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Transition to turbulence in shock-driven mixing: a Mach number study

Lombardini, M. and Pullin, D. I. and Meiron, D. I. (2012) Transition to turbulence in shock-driven mixing: a Mach number study. Journal of Fluid Mechanics, 690 . pp. 203-226. ISSN 0022-1120.

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Large-eddy simulations of single-shock-driven mixing suggest that, for sufficiently high incident Mach numbers, a two-gas mixing layer ultimately evolves to a late-time, fully developed turbulent flow, with Kolmogorov-like inertial subrange following a -5/3 power law. After estimating the kinetic energy injected into the diffuse density layer during the initial shock–interface interaction, we propose a semi-empirical characterization of fully developed turbulence in such flows, based on scale separation, as a function of the initial parameter space, as (η_(0^+)Δu/ν)(η_(0^+)/L_ρ)A^+/√(1-A^(+)^2) ≳ 1.53 × 10^4/C^2, which corresponds to late-time Taylor-scale Reynolds numbers ≳250. In this expression, η_(0^+) represents the post-shock perturbation amplitude, Δu the change in interface velocity induced by the shock refraction, ν the characteristic kinematic viscosity of the mixture, L_ρ the inner diffuse thickness of the initial density profile, A^+ the post-shock Atwood ratio, and C(A^+, η_(0^+)/λ_0)≈0.3 for the gas combination and post-shock perturbation amplitude considered. The initially perturbed interface separating air and SF_6 (pre-shock Atwood ratio A ≈ 0.67) was impacted in a heavy–light configuration by a shock wave of Mach number M_I = 1.05, 1.25, 1.56, 3.0 or 5.0, for which η_(0^+) is fixed at about 25% of the dominant wavelength λ_0 of an initial, Gaussian perturbation spectrum. Only partial isotropization of the flow (in the sense of turbulent kinetic energy and dissipation) is observed during the late-time evolution of the mixing zone. For all Mach numbers considered, the late-time flow resembles homogeneous decaying turbulence of Batchelor type, with a turbulent kinetic energy decay exponent n ≈ 1.4 and large-scale (k⟶0) energy spectrum ~k^4, and a molecular mixing fraction parameter, Θ ≈ 0.85. An appropriate time scale characterizing the Taylor-scale Reynolds number decay, as well as the evolution of mixing parameters such as Θ and the effective Atwood ratio A_e, seem to indicate the existence of low- and high-Mach-number regimes.

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Meiron, D. I.0000-0003-0397-3775
Additional Information:© 2011 Cambridge University Press. Received 8 March 2011; revised 12 July 2011; accepted 25 September 2011; first published online 21 November 2011. This work has been supported in part by the Department of Energy under subcontract no. DE-AC52-06NA25396.
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Department of Energy (DOE)DE-AC52-06NA25396
Subject Keywords:shock waves; transition to turbulence; turbulent mixing
Record Number:CaltechAUTHORS:20120227-122525364
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Official Citation:M. Lombardini, D. I. Pullin and D. I. Meiron (2012). Transition to turbulence in shock-driven mixing: a Mach number study. Journal of Fluid Mechanics, 690 , pp 203-226 doi:10.1017/jfm.2011.425
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:29487
Deposited By: Jason Perez
Deposited On:28 Feb 2012 21:05
Last Modified:09 Mar 2020 13:19

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