Asymptotic Analysis of Cyclic Oscillations in a Nonlinear Lumped Parameter Pulse Combustor Model

Abstract

An asymptotic solution is generated for the equation governing the cyclic pressure pulsations which are predicted by a lumped parameter model of pulse combustor operation. The study is based on a Poincaré-Lindstedt perturbation analysis of the type which has been employed for other nonlinear ordinary differential equations associated with self-sustained oscillations. The asymptotic solution yields an approximation for the period of cyclic pulse combustor pressure oscillations which reflects its dependence on both physical and geometrical design parameters.