This paper develops a fully coupled time domain Reduced Order Modelling (ROM) approach to model unsteady combustion dynamics in a backward facing step combustor. The acoustic field equations are projected onto the canonical acoustic eigenmodes of the systems to obtain a coupled system of modal evolution equations. The heat release response of the flame is modelled using the G-equation approach. Vortical velocity fluctuations that arise due to shear layer rollup downstream of the step are modelled using a simplified 1D-advection equation whose phase speed is determined from a linear, local, temporal stability analysis of the shear layer, just downstream of the step. The hydrodynamic stability analysis reveals a abrupt change in the value of disturbance phase speed from unity for Re < Recrit to 0.5 for Re > Recrit, where Recrit for the present geometry was found to be ≈ 10425. The results for self-excited flame response show highly wrinkled flame shapes that are qualitatively similar to those seen in prior experiments of acoustically forced flames. The effect of constructive and destructive interference between the two contributions to flame surface wrinkling results in high amplitude wrinkles for the case when Kc → 1.
