Perturbation analysis of self-sustained oscillations in a pulse combustion model

A lumped parameter model of pulse combustion is constructed which incorporates a valve submodel exhibiting continuous mass reactant flow. Unlike earlier models based on the orifice flow equations, the rate of change of the mass reactant flow, while discontinuous as the valve transitions from open to closed, exhibits a finite jump discontinuity. The model equations are analyzed by combining Fourier series expansions with regular perturbation expansions; this yields asymptotic expansions for both the combustion chamber pressure and tailpipe velocity oscillations. A numerical study of the perturbation expansions yields important information concerning the behavior of the pulse combustor as various physical and geometrical parameters are varied.