## 6 Optimal Results and Discussion  
Two new airfoils with the maximum relative thickness of about 30% are optimized by the above two schemes. The airfoil designed by scheme 1 is named WQ-A300, and the airfoil designed by scheme 2 is named WQ-B300. The profiles of the new airfoils and the classic DU97-W-300 airfoil which was designed by Delft University are plotted in Figure 6.  
To verify the superiority of the aerodynamic characteristics of the optimized airfoils, the aerodynamic performance of the new airfoils and the DU97-W-300 airfoil were compared. Figures 7 and 8 show a comparison of the aerodynamic performance of the new airfoils with that of the DU97-W-300 airfoil (Reynolds number Re = 3.0 \(\times\) 10\({}^{6}\), Mach number Ma = 0.15). The key aerodynamic parameters of the WQ-A300, WQ-B300, and DU97-W-300 airfoils are listed in Table 4. The aerodynamic characteristics of wind turbine airfoils are calculated by the RFOIL software. The accuracy and reliability of the theoretical values calculated by the software have been verified in some relevant studies [3; 4]. According to the figures and table, compared to the DU97-W-300 airfoil, the WQ-A300 and WQ-B300 airfoils exhibit a better lift coefficient and lift-drag ratio under both smooth and rough conditions. Under the smooth condition, the maximum lift coefficient and lift-drag ratio of the WQ-A300 airfoil are 1.889 and 141.756 respectively, an increase by 15.38% and 15.6%, and the maximum lift coefficient and lift-drag ratio of the WQ-B300 airfoil are 1.823 and 139.647 respectively, an increase of 11.8%, and 13.9%. Under the rough condition, the maximum lift coefficient and lift-drag ratio of the WQ-A300 airfoil are 1.326 and 66.391 respectively, an improvement by 4.57% and 7.27%, and the maximum lift coefficient and lift-drag ratio of the WQ-B300 airfoil are 1.295 and 64.798 respectively, an improvement of 2.1%, and 4.7%. Figure 6: Profiles of the new airfoils and the DU97-W-300 airfoil. Figure 7: **(a)** Lift coefficients of the new airfoils and the DU97-W-300 airfoil (smooth condition); **(b)** Lift coefficients of the new airfoils and the DU97-W-300 airfoil (rough condition). The profiles of the airfoil with a 30% thickness in literature [32] and the WQ-B300 airfoil are plotted in Figure 9. The aerodynamic characteristic of the WQ-B300 airfoil is compared with that of the airfoil in literature [32] (as shown in Figures 10 and 11). Table 4 lists the key aerodynamic parameters. Compared with that of the airfoil in literature [32], the maximum lift-drag ratio \(C_{L}\)/\(C_{D}\) of the WQ-B300 airfoil is 139.647, increased by 8.718% under the smooth condition. The other aerodynamic parameters are more or less the same with that of the airfoil in literature [32]. \begin{table}
\begin{tabular}{c c c c c} \hline \hline  
\end{table} 
Table 4: The comparisons of the key aerodynamic performance. Figure 8: (a) Lift-drag ratio of the new airfoils and the DU97-W-300 airfoil (smooth condition); (b) Lift-drag ratio of the new airfoils and the DU97-W-300 airfoil (rough condition). Figure 9: Profiles of the airfoil in literature [32] and the new airfoil. The comparison of the cross-sectional plying parameters of the WQ-A300 airfoil and the WQ-B300 airfoil is shown in Figure 12. The variety of the main beam location of the WQ-B300 cross-section is shown in Figure 13. It should be explained that the original structural parameters of the new blade cross-section are from the data of the 2.1 MW wind turbine blade (see Tables 1 and 2 for details). The cross-sectional plying parameters of the WQ-A300 airfoil is the same as that of the DU97-W-300 airfoil. Table 5 gives the comparisons of the cross-sectional layer parameters of the WQ-A300 airfoil and the WQ-B300 airfoil. From the above figures and table, we can see that the thickness of the uniaxial lamination of the WQ-B300 cross-section is decreased and the thickness of the biaxial and triaxial lamination is increased by optimizing the layer parameters of the blade cross-section and the position of the main beam.