Mathematical Sciences: The Modulation of Flames of Various Types in a Premixed Reactive Atmosphere

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9403798 Booty Steady, one-dimensional, premixed flames (or "deflagration waves") involving reactions that are highly activated can be categorized by their propagation Mach number, with flames of different Mach number having a different mathematical structure. In practice, however, most flames are spatially narrow and continually adjust both their speed and shape in accordance with the local environment through which they travel. The aim of the project is to clarify some of the outstanding issues regarding the unsteady and nonplanar propagation of different types of flames. These are governed by a coupled system of nonlinear partial differential equations, viz. the reactive Navier-Stokes equations, of which approximate solutions will be sought by (i) the systematic use of asymptotic and perturbation methods, for identifying significant or distinguished limits, and (ii) numerical methods. Steady, one-dimensional flames can be categorized by their propagation speed, with flames of different speed having a different mathematical structure. In practice, however, most flames are spatially narrow and continually adjust both their speed and shape in accordance with the environment through which they travel. The aim of the project is to address some of the outstanding issues regarding the unsteady and nonplanar propagation of different types of flame. In particular, (i) circumstances should be established under which a freely propagating, low-speed flame can either be extinguished or develop into a high-speed detonation wave, and (ii) the mechanism determining the different ways in which these events can occur should be clarified. This has applications to the control and safety of combustion phenomena in various different contexts.