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

Lombardini, M. and Hill, D. J. and Pullin, D. I. and Meiron, D. I. (2011) Atwood ratio dependence of Richtmyer-Meshkov flows under reshock conditions using large-eddy simulations. Journal of Fluid Mechanics, 670 . pp. 439-480. ISSN 0022-1120.

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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–CO_2, air–SF_6 and H_2–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.

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Meiron, D. I.0000-0003-0397-3775
Additional Information:© 2011 Cambridge University Press. Received 11 January 2010; revised 18 September 2010; accepted 8 October 2010; first published online 1 February 2011. This work has been supported in part by the Department of Energy under subcontract no. DE-AC52-06NA25396.
Funding AgencyGrant Number
Department of Energy (DOE)DE-AC52-06NA25396
Subject Keywords:instability; shock waves; turbulent mixing
Record Number:CaltechAUTHORS:20110323-142306126
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:23079
Deposited By: Tony Diaz
Deposited On:29 Mar 2011 17:54
Last Modified:09 Mar 2020 13:19

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