## 3 Methodology
### Mesh Generation  
To eliminate the effect of the domain, the flow domains of the airfoil were subdivided into smaller subdomains to analyze the fluid flow. The computational domain was discretized into nodes by ANSYS-ICEM CFD, and the governing equation was used to solve each and every node. To ensure that the interface boundaries had a 1:1 node connection, a meshing topology was adopted for both domains to avoid interpolation losses in the interface. The O-grid topology was employed to generate a structured grid for the overall computational domain. This type of blocking ensures reduced computational cost and interpolation losses. In addition to this, the fine mesh was maintained to achieve a turbulence model dependent \(y^{+}\) (\(<\)1 for the SST turbulence model) [36]. Figures 6 and 7 depict the details of the mesh topology and the grid generation around the computational domain. The main purpose for adopting the O-grid topology was to have better and more uniform control of the near-wall mesh. The \(y^{+}\) value should be always maintained at a value less than 1 within the domain of the airfoil to get the benefit of the SST turbulence model [13]. The \(y^{+}\) value is a function of \(\Delta y\) (first node's distance from the wall), \(Re\), and the flow length (\(L\)). The relation given in Equation (32) was used to calculate the value of \(\Delta y\) and to  
\begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline Units & m/s & \(-\) & \(-\) & \(-\) & kg/ms & kg/m\({}^{3}\) & m & k & J/kg & \(-\) & P\({}_{\mathrm{a}}\) \\ \hline NREL S809 & 7 & 0.02 & \(0.75\times 10^{6}\) & 0 \& 6.2 & \(1.82\times 10^{-5}\) & 1.258 & 0.34 & 288 & 287 & Air & \(475,858\) \\ \hline \hline \end{tabular}
\end{table}
Table 3: Operating parameters for the airfoil.  
get the \(y^{+}\) value [28]. The equation to calculate \(\Delta y\) was derived for the flow over the flat plate; therefore, it only provided initial estimates of \(\Delta y\) for the airfoil geometries. To get a \(y^{+}\) value, no more than a few iterations were required to finalize the value of \(\Delta y\) for a specific set of boundary conditions:  
\[\Delta y=Ly^{+}\sqrt{74}Re_{L}{}^{-\frac{13}{\Omega}} \tag{32}\]  
Figure 6: The C-type mesh for the baseline airfoil of a wind turbine at an angle of attack (AOA) of \(6.2^{\circ}\). (**a**) Overall blocking structure; (**c**) the mesh; and (**b**) zoomed-in mesh image.  
Figure 7: Mesh distribution of the airfoil at AOA = \(6.2^{\circ}\).  
Besides having a certain value of \(y^{+}\), some different values for the minimum number of nodes (\(n_{min}\)) within the boundary layer thickness (\(\delta\)) were also required. For the SST turbulence model, the condition for (\(n_{min}\)) is stated in Equation (33):  
\[\left\{\begin{array}{c}y_{n}(n_{min})\ \leq\delta\\ for\ SST\ n_{min}\ =15\\ y_{n}(15)\ \leq\delta\end{array}\right. \tag{33}\]  
where \(y_{n}(15)\) is the distance of the fifteenth node. The relation given in Equation (34) was used to calculate the value of the boundary layer thickness at a specific value of \(Re\) and \(L\):  
\[\delta=0.035\ LRe_{L}^{-\frac{1}{\beta}} \tag{34}\]  
The value of the boundary layer thickness calculated in Equation (34) was assigned to \(y_{n}(n_{min})\), and the mesh growth rate (\(r_{m}\)) from the wall side was computed by the relations of geometric progression shown in Equations (35) and (36) within the boundary layer thickness:  
\[r_{m}=\left[\ \frac{y_{N}(n_{min})}{\Delta y}\ \right]^{1/(n_{min}-1)} \tag{35}\]  
\[r_{m}=\left[\ \frac{y_{n}(15)}{\Delta y}\ \right]^{1/14} \tag{36}\]