On the noise prediction for serrated leading edges

Abstract

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]

Rapid noise prediction models for serrated leading and trailing edges

“…Based on this, it can be shown that Π l (ω, k 2 ), i.e. the wavenumber frequency spectrum of the incoming vertical fluctuation velocity, can be written as [1,26,23] Π l (ω,…”

“…As mentioned in Section 1, the TE and LE noise problems bear a striking similarity between each other. In either case, to allow the analytical derivation to continue, the serrated airfoil is often assumed to be a semi-infinite plate [1,32,4,23,25] placed in a uniform incoming flow of constant densityρ and velocityŨ at zero angle of attack, as shown in figure 1. The speed of sound is denoted bỹ c 0 .…”

“…Experiments and theories have shown that narrow serrations (a small serration wavelength) are more effective than wide serrations in reducing the LE noise [29,23]. This is related to the spanwise correlation length of the incoming gust, hence to the integral scale of the incoming turbulence.…”

“…This is related to the spanwise correlation length of the incoming gust, hence to the integral scale of the incoming turbulence. A detailed discussion was given by Lyu and Azarpeyvand [23] and Lyu et al [27]. Consequently, for practical usage, we only need to restrict our attention to narrow serrations.…”

“…A serrated LE has been proposed as one of the most promising approaches to reduce LE noise [7,12,31,15,29], and extensive research has been carried out to study its noise reduction performance and mechanisms. This includes experimental studies such as those by Hansen et al [15] and Narayanan et al [29], numerical investigations carried out by Lau et al [21], Kim et al [20] and Turner and Kim [35], and analytical examinations such as those by Lyu and Azarpeyvand [23] and Ayton and Chaitanya [4].…”