Modelling chordwise-varying porosity to reduce aerofoil-turbulence interaction noise

Abstract

We consider a finite perforated plate and study the effects of smoothly varying chordwise porosity on turbulence-aerofoil interaction noise. To study this problem, we use a novel Mathieu function collocation method, rather than a traditional Wiener–Hopf approach which would be unable to deal with chordwise varying quantities. Our main focus is on two bio-inspired porosity distributions, which are modelled based on air flow resistance data from the wings of barn owls and common buzzards. As expected, trailing-edge noise is much reduced for the owl-like distribution. However, and perhaps surprisingly, so too is leading-edge noise, despite both wings having similar porosity values at the leading edge. We then consider a general monotonic variation. Our study indicates that there may be a significant acoustic impact of how the porosity is distributed along the whole chord of the plate (i.e. not just its values at the scattering edges). Indeed, a plate whose porosity continuously decreases from the trailing edge to a zero-porosity leading edge can, in fact, generate lower levels of trailing-edge noise than a plate whose porosity remains constant at the trailing-edge value.