## 4 Results and Discussion
### Verification and Validation  
In this section, the results from the studies performed on airfoil optimization are discussed and presented. First, the ability of the CST method employed with a genetic algorithm to produce an optimized S809 airfoil was tested. Secondly, the PARSEC method was coupled with the GA to generate an optimized airfoil from the existing baseline S809 airfoil. The flow field conditions used by the optimization process to investigate the \(C_{I}\), \(C_{d}\) and lift-to-drag (\(L\)/\(D\)) ratio were \(Re=0.75\) million, AOA = \(0^{\circ}\) and \(6.2^{\circ}\), Mach number (Ma) = 0.02, and a wind velocity of 7 m/s. To normalize the chord length (c) for the airfoil, it was set to 0.34 m. During the optimization process, the CST and PARSEC variable \begin{table}
\begin{tabular}{c c c c c c c c c c c c c} \hline \hline M-i & N\({}_{\text{U}}\) & F\({}_{\text{LE}}\) & N\({}_{\text{D}}\) & N\({}_{\text{CL}}\) & F\({}_{\text{D}}\) & N\({}_{\text{TE}}\) & N\({}_{\text{LE}}\) & y\({}^{+}\) & \(C_{d}\) & \(C_{l}\) & N\({}_{\text{t}}\) & [MB] & t\({}_{\text{cpu}}\)[s] \\ \hline M1 & 125 & 75 & 125 & 75 & 75 & 250 & 150 & 0.7 & 0.0174 & 0.963 & 3.6 & 595 & 68 \\ M2 & 125 & 100 & 125 & 75 & 100 & 300 & 200 & 0.7 & 0.0156 & 0.973 & 4.9 & 796 & 95 \\ M3 & 125 & 125 & 125 & 75 & 125 & 350 & 250 & 0.7 & 0.0147 & 0.985 & 6.3 & 1023 & 122 \\ M4 & 125 & 150 & 125 & 75 & 150 & 400 & 300 & 0.7 & 0.0146 & 0.985 & 8 & 1278 & 157 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Distribution of mesh in the computational domain for the mesh independence study. parameters played an important role in describing the airfoil shape. Further airfoil shaping was defined by the upper and lower curvatures of the airfoil, which provided a design set of data. For every design variable, the lower and upper bound values were defined in the GA optimization code in MATLAB. As a result, the GA produced the best sets of CST and PARSEC parameters and, hence, an optimized airfoil profile was generated. These optimized airfoils were tested at a given set of conditions for the calculation of the \(C_{I}\), \(C_{d}\), and pressure distribution curve with the in-house MATLAB program XFOIL. The new \(C_{I}\), \(C_{d}\), and \(L\)/\(D\) ratio obtained after the optimization process were compared with the original airfoil, based on the NREL experimental data provided by OSU [37]. The performances of the initial and optimized airfoils are compared and displayed in Table 6. As a result, it can be seen that the optimized result of the CST method was better than the NREL-based experimental data of the original NREL S-809 airfoil. From Table 6, it can be seen that the \(C_{I}\) was maximized and the \(L\)/\(D\) ratio was better for the S809 airfoil optimized by the CST method in comparison with both the baseline airfoil and the airfoil optimized by the PARSEC method. While comparing the CST and PARSEC methods with the experimental results of the S809 airfoil, it can be observed that the optimized airfoils for CST and PARSEC showed improvements of 11.8% and 10.1%, respectively, in the coefficient of lift (\(C_{I}\)). However, this increment in the \(C_{I}\) led to an improvement in the \(L\)/\(D\) ratio by 9.6% for the CST method, while the PARSEC method showed a decrease in the \(L\)/\(D\) ratio by 2% compared with the experimental results. From this, it can be concluded that optimization by CST gives better performance than another parameterization method. Figure 9 displays the optimized S809 airfoil profile generated by the CST and PARSEC methods and the baseline airfoil. Figure 10 demonstrates the variation of lift coefficient with the increase in the angle of attack. It is observed that \(C_{I}\) increased in all three profiles as the angle of attack increased from 0\({}^{\circ}\) to 6.2\({}^{\circ}\). By looking at the figure, it can be concluded that the optimized CST airfoil