## 4 Results and Discussion
### Subsonic (NREL S-821) and Transonic (RAE-2822) Airfoil Design
Pressure distribution across the airfoil surface calculated by XFOIL works on the panel technique method. In the panel technique method, the whole airfoil is divided into different flat panels and the near trailing and leading edges panel is increased to capture the curve perfectly. In every panel, the middle point is the control point of the panel, and the vortex is generated at the middle point of every panel. By the summations of all the vortex produced in airfoil results in the generation of lift in an upward direction perpendicular to the fluid flow. Meanwhile, drag is calculated far away from the trailing edges which are parallel to the fluid flow in opposite direction. Figure 10: The shape comparison of an original and optimized airfoil (RAE-2822). Figure 9: Comparison of original and optimized airfoil shape (NREL S-821). In Figure 12a, at 20% of the chord length, it is observed that more negative pressure is generated at the upper surface in the original airfoil than optimized airfoil due to fluid flow around the surface whereas in the lower surface of the original airfoil more pressure is generated than optimized airfoil. Due to the high-pressure generation in the original airfoil, more lift is depicted for the original airfoil compared to an optimized airfoil. However, drag is minimized in optimized airfoil due to a decrement in the thickness of the optimized airfoil. As a result, the L/D ratio shows an improvement of 7.4% in the optimized airfoil. From Figure 12b, it can be said that negative pressure is higher on the upper side of the surface of the original airfoil from 30% to 80% of the chord length whereas the lower side of the surface of the optimized airfoil has higher pressure than original airfoil RAE-2822. Therefore the lift produced by the optimized airfoil is better than the original airfoil RAE-2822. As a result, it can be concluded that the L/D ratio of an optimized airfoil is better than that of baseline airfoil RAE-2822. The optimized airfoil S-821 and RAE-2822 have a greater \(C_{P}\) value than the original airfoil. The convergence graph of an optimized airfoil with six and eight design parameters is shown in Figure 13. The error bars and the pressure distribution curve at AOA 3\({}^{\circ}\) with regards to the number of iteration are displayed in Figure 13. The pressure residual at the surface of an airfoil is very small and the geometry residuals are below 3 \(\times\) 10\({}^{-3}\). The comparison of optimized results between CST (\(n\) = 6) and CST (\(n\) = 8) was done and it was  
Figure 11: Comparison of coefficient of Lift to drag (L/D) ratio with respect to AOA (**a**) NREL-8821, (**b**) RAE-2822. Figure 12: Distribution of pressure over the surface of an initial and optimized airfoil (**a**) NREL S-821; (**b**) RAE-2822. concluded that the optimized airfoil with eight design CST parametric variables shows better results than six parameters variables. In the figure below, the blue and red color in the first part of every figure signifies airfoil and \(\rm C_{P}\) at normalized chord length, respectively. While in the second part of each figure, yellow denotes residual error, red and blue denote the convergence plots. Figure 13: The convergence process and error bars with the generation corresponding to CST method. (**a**) NREL S-821 (\(n\)=6), (**b**) NREL S-821 (\(n\) = 8), (**c**) RAE-2822 (\(n\) = 6), (**d**) RAE-2822 (\(n\) = 8).