1 Introduction

The aerodynamic design of wind turbine blades is one of the core technologies for the design of wind turbine power generator system (WTGS) , since the aerodynamic performance of the blades can dramatically affect the wind-energy capture, the load characteristics, and the noise level of the wind turbine. The sectional profiles, called airfoils, play a crucial role on determining the shape of the blades, and in turn strongly affect the performance of the wind turbine. Hence, the design and verification of wind turbine dedicated airfoils are of great significance for improving the capability of the wind-energy capturing and reducing the structural weight as well as the system loads.

Since the late of 1980s and the beginning of 1990s, the United States and Europe have been researching the design and verification of advanced airfoil families dedicated for wind turbines, such as the S series^{[ 1- 2]}, the DU series^{[ 3- 5]}, the Risø series^{[ 6- 8]}, the FFA series^{[ 9- 10]}, and the FX 77-W series^{[ 11]}. Significant contributions have been made by Tangler and Sommers^{[ 1- 2]} from American National Renewable Energy Laboratory (NREL) , Timmer and van Rooij^{[ 3- 4]} and van Rooij and Timmer^{[ 5]} from Delft University of Technology (TU Delft) of the Netherlands, Fuglsang and Bak^{[ 6- 7]}, and Fuglsang et al. ^{[ 8]} together with their colleagues from Risø National Laboratory of Denmark, and Björk^{[ 9- 10]} from Flygtekniska Forsoksanstalten Aeronautical Research Institute of Sweden (FFA) . Their pioneer works about the design and wind-tunnel experiments for wind turbine dedicated airfoils greatly inspire the research and development in this field^{[ 12- 21]}. In China, an airfoil family, called the NPU-WA series^{[ 12- 14]}, has been developed since 2005 by Northwestern Polytechnical University (NPU) of China for megawatt-size (MW-size) wind turbines. It has been verified by intensive wind-tunnel experiments that the NPU-WA series features excellent high lift-to-drag ratio at high lift coefficient and high Reynolds number conditions while keeping a low level of sensitivity to the leading-edge roughness. The CAS-W airfoils^{[ 15- 16]} have been developed in the Institute of Engineering Thermophysics (IET) of Chinese Academy Science (CAS) for the wind turbine blades working at moderate lift coefficient and moderate Reynolds number conditions. The NPU-WA and CAS-W series are Chinese earliest airfoil families for large-size wind turbines.

The remainder of this article is organized as follows. In Section 2, an overview of wind-wide wind turbine airfoil families developed since 1990s is firstly presented. The research activities and progresses on the development of the NPU-WA series for MW-size wind turbines are summarized in Section 3, including the design process and wing-tunnel tests. The further improvement of the NPU-WA series towards lower sensitivity of the maximum lift coefficient to the leading-edge roughness is reviewed in Section 4. The outlook on developing the new NPU-MWA series dedicated for multi-megawatt size wind turbines is presented in Section 5. The last section gives five conclusions.

2 State of art for wind turbine airfoil families

Before 1990s, when wind turbine blades were designed, it was a common practice to use existing aviation airfoils^{[ 3]}, e. g. , the four-digit NACA 44xx and NACA 63$_{x}xxx$ series^{[ 22]}. Aviation airfoils are usually thin airfoils. To obtain thick airfoils, which are needed at the middle and root parts of wind turbine blades, linear scaling is usually made on the basis of the coordinates of thin airfoils. However, the aerodynamic performance of the scaled NACA airfoils is severely degraded due to the premeasured transition^{[ 4]}. It has been recognized by the community that the utilization of traditional aviation airfoils cannot meet the design requirements of higher power coefficients and lower loads for large-size wind turbine blades. Besides, it has proven that aviation airfoils cannot satisfy the operating needs under extreme environments.

Since 1990s, increasing efforts have been devoted in the United States and Europe in developing the new airfoils dedicated for wind turbines. As a result, various wind turbine airfoil families have been developed by different institutes, each of which usually includes a series of airfoils with varying relative thickness so as to cover the entire span of the wind turbine blade and to keep good geometric compatibility.

2. 1 S series

The NREL started the research on wind turbine dedicated airfoils in 1984^{[ 1]} under the financial support from the United States Department of Energy. Up to 1990s, nine families of wind turbine airfoils have been developed for various types of wind turbines^{[ 2]}. These wind turbine airfoils can be classified by the size of the target wind turbine blades and their regulation types, e. g. , stall-regulated wind turbines and variable-speed and pitch-control wind turbines. The airfoils of the S series are named as S 8xx, where "xx" denotes the corresponding sequence number. The airfoils S 819, S 820, and S 821 form a family of airfoils suited for the stall-regulated wind turbines with the medium blade diameter ranging from 10 m to 20 m and the power ranging from 20 kW to 150 kW. The S 819, with a relative thickness of 21% chord, is the main airfoil to be used at around 75% span of the blades. The S 820 airfoil, with a relative thickness of 16% chord, is to be used at the about 95% span of the blades. The S 821 airfoil, with a relative thickness of 24% chord, is to be used at the around 40% span of the blades. It has been proven that the utilization of the new airfoils can dramatically increase the power output of wind turbines, especially for the stall-regulated wind turbines. As a result, the annual power production can be increased from 10% to 35%. Note that the airfoils S 819, S 820, and S 821, which are designed for small size general wind turbines, feature low design lift coefficient (${{C}_{\text{l}}}$) and low maximum lift coefficient ($C_{{\rm l}, \max}$) . In 2005, the new airfoils called S 831 and S 830^{[ 23]} with relative thickness of 18% and 21%, respectively, were developed in the NREL to meet the requirements of larger-size wind turbine blades. The NREL reported that the maximum lift coefficients of the new airfoils predicted with the calculational fluid dynamics (CFD) method were as large as 1. 5 and 1. 6, respectively, while both the design lift coefficients are 1. 2. Figures 1 and 2 show the schematics of the NREL thick airfoils dedicated for mid-size wind turbine blades and the NREL high-lift airfoils dedicated for large-size wind turbine blades, respectively.

2. 2 DU series

Mainly funded by the European JOULE program and the Netherlands Agency for Energy and the Environment (NOVEM) , Delft University of Technology developed the DU airfoils^{[ 3]}. The general designation of the DU airfoils is DU yy-W (n) -xxx, where "DU" stands for Delft University of Technology, "$yy$" indicates the year in which the airfoil is designed, "W" denotes the wind-energy application, "n" denotes thenth design, and "$xxx$" gives 10 times the airfoil maximum thickness in percentage of the chord. For example, the DU 91-W2-250 airfoil and the DU 93-W-210 airfoil are two typical airfoils with the relative thickness of 25% chord and 21% chord and were designed in 1991 and 1993, respectively. In the case of the DU 91-W2-250 airfoil, the additional number "2" follows the means of "W" that there are more than one design for the airfoil with the relative thickness of 25% chord in 1991. Both the DU 91-W2-250 airfoil and the DU 93-W-210 airfoil have been extensively tested in low-speed and low-turbulence wind-tunnel s by the Faculty of Aerospace Engineering of Delft University of Technology, with the Reynolds number ranging from 1. 6×10⁶ to 3. 0×10⁶. With growing knowledge of mechanism behind the wind turbine blade noise and the effect of rotation^{[ 4]}, the DU wind turbine airfoil family is further enriched by the airfoils with relative thickness ranging from 15% chord to 40% chord, including 18% chord (DU-W-180, DU 96-W-180) , 30% chord (DU 97-W-300) , 35% chord (DU 00-W-350) , and 40% chord (DU 00-W-401) thick airfoils. The design principles of these airfoils are quite different. For the outboard airfoils to be deployed at the tip part of the blades, a high lift-to-drag ratio is always pursued, while the stall performance is expected to be moderate, and the roughness sensitivity as well as the noise should be as low as possible^{[ 5]}. For the inboard airfoils to be deployed at the root part of the blades, more considerations are given to the structural requirements and geometric compatibility at some expense of declined aerodynamic performance. Compared with traditional aviation airfoils, the DU airfoils have smaller upper-surface thickness (to reduce the roughness sensitivity) and larger aft loading. So far, the DU airfoils have been successfully applied to over 10 different types of wind turbines with the blade diameter ranging from 29 m to 100 m, corresponding to the maximum power from 350 kW to 3. 5 MW. Figure 3 shows the schematics of the shapes of the DU airfoil family.

2. 3 Risø series

In the late 1990s, the Risø National Laboratory in Denmark developed the Risø-A1 airfoil family^{[ 6]}, including three airfoils, i. e. , Risø-A1-18, Risø-A1-21, and Risø-A1-24. These airfoils are designed with the advanced tool based on the CFD method, and have been tested in the VELUX wind-tunnel at the Reynolds number 1. 6×10⁶. This Risø airfoil family is mainly applied to the wind turbines with 600 kW or higher power production. The field testing reveals that the Risø-A1 airfoils are well suited for both passive and active stall-regulated wind turbines, yet the roughness sensitivity is slightly higher than expected. For a 600 kW wind turbine with active stall regulation, the fatigue load could be decreased by 15% for the same amount of power production. Meanwhile, the weight and solidity of the wind turbine blades can be reduced. In addition to the Risø-A1 family, Risø-P and Risø-B1 airfoils^{[ 7- 8]} were developed in the same lab. The Risø-P airfoils are dedicated for pitch-regulated wind turbines with the particular consideration of lower roughness sensitivity, while the Risø-B1 airfoils^{[ 7]} are suited for MW-size wind turbines with variable speed and pitch control. The Risø-B1 airfoil family features the relative thickness ranging from 15% to 53% chord, covering the entire span of a wind turbine blade. Seven airfoils with high ${{C}_{\text{l}, \max }}$ were designed so as to allow a slender flexible blade maintaining high aerodynamic efficiency. The wind-tunnel tests for both the Risø-P airfoils and the Risø-B1 airfoils have been carried out in the VELUX wind-tunnel at the Reynolds number 1. 6×10⁶. It is shown that the maximum lift coefficient of the Risø-B1-18 airfoil is as large as 1. 64 and $C_{{\rm l}, \max }$ is reduced by only 3. 7% when the transition is forced near the leading edge by the roughness introduced by a standard zigzag tape. More severe roughness can result in the reduction of $C_{{\rm l}, \max}$ ranging from 12% to 27%. The wind-tunnel tests also show that, for the Risø-B1-24 airfoil, $C_{{\rm l}, \max }$ is 1. 62 for the clean airfoil and decreases by 7. 4% for the standard case of leading edge roughness. When combined with both the vortex generator and the GUIRNEY flap, $C_{{\rm l}, \max }$ of the Risø-B1-24 airfoil can be increased up to 2. 2 (32%) . Through the comparative study, it is found that the Risø-B1 airfoils feature lower roughness sensitivity. The schematics of the geometric shape of the partial Risø airfoils are shown in Fig. 4 and Fig. 5.

2. 4 FFA series

In 1990s, FFA developed the FFA-W3-211 airfoil and two thicker airfoils FFA-W3-241 and FFA-W3-301^{[ 10]}. According to their naming rule, "FFA" stands for the Aeronautical Research Institute of Sweden, "W" denotes the wind-energy application, the last three digits give 10 times the airfoil maximum thickness in the percentage of chord. Wind-tunnel experiments have been conducted in the L2000 wind-tunnel and the VELUX wind-tunnel, respectively. The results showed that the FFA airfoils, compared with the NACA series, featured larger relative thickness and better high-lift characteristics. Figure 6 shows the schematics of the geometric shapes of the FFA airfoil family.

In addition to the aforementioned airfoil families, there are other developments about wind turbine airfoils, such as the FX 77-W airfoils^{[ 11]} developed by Germany, the CQU-DTU airfoils^{[ 17]} developed by Chongqing University of China and Technical University of Demark, the ECN airfoils^{[ 18- 20]} developed by the Energy Centre of the Netherlands, and the Alstom airfoils^{[ 21]} developed by Spain. The detailed description and discussion about these airfoils are beyond the scope of this article.

3 Design and verification of NPU-WA series 3. 1 Design philosophy and objectives

Funded by the National High Technology Research and Development Program of China (863 Program) since 2007, NPU has made continuous efforts on the design of airfoils dedicated for MW-size wind turbines, which is called NPU-WA airfoils. Since the power production of a wind turbine is proportional to the square of the blade radiusR, in recent years, there has been a trend to continuously increase the size of wind turbines so as to capture more wind-energy. Larger size of wind turbine blades means higher Reynolds number, more structural weight, larger cost (proportional to R^2.4) , larger gust loads, and more limits due to vibration and fatigue. Therefore, the main design objectives of large-size wind turbine blades are to promote the capability of wind-energy capturing^{[ 24]} so as to reduce the blade weight, to cut down the costs of manufacturing and transportation, and to decrease the inertial loads, gust loads, and the corresponding system loads. Due to the fact that the main sections of large-size wind turbine blades are operating at very high Reynolds number, high aerodynamic efficiency at high Reynolds number is pursued for the design of the airfoils dedicated for large-size wind turbines. Furthermore, the airfoils dedicated for large-size wind turbines should have high design lift coefficient, which is beneficial to reduce the solidity (or blade chord) and blade planar area so as to reduce the structural weight, the cost due to manufacturing and transportation, the gust loads, and the inertial loads. Moreover, a high design lift coefficient is helpful in increasing the capability of the wind-energy capture when the wind speed is lower than the annual average speed, resulting in an increase in the annual power production.

The main design philosophy of the NPU-WA airfoil series can be summarized as follows. For variable-speed and pitch-control wind turbines, a family of airfoils is designed to promote the capability of the wind-energy capture and to reduce the blade structural weight and loads. The airfoils are expected to have two important characteristics at high Reynolds number and high lift coefficient conditions. The first condition is that the outboard airfoils should have high lift-to-drag ratio, high maximum lift coefficient $C_{{\rm l}, \max}$, gentle stall, and low sensitivity of $C_{{\rm l}, \max}$ to the leading edge roughness. The second condition is that, for inboard airfoils, high $C_{{\rm l}, \max}$, good structural performance, and geometric compatibility are emphasized.

Based on the philosophy stated above, Prof. QIAO et al. proposed the following design objectives for the NPU-WA airfoils:

(I) For the main airfoils to be used at around 75% span of the blades, the design lift coefficient $C_{\rm l}$ is 1. 2 at the angle of attack around 6°. It is required that the design lift coefficients of the main and outboard airfoils are either equal to or higher than 1. 2.

(ii) For the main and outboard airfoils, the design Reynolds number is 6×10⁶. Under high Reynolds number and high lift coefficient conditions, the NPU-WA airfoils should have a higher lift-to-drag ratio than the existing airfoils. At the off-design Reynolds numbers lower than 1. 5×10⁶, the NPU-WA airfoils should maintain a comparable lift-to-drag ratio in contrast to the existing airfoils.

(iii) The maximum lift coefficient $C_{{\rm l}, \max}$ of the NPU-WA airfoils is higher than that of the existing airfoils. When the angle of attack increases, separation may occur firstly from the trailing edge, and the stall will become gentle and progressive.

(iv) The moment coefficients of the main and outboard airfoils are at the same level with that of the NACA airfoils. Meanwhile, the moment coefficients of the inboard airfoils regarding with the aerodynamic center are no less than $-0. 15. $

(v) Under full turbulent flow conditions, i. e. , rough configurations, the lift-to-drag ratios of the NUP-WA airfoils are higher than those of the other high-lift wind turbine airfoils with the same relative thickness. Besides, the maximum lift coefficients of the NPU-WA airfoils are insensitive to the leading edge roughness. The roughness sensitivity should be less than 15% and 25% for the outboard airfoil and the inboard airfoil, respectively.

(vi) The relative thickness of the NPU-WA airfoil series are set as 15% chord, 18% chord, 21% chord, 25% chord, 30% chord, 35% chord, and 40% chord, respectively. Considering the manufacturing, the location of the maximum thickness for all airfoils is around at the 30% chord-wise location, and a small thickness is prescribed for the trailing edge. Table 1 gives the various trailing edge thicknesses for the NPU-WA airfoils when we take the chord length as 100.

3. 2 Design methodology

The design of the NPU-WA series is completed through the use of various design and calculation methods. The detailed information can be found in the corresponding references. Here, only some brief introduction is given.

(I) Inverse design

Three optional inverse design methods are available. The first one is to design an airfoil inversely by matching the given target pressure distribution at a relatively small angle of attack (or a relatively small design lift coefficient) . The second method is based on the subsonic potential equations with mixed boundary conditions^{[ 25]}, and aims to reach a hybrid target, which specifies the pressure distribution on the part of the surface and optimizes the geometric shape of the rest surface. The third one is based on the Navier-Stokes equations. It tries to match the desired pressure distribution at a high angle of attack (or a high lift coefficient) so that the resulting airfoils fit for various angles of attack and Reynolds numbers.

(II) Airfoil design via numerical optimization

The numerical optimization technique, which is capable of dealing with multi-objective multi-constraint problems, is coupled with the CFD solvers with varying fidelity, such as the Navier-Stokes equations^{[ 26- 28]} and the linearized potential equations coupled with the boundary-layer equation solution^{[ 25]}. The objective is to maximize the lift-to-drag ratio at high lift coefficient and high Reynolds number, whereas the constraints are set about the off-design conditions (moderate lift coefficient, low Reynolds number, etc. ) , the moment coefficient, and the thickness (including the maximum thickness location) .

(III) Direct modification of airfoil

This is a "cut-and-try" method with the man-machine interaction between the designer and the computer. The designer makes direct modifications to the airfoil shape on the computer screen, then performs the calculation for the resulting airfoil, and checks if these modifications can give the desired effects^{[ 29]}. This process is repeated until satisfied airfoils are obtained. Since the optimization techniques can hardly make very large modification to the airfoil shape, the direct airfoil modification with the man-machine interaction is necessary as a complementary tool to the numerical optimization process. Meanwhile, the direct airfoil modification is also a tool to make proper changes to the airfoil in order to meet the requirements under the off-design conditions.

(IV) Posterior evaluation

This step is intended to evaluate the performance of the airfoils designed with the above methods under both the design and off-design conditions. The XFOIL software^{[ 30]} is mostly used at small angle of attack or low lift coefficient conditions, while at high angle of attack or high lift coefficient conditions, an in-house flow solver^{[ 31]} based on the Reynolds-average Navier-Stokes equations is utilized.

Figure 7 gives the comparison of typical pressure distributions at the design state between the NPU-WA-210 airfoil and other wind turbine airfoils of the same relative thickness.

3. 3 Designation and geometric shape of NPU-WA series

According to the design requirements stated above, seven airfoils with the relative thickness of 15% chord, 18% chord, 21% chord, 25% chord, 30% chord, 35% chord, and 40% chord have been designed by Prof. QIAO et al. to form the NPU-WA wind turbine airfoil family. The designation follows the general format of the NPW-WA-$xxx$ airfoils, where "NPU" stands for NPU, "WA" denotes the wind turbine application, and "$xxx$" gives 10 times of the airfoil maximum relative thickness in percentage of the chord. Following this rule, the NPU-WA airfoils were named as NPU-WA-150, NPU-WA-180, NPU-WA-210, NPU-WA-250, NPU-WA-300, NUP-WA350, and NPU-WA-400, respectively.

Figure 8 shows the geometric shapes of the NPU-WA airfoils.

3.4 Wind-tunnel experiment

In 2009 and 2010, wind-tunnel experiments (see Fig. 9) for the NPU-WA airfoils were carried out in the NF-3 wind-tunnel , which is located in the old campus of NPU and has a 2D test section of 1. 6 m×0. 8 m. The experiments were conducted under both free and fixed transition conditions at the Reynolds number ranging from 1×10⁶ to 5×10⁶ and the angle of attack ranging from -10° to +20°. The results of the surface pressure distributions and wake measurements were collected for around 2 000 conditions, and put into a database of wind turbine airfoils. Compared with the experimental results available in the literatures at the Reynolds number ranging from 1×10⁶$ to 3×10⁶, more experimental results of the NPU-WA airfoils were given at higher Reynolds number so as to enrich the data. Please note that only parts of the experimental results are presented in this section due to the consideration of the article length limit.

3. 4. 1 High-lift characteristics

Figure 10 shows the high-lift characteristics of the NPU-WA-180 airfoil and the NPU-WA-210 airfoil, which represent the outboard airfoil and the main airfoil, respectively. In Fig. 10, $C_{\rm l}$ is the lift coefficient, $\alpha$ is the angle of attack, and $C_{\rm d}$ is the drag coefficient. It can be seen that the design lift coefficients are over 1. 2, and the lift coefficient corresponding to the maximum lift-to-drag ratio is very close to the value of $C_{{\rm l}, \max }$, which is one of the important characteristics for the NPU-WA airfoils. Furthermore, it is shown that the NPU-WA airfoils feature higher lift-to-drag ratios under high-lift conditions, comparing with the existing NACA airfoils and DU airfoils of the same relative thickness. Note that the experimental data of the DU 93-W-210 airfoil is updated by the latest experiments conducted in the NF-3 wind-tunnel in 2013.

3. 4. 2 Performance at high Reynolds number

Limited by the wind-tunnel facility, the highest Reynolds number in the experiments is 5 million for a test model with a chord length of 800 mm, which means that no experimental verification has been done yet for the NUP-WA airfoils at a design Reynolds number of 6 million. However, compared with similar experiments for other wind turbine airfoils (the Reynolds number is usually below 3 million) , the NPU-WA airfoils would be the airfoil family that has been intensively tested in the wind-tunnel at the Reynolds number up to 5 million. Through the wind-tunnel experiments, the performance of the NPU-WA airfoils at high Reynolds number is verified. Figure 11 gives the comparisons of the lift-to-drag ratio versus the Reynolds number between the NPU-WA-210 airfoil and the DU 93-W-210 airfoil at both free and fixed transition conditions. It can be observed that, the aerodynamic performance of the NPU-WA-210 airfoil changes slowly when the Reynolds number increases, and a high lift-to-drag ratio can be well maintained until at a Reynolds number up to 5 million.

3. 4. 3 Sensitivity of $C_{{\rm l}, \max}$ to leading-edge roughness

With the experimental results, the roughness sensitivities of the NPU-WA airfoils are obtained. The sensitivity of $C_{{\rm l}, \max}$ to the leading-edge roughness is defined by

where subscripts "free" and "fixed" denote the free and fixed transitions, respectively. Generally, both high design lift coefficient and large relative thickness would make the airfoils more sensitive to the leading-edge roughness. For the outboard airfoils (NPU-WA-150 and NPU-WA-180) , the sensitivities of ${{C}_{\text{l}, \max }}$ to the leading edge roughness are all below 10% over the whole Reynolds number range. The roughness sensitivity is in the range from 4. 9% to 7. 6% for the NPU-WA-150 airfoil and from 5. 2% to 9. 5% for the NPU-WA-180 airfoil, indicating that both the airfoils are insensitivity to the leading-edge roughness. The main airfoil (NPU-WA-210) has the roughness sensitivity of 9. 7% at the high Reynolds number 5. 0×10⁶ and 12. 3% at the moderate Reynolds number 3. 0×10⁶ (see Fig. 12) . The roughness sensitivities of the inboard airfoils are generally unimportant. Therefore, higher roughness sensitivities are allowed, but no more than 25%.

3. 4. 4 Aerodynamic performance of thick airfoils

Due to the lack of published wind-tunnel experimental results for thick wind turbine airfoils, the experimental results of an inboard airfoil NPU-WA-300 are presented in Fig. 13, without any comparison with other airfoils.

4 Design and verification of improved NPU-WA series

The wind-tunnel results have confirmed that the NPU-WA airfoils achieved the main design goals, i. e. , high lift-to-drag ratio at high Reynolds number and high lift conditions and insensitivity to the leading edge roughness for the outboard airfoils. However, after a comprehensive analysis of the wind-tunnel experimental results, Prof. QIAO pointed out that: (i) the NPU-WA-210 airfoil features relatively higher roughness sensitivity at moderate and low Reynolds number; (ii) the laminar-turbulent transition observed in the experiments at high $C_{\rm l}$ and high Reynolds number occurrs earlier than the theoretical prediction, resulting in lower lift-to-drag ratio at high $ C_{\rm l}$ and higher Reynolds number than the design targets. Hence, to fulfill the industrial requirements, further improvements and corresponding wind-tunnel tests are needed.

4. 1 Design objectives and methods

According to the recommendations from Prof. QIAO, considering the airfoil of 25% relative thickness would become the main airfoil of MW-size wind turbine blades with a diameter of around 100 m, the authors of this article raised the following design objective for improving the NPU-WA-210 and NPU-WA-250 airfoils:

(i) The design lift coefficient ranges from 1. 1 to 1. 2, the design angle of attack is between 5° and 6°, and the design Reynolds number ranges from 5 million to 6 million.

(ii) At high Reynolds number and high $C_{\rm l}$ conditions, the lift-to-drag ratio of the improved 21% thick airfoil should be comparable to that of the NPU-WA-210 airfoil and higher than that of the DU 93-W-210 airfoil.

(iii) Similarly, at high Reynolds number and high $C_{\rm l}$ conditions, the lift-to-drag ratio of the improved 25% thick airfoil should be higher than those of the NPU-WA-250 airfoil and the DU 91-W2-250 airfoil.

(iv) The improved airfoils should have a high maximum lift coefficient and a gentle stall.

(v) With the transition fixed at 5% from the leading edge, the improved airfoils with 21% and 25% relative thickness should have higher lift-to-drag ratios than the previous designs.

(vi) At moderate and low Reynolds numbers (around 3 million and 1 million, respectively) , the sensitivity of the maximum lift coefficient to the leading-edge roughness for the improved airfoils should be significantly lower than the previous designs and close to the low level of the DU airfoils.

(vii) The moment coefficients of the improved airfoils should be comparable to those of the previous designs and no less than $-0. 14$.

For improving the NPU-WA airfoils, some newly developed design tools and methods are used. The design tools employ the aerodynamic shape optimization technology, which integrates the CFD codes within the framework of a surrogate-based optimization. The aerodynamic characteristics of the candidate airfoils at small angles of attack (or low $C_{\rm l}) $ are evaluated by the MSES software developed by Prof. DRELA, while at large angles of attack (or high $C_{\rm l}) $, the aerodynamic performance are calculated by the PMNS2D, an in-house RANS solver with the functionality of the automatic transition prediction based on the linear-stability analysis and e$. {N}$ method. The latest version of an in-house optimization code SurroOpt^{[ 32]} is utilized to drive the design process towards the optimum airfoils. The "SurroOpt"^{[ 32- 37]} is a code for solving generic multi-objective and multi-constraint optimization problems. Firstly, the design of experimental method, e. g. , the Latin hypercube sampling (LHS) and the uniform design (UD) , is used to generate the initial sample shapes, whose aerodynamic response is evaluated by the CFD code. Then, the surrogate models^{[ 37- 40]} for the objective and constraint functions are built on the sampled data through the quadratic response surface model (RMS) , the Kriging model, or the radial basis functions (RBFs) . New sample points are generated by the sub-optimization defined by the infilling-sampling criteria. The sub-optimization is solved by a hybrid strategy combing the conventional optimization algorithms, e. g. , the genetic algorithm (GA) , the Broyden-Fletcher-Goldfarb-Shanno (BFGS) quasi-Newton method, the sequential quadratic programming (SQP) , and the Hooke & Jeevs pattern search method. Since the function evaluation of the sub-optimization is based on the surrogate models, the computational cost is usually neglectable, compared with the cost of the expensive CFD analysis. The new sample points are evaluated by the CFD analysis again, and then the surrogate models are updated. This process is repeated until the termination criterion is satisfied. It has been proven by practice that, the SurroOpt code is capable of finding the global optimum, and the optimization efficiency is much higher than the evolutionary method such as the genetic algorithm. The flowchart of the SurroOpt code is sketched in Fig. 14.

4. 2 Experimental verification of improved airfoils

At the end of 2012, the wind-tunnel experiments for improved NPU-WA airfoils were carried out in the NF-3 wind-tunnel of NPU. In order to make a comparative study to verify the improvement, the experiments for the original NPU-WA airfoils and DU airfoils with the same relative thickness are conducted. The experimental Reynolds number ranges from 1. 0×10⁶ to 5. 0×10⁶. Please note that only parts of the experimental results are presented in this section due to the consideration of the length limit of the article.

4. 2. 1 Experimental verification of improved NPU-WA-210 airfoil

Figure 15 shows the lift and drag curves of the lift coefficient $C_{\rm l}$ versus the angle of attack $\alpha$ and the lift coefficient $C_{\rm l}$ versus the lift-to-drag ratio $C_{\rm l}/C_{\rm d}$ of the improved NPU-WA-210 airfoil (represented by NPU-WA-210{\_}new) . The experimental results of the original NPU-WA-210 airfoil and the DU-93-W1-210 airfoil at the same conditions are also presented. From the figure, we can see that, at the Reynolds number 3 million, the improved NPU-WA-210 airfoil experiences a slight decrease with the increases in $C_{l, \max }$ and the lift-to-drag ratio when the design lift coefficient is 1. 2. The results are better than the DU airfoil.

Figure 16 presents the sensitivity of $C_{{\rm l}, \max}$ to the leading edge roughness for different Reynolds numbers. Obviously, the sensitivity of $C_{{\rm l}, \max}$ to the leading edge roughness is dramatically reduced at moderate and low Reynolds numbers, while at high Reynolds number, it is at the same level of the DU airfoil. In brief, the performance of the improved NPU-WA-210 airfoil is verified by the wind-tunnel experiments. The sensitivity of $C_{{\rm l}, \max}$ to the leading edge roughness is considerably reduced, while the characteristics of $C_{{\rm l}, \max}$ and $C_{\rm l}/C_{\rm d}$ are well maintained, well matching the design goals and indicating that the improved design is successful.

4. 2. 2 Experimental verification of improved NUP-WA-250 airfoil

Figure 17 shows the lift and drag characteristics of the improved NPU-WA-250 airfoil (denoted by NPU-WA-250_new) . The experimental results of the original NPU-WA-250 airfoil and the DU airfoil under the same conditions are also included. From the figure, we can see that, at the Reynolds number 3 million, the improved NPU-WA-250 airfoil increases with the increases in both $C_{l, \max }$ and the lift-to-drag ratio when the design lift coefficient is 1. 2, comparing with the original NPU-WA-250 airfoil. The improvement even makes it have better lift and drag characteristics than the DU airfoil.

Figure 18 presents the sensitivity of the maximum lift to the leading edge roughness for the Reynolds number ranging from 1. 0×10⁶ to 5. 0×10⁶. It is shown that, the roughness sensitivity is remarkably reduced at moderate and low Reynolds numbers, and is more close to the level of the DU airfoil, while at high Reynolds number, it remains the same level with the original design. In brief, the characteristics of $C_{{\rm l}, \max}$ and the lift-to-drag ratio are improved while the sensitivity of $C_{{\rm l}, \max}$ to the leading edge roughness decreases at moderate and low Reynolds numbers, indicating that the improved design for the NPU-WA-250 airfoil is successful.

5 Outlook of multi-megawatt-size wind turbine airfoils

In recent years, the technology of applying the wind turbine dedicated airfoil family to MW-size wind turbines ([1. 0 MW, 3. 0 MW]) have matured. Much attention has been paid on the development of the new airfoil families dedicated to larger wind turbines, which are called multi-megawatt (MMW) -size wind turbines ([3 MW, 10 MW]) , especially for the offshore wind-energy applications. In Germany and Belgium, the 6 MW and 7 MW wind turbines designed by Enercon have been operated successfully. Meanwhile, the 6 MW wind turbines from Vestas have been installed. Besides, the design processes of the 10 MW wind turbines in Vestas, the 7 MW wind turbines in Germany and Belgium, and the 6 MW wind turbines in the DOWEC are ongoing. The rapid development of MMW-size wind turbines inspires the research and design of new airfoil families.

According to the operating conditions of MMW-size wind turbines, new challenges arise for the design and verification of new airfoil families. The airfoils dedicated for MMW-size wind turbines are expected to have excellent aerodynamic performance at even higher design lift coefficient and higher Reynolds number, and have higher maximum lift coefficient than the airfoils dedicated for MW-size wind turbines. The operating Reynolds number of the main airfoil can easily reach at least 9 million, and the design lift coefficient can be larger than 1. 2. The breakthrough on the following key technologies are in demand:

(i) For outboard airfoils, high aerodynamic performance is required at higher Reynolds number (at least 9 million) and higher design lift coefficient (at least 1. 2) so that the blade solidity and chord length can be reduced as much as possible for the consideration of reducing the blade weight and gust loads;

(ii) For inboard airfoils, special tailored flat-back airfoils with very large trailing-edge thickness should be developed to promote the blade structural performance and at the same time to take into account of the high-lift aerodynamic characteristics at a price of increased drag;

(iii) Wind-tunnel tests are of great importance to verify the performance of MMW-size wind turbine airfoils at high Reynolds number ranging from 6. 0×10⁶ to 1. 0×10⁷. Moreover, special attention should be paid to the new technologies of the wind-tunnel experiments dedicated for very thick airfoils (the relative thickness ranges from 40% to 60%) , since the wall interference can be significantly larger than the experiments for thin airfoils.

The design and verification of the new NPU-WA airfoil family dedicated for MMW-size wind turbines are our ongoing work with the support of the National High Technology Research and Development Program of China (863 Program) . Eight airfoils with the thickness-to-chord ratio ranging from 15% to 60% will be designed to cover the entire span of an MMW-size wind turbine blade. It is expected that the new NPU-WA airfoil family will be verified by the wind-tunnel experiments at higher Reynolds number.

6 Conclusions

In this article, the development of the airfoil families dedicated for large-size wind turbines since 1990s is reviewed. The S series, DU series, Risø series, and FFA series are mainly concerned. Then, the design and verification of the NPU-WA airfoil series are presented, including design philosophy and methods, wind-tunnel experiments, and further improvement. The outlook of the developing new NPU-WA series for multi-megawatt-size wind turbines is given.

About the NPU-WA airfoils, some conclusions can be drawn as follows:

(i) The NPU-WA series has good performance at high Reynolds number (e. g. , 6 million) and high design lift coefficient (e. g. , 1. 2) . Therefore, it is well suited for the design of MW-size wind turbine blades;

(ii) The improvement of the NPU-WA airfoils has been conducted by the newly developed CFD and numerical optimization tools. It has been verified by the wind-tunnel experiments that the sensitivity of $C_{{\rm l}, \max}$ to the leading edge roughness is significantly reduced, while the lift and drag performances are either improved or only slightly degraded.

Acknowledgements This article is dedicated to Prof. Zhide QIAO, who is a senior professor of NPU, a famous aerodynamicist, a winner of the national model worker, and the founder of the National Key Laboratory of Science and Technology on Aerodynamic Design and Research. Prof. QIAO has devoted his life to the development of the NPU-WA airfoils during the period of the 11th Five-Year Plan, and has given numerous pivotal suggestions on the project of wind turbine airfoils during the period of the 12th Five-Year Plan. Here, we'd like to express our sincere respect and deep yearning to Prof. QIAO. The authors are also deeply grateful to Prof. Dexin HE, the chair of Chinese wind-energy Association, for his long-term support and guidance. In addition, this article has benefited greatly from the instructions and recommendations from Prof. Wenrui HU, an academician of Chinese Academy of Sciences. Thanks also go to all the colleagues in the research group of wind turbine airfoil design, e. g. , Jianhua XU, Lei YU, Jun LIU, Fangliang LIU, Yijian HUANG, Xiaochao XIAN, and Fan LI.