## 4 Results and Discussion
### Subsonic (NREL S-821) and Transonic (RAE-2822) Airfoil Design  
The flow field conditions for subsonic (NREL S-821) and transonic (RAE-2822) were studied at Mach number (Ma) 0.1 and 0.7, respectively and Reynolds number (Re) was 8 million at 3\({}^{\circ}\) angle of attack. Total drag was minimum on the airfoil between the range of 3\({}^{\circ}\) to 5\({}^{\circ}\) angles of attack. We considered 0.34 m as chord length (c) for both the airfoil. The CST parameters play a crucial role during the optimization process in describing the shape of an airfoil. The further shape of an airfoil was defined by two curvatures of an airfoil, i.e., upper and lower parts. During the optimization process, lower and upper bound values are defined for every design variable in GA MATLAB code. As a result, the corresponding airfoil profile is generated using the best set of CST parameters produced by GA. Then the airfoil is tested at the given above condition for both subsonic and transonic airfoil. XFOIL calculates Cl, Cd, and pressure distribution on the airfoil surface which is called the in-house MATLAB program. The performance of the baseline and optimized airfoils were compared and summarized in Table 5. As a result, it can be concluded by comparing both results obtained from XFOIL, that the optimized airfoil with eight design variables shows better results than the original subsonic NREL S-821 and transonic RAE-2822 airfoil. From Table 5, it is observed that Cd is minimized and the L/D ratio is better for optimized airfoil on comparing with original airfoil for both NREL S-821 and RAE-2822. Since Cd for the optimized airfoil NREL S-821 is 0.009 and for RAE-2822 is 0.007 which is lower than baseline airfoil by 10% and 12%, respectively. This shows an improvement in L/D ratio by 7.4% and 15.9% for an optimized airfoil NREL S-821 and RAE-2822, respectively. The comparison of the airfoil profile between the original and the optimized airfoil NREL S-821 and RAE-2822 is demonstrated in Figures 9 and 10, respectively. Figure 9 depicts that at 20% of the chord length, the optimized airfoil passes through \(-\)0.12 and the original airfoil from \(-\)0.15 at the y-axis, whereas another part of the airfoil overlaps each other. This shows that an optimized airfoil is reduced by 6% in its width of an airfoil. As a result, changes are shown in the pressure coefficient near about 20% of the chord length. The best-optimized airfoil is found whose thickest point occurs at x/c = 0.21. Figure 10 shows changes from 20% to 50% of chord length where less negative pressure is generated by a fluid in optimized airfoil compare to the original airfoil. RAE-2822 optimized airfoil is reduced by 3% of chord length and its thickest point occurs at x/c = 0.392. As a result, drag is minimized for optimized airfoil due to changes in the thickness of the airfoil. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Variables** & **RAE-2822** & **S-821** \\ \hline \(A_{1}^{0}\) & \(-\)0.1232 & \(-\)0.4750 \\ \(A_{1}^{1}\) & \(-\)0.1734 & \(-\)0.3828 \\ \(A_{1}^{2}\) & \(-\)0.1791 & \(-\)0.0710 \\ \(A_{1}^{3}\) & 0.0586 & 0.1254 \\ \(A_{0}^{0}\) & 0.12 Figure 11 demonstrates the L/D ratio concerning 3\({}^{\circ}\) AOA for both optimized and original airfoil. Both figures for NREL S-821 and RAE-2822 depict that the optimized airfoil has an increment in comparison to the original airfoil. By looking at the figures, it can be concluded that the lift to drag ratio is higher which implies good off-design property for small wind turbine blades. The pressure distribution curve over the surface of the original and the optimized airfoil at 3\({}^{\circ}\) AOA are compared and shown in Figure 12. Lift, drag, and pressure data are calculated by XFOIL flow solver in which the C\({}_{\text{P}}\) values are relatively high for both the optimized airfoils NREL S-821 and RAE-2822. These are the aerodynamic properties of an airfoil that are directly obtained from the given design objective.