Asymptotic approximations for the sound generated by aerofoils in unsteady subsonic flows
This thesis considers the sound generated by unsteady perturbations interacting with solid aerofoils in background steady flows, in an attempt to further develop analytic models for the noise generated by blades within turboengines. Specifically, high-frequency unsteady gust and sound wave perturbations are considered and asymptotic results are obtained for, primarily, the far-field noise. Previous analytic work has examined high-frequency gust-aerofoil interactions in steady uniform flows using rapid distortion theory, and has focused on aerofoils with simple geometries. We extend this to deal with aerofoils with more realistic geometries (by including camber, thickness, and angle of attack), as well as considering the new topic of sound-aerofoil interactions in steady uniform flows for aerofoils with realistic geometries. The assumption of a steady uniform flow is later relaxed and we investigate the sound generated by high-frequency gust-aerofoil interactions in steady shear flows. Throughout all of the aforementioned work, the key process involves identifying various asymptotic regions around the aerofoil where different sources dominate the generation of sound. Solutions are obtained in each region and matched using the asymptotic matching rule. The dominant regions producing noise are the local, “inner”, regions at the leading and trailing edges of the aerofoil. Approximations for the far-field noise (in the “outer” regions) are the principal results, however one can also extract approximations for the unsteady pressure generated on the surface of the aerofoil. The surface pressure generated by high-frequency gust-aerofoil interaction in uniform flow is found to contain a singularity at the leading-edge stagnation point, thus the final piece of work in this thesis focuses more closely on turbulent interactions with solid body stagnation points in uniform flow, eliminating this singularity.