The acoustics of short circular holes opening to confined and unconfined spaces

The sound generated or absorbed by short circular holes with a mean flow passing through them is relevant in many practical applications. Analytical models for their acoustic response often ignore the fact that such holes open to a confined or finite space either side, or account for this effect simply by adding an end mass inertial correction. The vortex-sound interaction within a short hole has been recently shown to strongly affect the acoustic response at low frequencies (D. Yang, A.S. Morgans, J. Sound Vib. 384 (2016) 294-311 [19]). The present study considers a semi-analytical model based on Green's function method to investigate how the expansion ratios either side of a short hole affect the vortex-sound interaction within it. After accounting for expansions to confined spaces using a cylinder Green's function method, the model is substantially simplified by applying a half-space Green's function for expansions to large spaces. The effect of both the up- and downstream expansion ratios on the acoustics of the hole is investigated. These hole models are then incorporated into a Helmholtz resonator model, allowing a systematic investigation into the effect of neck-to-cavity expansion ratio and neck length. Both of these are found to affect the resonator damping.