Superadiabatic small-scale combustors: asymptotic analysis of a two-step chain-branching combustion model

Abstract

An asymptotic study for a counterflow burner consisting of thin channels with heat exchange is proposed. The focus is made on the cases of ultra lean burning using a model of a two-step chain-branching chemistry. The ratio of the channel length to the thermal flame thickness is used as a natural large parameter. Then, the solution is constructed by the method of asymptotic expansions using this parameter. Finally, the obtained asymptotic for the flame position is satisfactorily compared with the exact solution of the problem. These explicit results have a clear advantage in that they facilitate considerably the parametric analysis. It is demonstrated that combustion of mixtures below the flammability limit can be carried out in the considered systems.