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Trapped acoustic modes in aeroengine intakes with swirling flow

A theoretical model of an aeroengine intake–fan system is developed in order to show the existence of acoustic resonance in the intake. In general this phenomenon can be linked to instabilities in aircraft engine inlets. The model incorporates a slowly varying duct intake and accounts for the swirling flow downstream of the fan. The slow axial variation in cross-section gives rise to turning points where upstream-propagating acoustic modes are totally reflected into downstream-propagating modes. The effect of the swirling flow downstream can be to cut off a mode which is cut on upstream of the fan. It is shown that these two aspects of the flow, coupled with the effects of the fan (represented by an actuator disc), can lead to acoustic modes becoming trapped in the intake, thus giving rise to pure acoustic resonance. A whole range of system parameters, such as axial, fan and swirl Mach numbers, which satisfy the conditions for resonance are identified. The effects of a stationary blade row behind the fan are also considered leading to a second family of resonant states. In addition we find resonance due to reflection of acoustic modes at the open (inlet) end of the duct.