# Noise Reduction Mechanisms of an Airfoil with Trailing Edge Serrations at Low Mach Number
## 1 Introduction  
In recent years, with the development of civil aviation and the increasing popularity of air travel, the number of airports close to the city limits has grown rapidly. The persisting problem of aircraft noise in residential areas has attracted more and more attention and stringent standards have therefore been set by the International Civil Aviation Organization (ICAO) for aircraft noise control [1; 2; 3]. Noise generated from aircraft can be divided into two categories: engine noise and airframe noise. Engine jet noise used to be the major noise source for a civil aircraft, while, with the introduction of turbofan engines with high by-pass ratios, significant reductions of jet noise have been achieved. Therefore, nowadays, the reduction of the airfoil self-noise from the engine fan and airframe's high lift devices has become more significant. Another industrial application in which the airfoil self-noise is also one of the dominant noise sources is the wind turbine. Wind turbines are an environmentally more acceptable form of energy, but noise nuisance, mainly radiated from the turbine blades, is created for communities living in close proximity [4]. Thus, for the aero-engine, airframe, and wind turbine industries, it is significant to reduce the airfoil self-noise [5; 6]. Airfoil self-noise is created by the interaction of airflow with a wing or a blade. In particular, the interaction of the turbulent boundary layer with the airfoil trailing-edge is one of the dominant sources of airfoil self-noise [5]. For the aforementioned applications, the trailing edge noise is the most relevant noise source, especially at low Mach numbers since the turbulent fluctuations are scattered efficiently over a solid trailing edge [7]. For alleviating this dominant trailing edge noise, several passive noise-mitigation solutions such as trailing-edge brushes [8; 9], sinusoidal and sawtooth serration [6; 10; 11; 12; 13; 14; 15; 16], slits [17; 18], and porous treatments [19; 20; 21] have been proposed. Among these passive methods, sinusoidal and sawtooth trailing edge serrations have been of important interest for researchers [3; 6]. Many theoretical [22; 23; 24; 25; 26; 27], experimental [10; 15; 16; 28; 29], and numerical [6; 30; 31] studies on trailing edge noise reduction using serrated trailing edges have been performed over the past decades. The first theoretical model for a serrated trailing edge was developed by [PERSON] [23; 24] in 1991. Under the frozen turbulence assumption, an analytical noise radiation model was derived for the semi-infinite flat plate with both sinusoidal and sawtooth trailing edge serrations at low Mach number flow. According to [PERSON]'s theory, since the effective spanwise length of the trailing edge that contributes to the trailing edge noise generation is reduced, trailing edge noise is consequently significantly reduced by the addition of trailing edge serrations. [PERSON]'s theory states that, at high frequency, the reduction of trailing edge noise is about \(10\times log_{10}(6h/\lambda)\) dB for the sinusoidal profile and is about \(10\times log_{10}[1+(4h/\lambda)^{2}]\) dB for the sawtooth profile, where \(h\) and \(\lambda\) are the amplitude and wavelength of the serrations, respectively. This theory is still widely used due to its simplicity. However, the predicted far-field noise spectra from this theory commonly deviate from experimental results [10; 14; 15; 17; 18; 28; 32]. Recently, [PERSON] et al. [26] proposed a more accurate semi-analytical model in which the predicted maximum noise reduction is better in agreement with measurements. However, some discrepancies concerning measurements are remaining due to the assumption of frozen turbulence [15; 17]. Actually, from the limitations of the applicability of the analytical models, for further improvement of its accuracy, a characterization of the statistical properties of the surface pressure fluctuation on the serrations and their frequency and spatial dependence is indispensable [6].