Strouhal number dependency of the aero-acoustic response of wall perforations under combined grazing-bias flow

The influence of low Mach number grazing-bias flow on the linear acoustic response of slit shaped wall perforations is determined in terms of a dimensionless acoustical impedance for Strouhal numbers based on the perforation width of order unity. The influence of edge geometries is studied by experiments. In particular, slanted slits under an angle of 30° with respect to the grazing flow direction are considered. Sound production, i.e. whistling potentiality corresponding to a negative real part of the impedance, is observed for various geometries and flow conditions. Sound production restricts the largest perforation size which can be used in practice for acoustical liners. Whistling in the limit cases of purely bias and purely grazing flows can be explained qualitatively in terms of Vortex Sound Theory. For combined bias/grazing flow, most of the oscillations in the impedance as a function of the Strouhal number are related to these limit behaviours. A configuration with thin sharp edges both upstream and downstream corresponds to commonly used theoretical models assuming an infinite thin wall. This configuration displays a behaviour drastically different from a more realistic perforation geometry with sharp square edges.