Effects of Tailpipe Friction on the Nonlinear Dynamics of a Thermal Pulse Combustor

Abstract

The effect of tailpipe friction on the combustion dynamics inside a thermal pulse combustor has been investigated using a nonlinear model consisting of four coupled first order ordinary differential equations. The dynamics of the system is represented through time series plots, time-delay phase plots, and Poincaré maps. The results indicate that as the tailpipe friction factor is lowered, the system undergoes a transition from steady combustion through oscillating combustion to an intermittent combustion with chaotic characteristics before extinction. The time series data are shown to be useful indicator for early detection of extinction. In one approach (thresholding), the occurrence of local peak pressures below a predefined threshold value is identified as an event and the number of events (event count) and largest number of successive cycles with such events (event duration) are recorded as the friction factor is lowered. In another approach, the statistical moments (kurtosis) of the data are used. Number of kurtosis peaks above a prescribed value and variance of the kurtosis values are recorded for decreasing values of friction factor. All these numbers sharply increase as the system approaches extinction.