## 5 Results and Discussion  
In the first section of the research results, some results from the flow simulations are presented. The iso-surface of Q-criterion (Q = 1) is given together with an instantaneous contour of x-velocity for the reference case in Figure 9. The vortex street is clear in the wake of the rod and the airfoil is exposed to turbulence. Mean pressure contours for all  
Figure 8: Comparison of far-field pressure spectral densities above the airfoil leading edge at 18.5c distance, showing results from the current LES, both experimental and LES data by [PERSON] et al. [1], and previous LES studies by [PERSON] and [PERSON] [8], [PERSON] et al. [11], and [PERSON] and [PERSON] [28]. Figure 7: Power spectral density (\(S_{uu}\)) of the streamwise velocity (\(u\)) plotted against the Strouhal number at points P1 and P2, showing results from the current LES, experimental data by [PERSON] et al. [1], and previous LES studies by [PERSON] and [PERSON] [8], [PERSON] et al. [11], and [PERSON] and [PERSON] [28]. designs are illustrated across two spanwise sections with the highest and lowest chord lengths for both regular (A1W1, A1W2, A2W1, and A2W2) and irregular (A3W2, A4W2, A5W2, and A6W2) serrations in Figure 10. The mean pressure contours are presented at two spanwise locations, identified as A (left) and B (right) in the bottom-right corner. Each contour is labeled with its configuration name followed by the section identifier (e.g., A1W1-A for configuration A1W1, section A). For the irregular serrations, they are specifically shown on the irregular serration for the highest and lowest chord lengths. This depiction is consistent for regular serrations since they remain the same throughout the span. The highest pressure values (\(p_{m}\approx 0.69\)) are observed near the tip of the longest chords, gradually decreasing towards the shortest chords, both for regular and irregular serrations. At the same spanwise locations, contours depicting the mean streamwise (\(\bar{u}\)) and spanwise (\(\bar{v}\)) velocity components are illustrated in Figure 11, where mean velocity contours for \(\bar{u}\) are presented in the left two columns, while the contours for \(\bar{v}\) are shown in the right two columns for the two spanwise locations marked as A and B. The presented figures reveal a discernible influence of serration types on the flow dynamics along the span. Notably, some irregular designs with greater chord lengths, exemplified by A3W2 and A5W2, exhibit slightly heightened velocity magnitudes in comparison to their corresponding regular designs. Conversely, some irregular designs with diminished chord lengths manifest lower velocities than their regular counterparts. Figure 10: Mean pressure contours at two spanwise locations, marked by red dashed lines in the bottom-right corner as A (**left**) and B (**right**) on each configuration. All contours are labeled with their configuration name followed by the section identifier (e.g., A1W1-A for configuration A1W1, section A). Figure 9: The iso-surfaces of Q-criterion (Q = 1) with instantaneous contour of x-velocity. Figure 11: Mean velocity contours, \(u_{m}\) (**left**, first two columns) and \(v_{m}\) (**right**, third and fourth columns), at two spanwise locations, marked by red dashed lines in the bottom-left (A1W1, A1W2, A2W1, and A2W2) and bottom-right (A3W2, A4W2, A5W2, and A6W2) corners as A (**left**) and B (**right**) on each configuration. All contours are labeled with their configuration name followed by the section identifier (e.g., A1W1-A for configuration A1W1, section A). Figure 12 presents the power spectral densities (PSDs) of the streamwise velocity component (\(S_{uu}\)) at two locations: \(x,y=-0.9,0.06\) (left column, subfigures a-c) and \(x,y=-0.8,0.07\) (right column, subfigures d-f). Each subplot includes the curves of three configurations: (a, d) show SLE, A1W1, and A1W2; (b, e) show A2W1, A2W2, and A3W2; and (c, f) show A4W2, A5W2, and A6W2.