Low-frequency still-air acoustic inertia of inclined circular aperture in an infinite flat plate of finite thickness

The acoustic inertia of the canonical configuration of inclined circular aperture(s) in a finite-thickness plate at the low frequency limit is investigated under the inviscid still-air condition. A hybrid approach combining modal expansion and boundary element method is applied to calculate the effective length of the aperture as a quantitative characterisation of its acoustic inertia. These calculations, covering different inclination angles up to 75°, are performed for a single isolated aperture with a selected range of plate thickness and the periodic aperture arrays of aligned and staggered arrangements with a selected range of aperture spacing respectively. The results are validated by the simulations carried out with the commercial software COMSOL. The parametric studies of geometric dimensions included in this work provide representative results for typical acoustic related engineering applications of finite-length inclined apertures. A link for access to the MATLAB programmes implementing the calculations is provided for interested readers. As an example of application, the hybrid method described in this work is used for the acoustic modelling of a representative multi-perforated liner studied in the literature for the problem of thermo-acoustic instability. The results compared well against those obtained from the Computational Fluid Dynamics simulations reported in the literature.