Frequency Domain Analysis of the Performance of a Valved Helmholtz Pulse Combustor

A theoretical study of the limit cycle characteristics of a gas fired, mechanically valved, Helmholtz pulse combustor is presented. The analysis is carried out in the frequency domain rather than the time domain in order to develop a performance prediction program that can be run on a personal computer. The pulse combustor is treated as a feedback system. The forward branch of the system consists of the acoustic resonator while the feedback loop consists of the combustion process and heat losses through the pulse combustor walls. The model is based upon an energy balance of the combustion chamber and an analysis of the acoustics of the tail pipe. A previously developed nonlinear model is used to describe the periodic inflow of reactants through the flapper valves and experimental data is used to develop a relationship between the reactants inflow and the magnitude of the oscillatory heat addition by the combustion process. The model predicts that the energy needed to drive the combustor oscillations near resonance is much smaller than the energy supplied by the combustion process. An order of magnitude analysis shows that known turbulent convective heat transfer processes cannot account for the difference between the predicted combustor energy utilization and the energy supplied by the combustion process. Consequently, the combustor cannot work near resonance unless the heat transfer through its walls is an order of magnitude larger than that predicted by known mechanisms and/or the phase difference between the pressure and the velocity oscillations in the tail pipe is significantly different than 90 degrees.