Extension of Amiet's theory to circular geometry

This paper proposes and presents derivations of two analytical methods based on Amiet's theory to predict the aerodynamic broadband noise of a thin annulus. The first approach extends the thin annulus model proposed by Roger [(2010). J. Fluid Mech. 653, 337-364] for leading-edge noise to trailing-edge noise by adapting Amiet's theory to a circular geometry. The second approach, referred to as the segmentation model, subdivides the annulus into noise-emitting flat plates, which are addressed with classical Amiet's theory. The results for the leading-edge thin annulus model matched well with the previously established results and experimental data. For the trailing-edge noise model, no reference results or experiments were available for direct comparison. The trailing-edge segmentation model showed good agreement with the thin annulus model, proving to be a valid method for trailing-edge noise prediction. Regarding the leading-edge segmentation model, an offset was observed, resulting in a consistent underprediction compared to the thin annulus model. Additional considerations were given about the ring's geometrical characteristics and their impact on the analytical model and noise predictions. These models provide a cost-effective approach, as the inputs can be derived from Reynolds-averaged Navier-Stokes simulations, making them suitable for numerous engineering applications, including ducted turbines, propellers, and other aerodynamic systems.