A semi-analytical model for the acoustic impedance of finite length circular holes with mean flow

Abstract

The acoustic response of a circular hole with mean flow passing through it is highly relevant to Helmholtz resonators, fuel injectors, perforated plates, screens, liners and many other engineering applications. A widely used analytical model [M.S. Howe. “Onthe theory of unsteady high Reynolds number flow through a circular aperture”, Proc. of the Royal Soc. A. 366, 1725 (1979), 205‐223] which assumes an infinitesimally short hole was recently shown to be insufficient for predicting the impedance of holes with a finite length. In the present work, an analytical model based on Green׳s function method is developed to take the hole length into consideration for “short” holes. The importance of capturing the modified vortex noise accurately is shown. The vortices shed at the hole inlet edge are convected to the hole outlet and further downstream to form a vortex sheet. This couples with the acoustic waves and this coupling has the potential to generate as well as absorb acoustic energy in the low frequency region. The impedance predicted by this model shows the importance of capturing the path of the shed vortex. When the vortex path is captured accurately, the impedance predictions agree well with previous experimental and CFD results, for example predicting the potential for generation of acoustic energy at higher frequencies. For “long” holes, a simplified model which combines Howe׳s model with plane acoustic waves within the hole is developed. It is shown that the most important effect in this case is the acoustic non-compactness of the hole.