An Efficient and Versatile Semi-Analytical Method for Acoustic Wave Scattering by Periodic Structures in Flow

The unified transform method is applied to industrially-motivated variations of the classical semi-infinite grating scattering problem. Previous applications of the unified transform method to scattering problems ignore the effects of flow, which limits their applicability to several important examples in engineering. Careful consideration is taken to implement mean flow into a periodic unit cell that has previously been used to represent porous structures in existing literature. An efficient and versatile analytical tool is constructed to investigate the scattering of an incident wave along a (potentially multi-layered) periodic grating in flow with the goal of producing a theoretical framework to improve the acoustic designs of scattering media in fluid flow. Initial results show that scattered noise can be mitigated by varying important geometrical properties of a suggested unit cell, such as the spacing between grating layers or the spacing between apertures. This methods paper brings attention to the procedure of the new technique based on the unified transform and highlights its versatility to varying geometries and plate parameters in scattering problems.