The acoustics of short circular holes with reattached bias flow

Abstract

One of the most important parameters influencing the acoustic response of holes that sustain a low-Mach-number bias flow is their length-to-diameter ratio. For sufficiently short holes, the bias flow is detached within the hole’s length, while in long holes the bias flow reattaches. The acoustic behaviour of each class is different and separate modelling approaches exist in the literature. For many technical applications, however, the length-to-diameter ratio falls in the range 1.5<Lh/Dh<3.0, where is not clear if the holes behave acoustically as short or long holes. In this work, the acoustics of such medium holes are explored numerically and analytically. The numerical approach is based on the linearisation of the compressible Navier–Stokes equations (LNSE) around a Reynolds-averaged mean flow. Medium holes are shown to whistle at higher Strouhal numbers than short holes although the mean flow reattaches within them. The underlying physics are further investigated by incorporating selected flow features of the LNSE results into a semi-analytical model accounting for vortex-sound interaction. It is shown that the perturbation field is determined by the three-way coupling of the two vortex sheets shed from the inlet and outlet edges of the hole with the acoustic field. Furthermore, the modelling of the growth of vorticity inside the hole is shown to be crucial to enable whistling in the semi-analytical model.