Simple analysis of flame dynamics via flexible convected disturbance models

Flame sheet modeling is a common approach for the determination of flame transfer functions for prediction and modeling of thermoacoustic combustion instabilities. The dynamics of the flame-sheet model for simple flame geometries can be shown to be equivalent to a basic model of convective disturbances interacting with a steady heat release region. This framework shows that the flame transfer functions predicted by linearized flame-sheet models are the Fourier transform of the steady heat release rate profile for the flamesheet geometry transformed into a Lagrangian convective time reference frame. This result is significant relative to existing flame-sheet modeling approaches in allowing the prediction of dynamic behaviors on the basis of steady information only. Multiple perturbations on the flame can be treated simply via superposition of individual perturbations. Analysis of results from these convective disturbance models illuminates the existence of two independent length scales governing the flame transfer function dynamics. Magnitude is governed by the tip-to-tail length of the flame, whereas phase is governed by the heat release rate profile center of mass calculated from the disturbance origin. The convective disturbance approach shows promise in its potential to derive flame transfer function predictions from a steady flame heat release rate profile.