Modeling of Richtmyer–Meshkov instability-induced turbulent mixing in shock-tube experiments

Abstract

A turbulence transport model for the analysis of shock interface interaction-induced turbulent mixing is presented. Results given by the one-dimensional (1-D) version of this model are compared with data obtained in shock-tube experiments. Calibrations are made from an air/He interface destabilized by a 1.3 incident shock wave Mach number, taking into account the successive interactions with the different reshocks on the shock tube end wall. Then, using the same set of model constants, different gas pairs with both various Atwood and incident shock wave Mach numbers are considered, in order to point out the influence of these main parameters on the results. Mixing zone thickness time evolutions and 1-D density profiles are presented and directly compared with experimental results. Profiles of other variables such as the space integral of the turbulent kinetic energy ∫k dx, translation energy ∫ρux2 dx, and the ratio ∫ρk dx/∫ρux2 dx, given by the computations, are also shown. Using two different initializations, in particular, to better describe the first phases of the phenomenon under study (i.e., taking into account the initial membrane in a horizontal shock tube configuration), we have found good agreement between calculations and experiments.