STAR · An Extended Local Scattering Theory for Acoustic-radiation and Receptivity of Trailing-edge Flows

An Extended Local Scattering Theory for Acoustic-radiation and Receptivity of Trailing-edge Flows

Trailing-edge flows arise in many technological applications, such as aircraft wings in aeronautics and mixing devices in chemical engineering. Two important and fundamental processes take place near the trailing edge, namely the acoustic radiation and receptivity, which refer to generation of sound by fluctuations within the flows and excitations of instability waves by ambient disturbances, respectively. This project will investigate (a) generation of instability waves in the wake as free-stream acoustic and vortical disturbances impinge on the trailing edge; (b) radiation of sound when Tollmien-Schlichting (T-S) waves in the upstream boundary layer propagate through, and interact with, the trailing-edge flow. Both processes will be analysed mathematically by developing a Local Scattering Theory, which we recently proposed as an appropriate framework for describing the coupling of distinct characteristic motions in a region of strong inhomogenuity. Furthermore, with radiation and receptivity being described properly, we will move on to investigate the so-called acoustic feedback loops, in which instability waves and acoustic waves are generated from each other, leading to self-sustained oscillations. First-principle theories will be developed to predict the tones (frequencies) of the oscillations. Although the proposed research is primarily of fundamental nature, the theoretical progress would be of considerable interest to aeronautic industry. Moreover, the study on the feedback loops reveals the mechanism of the airfoil tonal noise, which provides potential opportunities for noise reduction strategy. The overall objectives of this project are twofold. Firstly, it provides a theoretical framework to predict the receptivity and acoustic radiation of trailing-edge flows, which is of high practical relevance to a variety of engineering applications. Secondly, from the methodology point of view, this project combines sophisticated asymptotic methods with highly accurate numerical computations, enabling us to tackle a greater range of complex problems, for which numerical or analytical method alone would be inadequate.

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