# Optimizing Airfoil Aerodynamic Characteristics by Using Proposed CSA-KJ Method
## 1 Introduction  
Wind energy is an important clean and renewable energy source. The design of wind turbines is an important aspect of wind energy utilization. One of the most critical components of wind turbines is the blade airfoil, as its design directly affects the power generation efficiency of wind turbines. However, with the increasing complexity of wind turbine operating conditions, the existing wind turbine blade airfoils cannot adapt to offshore conditions, which leads to the problem of low power generation efficiency of wind farms. The reliability of a wind turbine depends on the careful design of its airfoil structure so that it can absorb energy with great efficiency, which plays a crucial role in the wind energy conversion system [1]. The lift-drag ratio coefficient of an airfoil is important to both the aircraft and wind turbines, and a high lift-drag ratio contributes to efficient energy conversion. The NACA550 airfoil used by [PERSON] et al. [2] has a higher lift drag ratio and thrust coefficient than other airfoils, and the wind turbine has higher wind energy conversion and output power under low Reynolds number conditions, providing effective power generation. [PERSON] et al. [3] proposed design standards for different types of NACA family airfoils for wind turbine blades and performed airfoil performance analysis using different possible values of the angle of attack. To achieve a high lift-drag ratio, it is necessary to enhance the lift of the airfoil, and the airfoil profile is the most importantfactor affecting the lift. Therefore, optimizing the airfoil profile is necessary to improve its lift-drag ratio. The Kutta-Joukowski (KJ) lift theorem is the most important theory of airfoil lift [4]. [PERSON] et al. [5] used [PERSON]'s theorem to calculate the lift in order to study the specific application of aerodynamics. [PERSON] et al. [6] estimated the quasi-steady lift at mid-downstroke based on the velocity field by applying the theorem. Meanwhile, [PERSON], [PERSON], and [PERSON] [7] proposed a Wake-Sectional Kutta-Joukowski (WS-KJ) model and predicted the time-averaged lift by considering the spatial evolutionary effects of the complex vortex structures in the wake. This has significantly improved the prediction accuracy of the time-averaged lift. In another instance, [PERSON], [PERSON], and [PERSON] [8] combined the forward stroke motion of the wing with the rapid pitching motion and used the Kutta-Joukowski theorem to build the mathematical model of rotational force mechanisms. [PERSON] et al. [9] established the hydraulic unbalance force model of the hydro-generator blades based on the KJ theorem. From these experiments, it can be seen that the KJ theorem has been widely applied in the calculation of airfoil lift and has a good application background. In terms of the selection of airfoil optimization tools, the Genetic Algorithm (GA) [10; 11; 12] and Particle Swarm Optimization Algorithm (PSOA) [13; 14] were used by many scholars. However, the classical swarm intelligence algorithms represented by the GA and PSOA still have certain deficiencies in optimization performance, which can lead to poor airfoil optimization results. [PERSON] [10] used the GA to optimize the airfoil shape considering a balance between the aerodynamic and structural performance of airfoils, but it was found it converged, in the region of interest, after 30 generations. [PERSON] et al. [11] optimized the lower and upper bound of airfoil profile values through GA MATLAB code, and the results showed that the optimized effect of airfoil profile (NREL S-821) by the GA was not obvious compared with the original airfoil shape. In order to obtain the optimal lift and drag coefficients, [PERSON] et al. [12] applied GA to optimize airfoil parameters, but the algorithm converged only after 15 generations; it can be seen that the premature convergence of GA has a limited effect on the improvement of airfoil performance.