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On Oscillatory Instability in Convective Burning of Gas-Permeable Explosives

I. Brailovsky, M. Frankel, L. Kagan, G. Sivashinsky (2010)

Mathematical Modelling of Natural Phenomena

The experimentally known phenomenon of oscillatory instability in convective burning of porous explosives is discussed. A simple phenomenological model accounting for the ejection of unburned particles from the consolidated charge is formulated and analyzed. It is shown that the post-front hydraulic resistance induced by the ejected particles provides a mechanism for the oscillatory burning.

On the Transition from Deflagration to Detonation in Narrow Channels

L. Kagan (2010)

Mathematical Modelling of Natural Phenomena

A numerical study of a two-dimensional model for premixed gas combustion in a narrow, semi-infinite channel with no-slip boundary condition is performed. The work is motivated by recent theoretical advances revealing the major role of hydraulic resistance in deflagration-to-detonation transition, one of the central yet still inadequately understood phenomena of gaseous combustion. The work is a continuation and extension of recently reported results over non-isothermal boundary conditions, wider...

Oscillatory Propagation of a Rich Premixed Spray Flame

L.S. Kagan, J.B. Greenberg, G.I. Sivashinsky (2010)

Mathematical Modelling of Natural Phenomena

Experimental evidence points to a rich variety of physical scenarios that arise when a laminar flame propagates through a pre-mixture of evaporating liquid fuel and a gaseous oxidant. In this paper new results of time-dependent numerical simulations of rich off-stoichiometric spray flame propagation in a two-dimensional channel are presented. A constant density model is adopted, thereby eliminating the Darrieus-Landau instability. It is demonstrated...

Reaction-diffusion-convection problems in unbounded cylinders.

Rozenn Texier-Picard, Vitaly A. Volpert (2003)

Revista Matemática Complutense

The work is devoted to reaction-diffusion-convection problems in unbounded cylinders. We study the Fredholm property and properness of the corresponding elliptic operators and define the topological degree. Together with analysis of the spectrum of the linearized operators it allows us to study bifurcations of solutions, to prove existence of convective waves, and to make some conclusions about their stability.

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