Airframe noise, the noise of an aircraft in flight not due to the engine or other mechanical devices, is often a major contribution to the sound heard from an aircraft during landing approach. Over the past few decades certification requirements have gradually tightened, reaching the point where the required noise reductions cannot be achieved through reducing engine noise alone. There are, similarly, restrictions on the noise output of wind turbines to reduce their impacts on local communities and wildlife. In practice this is achieved by braking the turbines at high speed, reducing energy outputs and efficiency. For both aircraft wings and turbine blades, the sharp trailing-edge is a well-understood and unavoidable source of noise, scattering vortical, hydrodynamic disturbances within the boundary-layer into far-field, acoustic, noise. Inspired by nature, for example the silent flight of owls, modification of the flow within the boundary-layer near the trailing-edge, either through passive or active devices, appears to offer methods of reducing far-field noise. The precise mechanisms are not completely understood, and this work focuses on the effect of varying boundary-layer parameters near the trailing-edge on the resulting far-field noise. Alternative methods of noise reduction include the addition of linings, for example via arrays of Helmholtz resonators. The junctions at the leading- and trailing-edges of such linings can again be a source of far-field noise, through a similar mechanism to that of a trailing-edge. This scattering is analysed within a simplified mathematical framework through an application of Rapid Distortion Theory, considering linearised perturbations to a transversely sheared background flow. Within this framework, the development of disturbances within a boundary-layer are investigated, both hydrodynamic and acoustic, over a variety of mixed boundary conditions. The inclusion of background shear requires numerical solution of differential equations, which are paired with complex variable techniques such as theWiener-Hopf method, constructed for the solution of boundary-value problems with discontinuous boundary conditions. The possibility of exact solutions using this technique allows asymptotic methods to be used to directly evaluate far-field noise.
mathematics, applied mathematics, acoustics, fluid dynamics, shear, scattering, wiener-hopf, owls
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