## 5 Conclusions  
In this paper, a genetic algorithm was coupled with the CST and PARSEC parameterization methods and employed to optimize the aerodynamic shape of a well-known wind turbine, the NREL S-809 airfoil, to improve its lift and drag characteristics in order to achieve its two objectives, those being to increase its lift and lift-to-drag ratio for a wind turbine. This has been presented and applied to find the optimal shape of the NREL Phase IV HAWT blades. The optimization scheme was carried out with MATLAB code, which utilized the XFOIL solver for an iterated process to calculate the lift, drag, and pressure data. At the final step, the commercially available ANSYS CFX software was used to simulate the flow field on a structured mesh using the Reynolds-averaged Navier-Stokes (RANS) equation in combination with the two-equation \(k\)-\(\omega\) and \(k\)-\(e\) SST turbulence model. However, the results showed significant improvement in the coefficient of lift and lift-to-drag ratio of the optimized airfoil compared with the original S809 airfoil. The following conclusions were derived:  
1. The airfoil optimized by CST showed an increment of 11.8% in the lift coefficient and 9.6% in the lift-to-drag ratio, while with PARSEC, it showed an improvement of 10% in the coefficient of lift and decrease of 2% in the overall lift-to-drag ratio while comparing both optimized NREL S809 airfoils;  
Figure 16: Velocity contour at 0\({}^{\circ}\) (left) and 6.2\({}^{\circ}\) (right) for the (**a**) baseline S809 airfoil and (**b**) optimized S809 airfoil. 2. The proposed methodology, in terms of the lift-to-drag ratio, which is the vital decisive factor in blade and wind turbine design, exhibited superior aerodynamic characteristics by 11.6% in the optimization process with CST compared with the PARSEC methodology;
3. The CFD analysis of the optimized airfoil showed an improvement of 24.6% in the lift coefficient and 12.4% in the lift-to-drag (L/D) ratio when comparing the optimized airfoil with the original S809 airfoil's experimental results (OSU);
4. The present aerodynamic optimization scheme was in close agreement with the previous results, and further application of the CST approach can be deployed with reasonable flexibility in other competitive optimization techniques;
5. A significant reduction in the number of different design parameters offered a smaller number of genes for the candidate solution, which further enabled the search algorithm to act comparatively more efficiently and, in a time, -bound manner. Conceptualization, methodology, formal analysis, and original draft preparation by [PERSON], M.-H.K. supervised the research and edited the manuscript. All authors have read and agreed to the published version of the manuscript. This research received no external funding. Not applicable. Data Availability Statement: Data is contained within the article. The authors declare no conflict of interest. The proposed methodology, in terms of the lift-to-drag ratio, which is the vital decisive factor in blade and wind turbine design, exhibited superior aerodynamic characteristics by 11.6% in the optimization process with CST compared with the PARSEC methodology;
3. The CFD analysis of the optimized airfoil showed an improvement of 24.6% in the lift coefficient and 12.4% in the lift-to-drag (L/D) ratio when comparing the optimized airfoil with the original S809 airfoil's experimental results (OSU);
4. The present aerodynamic optimization scheme was in close agreement with the previous results, and further application of the CST approach can be deployed with reasonable flexibility in other competitive optimization techniques;
5. A significant reduction in the number of different design parameters offered a smaller number of genes for the candidate solution, which further enabled the search algorithm to act comparatively more efficiently and, in a time, -bound manner. Conceptualization, methodology, formal analysis, and original draft preparation by M.T.A., M.-H.K. supervised the research and edited the manuscript.