Abstract
Intrinsic thermoacoustic modes are studied in the case of self-igniting flames stabilised in the diverging section of a converging-diverging nozzle with Mach number in the range M = 0.6. Since auto-ignition is largely influenced by the pressure and static temperature conditions in the entire region upstream of the flame, the subject of intrinsic thermoacoustic modes, i.e. modes due to the closed-loop feedback between the flame behaviour and the upstream acoustic field in the absence of reflection from the upstream and downstream boundaries, is particularly interesting and relevant. These types of modes, which are very different in nature from those due to the closed-loop reflection of acoustic waves from the inlet and outlet boundaries, have been studied by several authors mostly in the case of conventional propagating premixed flames. In this work, the flame response to incident acoustic waves is determined analytically based on the linearised Rankine-Hugoniot relations applied to the instantaneous infinitesimally thin auto-ignition boundary. Acoustic wave propagation in the flow upstream and downstream of the flame is resolved by the Magnus expansion. Intrinsic thermo-acoustic modes are found by two different methods: a) as solutions of the closed-loop stability problem when the reflection coefficients at the inlet and outlet boundaries tend to zero, b) as poles of the flame scattering matrix. It is shown that the intrinsic modes obtained in this way coincide in the case of self-ignition in a straight duct, but differ in the case of a flame stabilised in a converging-diverging duct. This apparent discrepancy is discussed and explained.
