The role of spontaneous waves in the deflagration-to-detonation transition in submillimetre channels

Abstract

Flame acceleration and transition to detonation in submillimetre two-dimensional planar and three-dimensional square channels were simulated by solving the compressible reactive Navier–Stokes equations. A simplified chemical–diffusive model was used to describe the diffusive transport and chemical reaction of a highly reactive mixture, such as stoichiometric ethylene and oxygen in 2D and 3D channels. The walls of the channels were modelled as no-slip and adiabatic. The initial flame acceleration and precursor shock formation were consistent with earlier results. Viscous dissipation in the boundary layer heats the reactants, which have been compressed by the precursor shock. The strength of the precursor shock and the amount of viscous dissipation increase until the temperature of the boundary layer is high enough to ignite the reactants. This produces a spontaneous wave, which, in most of the cases considered, initiates the detonation. The spontaneous wave first forms where the flame attaches to the wall in the planar channels, and forms at the corner where two walls meet in the square channels. In a separate study, the boundary layer also ignited in a computation for a circular tube containing a mixture hydrogen and oxygen represented by a detailed chemical reaction mechanism. The formation of spontaneous waves to the extent studied appears to be robust, and is relatively insensitive to channel geometry, fuel and oxidiser mixture, and the level of detail in the chemical–diffusive models used.

Keywords:

• flame acceleration
• deflagration-to-detonation transition
• spontaneous wave
• numerical simulation
• shock wave

Acknowledgements

Grisha Sivashinsky is a wonderful friend and colleague. Through the years, our appreciation of his pioneering theoretical analyses has grown exponentially. His work has been fundamental to our understanding of the deflagration-to-detonation transition and flame instability. Additionally, he helped in the developement of many concepts, such as reactivity gradients and hot spots, which are now considered common knowledge. This paper would simply not have been possible without his previous work. Thank you, Grisha.

The authors acknowledge the University of Maryland (http://www.it.umd.edu/hpcc) and Department of Defense High Performance Computing Modernization Program supercomputing resources made available in conducting the research reported in this paper.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was sponsored in part by the Office of Naval Research [grant number N00014-14-1-0177] and in part by the University of Maryland through Minta Martin Endowment Funds in the Department of Aerospace Engineering, and through the Glenn L. Martin Institute Chaired Professorship at the A. James Clark School of Engineering.