Nonlinear global flame response behaviors for triggering of combustion instabilities.

This article focuses on the nonlinear global heat release characteristics that enable a linearly stable combustor to exhibit bi-stable behavior, known as "triggering," where a sufficiently large disturbance can destabilize the system. Using a fifth-order expansion of the global unsteady heat release rate in disturbance amplitude, the study derives analytical constraints on the phase relationships between third- and fifth-order nonlinear flame responses under assumptions of linear damping and either zero or non-zero linear flame response. These constraints define narrow parameter regions where triggering can occur, with the presence of non-zero linear response broadening the triggering parameter space. The methodology includes a physics-based fitting strategy applied to experimental datasets, validating the theoretical predictions, and is further illustrated through a nonlinear model of an axisymmetric premixed flame, identifying flame angles and frequencies conducive to triggering. The work highlights the importance of nonlinear flame dynamics in combustion instability and provides a framework for screening experimental data to assess triggering tendencies.