Periodic Pulsation in Lean Premixed Combustors and Nonlinear Dynamical Systems

Abstract

Lean-premixed combustors have seen increased use due to the combined benefits of increased fuel efficiency and reduced pollutant emissions; however, these systems are prone to combustion instabilities and flashback. We have analyzed the dynamical behavior of one particular type of instability – which we refer to as periodic pulsation – using a reduced-order combustion model for lean-premixed combustors. From the combustion model we have established a set of criteria for the appearance of periodic pulsation, and we have demonstrated that applying similar conditions to two other dynamical systems (including the Van der Pol oscillator) produces the periodic pulsation phenomenon in those systems. The phenomenon is distinguished by regular pulses of high-amplitude oscillation in time separated by periods of relative calm – visually similar to an ultrashort pulse found in nonlinear optics. Although every pulse repeats periodically from a macroscopic point of view, we have shown that the state space trajectory behavior of periodic pulsation must inherently be quasi-periodic – regardless of the dynamical system in question. We have found that under certain conditions the trajectories of periodic pulsation can resemble the ECG signal of heartbeats; furthermore, the two systems studied besides the combustion model can exhibit what is best described as ’arrhythmias’ in the periodic pulsation signal