# Noise Reduction Mechanisms of an Airfoil with Trailing Edge Serrations at Low Mach Number
## 5 Effect of Serrations on the Hydrodynamic Field
Consequently, the development of these mainstream vortices will greatly affect the fluctuation components in the vertical cross section of the mainstream direction. Figures 9 and 10 show the distributions of Reynolds stress \(R_{ij}\) near the trailing edge of the flow around the NACA0012 airfoil and around the trailing edge serrated NACA0012 airfoil. Reynolds stress is defined by \(R_{ij}=\tilde{\rho}\overline{u_{i}^{\prime}u_{j}}\). Figure 9 shows an iso-surface of \(R_{22}=0.05\), and Figure 10 shows an iso-surface of \(R_{33}=0.02\). In the case of the flow field around the baseline NACA0012 blade, \(R_{22}\) is distributed in the spanwise direction on the airfoil surface near the trailing edge and near the wake, while, in the case of the trailing edge serrated airfoil, the distribution of \(R_{22}\) is almost limited near the wake. Meanwhile, \(R_{33}\) is widely distributed near the wake of the serrated airfoil, while it is hardly found near the wake of the baseline airfoil. From this, it is found that the development of the vortices in the main flow direction due to the trailing edge serrations of airfoil results in a decrease in velocity fluctuations in the vertical cross-section of the mainstream direction. Figure 7: Instantaneous profile of iso-contours of \(Q=400\) colored by \(|\omega_{x}|\leq 100\): (a) NACA0012 airfoil; and (b) serrated airfoil. Figure 8: Time evolution of instantaneous vortex structure: \(Q=2000\) colored by \(|\omega_{x}|\leq 100\) (\(T_{0}\) means an abitrary initial moment, \(\Delta T\) time interval, as in \(1.5\times 10^{-3}\) s). (**a**) \(T_{0}\); (**b**) \(T_{0}+\Delta T\); (**c**) \(T_{0}+2\Delta T\). Figure 9: Iso-contours of Reynolds stress \(R_{22}=0.05\) near the trailing edge: (**a**) NACA0012 airfoil; and (**b**) serrated airfoil. Figure 11 shows the pressure fluctuation distribution of the airfoil surface near the trailing edge of baseline NACA0012 airfoil and that with the trailing edge serrations. In the case of the NACA0012 airfoil shown in Figure 11a, a strong pressure fluctuation distribution is observed across the entire spanwise direction near the trailing edge, while, in the case of the serrated airfoil shown in Figure 11b, the pressure fluctuation is weaker and mainly concentrated at the tips of the serrations. The profiles of pressure fluctuation near the trailing edge of the baseline NACA0012 airfoil and the serrated airfoil are similar to the distribution of Reynolds stress in Figure 9. It is therefore believed that the distribution of Reynolds stresses affects the strength of the pressure fluctuation. From the above discussion, although the trailing edge serrations cause an increase in pressure drag on the airfoil, they prevent the growth of spanwise vortices near the trailing edge and promote the development of the streamwise direction vortices. Meanwhile, the velocity fluctuation in the vertical cross-section of the mainstream direction is mitigated due to the trailing edge serrations, and, as a result, brings a decrease in the pressure fluctuation near the trailing edge. Figure 10: Iso-contours of Reynolds stress \(R_{33}=0.02\) near the trailing edge: (**a**) NACA0012 airfoil; and (**b**) serrated airfoil.