A One-Dimensional Model of a Pulse Combustor

Abstract

A numerical model of a pulse combustor has been developed to simulate the nonlinear wave motion resulting from the periodic combustion process. The wave pattern is followed in time by integrating the unsteady, one-dimensional equations of continuity, momentum and energy for vairable-are geometry, including losses due to friction and heat transfer. The resulting periodic wave pattern is governed by the pulse combustor geometry, the fuel mixture, and the combustion and injection processes. The simplified pulse combustor used in in this paper coasists of a combustion chamber and tail pipe joined by a short transition section. The resulting periodic wave patern is governed by the pulse combustor geometry, the fuel mixture, and the combustion and injection processes. The simplified pulse combustor used in in this paper coasists of a combustion chamber and tail pipe joined by a short transition section. The model for the combustion process is guided by experimentally obtained chemiluminescence measurements taken in an operating pulse combustor of similar design. The injection of fuel and an is also prespecified by experimentally measured rates. We base our method of determining the "optimal" operating frequency of the pulse combustor on Rayleigh's critierion, which states that for stable combustion-driven flow oscillations the energy release must be in phase with the resonant pressure wave. We quantify the phase relation between the heat release and the combustion chamber pressure, called to the Rayleigh efficiency n, and compare the magnitudes obtained at different forcing frequencies. Since the Rayleigh efficiency reaches a maximum when the combustion process provides the strongest reinforcement of the pressure waves, the "optimal" operating frequency occurs when n is a maximum. This procedure is confirmed by the simulation of an experimental pulse combustor with this one-dimensional model. Using reasonable estimates of heat transfer and friction, the numerical prediction of n peaks at a frequency corresponding to the experimentally observed operating frequency of the pulse combustor. A comparison of the cyclic velocity at this frequency with experimentally measured quantities shows particularly good agreement considering the current understanding of loss coefficients in pulsating flows We have also used the Rayleigh efficiency to quantify the sensitivity of the combustor performance to changes in system parameters. We find that the system is very sensitive to parameters which affect the temperature of the gas, such as heat transfer coefficients or equivalence ratio of the reactants. The friction coefficient affects the magnitude of the pulsations but not the operating frequency. The Rayleigh efficiency is shown to be a powerful tool. By comparing the Rayleigh efficiencies for different design conditions we can identify the "optimal" operating parameters, those that produce the strongest pulsations, providing useful guidance for the design engineers.