilities. In complex applications, the Reynolds-averaged Navier–Stokes model analysis continues to play a major role. However, there are very few turbulence models that facilitate unified predictions of the outcome of reshocked RM mixing experiments under different physical conditions. Thus, we aim to achieve this objective using the K-L model based on three considerations: deviatoric shear stress is considered when constructing Reynolds stress tensor; the model coefficients used are derived based on a new systematic procedure; the performance of different numerical schemes are studied to ensure high resolution but basically no numerical oscillation. Consequently, a unified prediction is obtained for the first time for a series of reshocked RM mixing experiments under incident shock Mach numbers Ma = 1.2–1.98, Atwood numbers At = ±0.67, and test section lengths 8 cm ≤ δ ≤ 110 cm. The results reveal the feasibility of demonstrating different reshocked RM processes using a single model, without adjusting the model coefficients, which sheds light on the further application of the present model to practical engineering, such as inertial confinement fusion.