Combustion instability analysis from the perspective of acoustic impedance

Abstract

This paper presents a one-dimensional thermoacoustic model for a dump combustor in terms of two acoustic impedances just before and after a flame/area-expansion location. A key findings is that, as long as combustion instability is concerned, those two impedances fully crystallize the geometry of a combustor, steady operating conditions and inlet-outlet boundary conditions. From this impedance-based thermoacoustic model and a formulation of combustion instability as a robust stability problem, it is shown that the existence of either a low frequency impedance matching or a low resonance frequency of a flame chamber associated with a closed left boundary at a flame location, can promote combustion instability. A sufficient condition for combustion stability which requires no knowledge of a flame transfer function except its peak gain, is also presented. Our sufficient condition is shown to be less conservative than existing ones in literature. A numerical example is presented to illustrate our developments and findings.