The development and commercial application of lean premixed aeronautical gas turbine combustors is currently hindered by the occurrence of thermoacoustic oscillations. It has been established that the acoustic energy input into a thermoacoustic system is notionally described by the coupling that exists between the pressure and heat release rate. 1 However, difficulties arise when attempting to understand and predict the feedback mechanisms that link pressure oscillations to heat release rate oscillations and promote the occurrence of self-excited thermoacoustic oscillations in realistic systems. This is due to the complexity and inter-connectivity of the coupling that exists through the dynamical turbulent flow, mixing, combustion, and acoustics. Aeronautical applications pose additional challenges when compared to land-based power systems due to the need to inject, vaporize, and mix liquid fuel directly in the combustion chamber, and because of the wide variety of operating conditions needed within a flight envelope. Changing air and fuel flow rates can dramatically affect the prevalence of self-excited dynamics and the resultant saturation pressure oscillation amplitude (p). There has been a substantial body of research directed at understanding the coupling mechanisms responsible for thermoacoustic oscillations. Heat release dynamics are affected by perturbations in the flow field, as well as fluctuations in the supply of reactants to the flame zone. 2 The relative strength of each of these factors depends on the specific conditions of the experiment. Lieuwen et al. 3, 4 found that heat release rate oscillations can result from fluctuations in the equivalence ratio, caused by pressure oscillations interacting with the incoming supply of reactants. Many studies have focused on the direct action of acoustically-induced velocity oscillations on the flame. 5–7 Using a perfectly premixed atmospheric laboratory combustor, Brisebois et al. 2 found that vortical distributances in the air supply to the flame zone determined the phase relationships between the pressure and heat release rate. Entropy waves were also found by Hield et al. 8 to drive low frequency oscillations. Models of thermoacoustic behaviour commonly employ time lags, where a disturbance in one of the aforementioned factors is propagated into a heat release rate fluctuation at a later time. 4, 8–11

Models aimed at determining oscillation frequencies generally assume a simplified acoustic geometry and perform a linear stability analysis to find the resonant modes of the combustion system. The dominant frequency of self-excited thermoacoustic oscillations generally corresponds with one of these modes. 12 For simple geometries, the resonant properties in both Helmholtz and organ tone oscillations are well understood. 13 In practical combustors however, there are complex acoustic boundary conditions, as well as many components with complex geometries that can potentially shift or add resonant frequencies. Flame transfer functions (FTF) provide an empirical means of representing the linear thermoacoustic response of a system as a function of frequency. 14 For limit-cycle oscillations, where the non-linear effects become significant, flame describing functions (FDF) can be used to determine the limit cycle amplitude of oscillations. 15 Both of these representations are determined experimentally by forcing the combustor of interest at a wide range of frequencies and amplitudes and establishing a transfer function of the combustor response. FTF/FDFs express the acoustic response in terms of a gain and phase shift, and thus provide little insight into the causal mechanisms responsible for the excited …