Stability analysis of thermoacoustic interactions in vortex shedding combustors using Poincaré map

Abstract

Vortex separation and breakdown are an important source of unsteady heat release rate fluctuations in thermoacoustic systems. The coupling between the acoustic field and the energy released by vortex breakdown can cause combustion instability. The objective of this work is to perform linear stability analyses and to quantify the stability of thermoacoustic interactions where vortex breakdown is the dominant cause of heat release rate fluctuations. The dynamics of the system is modelled as a kicked oscillator, where the energy released by vortex breakdown is represented as the kick. Assuming small fluctuations, periodic and low values of kick, a Poincaré map is derived analytically. The stability of the system is determined from the eigenvalues associated with the Poincaré map. The results allow us to identify the region where vortex shedding or the acoustic mode is dominant. Previous experimental investigations report the transition between the two modes for variation in the flow Mach number. Similar transitions are observed in the present study.