Nonlinear acoustics of an aperture under grazing flow

Abstract

This work presents a mathematical model of a dynamically forced, acoustically compact aperture subject to one-sided mean grazing flow in two or three dimensions. By contrast to other simplified theoretical representations of a grazed aperture, the one proposed in this contribution considers some of the nonlinear effects a reduced order model should naturally inherit from the conservation equations governing the primary system’s dynamics. Furthermore, unlike other nonlinear developments, this one is able to reproduce the acoustic forcing amplitude dependence of the fundamental-frequency-based impedance, measured in recent experiments, without relying on empirical parameters. This nonlinear model offers further insight into the dominant physical mechanisms determining the aforementioned behaviour and allows reasonable a priori estimates of the aeroacoustic dynamics of the aperture. This could be used as a building block of more sophisticated systems or for the derivation of even simpler representations suitable for acoustic network modelling.