Nonlinear dynamical features of vortex-acoustic lock-on in a backward-facing step combustor

Abstract

Unstable shear layers characteristic of step combustors display strong vortex shedding and play a dominant role in combustion instability. Past non-premixed flame experiments with Reynolds number (Re) as the bifurcation parameter showed that during instability, the frequency of acoustic oscillations locks-on to the natural vortex shedding mode for a range of Re. In the present work, we study the dynamical features of this type of lock-on. We employ a vortex model to bring out the nonlinearity in the flame response to vortical perturbations. This is coupled with a Galerkin model for the acoustic field. Regimes of aperiodic oscillations, low-amplitude lock-on and high-amplitude lock-on are predicted in agreement with experimental trends. Phase portraits show a transition to instability during lock-on via a supercritical Hopf bifurcation with an increase in limit cycle amplitudes. Synchronisation between the acoustic pressure and vortex-driven heat release perturbation is studied using recurrence analysis. The system transitions from asynchronous to phase synchronisation in the low-amplitude lock-on regime, characterised by an increasing degree of phase correlation. In the high-amplitude lock-on regime, a state of generalised synchronisation exists, where in addition to the phase, the amplitudes also show strong correlation.