## 4 Results and Discussion
### Numerical Validation  
Based on CST and GA, optimized geometry and original airfoil were validated in the CFD-CFX environment using the RANS equation. One of the important motivations of this work was to make the RANS-based aerodynamic shape optimization of the airfoil with rapid changes using high-performance computing resources. Simulations were performed using the RANS model to compute the performance of the optimized airfoil along with \(k-\omega\) SST turbulence model. Airfoil NREL S-821 designed by combining CST and GA optimization process was validated numerically. Simulation of airfoil NREL S-821 was done at 3\({}^{\circ}\) AOA and at different conditions presented in Table 1 to compare the results with the existing experimental data from reliable NREL-based data sources [38]. Some forces exerted on the airfoil are usually broken down into two different forces and moments. The total component of the net force acting perpendicular to the inflow is called lifting force, and the net force acting parallel to the inflow is called drag forces. In Table 6 the lift and drag coefficient of the baseline and optimized airfoil by the computational model are shown and compared with the experimental data at 3\({}^{\circ}\) AOA. The lift to drag ratio for an optimized airfoil is about 2.2% higher than the baseline airfoil NREL S-821 CFD data. It is observed that Cd for an optimized airfoil is 7.22% better compared with the baseline CFD results. However, on comparing baseline airfoil CFD results with the experimental data, there is a slight increment of 2.1% in the lift to drag coefficient. Simulation outcomes of static pressure are presented in Figure 14 over the original and optimized airfoils at an angle of attack 3\({}^{\circ}\). The original airfoil is shown on the left side while the optimized airfoil is displayed on the right side. Pressure over the upper surface of the original airfoil is observed more negative than that of an optimized airfoil. While there is higher pressure on the lower surface of both the original and optimized airfoil than that of the incoming flow stream. Therefore, the airfoil is effectively pushed upward, perpendicular to the incoming airflow. The contours of velocity components at 3\({}^{\circ}\) AOA are shown in Figure 15. The left-hand side and right side displays initial airfoil and optimized airfoil, respectively, generated by GA code in MATLAB. After comparing the velocity on both the airfoils it was found \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & \multicolumn{2}{c}{**NREL S-821**} & \multicolumn{2}{c}{**Relative Variation**} \\ \hline \hline  & **Experimental Data [32]** & **Baseline Airfoil (CFD)** & **Optimized Airfoil (CFD)** & **Baseline with Exp.** & **Optimized with Baseline** \\ \hline Cl & 0.61 & 0.59 & 0.56 & \(-\)3.4\% & \(-\)5.08\% \\ Cd & 0.019 & 0.018 & 0.0167 & +5.50\% & +7.22\% \\ L/D & 32.1 & 32.77 & 33.53 & +2.1\% & +2.2\% \\ AOA & 3\({}^{\circ}\) & 3\({}^{\circ}\) & 3\({}^{\circ}\) & \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Detailed comparison of CFD performance of baseline and optimized airfoils with experimental results (NREL S-821). Figure 14: Pressure contour for the original (**left**) and the optimized airfoil (**right**) (NREL S-821). that the upper surface experienced higher velocity compared to the lower surface of the airfoil. With the change of angle of attack the stagnation point changes for the airfoil. By increasing the angle of attack, the upper surface velocity increases and lower surface velocity decreases. Contours of Mach number are shown in Figure 16 at 3\({}^{\circ}\) angle of attack over the original airfoil and optimized airfoil. The Mach number in the flow field is higher over the original airfoil than that of an optimized airfoil. This is because an optimized airfoil upper surface is much flatter than that of an original airfoil. Consequently, causes the flow to accelerate at low speed over the upper surface of the optimized airfoil. This leads to the reduction in the coefficient of drag for the optimized airfoil.