To investigate the acoustic properties of a slit resonator attached to a pipe with flow

a theoretical model based on the discrete vortex method was set up.The discontinuity conditions at the joint between the pipe and the resonator were formulated using the mass and momentum conservations

then combined with a discrete vortex model the acoustic impedance and the absorption coefficient of the resonator were computed.The numerical simulation indicates that the flow field around the slit is dominated by the rolling-up and flapping motion of the shed vortex sheet

which agrees with the previous flow visualization results and validates the "lip" assumption of the shear layer at the slit in the semi-empirical models.The present results reveal that the acoustic resistance of the resonator is mainly determined by the sound pressure levels and the grazing flow speed

while the acoustic reactance is dominated by the depth of the cavity

the thickness of the plate and end correction.