Flame-acoustic coupling of combustion instability in a non-premixed backward-facing step combustor: the role of acoustic-Reynolds stress

Combustion instability in a laboratory scale backward-facing step combustor is numerically investigated by carrying out an acoustically coupled incompressible large eddy simulation of turbulent reacting flow for various Reynolds numbers with fuel injection at the step. The problem is mathematically formulated as a decomposition of the full compressible Navier–Stokes equations using multi-scale analysis by recognising the small length scale and large time scale of the flow field relative to a longitudinal mode acoustic field for low mean Mach numbers. The equations are decomposed into those for an incompressible flow with temperature-dependent density to zeroth order and linearised Euler equations for acoustics as a first order compressibility correction. Explicit coupling terms between the two equation sets are identified to be the flow dilatation as a source of acoustic energy and the acoustic Reynolds stress (ARS) as a source of flow momentum. The numerical simulations are able to capture the experimentally observed flow–acoustic lock-on that signifies the onset of combustion instability, marked by a shift in the dominant frequency from an acoustic to a hydrodynamic mode and accompanied by a nonlinear variation of pressure amplitude. Attention is devoted to flow conditions at two Reynolds numbers before and after lock-on to show that, after lock-on, the ARS causes large-scale vortical rollup resulting in the evolution of a compact flame. As compared to acoustically uncoupled simulations at these Reynolds numbers that show an elongated flame with no significant roll up and disturbance in the upstream flow field, the ARS is seen to alter the shear layer dynamics by affecting the flow field upstream of the step as well, when acoustically coupled.