Linear instability of a premixed slot flame: Flame transfer function and resolvent analysis

The response to forcing of a 2D laminar premixed slot flame is investigated by means of linear analysis, based on the compressible flow equations with a two-step reaction scheme for methane combustion. The flame transfer function (FTF) is computed from this linear model, in excellent agreement with reference nonlinear calculations. The input-output gain between externally applied forcing and the global heat release rate response is computed, and peaks in the gain are related to intrinsic thermoacoustic (ITA) modes. The receptivity of the flame to arbitrary flow forcing is characterised by the resulting amplitude of global heat release rate fluctuations. Linear resolvent analysis is used to identify optimal forcing structures and their associated flame response, leading to a discussion of the dominant mechanisms for the amplification of flow perturbations, which trigger flame oscillations. These seem to involve a resonance with ITA instability modes.