# Noise Reduction Mechanisms of an Airfoil with Trailing Edge Serrations at Low Mach Number
## 1 Introduction
Many experimental studies on trailing edge serrations have examined the disagreement between analytical predictions and experiments. [PERSON] [33] measured surface pressure fluctuations on serrations and showed that a larger spanwise magnitude-squared coherent of the surface pressure fluctuation on the straight trailing edge. Through incorporating surface pressure and surface heat transfer measurements, [PERSON] and [PERSON] [14] showed the presence of pressure-driven edge-oriented vortices and concluded that the measured far-field noise is influenced by the angle between the edge-oriented vortices and the local streamline. [PERSON] et al. [15] showed the spanwise correlation length of the spanwise velocity component decreases from the root to the tip of serrations, while the convective velocity of the streamwise velocity component increases from the root to the tip and concluded that trailing edge noise is mainly generated at the root of the serrations. Based on the aforementioned experimental studies, it is possible to obtain further improvements with a better understanding of the effects of serrations on the wall pressure statistics. However, it has always been challenging for experimentalists to measure the surface pressure fluctuations on thin surfaces without perturbing the flow [14; 33]. Computations of the flow organization and acoustic propagation around trailing edge serrations have been conducted in the past [6; 11; 30; 31; 34]. By performing numerical analyses, both flow and pressure fields can be obtained and one has the advantage of overcoming the experimental limitations mentioned above. [PERSON] and [PERSON] [11] found the formation of horse-shoe vortices in the space between the serrations. [PERSON] et al. [6] showed that the spanwise correlation length and convective velocity of surface pressure fluctuations influence both the intensity and the frequency range of noise reduction. [PERSON] [35] confirmed that the combed teeth give noise reductions largerthan the standard teeth due to an improvement in the streamline angles: in general, the flow tends to be less three-dimensional and more aligned with the serration edge. Although trailing edge serrations have proven to be valid solutions of trailing edge noise reduction, its underlying noise reduction mechanism is still not fully understood. A variation in the hydrodynamic field due to the spanwise varying geometry is a possible explanation. However, the complex three-dimensionality of the flow around the serrated trailing edges is not straightforward. An improvement in serration design can be realized with a better understanding of this underlying mechanism. Thus, the goal of this study was to show the variation in the hydrodynamic field caused by the trailing edge serrations and find the relation between the hydrodynamic field characteristics and noise-reduction. For this goal, the flow field around the NACA0012 airfoil with a straight trailing edge and sinusoidal serrated trailing edge at zero-angle of attack in low Mach number range were carefully investigated and compared. To overcome the experimental limitation, an efficient hybrid computational method for hydrodynamic field and aeroacoustic field was selected. The turbulent flows around NACA0012 airfoil with or without trailing edge serrations were computed through large-eddy simulation (LES) with an improved one-equation dynamic subgrid-scale (SGS) model. The weak compressibility at low Mach number was taken into account by modifying the pressure equation. The computational results were validated against experimental data. Acoustic perturbations were obtained utilizing a derived sound source formulation. This makes it possible to extend the hybrid method from zero to low or moderate Mach number region. A similar numerical methodology has been validated against experiments before, as presented in [36; 37; 38].