Direct numerical simulations of trailing-edge noise generated by boundary-layer instabilities

Direct numerical simulations (DNS) are conducted of noise generated at an infinitely thin trailing edge (TE). The aim is to predict the far-field sound and the near-field hydrodynamics, thereby providing an insight into the physical mechanisms of sound generation at airfoil TEs and potentially helping to validate acoustic theories. One of the theories widely used is the classical inviscid theory of Amiet, where the far-field sound can be evaluated in closed form if the convecting surface pressure spectrum upstream of the TE is known. For the first time, data from DNS including viscous effects are compared to the classical inviscid TE noise theory. In the present investigation, Tollmien–Schlichting waves are introduced close to the inflow boundary. The disturbances propagate downstream producing pressure fluctuations at the TE. In conducting two-dimensional DNS the theoretical method requires modification to account for the radiation of the total pressure difference in two dimensions only, as opposed to the three-dimensional sound radiation originally considered by Amiet. The modified theoretical analysis and a comparison between DNS and theoretical results are presented, scrutinizing the assumptions made in the derivation. Amietʹs surface pressure jump transfer function is found to predict the scattered pressure field accurately. Directivity plots of DNS data show that viscous effects appear to smear individual lobes and that a downstream pointing lobe is present at higher Mach number which is attributed to an additional wake source.