  Abrupt transitions to the state of thermoacoustic instability (TAI) in gas
turbine combustors are a significant challenge plaguing the development of
next-generation low-emission aircraft and power generation engines. In this
paper, we present the observation of abrupt transition in three disparate
turbulent thermoacoustic systems: an annular combustor, a swirl-stabilized
combustor, and a preheated bluff-body stabilized combustor. Using a low-order
stochastic thermoacoustic model, we show that the reported abrupt transitions
occur when an initially stable, supercritical limit cycle becomes unstable,
leading to a secondary bifurcation to a large amplitude limit cycle solution.
The states of combustion noise and intermittency observed in these turbulent
combustors are well captured by the additive stochastic noise in the model.
Through amplitude reduction, we analyze the underlying potential functions
affecting the stability of the observed dynamical states. Finally, we make use
of the Fokker-Planck equation, educing the effect of stochastic fluctuations on
subcritical and secondary bifurcation. We conclude that a high enough intensity
of stochastic fluctuations which transforms a subcritical bifurcation into an
intermittency-facilitated continuous transition may have little effect on the
abrupt nature of secondary bifurcation. Our findings imply the high likelihood
of abrupt transitions in turbulent combustors possessing higher-order
nonlinearities where turbulence intensities are disproportionate to the large
amplitude limit cycle solution.
