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Influence of turbulent fluctuations on detonation propagation

Published online by Cambridge University Press:  05 April 2017

Brian McN. Maxwell Open the ORCID record for Brian McN. Maxwell [Opens in a new window] ,
R. R. Bhattacharjee ,
S. S. M. Lau-Chapdelaine ,
S. A. E. G. Falle ,
G. J. Sharpe  and
M. I. Radulescu
Brian McN. Maxwell*
Affiliation:
Department of Mechanical Engineering, University of Ottawa, 161 Louis Pasteur, Ottawa, K1N 6N5, Canada
R. R. Bhattacharjee
Affiliation:
Department of Mechanical Engineering, University of Ottawa, 161 Louis Pasteur, Ottawa, K1N 6N5, Canada
S. S. M. Lau-Chapdelaine
Affiliation:
Department of Mechanical Engineering, University of Ottawa, 161 Louis Pasteur, Ottawa, K1N 6N5, Canada
S. A. E. G. Falle
Affiliation:
School of Mathematics, University of Leeds, Leeds LS2 9JT, UK
G. J. Sharpe
Affiliation:
Blue Dog Scientific Ltd, 1 Mariner Court, Wakefield WF4 3FL, UK
M. I. Radulescu
Affiliation:
Department of Mechanical Engineering, University of Ottawa, 161 Louis Pasteur, Ottawa, K1N 6N5, Canada
*
†Email address for correspondence: [email protected]
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Abstract

The present study addresses the reaction zone structure and burning mechanism of unstable detonations. Experiments investigated mainly two-dimensional methane–oxygen cellular detonations in a thin channel geometry. The sufficiently high temporal resolution permitted the determination of the probability density function of the shock distribution, a power law with an exponent of $-3$, and the burning rate of unreacted pockets from their edges – through surface turbulent flames with a speed approximately 3–7 times larger than the laminar one at the local conditions. Numerical simulations were performed using a novel large-eddy simulation method where the reactions due to both autoignition and turbulent transport were treated exactly at the subgrid scale in a reaction–diffusion formulation. The model is an extension of Kerstein and Menon’s linear eddy model for large-eddy simulation to treat flows with shock waves and rapid gas-dynamic transients. The two-dimensional simulations recovered well the amplification of the laminar flame speed due to the turbulence generated mainly by the shear layers originating from the triple points and subsequent Richtmyer–Meshkov instability associated with the internal pressure waves. The simulations clarified how the level of turbulence generated controlled the burning rate of the pockets, the hydrodynamic thickness of the wave, the cellular structure and its distribution. Three-dimensional simulations were found to be in general good agreement with the two-dimensional ones, in that the subgrid-scale model captured the ensuing turbulent burning once the scales associated with the cellular dynamics, where turbulent kinetic energy is injected, are well resolved.

JFM classification

Compressible Flows: Compressible Flows Compressible Flows: Detonation waves Mixing: Turbulent mixing
Type
Papers
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Journal of Fluid Mechanics , Volume 818 , 10 May 2017 , pp. 646 - 696
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© 2017 Cambridge University Press 

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