Incompressible large eddy simulations coupled with acoustics are performed to predict combustion noise and instability in a partially premixed based backward facing step combustor. The computational analysis adopts a simultaneous multi-scale spatio-temporal framework for flow and acoustics such that the flow/acoustics varies at a shorter/longer length scale and a longer/shorter time scale respectively. This engenders flow dilatation and acoustic Reynolds stress (ARS) as the external source terms in the acoustic energy and flow momentum respectively. Numerical results are presented for three cases, at a particular Reynolds number, wherein two of them constitute acoustically coupled (coupled long duct case) and its uncoupled counterpart (no acoustic feedback). The third corresponds to a shorter combustor length (coupled short duct case). These three cases contrast the strong acoustic feedback in the short duct case, both of which are compared with the acoustically uncoupled LES that is common to them. It is found that combustion occurs predominantly in the large-scale vortical structures in the coupled long duct case due to enhanced mixing between the reactants brought about by the strong acoustic feedback (ARS). Thus, the present work is able to not only distinguish between the flow and acoustic processes, but also handle both combustion noise and instability within the same framework.

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