A new analytical model is developed for the prediction of noise from serrated trailing edges. The model generalizes Amiet's trailing-edge noise theory to sawtooth trailing edges, resulting in a complicated partial differential equation. The equation is then solved by means of a Fourier expansion technique combined with an iterative procedure. The solution is validated through comparison with the finite element method for a variety of serrations at different Mach numbers. The results obtained using the new model predict noise reduction of up to 10 dB at 90 • above the trailing edge, which is more realistic than predictions based on Howe's model and also more consistent with experimental observations. A thorough analytical and numerical analysis of the physical mechanism is carried out and suggests that the noise reduction due to serration originates primarily from interference effects near the trailing edge. A closer inspection of the proposed mathematical model has led to the development of two criteria for the effectiveness of the trailing-edge serrations, consistent but more general than those proposed by Howe. While experimental investigations often focus on noise reduction at 90 • above the trailing edge, the new analytical model shows that the destructive interference scattering effects due to the serrations cause significant noise reduction at large polar angles, near the leading edge. It has also been observed that serrations can significantly change the directivity characteristics of the aerofoil at high frequencies and even lead to noise increase at high Mach numbers.

An analytical model is developed for the prediction of noise radiated by an aerofoil with leading edge serration in a subsonic turbulent stream. The model makes use of the Fourier Expansion and Schwarzschild techniques in order to solve a set of coupled differential equations iteratively and express the far-field sound power spectral density in terms of the statistics of incoming turbulent upwash velocity. The model has shown that the primary noise reduction mechanism is due to the destructive interference of the scattered pressure induced by the leading edge serrations. It has also shown that in order to achieve significant sound reduction, the serration must satisfy two geometrical criteria related to the serration sharpness and hydrodynamic properties of the turbulence. A parametric study has been carried out and it is shown that serrations can reduce the overall sound pressure level at most radiation angles, particularly at small aft angles. The sound directivity results have also shown that the use of leading edge serration does not particularity change the dipolar pattern of the far-field noise at low frequencies, but it changes the cardioid directivity pattern associated with radiation from straight-edge scattering at high frequencies to a tilted dipolar pattern.

An analytical model is developed for the prediction of noise radiated by an aerofoil with leading edge serration in a subsonic turbulent stream. The model makes use of the Fourier Expansion and Schwarzschild techniques in order to solve a set of coupled differential equations iteratively and express the far-field sound power spectral density in terms of the statistics of incoming turbulent upwash velocity. The model has shown that the primary noise reduction mechanism is due to the destructive interference of the scattered pressure induced by the leading edge serrations. It has also shown that in order to achieve significant sound reduction, the serration must satisfy two geometrical criteria related to the serration sharpness and hydrodynamic properties of the turbulence. A parametric study has been carried out and it is shown that serrations can reduce the overall sound pressure level at most radiation angles, particularly at downstream angles close to the aerofoil surface. The sound directivity results have also shown that the use of leading edge serration does not particularity change the dipolar pattern of the far-field noise at low frequencies, but it changes the cardioid directivity pattern associated with radiation from straight-edge scattering at high frequencies to a tilted dipolar pattern. † Email address for correspondence: bl362@cam.ac.uk arXiv:1706.04509v1 [physics.flu-dyn]

This paper is concerned with the development of a theoretical model for the prediction of the sound radiated by serrated trailing-edges. The proposed model is based on Fourier expansion and Amiet's formulation. By using an iterative PDE-solving procedure, the scattered pressure field on the surface of an airfoil with sawtooth trailing-edge serrations is obtained. The far-field sound is then evaluated using the surface pressure integral based on the theories of Kirchhoff and Curle. The power spectral density (PSD) of the farfield sound is then related to the wavenumber spectral density of the hypothetical surface pressure under the turbulent boundary layer that would exist when the trailing-edge is absent. Numerical evaluation of the new model has shown better agreement than that obtained using Howe's model. Based on the new model, the sound reduction achieved by a trailing-edge with sharp sawtooth serrations is around 5-10 dB for a wide frequency range. This result better agrees with experiments, in which the average sound reduction is reported to be 5-7 dB. The results obtained using the new analytical model also agree well with FEM computations, suggesting that the model developed in this paper can capture the essential physics and give correct predictions for the sound generated by serrated trailingedges. In the end, the physical mechanism of noise reduction is found to be the destructive interference effect of the scattered pressure field.

A semi-analytical model for installed jet noise is proposed in this paper. We argue and conclude that there exist two distinct sound source mechanisms for installed jet noise and the model is therefore composed of two parts to account for these different sound source mechanisms. Lighthill's acoustic analogy and a fourth-order space-time correlation model for Lighthill stress tensor are used to model the sound induced by the equivalent turbulent quadrupole sources, while the trailing-edge scattering of near-field evanescent instability waves are modelled using Amiet's approach. A non-zero ambient mean flow is taken into account. It is found that, when the rigid surface is not so close to the jet as to affect the turbulent flow field, the trailing-edge scattering of near-field evanescent waves dominates the low frequency amplification of installed jet noise in the far-field. The high-frequency noise enhancement on the reflected side is due to the surface reflection effect. The model agrees well with experimental results at different observer angles apart from deviations caused by mean-flow refraction effect at high frequencies at low observer angles.