Optimal Mass Reactant Flows in Pulse Combustion

Abstract

An essential ingredient in any lumped parameter model of pulse combustion is the particular submodel chosen for the mass reactant flow rate $\dot{m}_R$, e.g., many previous efforts at lumped parameter modelling of pulse combustion employed the orfice flow equations to simulate the flow of air and fuel into the pulse combustor. We demonstrate that it is possible to choose a sequence $\dot{m}_{R}^{(k)}$ of mass reactant flows with the property that the corresponding sequence $A^{(k)}$ of amplitudes, associated with stable pressure oscillations in the combustion chamber, satisfies $A^{(k)} \rightarrow \infty$, as $k \rightarrow \infty$, while the sequence of periods $T_{p}^{(k)}$ associated with those oscillations satisfies $T_{p}^{(k)} \rightarrow 0$, as $k \rightarrow \infty$.