Broadband noise prediction for aerofoils with a serrated trailing edge based on Amiet’s theory

Abstract

Trailing-edge serrations are used as means to reduce aerofoil broadband self-noise in various industrial applications. However, a reliable prediction of the reduced noise level has not been established to date. In this paper, the authors suggest that Amiet’s theory can be used to accurately predict the sound radiated from serrated trailing edges. A plausible explanation as to how the classical theory, originally derived from non-serrated (straight) trailing edges, also works for the serrated trailing edges is provided. Besides, the authors propose a directivity correction to the Amiet’s original model to account for realistic aerofoil geometry. The directivity correction provides a significantly improved prediction of the noise level in the upstream and downstream directions for both serrated and baseline trailing edge cases. This study is based on wall-resolved large-eddy simulations of Joukowski aerofoils with multiple serration geometries and in different flow conditions.

Introduction

Aerodynamic noise is critical to many industrial applications such as wind turbines. It is well-known that aerodynamic noise generated by aerofoils is of numerous natures [1]. Trailing-edge (TE) noise results from the scattering, at the aerofoil trailing edge, of surface pressure fluctuations convecting within the turbulent boundary layer. It has been shown by Oerlemans [2] that TE noise constitutes the main source of aerodynamic sound coming from a wind turbine and it has been investigated extensively through a wide range of approaches whether it be analytical [3], [4], [5], [6], [7], [8], [9], [10], [11], [12], experimental [13], [14], [15] or computational [16], [17].

The use of a serrated trailing edge (STE) as a means of broadband TE noise reduction has been investigated for decades by numerous authors. TE serrations can refer to all sorts of spanwise-varying TE geometries. The most common is the sawtooth geometry since it provides satisfying noise abatement performances and is easily applicable to industrial scale but different shapes have been tested in the literature [18]. Multiple experimental studies have been carried out over the last thirty years. Dassen et al. [19] conducted some experiments on NACA aerofoils and flat plates and showed that the expected noise reduction from STE was around 5 dB which was later confirmed by Oerlemans et al. [20] who found a figure of 3.2 dB. Gruber et al. [21] investigated the noise reduction mechanisms and suggested that the serration amplitude (root to tip) should be longer than the turbulent boundary layer thickness to achieve a significant noise reduction. Moreau and Doolan [22] showed that the assumption of frozen turbulence usually employed in analytical models is incorrect and may explain the differences observed between measurements and analytical predictions. Additionally, they suggested that the change of the hydrodynamic field near the serrations is more impactful on noise reduction than the change of diffraction properties. The most recent experiments [23], [24], [25] are based on PIV measurements and allow more detailed analysis of the flow features. The observations made by Avallone et al. [26] show that the turbulent intensity is higher at the root of sawtooth serrations than at the tip. Chong and Vathylakis [27] studied the viscid–inviscid interaction between the turbulent eddies and the oblique vortical structures along the TE. Computational methods have also been used to investigate STEs [28], [29], [30], however, no consensus has yet been found on the mechanism of STE broadband noise reduction. Thus, in contrast with the observations of Moreau and Doolan [22], all analytical models developed since the 1990s are based on a destructive phase interference mechanism. This includes the pioneering theoretical work of Howe [31] who published a Green’s function-based analytical model for noise prediction of a semi-infinite serrated flat-plate. Lyu’s and Ayton’s [32], [33], [34] approaches are both based on the same governing equation but the Wiener–Hopf technique used in their most recent work considerably reduces the number of sums to compute in the model resulting in a much faster implementation. These models essentially spread a modulated single-point wall pressure fluctuations spectrum along the serrated edge and only account for cut-on modes. In other words, the source magnitude does not depend on the position along the edge.

This paper aims to develop an accurate prediction method of noise generated from serrated trailing edges. In this respect, high-resolution numerical simulations are carried out in order to obtain accurate wall pressure data near the aerofoil trailing edge. This highly accurate noise source data is then used in two different approaches namely, Ffowcs-Williams & Hawkings’ [35] and Amiet’s [3], [4], to calculate the radiated sound in the far-field. In this work, the authors take the Ffowcs-Williams & Hawkings (FW–H) solution as a reference solution and examine the accuracy of Amiet’s solution relative to it. In this framework, the authors investigate the feasibility of using Amiet’s model for the prediction of STE noise, which has not been reported to date. It is a controversial approach because Amiet’s model was originally derived for a non-serrated (straight) trailing edge only. The authors also investigate a possible modification to Amiet’s model to improve the accuracy of the STE noise prediction in a wide observer angle.

The paper is organised in the following order. Section 2 provides a case description as well as computational details. In Section 3, Amiet’s noise prediction technique is used to predict the sound from LES data. Section 4 presents some numerical results explaining why this straight TE theory also works for STEs. Section 5 introduces a directivity correction factor to rectify the noise under-prediction in the upstream and downstream directions in Amiet’s model. The capability of Amiet’s model in the prediction of serrated trailing-edge noise reduction is exhibited in Section 6 before conclusions are drawn in Section 7.