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Triggering in Thermoacoustics

Under certain conditions, the flow in a combustion chamber can sustain large amplitude oscillations even when its steady state is linearly stable. Experimental studies show that these large oscillations can sometimes be triggered by very low levels of background noise. This theoretical paper sets out the conditions that are necessary for triggering to occur. It uses a weakly nonlinear analysis to show when these conditions will be satisfied for cases where the heat release rate is a function of the acoustic velocity. The role played by non-normality is investigated. It is shown that, when a state triggers to sustained oscillations from the lowest possible energy, it exploits transient energy growth around an unstable limit cycle. The positions of these limit cycles in state space is determined by nonlinearity, but the tangled-ness of trajectories in state space is determined by non-normality. When viewed in this dynamical systems framework, triggering in thermoacoustics is seen to be directly analogous to bypass transition to turbulence in pipe flow.