# Noise Reduction Mechanisms of an Airfoil with Trailing Edge Serrations at Low Mach Number
## 5 Effect of Serrations on the Hydrodynamic Field  
In this section, the results of flow fields around baseline NACA0012 airfoil and that with sinusoidal trailing edge serrations at zero angle of attack, Mach number \(M=0.0875\), Reynolds number based on the chord length and the mainstream velocity \(Re=2\times 10^{5}\) are compared to discuss the effect of serrations on the hydrodynamic field and then to understand the underlying noise reduction mechanism of trailing edge serrations. Figure 6 shows the mean velocity distribution in the main flow direction around the straight and serrated NACA0012 airfoils, i.e., around the baseline NACA0012 airfoil in Figure 6a and around the cross-section \(A^{\prime}A\), and \(B^{\prime}B\) of the serrated airfoil in Figure 6b. In Figure 6a, the separation appears near the trailing edge and the region of separation is small. However, in the case of an airfoil with trailing edge serrations shown in Figure 6b, a wide separation area is seen near the root of the serration (cross-section \(A^{\prime}A\)) compared to the average velocity distribution around the straight airfoil. The expansion of the separation area near the trailing edge delays the pressure recovery and leads to an increase in pressure drag on the serrated airfoil. As a result, the drag coefficient of the serrated airfoil is larger than that of the baseline NACA0012 airfoil, that is, \(C_{D}=1.27\times 10^{-2}\) and \(1.13\times 10^{-2}\) for the serrated and straight airfoils, respectively. It is therefore confirmed that the pressure drag is slightly increased by the trailing edge serration. To investigate the variation of the vortex structure due to the trailing edge serration, the iso-surface of the second invariant \(Q=400\) of the instantaneous velocity gradient tensor is shown in Figure 7. The value of the mainstream direction vorticity \(\omega_{x}\) is expressed in color gradation on the \(Q\) iso-surface, where the red corresponds to \(\omega_{x}=100\) and blue corresponds to \(\omega_{x}=-100\). In the case of the flow around the NACA0012 airfoil in Figure 7a, spanwise vortices with a numerical value of \(Q=400\) or more are observed from around \(X/C=0.82\), and it is confirmed that these vortices are three-dimensionalized and collapse into small vortices while advancing downstream along the airfoil surface. Finally, vortices structures with large values of \(\omega_{x}\) in the near wake are hardly found. In the case of the flow around the trailing edge serration in Figure 7b, by contrast, almost no spanwise  
Figure 6: Profile of mean velocity distribution around straight and serrated airfoils: (**a**) NACA0012 airfoil; and (**b**) serrated airfoil. vortices with a value of \(Q=400\) or more can be seen near \(X/C=0.82\), and the vortices structure with finer space scales including mainstream and spanwise vortices is generated near the trailing edge. Meanwhile, it is observed that large vortex structures including strong streamwise direction vortexes are developed in the near wake. For the sake of investigating the behavior of the vortices near the trailing edge serrations in more detail, Figure 8 shows the time evolution of the instantaneous vortical structure (\(Q~{}=~{}2000\) iso-surface) colored by \(|\omega_{x}|\leq 100\) near the trailing edge of the serrated airfoil (time interval is about \(1.5\times 10^{-3}\) s). Focusing on the red-lined vortices in Figure 8a, the three dimensional small vortices seen near the root of serration are stretched as they move downstream in the near tip of the serration, as shown in Figure 8b, and then they become larger-scale mainstream direction vortices in the near wake in Figure 8c. From the above observations, it is confirmed that the growth of the spanwise vortices near the trailing edge is impeded by the trailing edge serration, and the main flow direction vortex is formed and developed from near the trailing edge to the wake for the flow field around the serrated airfoil.