Analytical Green's function for the acoustic scattering by a flat plate with serrated edges

Serrations have attracted considerable attention in recent years owing to its capability to reduce trailing-edge and leading-edge noise in applications such as wind turbines and various rotating fans. Amiet's approach of modelling turbulence as gusts is widely used in recent analytical attempts. The approach of using Green's function, apart from an earlier attempt of Howe, is still rare, but it is very useful because it allows a direct comparison with experiments using laser-induced monopoles and offers the extensibility of including more realistic effects such as non-zero angle of attack. In this paper, we develop an analytical Green’s function for the serrated edge scattering problem using the Wiener-Hopf technique. A closed-form analytical Green’s function is obtained for sawtooth serrations and compared with the canonical Green’s function for straight edges. The analytical Green's function is verified using the finite element method. Both noise reduction spectra and directivity patterns are studied as a function of source position. Physical mechanism of sound reduction is discussed. This analytical Green’s function can be used to developed more accurate trailing-edge and leading-edge noise models and used as a benchmark solution for various numerical simulations.