## 3 Discussion and Results
### Morphing Trailing Edge Optimization
(**a**) the initial (reference) versus the final (optimized or mor-phed) airfoil shape, (**b**) the convergence trend for the minimum drag optimization function. Figure 20: Lift coefficients versus angle of attack at two optimized design configurations; (**a**) the variations of lift coefficients with the angles of attack at Flight Condition I (**b**) the variations of lift coefficients with the angles of attack at Flight Condition II; (**c**) the variations of lift coefficients with the angles of attack at Flight Condition III; (**d**) the lift coeffi-cient variations for all three flight conditions for Opt. Case I.  
Figure 21: Lift coefficients versus drag coefficients for various optimized design configurations. (**a**) the drag polar at Flight Condition I; (**b**) drag polar at Flight Condition II; (**c**) drag polar at Flight Condition III; (**d**) drag polar for all three flight conditions for Opt. Case I.  
Figure 22: Pressure coefficients for different MTE design configurations. (**a**) at angles of attack of \(4^{\circ}\); (**b**) at angles of attack of \(10^{\circ}\). Figure 23 illustrates the initial (reference) versus the final (optimized or morphed) airfoil shape, while Figure 23 presents the convergence graph of the aerodynamic endurance optimization for the given MTE optimized airfoil while utilizing the PSO algorithm with pattern search. Figure 23 shows that the algorithm performs well and improves the airfoil shape to maximize the endurance. The optimization process using the endurance maximization objective function led to improved endurance performance in the optimized airfoils with respect to the endurance performance of the baseline airfoil. The performance measured in terms of \(\text{C}_{\text{L}}^{3/2}/\text{C}_{\text{D}}\) variation with \(\text{C}_{\text{L}}\) is shown for three different flight conditions in Figure 24. The endurance performance of each optimized airfoil shows a higher value in the MTE Opt. Case I with respect to its baseline airfoil configurations. For the same endurance performance defined by the \(\text{C}_{\text{L}}^{3/2}/\text{C}_{\text{D}}\) ratio, the lift coefficients were found to be 1.17 for the baseline airfoil and 1.45 for the MTE airfoil configuration for the optimized flight condition II, respectively. Furthermore, as seen in Figure 24, the efficiency of \(\text{C}_{\text{L}}^{3/2}/\text{C}_{\text{D}}\) increased by approximately 10.25% for flight condition III; this finding indicates the improved endurance performance of the UAS-S45 airfoil. The difference between the results obtained by the two objective functions of drag minimization and endurance maximization to obtain optimal airfoil configurations was determined. The optimized airfoil geometrical shapes were obtained for drag minimization and endurance maximization as shown in Figure 25. The main difference observed in the airfoil geometries, as shown in Figure 25, is that the trailing edge obtained with the drag minimization objective function gave a smaller deflection than the baseline airfoil. Likewise, the endurance maximization objective function requires higher airfoil deflection with a continuous trailing edge. Figure 23: Optimized airfoil and convergence history for endurance maximization function. (**a**) the initial (reference) versus the final (optimized or morphed) airfoil shape; (**b**) the convergence graph of the aerodynamic endurance optimization. The contour plots of the velocity magnitude and of the turbulent kinetic energy are visualized for the baseline airfoil and for the airfoils optimized by the Transition \((\gamma-R\epsilon_{\theta})\) SST turbulence model in Figure 26. These contour plots reveal that for a given MTE deflection, larger TE separation regions are found at 4\({}^{\circ}\) angles of attack than at 10\({}^{\circ}\) angles of attack. Similarly, the vertex of turbulent kinetic energy (TKE) originating from the MTE at an angle of attack of 40\({}^{\circ}\) has more strength than the vertex an the angle of attack of 10\({}^{\circ}\).