## 5 Discussion  
In the present study, a methodology for designing high-lift mechanisms for aircraft wings is developed, applying a combination of LE droop nose and TE flap morphing. Airfoils of increased maximum lift are produced through an optimization process, where smooth polynomial curves approximate the morphing parts in the LE and TE regions of the airfoil, while a viscous-inviscid fast interaction code is used for the prediction of the aerodynamic characteristics. Results indicate that significant increase in maximum lift coefficient and stall angles of attack are achievable. The contribution of each morphing mechanism (LE droop nose, TE flap) to the total \(\mathrm{C_{L,max}}\) increase is investigated. When only LE droop nose is applied stall is delayed and, as a result, lift coefficient increases allowing the airfoil to operate at higher angles of attack. On the other hand, when only TE flap is applied the effective camber line increase at the TE region results in the shifting of the entire \(\mathrm{C_{L}}\) polar towards lower AoA. The entire level of the \(\mathrm{C_{L}}\) curve increases, but stall occurs at lower AoA. The combined effect is a delayed stall along with a shift of the \(\mathrm{C_{L}}\) curve to a higher level. The above conclusions are verified using a high fidelity CFD solver. CFD predictions exhibit an even higher \(\mathrm{C_{L,max}}\) increase due to delayed stall and higher pressure peaks at the suction side of the LE, suggesting that the optimization results derived with the fast viscous-inviscid interaction code are conservative at least for the current airfoil study. The imposed curvature and inclination constraints prevent the appearance of geometric irregularities and flow disturbances at the connections between the undeformed and the morphing parts. This is reflected on the predicted smooth pressure distributions and the velocity contours. The present work focuses on the achievable increase of the maximum lift, which is desirable during take-off and landing flight procedures; aerodynamic performance is not considered in the optimization process. However, the predictions of the CFD solver demonstrate that although morphing airfoils produce an increased drag, they are still capable of operating with much higher aerodynamic performance (\(\mathrm{C_{L}}/\mathrm{C_{D}}\)). This interesting outcome ensures the overall aerodynamic effectiveness of the designed airfoils and indicates the potential of the developed optimization methodology to be applied to other contiguous technologies, such as wind energy, where maximization of \(\mathrm{C_{L}}/\mathrm{C_{D}}\) is likely to be the most relevant design objective for maximum energy yield. Finally, fully turbulent flow simulations are performed to investigate the effect of a potential increase of the surface roughness. As expected, fully turbulent calculations predict lower values of the maximum lift. It is observed that in fully turbulent conditions, PSO and ES optimized airfoils produce a similar \(\mathrm{C_{L,max}}\), whilst in transitional conditions, the PSO airfoil produces a considerably higher \(\mathrm{C_{L,max}}\). Therefore, changing from transitional to turbulent conditions mitigates maximum lift increase to the same level for both airfoils. Conceptualization, V.R. and J.P.; methodology, C.T., N.-G.M., J.P., V.R., G.S. and G.P. ; software, G.S. and G.P. ; validation, C.T. and N.-G.M. ; formal analysis, C.T. and N.-G.M. ; writing--original draft preparation, C.T. and N.-G.M. ; writing--review and editing, J.P. and V.R. ; visualization, C.T., N.-G.M. and J.P.; supervision, J.P. and V.R. All authors have read and agreed to the published version of the manuscript. This research received no external funding. Not applicable.