Combustion Instability Control Through Acoustic Modulation at the Inlet Boundary: Analysis

A linear modal analysis is undertaken to investigate the effects of acoustic modulation at the inlet boundary on the longitudinal instability modes of a dump combustor. This study complements an accompanying experimental investigation that demonstrates combustion instability control through single-frequency acoustic modulation at the inlet [Bennewitz, J. W., Frederick, R. A., Jr., Cranford, J. T., Lineberry, D. M., "Combustion Instability Control Through Acoustic Modulation at the Inlet Boundary: Experiments," Journal of Propulsion and Power (to be published)]. The modal analysis employs acoustically consistent matching conditions instead of the conventional mass, momentum, and energy balances. A specific impedance boundary condition at the inlet is derived through a mass-spring-damper model of a speaker diaphragm that provides the acoustic modulation. The speaker model constants are obtained from an apparatus consisting of a speaker attached to a short hard-wall-terminated duct. At first, the modal analysis is shown to predict a naturally unstable first longitudinal mode in the absence of acoustic modulation, consistent with the spontaneously excited combustion instability mode observed experimentally. Subsequently, a detailed investigation involving variation of the modulation frequency from 0 to 2500 Hz and a mean combustor temperature from 1248 to 1685 K demonstrates the unstable to stable transition of a 2300-2500 Hz first longitudinal mode. The model-predicted mode stability transition is consistent with experimental observations, thereby supporting the premise that inlet acoustic modulation is a means to control high-frequency combustion instabilities. From the modal analysis, it may be deduced that the inlet impedance provides a damping mechanism for instability suppression.