Turbulence-distortion modelling for Amiet’s theory enhancement

Abstract

When applied to aerofoils with non-negligible thickness, Amiet’s theory for turbulence-interaction noise prediction does not account for the alterations in the velocity field and acoustic response induced by the surface, resulting in an overestimation of the radiated noise. This study proposes a semi-analytical method that models turbulence distortion in the immediate vicinity of the surface starting from upstream flow conditions and considers the resulting effects on the acoustic response of the aerofoil. The distorted spectrum of the upwash velocity component is calculated using the asymptotic results of the rapid distortion theory (RDT) for very large- and small-scale turbulence, overcoming the need to define a representative location where turbulence characteristics are sampled. This distorted spectrum is characterised by an increased energy content that is encompassed in the model by scaling the analytical flat-plate formulation of the aeroacoustic transfer function. The proposed approach relies on defining the aerofoil geometrical feature that affects distortion mechanisms, required to extend the RDT results to such geometries. This parameter is identified as the path travelled by the turbulent eddies from the stagnation point to the position of maximum surface-pressure fluctuations, which is, in turn, related to flow acceleration and leading-edge sharpness. The accuracy of this methodology in enhancing noise prediction is demonstrated using numerical and experimental data of grid-generated turbulence interacting with different aerofoils.