# Wind Turbine Enhancement via Active Flow Control Implementation
## 2 Numerical Method
### Mesh Assessment
Figure 4: Full view of the mesh in the computational domain (**a**), zoomed view of the structured mesh in the leading (**(b) top**) and trailing (**(b) bottom**) edges for FFA-W3-301 airfoil type. Figure 5: Synthetic jet position and associated parameters (**a**). Detailed view of the AFC mesh implementation in Section 54. (**b**)  
The simulations carried out encompassed a 28 \(s\) duration, wherein the average lift and drag coefficients were derived from a sampling window spanning the concluding 8 s of the simulation. The numerical outcomes of the averaged aerodynamic coefficients, coupled with the corresponding relative error denoted as \(\text{Error}C_{l}\) in percentage and versus the value obtained by [51], are presented comprehensively in Table 4. The number of cells used for each mesh, the minimum and maximum \(y+\) at the airfoil surface, the airfoil efficiency \(\eta\), as well as the boundary layer separation point denoted as \(x_{s}/C\), are presented in the same table. Upon careful examination, it becomes evident that as the maximum \(y^{+}\) is reduced, the error in the lift coefficient drastically drops, becoming negligible between the two finest meshes. For instance, the discrepancy stands at 4.45% between the \(C_{l}\) obtained for maximum \(y^{+}=4.29\) and the value obtained by [51]; such discrepancy is reduced to 2.51% when comparing the reference value and the one obtained in meshes C and D. It is relevant to note that meshes C and D generate identical results for \(C_{l}\) and for the boundary layer separation \(x_{s}/C\), and minor discrepancies are observed in the \(C_{d}\) values generated by these two meshes. A discrepancy of around 32% is observed when comparing the reference \(C_{d}\) with the one obtained in mesh C; this large discrepancy is understood when noting that the airfoil chord used in reference [51] was the unity, the Reynolds number being \(Re=10^{7}\). In the present study, the chord associated with Section 54 is 6.2 m, and the Reynolds number is \(12.7\times 10^{6}\), therefore clarifying why the drag coefficient, is a bit larger in the present study. Considering the notable accuracy achieved by Mesh C and the manageable computational time entailed in its simulation, it has been judiciously chosen as the preferred candidate for subsequent simulations. For a visual and perhaps more precise comparison of the outcomes, an illustrative representation has been generated to showcase the variation in pressure and friction coefficients across the chord length and for the four distinct tested meshes, as exhibited in Figure 6a,b. Examining the pressure distribution over both the upper and lower surfaces of the airfoil reveals a remarkably uniform behavior across all the meshes. Notably, there exists a consistent and gradual pressure recovery on the upper surface. The sole discernible divergence in pressure coefficients among all the meshes manifests near the \(1.5\,\text{m}\ =x/C=0.24\) mark along the chord. Nevertheless, the graph depicting \(C_{p}\) presents a strikingly analogous pattern for all the meshes. In the realm of the friction coefficient graph, as depicted in Figure 6b, distinctions emerge among the meshes. Notably, the lower \(y^{+}\) meshes, namely Mesh A and B, exhibit some variations in the boundary layer separation point, \(x_{s}/C\). Conversely, Mesh C closely mirrors the \(C_{f}\) trends observed in Mesh D, aligning with the minor errors observed in the averaged aerodynamic coefficients. This alignment renders Mesh C the optimal selection for future simulations. \begin{table}
\begin{tabular}{l c c c c c c c} \hline \hline
**Mesh** & \(\mathbf{N_{cell}}\) & **Min \(\mathbf{y^{+}}\)** & **Max \(\mathbf{y^{+}}\)** & \(\mathbf{x_{s}/C}\) & \(\mathbf{C_{l}}\) & \(\mathbf{C_{l}}\) & **Error [\%]** & \(\mathbf{C_{d}}\) & \(\mathbf{\eta(C_{l}