Low-order modeling of low-frequency combustion instabilities in aeroengines

Rumble is a combustion-induced instability occurring in aeroengines during start-up. Characteristically, low-limit-cycle frequencies between 50 and 150 Hz are obtained. Two basic feedback mechanisms are susceptible to promote rumble: entropy waves being reflected as pressure waves at the (nearly) choked combustor outlet and the purely thermoacoustic mode, originating from an in-phase oscillation of the heat release and the combustor pressure. Prior experiments on a generic rich-quench-lean (RQL) combustor have shown that the thermoacoustic mode determines the instability behavior over a wide range of operating conditions. A low-order model is developed for the staged RQL combustor to replicate theoretically the experimental findings and to investigate further the interaction of entropy waves and the purely thermoacoustic mode. The model accounts for dispersion and incorporates a simple flame transfer function, developed for spray combustion with negligible prevaporization. The model results confirm the experimental findings indicating a dominating thermoacoustic mode in the spectrum. The characteristically low-limit frequencies are a result of the characteristic timescales of droplet transport and combustion in the primary zone. It is further shown that the prevailing instability mode is strongly dependent on the dispersive properties of the primary zone and in the dilution sector of the combustor.