Journal of Fluid Mechanics

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Atwood ratio dependence of Richtmyer–Meshkov flows under reshock conditions using large-eddy simulations

M. LOMBARDINIa1 c1, D. J. HILLa1, D. I. PULLINa1 and D. I. MEIRONa1

a1 Graduate Aeronautical Laboratories, California Institute of Technology, Pasadena, CA 91125, USA

Abstract

We study the shock-driven turbulent mixing that occurs when a perturbed planar density interface is impacted by a planar shock wave of moderate strength and subsequently reshocked. The present work is a systematic study of the influence of the relative molecular weights of the gases in the form of the initial Atwood ratio A. We investigate the cases A = ± 0.21, ±0.67 and ±0.87 that correspond to the realistic gas combinations air–CO2, air–SF6 and H2–air. A canonical, three-dimensional numerical experiment, using the large-eddy simulation technique with an explicit subgrid model, reproduces the interaction within a shock tube with an endwall where the incident shock Mach number is ~1.5 and the initial interface perturbation has a fixed dominant wavelength and a fixed amplitude-to-wavelength ratio ~0.1. For positive Atwood configurations, the reshock is followed by secondary waves in the form of alternate expansion and compression waves travelling between the endwall and the mixing zone. These reverberations are shown to intensify turbulent kinetic energy and dissipation across the mixing zone. In contrast, negative Atwood number configurations produce multiple secondary reshocks following the primary reshock, and their effect on the mixing region is less pronounced. As the magnitude of A is increased, the mixing zone tends to evolve less symmetrically. The mixing zone growth rate following the primary reshock approaches a linear evolution prior to the secondary wave interactions. When considering the full range of examined Atwood numbers, measurements of this growth rate do not agree well with predictions of existing analytic reshock models such as the model by Mikaelian (Physica D, vol. 36, 1989, p. 343). Accordingly, we propose an empirical formula and also a semi-analytical, impulsive model based on a diffuse-interface approach to describe the A-dependence of the post-reshock growth rate.

(Received January 11 2010)

(Revised September 18 2010)

(Accepted October 08 2010)

(Online publication February 01 2011)

Key words:

  • instability;
  • shock waves;
  • turbulent mixing

Correspondence:

c1 Email address for correspondence: manuel@caltech.edu

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