# Aerodynamic Efficiency Improvement on a NACA-8412 Airfoil via Active Flow Control Implementation
## 2 Numerical Method
### Mesh Assessment
the first cell height, which certifies that the mesh was properly designed and ensured the condition of \(y^{+}<1\) necessary to evaluate the boundary layer. In order to further check the mesh to be employed, the pressure coefficient \(C_{P}\) evaluated at each point of the airfoil surface and for all \(y^{+}\) studied is presented in Figure 6. The \(C_{P}\) distribution along airfoil lower surface showed a very similar behaviour for every mesh candidate, despite that \(y^{+}=1\) and \(y^{+}=0.7\) showed a slightly lower \(C_{P}\) value for approximately the 80% of the chord. A more notable difference can be observed in the airfoil upper surface, where \(C_{P}\) progressively grows as \(y^{+}\) decreases. It can be observed how \(C_{P}\) in the airfoil upper surface for \(y^{+}=0.3\) and \(y^{+}=0.5\) are very similar along the whole chord, only showing a minor difference between the leading edge of the airfoil and \(x/C=0.3\). When considering the friction coefficient, see Figure 7, no notable differences can be noticed between the \(C_{F}\) distribution for the different meshes studied. The separation point is well predicted by all meshes evaluated, while small differences are observed in the reattachment point. After analyzing the \(C_{P}\), \(C_{F}\), \(C_{I}\) and \(C_{d}\) coefficients, we can conclude that the results obtained for the mesh with an estimated \(y^{+}=0.5\) are representative and almost mesh independent. This mesh was selected for the baseline case evaluation as well as for the later AFC implementation simulations. In addition, selecting this mesh exploited the fact that the computational time required to complete the simulations was drastically lower than for the most dense mesh, without compromising the solution in a great extent. To conclude with the baseline case analysis, the streamlines of the averaged flow field are presented in Figure 8. A huge separation bubble is generated very close to the airfoil LE, as indicated in Figure 7, and it extends up to the vicinity of the TE, where a counter rotating vorticular structure is generated. Notice that the boundary layer separation point is observed to be at about 10% of the chord, \(x/C=0.1045\). The objective of the AFC implementation is to postpone the boundary layer separation, breaking this large vorticular \begin{table}
\begin{tabular}{c c c c c c c} \hline \(y^{+}\) & \(N_{cell}\) & \(C_{I}\) & \(C_{d}\) & \(C_{I}Error\) \% & \(C_{d}Error\) \% & **Calculated Maximum \(y^{+}\)** \\ \hline
1 & 120,879 & 1.0797 & 0.2218 & 14.93 & 9.14 & 0.9127 \\ \hline
0.7 & 139,551 & 1.1153 & 0.2267 & 12.12 & 7.13 & 0.6544 \\ \hline
0.5 & 160,557 & 1.2267 & 0.2393 & 3.35 & 1.97 & 0.4728 \\ \hline
0.3 & 183,897 & 1.2692 & 0.2441 & - & - & 0.2887 \\ \hline \end{tabular}
\end{table} 
Table 2: Mesh candidates for the Mesh Independence Test. Figure 6: Baseline case pressure coefficient comparison. structure onto smaller ones, or even completely suppressing it. This will reduce the drag generated by the large vortex and increase the lift generated by the airfoil.