On the structure of the deflagration for the generalized reaction-rate model (Q1286265)

Summary: 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, \(\beta =T_a/T_b\), greater than order unity, for the generalized reaction-rate-model case of (1) the heat-addition-temperature ratio, \(\alpha=(T_b-T_u)/T_u\), of order unity [where \(T_a, T_b\), and \(T_u\) are 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.