## 4 Validation  
Three grids containing 40, 152 and 293 million cells are tested for the grid convergence study. The grid is refined around the rod and airfoil to ensure capturing the flow in the boundary layer which is crucial for LES and acoustic simulations. For the grid convergence study, mean x-velocity profiles are collected. Averaging is an important part of this work since the averaged results are also used in CAA simulations. Before starting the averaging process, the simulation is run for nearly \(\bar{t}=86\). For averaging, the data are sampled for a period of \(\bar{t}=91\), which corresponds to approximately 0.026 s in real time and about 35 shedding periods. Generally, 4096 cores are used for the calculations. The results for the tested grids for two different locations, x = \(-1.255\) and \(-0.75\) as shown in Figure 1 as lines L1 and L2 (TE of the airfoil is the reference, x = 0), are presented in Figure 4. As it can be seen from the figure, the grid with 152 million cells is found to be sufficient for the work. Additionally, the Grid Convergence Index (GCI) is calculated using the minimum and maximum values of the mean streamwise velocity profiles shown in  
Figure 3: Airfoils with regular (**left**) and irregular (**right**) LE serrations: Regular serrations maintain a constant amplitude across the span, whereas irregular geometries alternate the amplitude of every second serration by \(\pm 50\%\) of their base values.  
Figure 4. Specifically, the minimum velocity is extracted from line L1 (left plot), and the maximum velocity from line L2 (right plot), for the medium (152M cells) and fine (293M cells) grids. In both cases, the GCI values are below 1%, confirming mesh independence for the selected resolution. The mesh structure of the grid with 152 m cells is presented in Figure 5. As it can be noted from Figure 5, the grid is refined close to the solid bodies. For the validation, the LES results are compared with the experimental data from the study by [PERSON] et al. [1]. In Figure 6, the LES results of x-component of the velocity distributions at lines L1 and L2 are compared with the experimental data. As seen in the figure, the results are generally in agreement. LES slightly over predicts the reduction in the velocity for the line; however, this is usually the case also for other LES studies like the studies by [PERSON] and [PERSON] [8] and [PERSON] et al. [11]. This could also be due to the \(y=-2\) mm shift between the rod axis and the airfoil chord mentioned in the experimental study [1].  
Figure 4. Mean x-velocity profiles at lines L1 (**left**) and L2 (**right**).  
Figure 5. Mesh structure.  
Figure 6. Comparison of mean streamwise velocity (\(u\)) profiles at lines L1 (**left**) and L2 (**right**), showing the current LES results alongside experimental data by [PERSON] et al. [1] and previous LES studies by [PERSON] and [PERSON] [8] and [PERSON] et al. [11].  
The velocity power spectral density (\(S_{uu}\)) of the x-velocity plotted against Strouhal number at points P1 and P2 is compared with the experimental and other available results from the literature in Figure 7[8; 11; 28]. As it can be seen, the results of the current study are in agreement with the experimental results and also other LES results. The current LES clearly displays the spectral peak and the broadband components.  
Finally, the experimental and LES far-field pressure spectral densities (PSD) above the leading edge at 18.5c distance are compared in Figure 8. It can be seen that LES results are in agreement with the experimental measurements. The hybrid LES/CAA model accurately predicts the Strouhal number (\(S_{t}\approx 0.195\)) corresponding to the peak \(S_{pp}\) value (\(S_{pp}\approx 90\ dB/St\)), with only a slight deviation.