## 3 Optimization Results
Figure 9: Effect of the combined LE droop nose/TE flap optimization on the lift coefficient polar. Comparison between the geometries derived from the PSO and Evolution Strategies (ES) optimization algorithms, the original geometry, and the reference deformation. Flow simulations were performed using Foil2w. Figure 11: Effects of the individual LE droop nose and TE flap morphing and their combination on the lift coefficient polar. ES algorithm with eight generations (1008 evaluations) was employed for the individual as well as the combined morphing optimization. Flow simulations were performed using Foil2w. Measurements for extended and drooped slat are reported in [2]. Figure 10: Effects of the individual LE droop nose and TE flap morphing and their combination on the lift coefficient polar. PSO algorithm with four generations (560 evaluations) was employed for the individual as well as the combined morphing optimization. Flow simulations were performed using Foil2w. Measurements for extended and drooped slat are reported in [2]. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{
\begin{tabular}{c} **Optimization** \\ **Algorithm** \\ \end{tabular} } & \multicolumn{3}{c}{\(\mathbf{C_{L,max}}\)} & \multicolumn{3}{c}{\% Difference with NACA 64A010} \\ \cline{2-7}  & **LE Droop Nose** & **TE Flap** & **Combined** & **LE Droop Nose** & **TE Flap** & **Combined** \\ \hline ES & 1.76 & 1.60 & 2.07 & 60.22 & 45.44 & 88.31 \\ PSO & 1.99 & 1.60 & 2.27 & 80.96 & 46.02 & 106.96 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Relative increase in CL,max applying optimized LE droop nose, TE flap, and combined morphing with the PSO and ES algorithms. Simulation of the flow field was performed by Foil2w. A closer look at the pressure distribution (presented in Figure 12) around the morphed shapes and the undeformed baseline NACA 64A010 can provide information for the physical interpretation of the attained \(\rm C_{L,max}\) increase. Pressure distributions are plotted for AoAs corresponding to the maximum value of the lift coefficient. This is at 17.5\({}^{\circ}\) and 14\({}^{\circ}\) for the morphed shapes predicted by PSO and ES algorithms, respectively, and 10\({}^{\circ}\) for the baseline NACA 64A010 (see Figure 9). Apparently, the larger extent of the high under-pressure pocket on the suction side in the vicinity of the LE region drives the increase in the maximum \(\rm C_{L}\). The PSO airfoil exhibits a suction pressure peak of about 25% higher than that of the ES airfoil. This explains the higher \(\rm C_{L,max}\) value obtained by this airfoil. Although the suction peak of the baseline airfoil is larger than those of both morphed shapes, the pressure of the baseline airfoil quickly recovers within a very short distance (less than 5%) from the LE point. The under-pressure of the morphed shapes remains high up to 10% of the chord distance from the LE. It is noted that for both morphed shapes, at the \(\rm C_{L,max}\) AoA, the flow remains almost attached over the whole suction side. A limited separation is obtained for both morphed airfoils at about 80% of the chord (seen as a plateau of the pressure coefficient beyond this chordwise position). Another interesting observation is related to the pressure variation at the connection points between the deformed and undeformed airfoil parts, where it is desirable to avoid steep flow disturbances. The plots of the pressure coefficient in Figure 12 do not present significant irregularities, confirming that the imposed curvature and slope constraints, integrated into the optimization procedure, prevent the occurrence of significant geometric discontinuities. Moreover, in the PSO airfoil, the additional fixed control points between the morphed and the undeformed part improve the continuity of the geometry at the connections (see Figure 8), and this effect is also reflected on the \(\rm C_{P}\) distribution (at least at the two connection points of the suction side and the TE connection point of the pressure side).