Convective Velocity Perturbations and Excess Gain in Flame Response as a Result of Flame-Flow Feedback

Convective velocity perturbations (CVPs) are known to play an important role in the response of flames to acoustic perturbations and in thermoacoustic combustion instabilities. In order to elucidate the flow-physical origin of CVPs, the present study models the response of laminar premixed slit flames to low amplitude perturbations of the upstream flow velocity with a reduced order flow decomposition approach: A linearized G-equation represents the shape and heat release rate of the perturbed flame, while the velocity perturbation field is decomposed into irrotational and solenoidal contributions. The former are determined with a conformal mapping from geometry and boundary conditions, whereas the latter are governed by flame front curvature and flow expansion across the flame, which generates baroclinic vorticity. High-resolution CFD analysis provides values of model parameters and confirms the plausibility of model results. This flow decomposition approach makes it possible to explicitly evaluate and analyze the respective contributions of irrotational and solenoidal flows to the flame response, and conversely the effect of flame perturbations on the flow. The use of the popular ad hoc hypothesis of convected velocity perturbation is avoided. It is found that convected velocity perturbations do not result from immediate acoustic-to-hydrodynamic mode conversion, but are generated by flame-flow feedback. In this sense, models for flame dynamics that rely on ad-hoc models for CVPs do not respect causality. Furthermore, analysis of the flame impulse response reveals that for the configuration investigated, flame-flow feedback is also responsible for “excess gain” of the flame response, that is, the magnitude of the flame frequency response above unity.