## 4 Validation with a High Fidelity Solver  
To verify the results obtained by Foil2w, the flow around the modified geometries is also simulated using MaPFlow, a CFD URANS solver. In both codes, transition modeling is realized using the same model \(\rm e^{N}\). For the CFD simulations, the computational grid is  
Figure 12: Pressure coefficient distribution for the airfoils produced by the PSO and ES optimization algorithms at the maximum \(\rm C_{L}\) angles of attack. Flow field was simulated using Foil2w. generated using the ANSYS ICEM software [29]. Special care is taken to generate a grid sufficiently dense within the boundary layer region and in the vicinity of the LE and TE regions. The distance of the first node from the surface is 10\({}^{-6}\) chords (y\({}^{+}\approx\) 1). In Figure 13, the mesh for the PSO-airfoil is depicted, whilst a similar mesh was created for the ES-airfoil. It consists of 606 wrap around nodes and 180 nodes in the normal to the surface direction. Out of the 180 nodes in the normal direction, 120 are distributed from the surface up to a distance of 0.13 chords using a geometrical progress with ratio 1.08. Figure 14 compares the MaPFlow and Foil2w predictions of the C\({}_{\rm L}\)-AoA polars for the optimized morphed airfoils. The MaPFlow and Foil2w polars for the original airfoil are also presented in the plot. Higher C\({}_{\rm L,max}\) values are systematically predicted by the CFD solver for the morphed airfoils, although the opposite applies for the baseline NACA 64A010. In general, compared to the original airfoil, the differences between the two codes increase, as the airfoil geometry is deformed. This is due to the fact that, as the geometry becomes more complex, and taking into account that transitional effects are included, the results become more sensitive to the simulation of viscous flow phenomena, such as the prediction of the transition locations and the appearance of separation. The maximum lift coefficient increases from 1.1 to 2.5 and 2.3 for the PSO and ES airfoils, respectively. This is due to the fact that in the CFD simulations stall takes place at higher angles of attack (19\({}^{\circ}\) for both PSO and ES). It is noticeable that in MaPFlow predictions the ES airfoil exhibits higher C\({}_{\rm L}\) values than the PSO airfoil at AoAs in the range 5-15\({}^{\circ}\), below the C\({}_{\rm L,max}\) AoA. In aeronautical applications, this region is outside the operation points of interest and it is probable that morphing is applied differently at the lower AoAs. In the case of wind energy applications, though, the operational region is broader indicating that a larger part of the polar should be taken into account. In Table 6, percentages of the maximum lift coefficient increase for the designed airfoils, as predicted using Foil2w and MaPFlow, are summarized and compared. It is underlined that CFD predictions indicate that PSO-airfoil reaches a 140% increase in C\({}_{\rm L,max}\), while ES-airfoil reaches a 125% increase. Therefore, MaPFlow exhibits an even higher increase in C\({}_{\rm L,max}\) (more than 100%), suggesting that the results of the optimization using the lower fidelity Foil2w solver are conservative at least for the particular airfoil studied in the present work. It is worth noting that contrary to the morphed airfoils, the C\({}_{\rm L,max}\) predicted by the CFD code for the baseline airfoil is slightly lower than the one provided by Foil2w. Figure 13: Computational grid (C type) for PSO airfoil, constructed using ICEM, ANSYS (2020). Velocity contour plots around the PSO airfoil are depicted in Figure 15, at the AoA where the maximum value of lift coefficient occurs (19\({}^{\circ}\)). The flow patterns of Figure 15 confirm the discussion made in the previous section.