## 3 Discussion and Results  
The aerodynamic optimization considered in this study applies to both Droop Nose Leading Edge Morphing (DNLE) and Morphing Trailing Edge (MTE) configurations. To utilize the full potential of the \"morphing\" concept, a baseline shape optimization was carried out followed by its morphing shape design at various flight conditions given in Table 5. These cases are based on various altitudes and Reynolds numbers that are  
Figure 5: Schematics of the Hybrid Optimizer/ Particle Swarm Optimization (PSO) algorithm combined with the Pattern Search algorithm. computed for the airspeed of 34 m/s. These given flight conditions are chosen because of the fact that the UAS-S45 can reach altitudes of 20,000 ft and a stall speed of 34 m/s. The design framework uses endurance maximization as an optimization function to enhance the performance of the UAS-S45 over a large part of its flight regimes. Figure 6 shows the flight envelope of UAS-S45. From a physical standpoint, every flight condition is defined by a specific Mach number, altitude (Reynolds number and temperature are calculated according to ISO standard atmosphere) and a fixed lift coefficient. The present study considered the optimization of the leading edge and trailing edge of the UAS S45 conventional wing that could be both morphed. The difference of performances obtained between the baseline airfoil and the morphed one demonstrate the overall benefits of morphing airfoil design. Figure 7 shows the design of Droop Nose Leading Edge (DNLE) and Morphing Trailing Edge (MTE) airfoil configurations versus the baseline airfoil. Figure 6(a) shows the basic concept of the morphing wing with combined morphing leading and trailing edge deflections and Figure 6(b) shows two cases of MTE designs. Figure 8 shows the aerodynamic coefficients \(\mathrm{C_{L}}\) and \(\mathrm{C_{D}}\) variations of the baseline UAS-S45 root airfoil for two Reynolds numbers Re = 1.2 \(\times\) 10\({}^{6}\) and Re = 2.4 \(\times\) 10\({}^{6}\), which were calculated using the XFoil and the Transition \((\gamma-Re_{\theta})\) SST in Ansys/Fluent software. As seen in Figure 8, the lift coefficients' variations with the angle of attack were predicted accurately, while small differences were found in drag coefficient variations with the angle of attack. These differences in the drag coefficients' variations are found largely at angles of attack higher than 4\({}^{\circ}\) because the pressure-based drag coefficient becomes the dominant component of the total drag coefficient and flow separation conditions result in a decreased friction-based drag coefficient. This result implies that drag forces are very sensitive to turbulence effects and the Transition \((\gamma-Re_{\theta})\) SST model can solve the turbulence problems more accurately than the XFoil solver. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Flight Condition** & **Altitude (Feet)** & **Reynolds Number** \\ \hline Flight Condition I & 0 & 2.40 \(\times\) 10\({}^{6}\) \\ Flight Condition II & 10,000 & 1.88 \(\times\) 10\({}^{6}\) \\ Flight Condition III & 20,000 & 1.45 \(\times\) 10\({}^{6}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Operating conditions for design problem of UAS-S45 at the airspeed of 34 m/s. Figure 6: Schematic of the flight regimes of UAS-S45. Figure 9a shows the friction coefficient variations with the chord for the angles of attack of \(0^{\circ}\), \(2^{\circ}\) and \(6^{\circ}\) obtained by use of the Transition \((\gamma-Re_{\theta})\) SST model; this figure indicates very good accuracy in predicting the flow separation phenomena as the skin friction coefficient increases slightly with the increase in angle of attack. Figure 9a,b also shows the initial flow separation, the separated region and its reattachment. It is seen in Figure 9b that the flow separation is not affected by the change in the flow separation phenomenon. Figure 8: Aerodynamic lift and drag coefficient variations using the XFoil and Fluent solvers.