## 1 Introduction  
Wind energy, as a clean and renewable energy, has attracted more and more attention from all over the world. Wind turbines that can transfer wind energy into electricity production have been developing rapidly in the world in recent years. The blades, as one of the key components of wind turbines, cost about 20% of the whole machine. Their good design, reliable quality, and superior performance are the decisive factors to improve the utilization rate of wind energy and ensure stable operation of wind turbines. The key factors for the design of wind turbine blades are the aerodynamic performance and the structural properties of wind turbine airfoils. At present, the design of airfoil profiles with medium thickness, in which the maximum relative thickness is between 25% and 35%, has been the focus of aerodynamic performance of wind turbine blades. [PERSON] and [PERSON] [1; 2] designed 35 kinds of airfoils named the NREL-S (National Renewable Energy Laboratory Special) airfoil series for various wind turbines using Eppler theory and inverse design method. The new airfoil families exhibit high maximum lift coefficients. DU airfoil families with a relative thickness of 15% to 40% were designed using mixed inverse design method [3; 4]. Airfoils with good aerodynamic performance can be designed by changing the upper-surface thickness and the S-shape lower surface. The result showed that the lift coefficient was improved and relatively insensitive to roughness. Compared with other airfoils, the DU (Delft University) airfoil families exhibited better aerodynamic performance. From the middle of 1990's, RISO airfoils were designed by RISO National Laboratory in Denmark [5]. In their work a direct design method for wind turbine airfoils based on mathematic optimization and the XFOIL software was presented. [PERSON] [6] presented a method named PARSEC (Pseudopotential Algorithm for Real-Space Electronic Calculations) to design airfoils; a modern airfoil was designed by controlling the airfoil geometry parameters. [PERSON] [7] presented an improved PARSEC method to design airfoils, and a brand-new airfoil was optimized. [PERSON] and [PERSON] [8] presented a new method for airfoil shape parameterization to optimize the airfoil at high Reynolds number turbulent flow conditions using a genetic algorithm. It was concluded that this method is capable of finding efficient and optimum airfoils in fewer generations. [PERSON] and [PERSON] [9,10] presented a general integral expression of airfoils based on a generalized functional and Trajkovski conformal transformation. CQU-DTU (Chongqing University) and WT (Wind Turbine) series airfoils have been designed successively using a multi-disciplinary optimal method. The aerodynamic performance of the airfoil series has been verified by wind tunnel experiments. [PERSON] and [PERSON] [11] studied performance improvement of airfoils for wind turbine blades with groove. It was confirmed that the shape of the groove contributed to recovering velocity around the airfoil wall, and the lift to drag the ratio improvement by the groove was maintained at the given range of Reynolds number. [PERSON] and [PERSON] [12] used this method combined with airfoil self-noise theory, as such CQU-DTU-LN1 airfoils were designed which exhibited low noise emissions. The noise characteristics of the airfoils were verified by wind tunnel experiments. [PERSON] and [PERSON] [13] presented an integrated optimal method of airfoil and blade for large wind turbines. The results indicated that the airfoils achieved a high power coefficient and were insensitive to surface roughness. [PERSON] [14] presented a multi-objective genetic algorithm with objective functions of minimum energy waste and maximum efficiency. The results show that using the second law approach along with the Pareto optimality concept leads to a set of precise solutions. [PERSON] [15,16] put forward a mathematical model of the overall optimization employing airfoil performance evaluation indicators.