Pulsed Control of Thermoacoustic Instabilities: Analysis and Experiment

Thermoacoustic instabilities in combustors have been suppressed using phase-shift algorithms pulsing an on-off actuator at the limit cycle frequency $(flc)$ or at the subharmonics of $flc$⁠. It has been suggested that control at a subharmonic rate may extend the actuator lifetime and possibly require less actuator bandwidth. This paper examines the mechanism of subharmonic control in order to clarify the principles of operation and subsequently identify potential advantages for combustion control. Theoretical and experimental arguments show that there must be a Fourier component of the subharmonic control signal at $flc$ in order to stabilize the limit cycling behavior. It is also demonstrated that the magnitude of that Fourier component must be equivalent to the signal magnitude for a linear phase-shift controller that operates directly at $flc$⁠. The concept of variable-subharmonic control is introduced whereby the actuator is pulsed at the instability frequency to initially stabilize the system and then is pulsed at a subharmonic frequency to maintain stability. These results imply that an actuator used for subharmonic control cannot be effective unless its bandwidth spans the instability frequency. The advantage of reduced cycling may still be realized but will require higher control authority to produce the same effect as an actuator pulsed at the instability frequency.