DNS 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, providing an insight into the physical mechanisms of sound generation and potentially helping to validate acoustic theories. In particular, the DNS data are compared with Amiet's theory, where the farfield sound can be evaluated in closed form if the convecting surface pressure spectrum upstream of the TE is known. For 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. For DNS, a high-order accurate numerical method is chosen which is free of upwinding, artificial dissipation or any form of explicit filtering, and employs a novel boundary treatment. The modified theoretical analysis and a comparison between DNS and theoretical results are presented, scrutinizing the assumptions made in the derivation. Amiet's 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 strong downstream pointing lobe is present which is attributed to an additional wake source.