1. Introduction
With the increase of energy consumption, ever-growing ecological, social and economic awareness and decreasing fossil fuels, governments and legislatures are more concerned about pollution-related challenges around the globe [
1,
2,
3,
4,
5]. Recently, the European Union and G8 leaders mutually decided to reduce carbon emissions by 80% before 2050 [
6]. As such, governments across the world are forced to spend more funds on alternative sources of energy. Due to global warming and rising world energy demands, trends in power generation are shifting toward renewable energy sources [
7]. Among these resources, wind energy has been credited for its high performance, sustainability and cost-effectiveness. Wind energy, a viable source of renewable energy with a minimal carbon footprint, and its availability in abundant quantities is an essential alternative to traditional fossil-based fuel sources. Therefore, to meet these essential needs, designing and selecting airfoils are important steps in the aerodynamic design of wind turbine blades. Day by day, wind energy production is rising, with an annual growth rate of 10.6% for 2016–2017 (487 GW to 539 GW), and it is expected to fulfill 20% of energy needs by the year 2030 [
8]. However, harnessing wind energy to its fullest is limited by several constraints: large land occupancy, high installation costs, land requirements, noise pollution and the structural limitations of the wind turbines. Therefore, to optimize the efficiency of the wind energy systems, different design concepts or optimized airfoils are needed for the blades to maximize their lift and lift-to-drag ratios. In recent years, several design concepts for wind energy systems have included high-altitude wind energy converters (HAWECs) and airborne wind energy (AWE).
Aerodynamic shape optimization (ASO) has become important for development in the aerospace and mechanical engineering fields. The aerodynamic shape parametric method, by obtaining an optimized result, plays an important role in ASO [
9]. The parametric method with fewer design parameters is efficient, less time-consuming during optimization and has the capability to handle a large, aerodynamic shape in the design space. Earlier, different types of aerodynamic shapes were designed with different aims and objectives. As we are moving toward the industrial revolution and transformation of new CFD techniques, different numerical tools are developed for the optimization of airfoils, instead of using the old flat plate theory for the design of airfoils [
10]. For the design of airfoil aerodynamics, the two main approaches are (1) inverse design (ID) and (2) direct numerical optimization (DNO) [
11,
12]. The ID method is used to solve the geometry and search different airfoil designs, which can satisfy the fluid dynamic structure and generate pressure distribution. DNO acts as a coupled geometry and performs aerodynamic analysis to generate an optimum design in an iterating process related to different objectives and constraints. However, the two methods discussed above indicate modification in an existing airfoil design, and to achieve better and new designs through local airfoil modifications, different parameterization techniques can be applied. This airfoil shape can be modified through smooth analysis of the original airfoil coordinates through a shape analytical function (e.g., Bernstein polynomials or Legendre) [
13]. ASO includes airfoil shape parameterization, optimization algorithms and airfoil design analysis. Optimization of the shape parameterization method has a great impact on the results and has the potential to accommodate a wider range of potential airfoil shapes with fewer design parameters in the design space [
9]. Different aerodynamic shape parameterization techniques have been developed for the airfoil design and its parameterization [
14]. There are several parametric methods for ASO, such as the parametric section (PARSEC) method, B-spline, Bezier curves and class shape transformation (CST), which are widely used to fit the size of the airfoil through interpolation methods. Hicks-Henne parameterizations, CST methods, Bezier curves and B-spline curves are useful for reconstructing the airfoil, but the relative position of the control point is difficult to manage [
15,
16]. Hicks and Henne [
17] reported in their work that analytical functions can be represented by airfoil families [
18]. The results produced from the analytical functions cannot be used as an essential new design concept, but they are robust enough to represent different types of airfoils. The airfoil shape is represented by parametric methods with different basis functions because the parameters used in the airfoil are greater in number, making it possible to find better design results [
19]. On the other hand, due to the increase in design variables, this results in the problem of finding a corrective algorithm that does not help to find the optimal design. Airfoil optimization plays an important role in maximizing the coefficient of lift (
), so the aerodynamic performance is improved, achieving benefits to the lift-to-drag (
L/D) ratio and better endurance. During the optimization process, the airfoil shape is changed in every iteration to obtain the desired results. However, it is too difficult to use all sets of design variables for the optimization process. Therefore, the design variables should be limited from a nearly infinite amount to a finite set, and the parameterization method is designed to represent a completely new airfoil or an existing airfoil [
20]. Samareh [
15] and Wu et al. [
16] conducted a survey and confirmed that the parameterization method has a great influence on the whole optimization process. Ulaganathan and Balu [
20] suggested that the polynomial approach based on parameterization schemes strongly influences the maximum design variables obtained as a result of the optimization.
Some physically intuitive methods facilitate the use of airfoil parameters to explain its shapes (e.g., the trailing edge angle, the airfoil thickness or the radius of the leading edge). Sobieczky [
21] presented a parameterization method called PARSEC. This method uses a total of 11 basic parameters to represent an airfoil shape. The parameters used in the PARSEC method are directly linked to the airfoil geometry (e.g., thickness, curvature, maximum thickness and abscess), and they give the designer a real idea of what the design will be. The geometry definition must be coupled with an optimization technique that must properly take the airfoil parameterization into consideration. In this work, an optimization process for airfoil geometry is introduced. This method is based on the genetic algorithm (GA) optimization method, finding the optimum results by the coupling parameterization method and producing the maximum lift-to-drag (
L/D) ratio. The results are then compared to the CST parameterization method and the CFD results. Kulfan [
15] and Bussoletti [
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 S809 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 F39aerospace applications. The panel technique is used by the XFOIL solver in the MATLAB environment to calculate
and
. 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. The results are described in detail and shown with an indicator of the pressure coefficient, convergence graphs, and a mesh independence study. The study conducted in this paper has adaptability for both symmetric and asymmetric airfoil shapes. Finally, the results are discussed and reported for the coefficient of drag (
), coefficient of lift (
) and lift-to-drag (
L/D) ratio for optimized airfoil geometries at 0°, 2°, 4°, and 6.2° angles of attack (AOAs).