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A Reduced Model for Flame-Flow Interaction

P. GordonM. FrankelG. Sivashinsky — 2010

Mathematical Modelling of Natural Phenomena

The paper is concerned with an extension of the classical relation between the flame speed and the curvature-flow stretch, valid only for high Lewis numbers (diffusively stable flames). At low Lewis numbers the corresponding flame-flow system suffers short-wavelength instability, making the associated initial value problem ill-posed. In this study the difficulty is resolved by incorporation of higher-order effects. As a result one ends up with a reduced model based on a coupled system of second-order...

On Oscillatory Instability in Convective Burning of Gas-Permeable Explosives

I. BrailovskyM. FrankelL. KaganG. 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.

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