Combustion of a finite quatity of gas released in the atmosphere

Abstract

Low Mach number and large activation energy asymptotic approximations are used to derive a model for the thermal behaviour of a finite planar, cylindrically or spherically symmetric fuel region released in an unconfined oxidant environment. A single one-step exothermic reaction is taken to occur. The induction stage has been studied in a previous paper [1] where it was shown that ignition occurs provided the fuel region exceeds a critical size. Below this size diffusive dilution starves the reaction too quickly for ignition to be possible. In this paper combustion of the system following ignition is studied. The analysis is equally valid whether ignition arises through self-heating or whether it is brought about by some other means such as a spark. Deflagration flames are formed which quickly consume the locally lean species at any point. A criterion is identified for any diffusion flame to exist after the passage of deflagration flames. A non-linear moving boundary formulation is developed to describe the progress and eventual collapse of such diffusion flames as the remaining fuel is consumed. The linearised version of these equations gives an upper limit for the time in which all combustion ceases.