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Viscous solution of the triple-shock reflection problem

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Abstract

The reflection of a triple-shock configuration was studied numerically in two dimensions using the Navier–Stokes equations. The flow field was initialized using three shock theory, and the reflection of the triple point on a plane of symmetry was studied. The conditions simulated a stoichiometric methane-oxygen detonation cell at low pressure on time scales preceding ignition when the gas was assumed to be inert. Viscosity was found to play an important role on some shock reflection mechanisms believed to accelerate reaction rates in detonations when time scales are small. A small wall jet was present in the double Mach reflection and increased in size with Reynolds number, eventually forming a small vortex. Kelvin–Helmholtz instabilities were absent, and there was no Mach stem bifurcation at Reynolds numbers corresponding to when the Mach stem had travelled distances on the scale of the induction length. Kelvin–Helmholtz instabilities are found to not likely be a source of rapid reactions in detonations at time scales commensurate with the ignition delay behind the Mach stem.

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Acknowledgments

This work was sponsored by a Natural Sciences and Engineering Research Council of Canada (NSERC) Discovery grant to M. I. Radulescu and a NSERC Alexander Graham Bell Canadian Graduate Scholarship to S. S.M. Lau-Chapdelaine. The authors wish to acknowledge Gary Sharpe for useful discussions.

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  1. Department of Mechanical Engineering, University of Ottawa, 161 Louis Pasteur, Ottawa, K1N 6N5, Canada

    S. S.-M. Lau-Chapdelaine & M. I. Radulescu

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  1. S. S.-M. Lau-Chapdelaine
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  2. M. I. Radulescu
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Correspondence to S. S.-M. Lau-Chapdelaine.

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Communicated by G. Ciccarelli.

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Lau-Chapdelaine, S.SM., Radulescu, M.I. Viscous solution of the triple-shock reflection problem. Shock Waves 26, 551–560 (2016). https://doi.org/10.1007/s00193-016-0674-8

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