Mathematical model of a pulsating combustor

Abstract

A pulsating combustor producing longitudinal acoustic oscillations was constructed and a mathematical model of the system developed. The combustor was a closed - open tube, combustion taking place at the closed end into which were fed air and propane. The two lowest modes of longitudinal, acoustic vibration were obtained. The fundamental occurring at low fuel flowrate up to a maximum flowrate corresponding to an energy • input of 12Kw, at which either the fundamental or first harmonic occurred and above which only the first harmonic was obtained up to the maximum flowrate of the system corresponding to an energy input of 20 Kw. The analysis of the system used the conservation equations of mass, momentum and energy from these suitably formed equations could be derived which were solved by the method of characteristics. The combustion model was governed by a simple overall-reaction rate equation. Plug flow was assumed with perfect radial mixing and no axial mixing, conduction or diffusion. The convective heat transfer coefficients were evaluated by means of the quasi-steady-state theory. The mathematical model predicted the gas temperature gradient and the distribution of pressure and velocity standing waves. Owing to the use of a much simplified combustion model, it was not possible to predict the acoustic energy required to determine the amplitude and frequency of oscillation. The amplitude was found to be highly dependent on the fuel injection system, Air/Fuel ratio and mode of oscillation. The practical results confirmed the higher rates of heat transfer associated with pulsating flow.