Numerical Simulation of Flame Acoustic Interaction with Consideration of Multiple Time and Length Scales Including Acoustic Damping

A generalized formulation of combustion-acoustic coupling at simultaneous multiple timeand length-scales is presented. The compressible Navier Stokes equations are expanded about the mean flow Mach number M and the ratio of flow and acoustic length scales h/L. This results in the equations separating into the one governing the incompressible base flow evolving at longer time and shorter length scale and the other, the acoustics evolving at shorter time and longer length scale. Explicit coupling terms, the dilatation of the base flow as a source of acoustic energy and the acoustic Reynolds stress (ARS) as the source to base flow momentum are identified. Simulations are carried out in a dump combustor. The flame acoustic system, initially in the multi-time/length scale regime, is shown to evolve towards the single-time/multi-length scale regime as a result of the coupling. The system approaches the single time multiple length scale regime much faster with increase in the flow velocity. Acoustic damping, when accounted for, limits the acoustic amplitude and flame/vortex roll-up, and its subsequent shedding is predicted by the coupled nonlinear system.