# Wind Turbine Enhancement via Active Flow Control Implementation
## 2 Numerical Method
### Mesh Assessment  
The blade considered in the present research is the DTU-10 MW offshore HAWT and consists of six different airfoil types, which, seen from the central axis to the blade tip, see Figure 3, are FFA-W3-600; FFA-W3-480; FFA-W3-360; FFA-W3-301; FFA-W3-241; and NACA0015. Note that DTU implemented a Gurney flap at the trailing edge of the FFA-W3-600 airfoil type, so in terms of meshing, this modification must be considered. The mesh independence study was performed using Section 54, which belongs to the FFA-W3-301 airfoil type. For a wind speed of 10 m/s, the Reynolds number associated with this section is \(Re=14.08\times 10^{6}\), and considering the angle of attack associated, boundary layer separation is expected to occur. For the FFA-W3-301 airfoil family, a C-type body-fitted structured mesh has been chosen for the region close to the airfoil. The C-type mesh comprises a curvilinear line surrounding the solid geometry, which is closed on the leading edge of the airfoil but open on the trailing edge. The region between the airfoil and the C-line is where the structured mesh is allocated; this region is usually called the \"halo.\" The halo thickness employed in the present research and measured perpendicular to the airfoil surface is about 3.2% of the chord; this value was kept constant for the two airfoils considered. A general view of the computational domain with the hybrid mesh employed is presented in Figure 4a. A zoomed view of the structured mesh zones at the airfoil's leading and trailing edges is presented in Figure 4b, where the details of the mesh at the trailing edge are observed. A small, rectangularly structured domain has been employed at the trailing edge region to properly capture the vortical structures due to possible flow detachment. The remaining portion of the computational domain has been designated with a non-structured mesh; see Figure 4a. This choice is rooted in the understanding that a certain level of reduced accuracy in regions distant from the airfoil surface is acceptable. Furthermore, opting for a hybrid mesh enables a more favorable balance between computational efficiency and accuracy of the results. Notwithstanding this, a heightened cell density has been strategically implemented in the vicinity of the airfoil to attain the desired level of precision. The implementation of the AFC technology using synthetic jets (SJ) requires the modification of the mesh in the location where the SJ is to be implemented. Figure 5b  
Figure 3: Blade diagram with the different airfoil profiles along the blade span. presents a zoom view of the mesh around the SJ, and Figure 5a introduces the main SJ-associated parameters that will be tuned via the corresponding parametric optimization. To ensure maximum accuracy in the simulated results, a thorough investigation of the mesh density is required, particularly in the halo region near the airfoil surface where the boundary layer develops and it is likely to separate. In this region, a drastic velocity and shear stress evolution in the normal direction to the airfoil surface is to be expected. Due to the lack of prior experimental investigations considering the Reynolds number and the airfoil type chosen and noting that the previous numerical investigations performed by reference [51] presented the time-averaged value for \(C_{l}\) and \(C_{d}\), a mesh independence study was performed to ensure a dissociation between mesh resolution and the outcomes produced, thus establishing a robust foundation for further analysis. The assessment for mesh independence involves generating four distinct meshes, all sharing identical overall geometries (depicted in Figure 4a), while varying the targeted \(y^{+}\) values. For the purpose of result validation, the approach chosen involves examining the time-averaged \(C_{l}\) and \(C_{d}\), as well as the distributions of \(C_{p}\) and \(C_{f}\) along the chord for each mesh resolution. This comparative study seeks to identify the \(y^{+}\) value at which substantial result deviations are absent.