Vortex sound radiation in a flow duct with a dipole source and a flexible wall of finite length

The noise attenuation of fan-ducted noise at low blade-passage frequency remains a challenge. The present study investigates the noise reduction mechanism of a tensioned membrane housing device that directly controls the sound radiation from the doublet which is enclosed in an infinitely long duct with a point vortex. The time dependent sound radiation mechanism and the vibro-acoustics coupling mechanism of the systems are studied by adopting the potential theory and matched asymptotic expansion technique. The silencing performance of such a passive approach depends on the amplitude and phase of the sound field created by the doublet and the acoustic pressure induced by the membrane oscillation in order to achieve sound cancellation. Results show that the response of membrane vibration is strongly associated with the flow field induced by the grazing uniform flow and also the fluid loading generated by the inviscid vortex. The geometrical property of the cavity and the mechanical properties of the flexible membranes play important roles in controlling the performance of the proposed device.