An Analytical Investigation Characterizing the Application of Single Frequency Acoustic Modulation for High Frequency Combustion Instability Suppression

Abstract

This research investigation presents a one dimensional acoustically consistent linear modal analysis based analytical method to analyze the stability of a fundamental longitudinal combustion instability mode when acoustic modulation is introduced. This analytical method was developed to qualitatively describe high frequency instability suppression trends seen in experiments in which strategic acoustic modulation was applied. This experimental liquid rocket engine combustor uses a speaker located in the oxidizer post, upstream of an injector to acoustically modulate the incoming propellant. This study provides a thorough derivation of an analytical method that was utilized to study the acoustic stability of the instability mode as single frequency acoustic modulation from the speaker was applied. Two ducts with different diameters were used to approximate the experimental rocket engine combustor geometry, with acoustically consistent matching conditions applied at the interface of the ducts. The boundary condition of the exit of the chamber was assumed to be acoustically closed, while the inlet boundary condition was derived in order to simulate a speaker introducing single frequency acoustic modulations into the combustor. Five case studies considering a fundamental longitudinal mode from f = 2, 300 − 2, 500Hz were investigated in order to determine the stability trend of the instability as acoustic forcing is applied. All cases consistently predicted a naturally unstable mode in the absence of acoustic forcing from the speaker, which is consistent with the spontaneously excited combustion instability observed experimentally without modulation from the speaker. It was found that the model was able to successfully predict trends in the stability of the mode observed in the experimental tests, which provides insight into the causes of suppression phenomena in the spontaneous longitudinal instability.