A second-order turbulence model for gaseous mixtures induced by Richtmyer—Meshkov instability

Abstract

A second order turbulence model for compressible one-dimensional mixing flows is used to calculate the experiment performed by Poggi et al. [18 Poggi, F., Thorembey, M.-H. and Rodriguez, G. 1998. Velocity measurements in turbulent gaseous mixtures induced by Richtmyer–Meshkov instability. Physics of Fluids, 10: 2698–2700. [CSA][CROSSREF][Crossref], [Web of Science ®] , [Google Scholar]] where mixtures were induced by Richtmyer–Meshkov instability. This R ij −ϵ model is supplemented by equations for the turbulent mass flux and the density variance . In Poggi's experiments, beside usual mixing length measurement, the laser Doppler anemometry technique gave temporal evolution of the turbulent kinetic energy. The present study shows that a statistical turbulence model can reproduce these strongly differential experimental data. Indeed, evolution of the radial component of the Reynolds stress tensor as well as that of the anisotropy are satisfactorily calculated. Nevertheless, discrepancies are observed at the very beginning of the process where the turbulence is probably not fully developed. The three-layer Meshkov experiment [16 Andronov, V. A., Bakhrakh, S. M., Meshkov, E. E., Nikiforov, V. V., Pevnitskii, A. V. and Tolshmyakov, A. I. 1982. An experimental investigation and numerical modeling of turbulent mixing in one-dimensional flows. Soviet Physic Doklady, 27: 393 [CSA] [Google Scholar]] is also successfully interpreted with the same procedure. In addition, the dependence of the evolution of turbulent quantities on the initial conditions is addressed.