## 3 Discussion of the Noise Results
### Effect of the Pore Diameter  
Figure 8 presents \(\Delta\)SPL as a function of free-stream velocity and frequency for structured porous trailing edges whose three subregions are covered by pores of the same diameter. It can be seen that the structured porous edges can significantly suppress airfoil self-noise, especially in the regimes corresponding to tonal noise. A maximum noise reduction of 28.09 dB and 36.62 dB are obtained for angles of attack of \(\alpha=0^{\circ}\) and \(\alpha=10^{\circ}\), respectively. However, noise increases of up to 22.58 dB and 21.58 dB are observed at \(\alpha=0^{\circ}\) and \(\alpha=10^{\circ}\), respectively. These increases can be divided into two types: Firstly, the increase around the peak frequency of the tonal noise is generally attributed to the frequency shift of the tonal noise. Figure 9 plots typical noise spectra between the structured porous trailing edges and the baseline trailing edge. As seen in these plots, the peak frequency of the tonal noise (see the black circle in Figure 9) at \(V_{\infty}=30\) m/s and \(\alpha=0^{\circ}\) shifts from 1256.25 Hz for the baseline trailing edge to 1350 Hz, 1343.75 Hz, and 1356.25 Hz for L04M04N04, L06M06N06, and L08M08N08, respectively. For \(V_{\infty}=60\) m/s and \(\alpha=10^{\circ}\), the peak frequency shifts from 3312.5 Hz to 3325 Hz, 2812.5 Hz, and 2206.25 Hz, respectively. Secondly, an increase in noise at frequencies larger than 6 kHz is consistent with published results, owing to the increase in the surface roughness noise [12; 26; 27]. This is supported by  
Figure 7: Tonal noise regimes of the baseline NACA 0012 airfoil. the fact that porous edges with bigger pores generally exhibit a higher surface roughness as well as more high-frequency noise emission. Another trend discernible from Figure 8 is that greater noise reduction was obtained by a structured porous edge with a larger pore diameter. This is further confirmed by Figure 10, where \(\Delta\)OASPL levels for the different configurations are plotted. It is shown  
Figure 8: \(\Delta\)SPL as a function of free-stream velocity and frequency for structured porous trailing edges with the same pore diameter: (**a**) L04M04N04 with \(\alpha=0^{\circ}\), (**b**) L06M06N06 with \(\alpha=0^{\circ}\), (**c**) L08M08N08 with \(\alpha=0^{\circ}\), (**d**) L04M04N04 with \(\alpha=10^{\circ}\), (**e**) L06M06N06 with \(\alpha=10^{\circ}\), and (**f**) L08M08N08 with \(\alpha=10^{\circ}\). Figure 9: Typical noise spectra between the structured porous trailing edges and the baseline trailing edge. (**a**) \(V_{\infty}=30\) m/s, \(\alpha=0^{\circ}\); (**b**) \(V_{\infty}=60\) m/s, \(\alpha=10^{\circ}\). Different colored circles in the zoomed inset figures illustrate the peak SPL of the different configurations. that a maximum OASPL reduction of 2.86 dB (see Table 2) and 4.66 dB (see Table 3) can be obtained by L08M08N08 at angles of attack of \(\alpha=0^{\circ}\) and \(\alpha=10^{\circ}\), respectively. The reason for this trend is that porous edges with a larger pore diameter have larger porosity (defined as the ratio of the cumulative volume of the pores to that of the total volume of the interchangeable trailing edge section [28]), and several experimental results from the references have demonstrated that noise reduction is more significant when the porosity increases [29; 30].