Combustion instabilities result in large combustor acoustic amplitudes due to a feedback loop between exciting acoustic/hydrodynamic disturbances and flame response. This article addresses the global heat release properties required for a seemingly stable combustor to exhibit bi-stable behavior; that is, linearly stable but destabilized by a large enough disturbance amplitude, commonly referred to as “triggering” in the combustion instability literature. The global unsteady heat release rate is expanded up to fifth order in the source disturbance amplitude to capture triggering behaviors. For a system with linear damping, results show that under zero linear flame response, the third and fifth order non-linearity must satisfy very specific relationships in phase with no constraints on relative amplitudes. Extending this to non-zero linear flame response shows shifts in the phase relationship constraints. The analysis is applied to experimentally measured datasets from the literature showing its applicability. In addition, an example problem for an anchored, premixed flame is used with the constraints, to find the combination of control parameters where triggering is possible. The ultimate goal for the presented results is that it can be used to screen datasets (such as from single nozzle flame characterization experiments) and identify parametric spaces where triggering tendencies are the highest.
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