Models for Flame-Vortex-Acoustic Interactions in a Backward-Facing Step Combustor - A Comparitive Study

A novel model for flame-vortex-acoustic interactions in a lean premixed step combustor is described. The distinctive role of vortex shedding motivates the use of a Lagrangian vortex method for the flow. Two flame models are compared, the G-Equation (GE) and Thermo-Diffusive model (TD). At stable operation, weak wrinkles propagate along the flame surface in both models and their instantaneous flame positions match. For larger equivalence ratios, a higher heat release perturbation q' causes a transition to limit-cycle behaviour in the TD where flame-vortex interactions over one cycle are predicted. When the velocity reaches a minimum, vortices in the recirculation zone merge with vortices at step upstream increasing the circulation Γ resulting in a large vortex that extends to the top wall. The flame wraps around the large vortex trapping reactants in its fold. The trapped reactants burn vigorously, marking the instant of highest q' in phase with acoustics-forced Γ. This contributes to the closed-loop feedback mechanism. In the GE, high u_θ/s_L due to strong Γ tend to cause large wrinkles and cusps that do not smooth out due to absence of kinematic restoration effects, otherwise captured by the TD. The TD dynamics and phase relationships are in excellent agreement with experiments.