On the structure of the deflagration for the generalized reaction-rate model

Abstract

The structure of the deflagration is examined by means of an asymptotic analysis of the physical-plane boundary-value problem, with Lewis-Semenov number unity, in the limit of the activation-temperature ratio,β=Ta/Tb, greater than order unity, for the generalized reaction-rate-model case of (1) the heat-addition-temperature ratio,α=(Tb−Tu)/Tu, of order unity [whereTa,Tb, andTuare the activation, adiabatic-flame (and/or burned-gas), and unburned-gas temperatures, respectively]; and (2) the exponent,a, which characterizes the pre-exponential thermal dependence of the reaction-rate term, unity. This examination indicates that the deflagration has a four-region structure. To obtain a uniformly valid solution of the problem, in addition to the (classical) upstream diffusion-convection and downstream diffusion-reaction regions, a far-upstream (or cold-boundary) region and a far-downstream (or hot-boundary) region must be introduced.