Application of the Wiener Hopf technique in the modelling of turbulent boundary layer trailing edge noise and supersonic jet screech

The Wiener Hopf Technique is used to solve two mixed boundary problems in aeroacoustics. In the first problem, an analytical Green’s function for the serrated edge wave scattering problem is solved using the Wiener Hopf technique. A closed form analytical Green’s function is obtained for piecewise linear 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. In the second problem, the generation of instability waves in a supersonic jet induced by acoustic wave impingement is examined. To obtain the newly excited instability wave, t he scattered sound field d ue to the acoustic impingement is first solved using the Weiner Hopf technique, with the kernel function factored using asymptotic expansions and overlapping approximations. Subsequently, the unsteady Kutta condition is imposed at the nozzle lip, enabling the derivation of the dispersion relation for the newly excited instability wave. A linear transfer function between the upstream forcing and the newly excited instability wave is obtained. T he amplitude and phase delay and their dependence on the frequency are examined. The new model shows improved agreement between the predicted screech frequencies and the experimental data compared to classical models.