## 5 Results and Discussion
These two points are selected due to their positions on similarly shaped airfoil sections close to the leading edge, taking into account that spanwise sections of each configuration have varying chord lengths along the span. In the proximity of the leading edge, \(S_{uu}\) tends to be slightly higher (peak values of nearly \(S_{u}u\approx-4\) dB/St) for some irregular serration configurations (e.g., A5W2) compared to their regular counterparts. Notably, the vortex shedding peak exhibits a slight diminishment for some designs such as A1W2, A3W2, and A6W2. This attenuation may be attributed to the improved damping of vortical structures shed by the rod during interaction with the leading edge, resulting in a reduction in noise. Figure 13 displays the power spectral densities (PSDs) of the wall-normal velocity component (\(S_{vv}\)) at two distinct spanwise locations: \(x,y=-0.9,0.06\) (left column, subfigures a-c) and \(x,y=-0.8,0.07\) (right column, subfigures d-f). As in the previous figure, each subplot contains the curves of three serration configurations. The highest peak values are approximately \(S_{vv}\approx-8\,dB/St\) at \(x,y=-0.9,\,0.06\) and \(S_{vv}\approx-10\,\,dB/St\) at \(x,y=-0.8,0.07\). Similar observations to those of the previous figure can be made here: the reduction in the vortex shedding peak may be causing the reduction in noise levels. Finally, the far-field power spectral density (PSD) of pressure fluctuations is presented for regular (top) and irregular (bottom) leading-edge treatments in Figure 14. The figures on the right provide differences in sound pressure levels, with positive values indicating noise reduction. Notably, all tested configurations demonstrate noise reduction, with the irregular A3W2 and A6W2 designs achieving superior performance--nearly 11 dB reduction in the Strouhal number range of 0.25-0.75. Among the regular serration configurations, designs with higher amplitudes (A1W1 and A1W2) show improved acoustic performance, with reductions reaching up to 10 dB. The A4W2 configuration demonstrates the lowest performance and even shows some noise increase between \(St=0.6\) and 0.8. The observed low performance of A4W2 may be attributed to its short amplitude characteristics. Specifically, A4W2 possesses a short amplitude similar to that of A2W2, which has been noted to demonstrate inferior noise mitigation performance relative to other variants. This correlation suggests that amplitude length plays a critical role in the effectiveness of noise reduction, with lower amplitudes potentially leading to diminished performance outcomes. At the peak Strouhal (\(St\)) location, noise reduction is generally modest across all designs, with a notable increase in noise reduction, especially for \(St>0.2\). The current study observes similar noise reduction characteristics and PSD trends in regular serrated designs to those reported by [PERSON] et al. (2011) for comparable serrated airfoil configuration, particularly in terms of amplitude-dependent performance variations. Additionally, these findings are consistent with the observations reported in [PERSON] et al. (2019), which indicate that noise reduction performance tends to exhibit a negative correlation with wavelength. It can be seen that the effectiveness of noise mitigation in irregular configurations is influenced by the base amplitude of their regular serration counterparts. Figure 12: PSD of u velocity (\(S_{uu}\)) at \((x,y)=(-0.9,0.06)\) (**a–c**) and at \((x,y)=(-0.8,0.07)\) (**d–f**) for different serration configurations: (**a,d**) SLE, A1W1, A1W2; (**b,e**) A2W1, A2W2, A3W2; (**c,f**) A4W2, A5W2, A6W2. The reference is 1 m\({}^{2}\)s\({}^{-2}\). The leading and trailing edges of the reference design are located at \((x,y)=(-1.0,0.0)\) and \((x,y)=(0.0,0.0)\), respectively. Figure 13: PSD of v velocity (\(S_{vv}\)) at \((x,y)=(-0.9,0.06)\) (**a–c**) and at \((x,y)=(-0.8,0.07)\) (**d–f**) for different serration configurations: (**a,d**) SLE, A1W1, A1W2; (**b,e**) A2W1, A2W2, A3W2; (**c,f**) A4W2, A5W2, A6W2.