Linear stability analysis of combustion oscillation systems delay-coupled by sound propagation in a tube

Combustion oscillation is a self-excited oscillation phenomenon that occurs in combustion systems. This instability should be mitigated for stable operation because it can cause loud noise, unexpected propagation of flame, and fatigue failure of mechanical components. Time-delayed coupling is a method to control self-sustained oscillations in identical oscillators or detuned oscillators by introducing mutual interactions with delay times. The coupling can lead to suppression of the oscillators, which is known as amplitude death. Previous studies have demonstrated the delay coupling, achieved by a gas-filled tube mediating sound waves, can stop combustion oscillations. The propagating time introduces the delay and the resulting acoustic interactions stabilize the systems without the need for complex sensors, controllers, or actuators. In this study, a novel analytical model of the delay coupling is proposed and the linear stability analysis of coupled systems was investigated. The death-inducing conditions can be found numerically using the length, radius, and location of the coupling tube as the control parameters. We conducted experiments on the amplitude death in simple combustors to validate the proposed model. [Work supported by Paloma Environmental Technology Development Foundation.]