Optimal burning rate sequences for a nonlinear pulse combustion model

Abstract

Within the context of a specific lumped parameter model of pulse combustion, the following issue is addressed: given a specific submodel for the reactant flow rate, can one exhibit a sequence of burning rates, which converge to a limiting burning rate, and for which the associated pressure amplitudes converge to an amplitude that is arbitrarily large while, at the same time, the associated periods of oscillation converge to zero; the existence of such optimal burning rate sequences is established and it is also shown that there exist burning rate sequences for which the associated pulse combustor pressure amplitudes converge to zero.