###### Abstract
[PERSON] [15] and [PERSON] [16] introduced new parameterization methods called Kulfan parameters, or the class shape transformation (CST) method. The CST method is a powerful method of parameterization because of its simplicity, robustness and ability to categorize the aerodynamic body in various possible forms. It uses equations to produce a wide array of aerodynamic shapes with minimal parameters and smooth geometries [22]. For designing a preliminary airfoil and its optimization, fewer parameters to give a particular shape with a lower-order polynomial are required. The CST method is very similar to the Bezier curves method, except CST equations are present in addition to the Bezier curves equation with a class function term. One of the advantages of CST over Bezier curves is that it can fit a curve to a particular airfoil with lower coefficients. The aerodynamic shapes are classified into a class function that forms the basis, and then different shapes are derived from this class function. There are different aerodynamic shapes of airfoils that can be transformed into an axisymmetric body or changed with the shape function to get a new shape design for an airfoil. These shapes are a biconvex airfoil, a Sears-Haack body, a round nose and a pointed aft-end airfoil, similar to the NACA airfoil, elliptic airfoil, wedge airfoil and other different airfoils. The shape function has its own shape for the geometry within the same class, as directed by the class function. The main goal of this paper is the optimization of the well-known National Renewable Energy Laboratory (NREL) airfoil, known as the S809 airfoil. The thickness of this airfoil is 21%, and the laminar flow airfoil's experimental results and design are given in [23]. Different blades, such as NREL Phase II, Phase III, and Phase VI HAWT blades, are designed based on the NREL 8809 airfoil from root to tip [24]. The airfoil NREL S809 is subject to low Mach number (almost incompressible) flow with a Reynolds number in the range of one to two million. Laminar and turbulent trailing edge separation occurs when the angle of attack is 0-5.13 degrees and the angle of attack increases, respectively [25]. Motivated by the above discussion, in this study, the PARSEC and CST methods are coupled with a genetic algorithm (GA) to propose an integrated scheme for aerodynamic shape optimization. The main aim is to achieve the optimized geometry from two separate parameterization methods with GA and compare the results with the NREL experimental data. The most common and best airfoil selected for this purpose is the NREL S-809 because of its high _L/D_ ratio at the stall angle and its common use for wind energy and F39 aerospace applications. The panel technique is used by the XFOIL solver in the MATLAB environment to calculate \(C_{l}\) and \(C_{d}\). The resulting _L/D_ ratio of the optimized and original airfoil is compared with the NREL experimental data provided by The Ohio State University (OSU) [26] to validate the proposed result. After further steps, numerical modeling work and CFD analysis is performed for the NREL S-809 to test the application of numerical simulations with airfoil confines inside the structural grid. It is an obvious fact the airfoil is the basic building profile of any wind turbine blade. The shape optimization of the chosen baseline airfoil has a major impact on the energy-harvesting operation of wind turbines. In this prospectus, the presented research also points out the possibility of applying the design solution to a range of wind turbines (e.g., off-shore wind turbines, on-shore wind turbines, and vertical axis wind turbines). Furthermore, the in-house code has been written in the widely used MATLAB, which has many library functions for supportive execution. Because of factors such as the simplicity of the CST method and the robustness of the code, it can be easily coupled to any other blade design program for the optimization of single or multiple airfoils along the span of the blade.