To enhance the aerodynamic performance of wind turbine blades, this study proposes the adoption of a bionic airfoil inspired by the aerodynamic shape of an eagle. Based on the blade element theory, a non-uniform extraction method of blade elements is employed for the optimization design of the considered wind turbine blades. Moreover, Computational Fluid Dynamics (CFD) is used to determine the aerodynamic performances of the eagle airfoil and a NACA2412 airfoil, thereby demonstrating the superior aerodynamic performance of the former. Finally, a mathematical model for optimizing the design of wind turbine blades is introduced and a comparative analysis is conducted with respect to the aerodynamic performances of blades designed using a uniform extraction approach. It is found that the blades designed using non-uniform extraction exhibit better aerodynamic performance.

Wind energy, as a green, pollution-free, and renewable energy source, has gradually become a focus of attention [

In the aspect of airfoil research, Rose et al. [

In-depth research has been conducted on the optimization design of wind turbine blades. However, these studies predominantly focus on either airfoil or blade design methods, with limited research on integrating both. This study applies a bionic airfoil design inspired by an eagle, implementing a non-uniform extraction method of blade elements based on the blade element theory for wind turbine blade optimization.

In nature, birds are the most adept at flying, with their wing shapes evolved through natural processes to achieve outstanding flight capabilities. The wings of the sparrowhawk are formed by a lateral arrangement of airfoil shapes. Through fluttering and clever utilization of aerodynamic principles, they generate upward lift and thrust to propel the body forward, resembling the operating conditions of wind turbines. This study employs a portable 3D scanner to scan the sparrowhawk airfoils and acquire a point cloud image. The resulting scan data is processed using image processing software called ImageWare, as illustrated in

Lastly, the final selected sparrowhawk airfoil section was derived, and the collection and fitting of coordinate points were carried out. Using Matlab software, the upper and lower airfoil profiles were fitted to obtain the coordinate equation of the airfoil. The resulting equation is presented below:

Upper wing type:

Lower wing type:

The airfoil is named QY-7305, where “QY” represents the initial capitalization of the Chinese name of the Sparrowhawk and “7305” indicates the cross section at −73.05 mm with the characteristic plane as the reference.

Mesh generation of the airfoil was conducted using the ICEM-CFD software, employing a structured grid. The computational domain was defined as a circular region with the leading edge of the airfoil as the center and a radius equal to 10 times the airfoil chord length. The first layer height of the mesh on the airfoil surface was set to 2.2 × 10^{−5}, with a boundary layer consisting of 10 layers. The wall mesh growth rate was set at 1.1. These conditions were maintained for mesh independent verification, ensuring that variations in cell size did not impact the accuracy of the computational results.

No. | Number of grids | Lift coefficient | Correlation error % |
---|---|---|---|

1 | 63942 | 1.5133 | 1.836 |

2 | 78635 | 1.5369 | 0.305 |

3 | 87985 | 1.5389 | 0.175 |

4 | 95960 | 1.5408 | 0.05 |

5 | 11658 | 1.5416 | 0 |

No. | Number of grids | Lift coefficient | Correlation error % |
---|---|---|---|

1 | 59689 | 0.7058 | 2.16 |

2 | 73659 | 0.7125 | 1.23 |

3 | 85460 | 0.7189 | 0.346 |

4 | 93567 | 0.7201 | 0.18 |

5 | 10563 | 0.7214 | 0 |

The total number of grids for the selected QY-7305 and NACA2412 airfoils in this study were 95960 and 93567, respectively. The mesh distribution of the QY-7305 airfoil is shown in

The study of the aerodynamic characteristics of wind turbine airfoils is essentially an investigation into the impact of turbulent flow on the aerodynamic properties of wind turbine airfoils. Turbulence is a complex and highly nonlinear flow, requiring a comprehensive understanding of numerical methods for turbulence computation to better simulate and predict various performance aspects of wind turbine airfoils. Considering the balance between computational accuracy and resource requirements, this paper adopts a method based on the Reynolds-Averaged Navier-Stokes approach. The flow velocity studied in this paper is lower than the Mach number of 0.3. Considering the influence of viscous forces, it is simulated as a steady-state incompressible flow.

Continuity equation:

Momentum equation:

Reynolds stress tensor equation:

In the equation,

The

The turbulent viscosity is calculated as follows:

In the equations,

Model constants | Value |
---|---|

α* | 1 |

α | 0.52 |

β* | 0.09 |

β_{i,1} |
0.075 |

β_{i,2} |
0.0828 |

σ_{k,1} |
1.176 |

σ_{k,2} |
1 |

σ_{ω,1} |
2 |

σ_{ω,2} |
1.168 |

The airfoil surface is set as a no-slip wall boundary, and the boundary conditions for the domain are chosen using a pressure far-field approach. The incoming flow velocity is adjusted by changing the Mach number setting. The angle of attack is altered by modifying the X and Y components of the incoming flow direction. The present study employs a pressure-based algorithm and a second-order upwind differencing scheme for discretization, using the SIMPLE pressure-velocity coupling method with double-precision solving. During the solving process, in addition to monitoring the residuals of the variables, lift coefficient (_{L}), and drag coefficient (_{D}) must also be tracked to ensure true convergence of the solution. The convergence criteria for all calculations are residuals less than 1 × 10^{−5} [

The analysis focuses on varying the incoming angle of attack, specifically examining the range of 0–12 degrees in this paper. As shown in

The lift-to-drag ratio is a key metric for assessing the aerodynamic performance of an airfoil. As shown in

The key design parameters for wind turbine blades include the selection and design of the blade airfoil, the number of blades (

The design parameters of the wind turbine in this paper are shown in

Rated power (kW) | Wind turbine drive efficiency |
Wind energy utilization factor _{P} |
Air density (kg/m³) | Design wind speed (m/s) | Number of blades |
Blade tip speed ratio |
Airfoil type |
---|---|---|---|---|---|---|---|

44 | 0.85 | 0.40 | 1.225 | 12 | 3 | 6 | QY-7305 |

The diameter of the wind turbine can be determined using the following equation for power of the airfoil:

It is calculated that the diameter of wind wheel

The Wilson design method, which is based on the blade element theory, divides the blade into equal sections and uses the maximum power coefficient of each section as the objective function for optimization and solution. Increasing the number of segmented elements in the Wilson design method leads to more element cross sections being aligned with the objective function, resulting in a wind turbine blade design that closely approaches an optimal shape and exhibits improved aerodynamic performance. Excessive elements complicate the calculation and modeling process, while insufficient elements compromise accuracy and lead to errors in fitting chord length and twist angle, thereby affecting the optimization of wind turbine blade shape design. This paper proposes a method for non-uniformly acquiring wind turbine blade elements, enabling the adjustment of element numbers within an optimal range to achieve high calculation accuracy. This approach facilitates the creation of 3D models and enhances wind turbine energy utilization. Additionally, relevant correction functions are employed to rectify the calculated element twist angle and element chord length parameters, thereby providing greater convenience for wind turbine blade design based on the easy 3D model generation.

The basic mathematical model for pneumatic shape calculation is as follows:

To maximize the wind energy utilization factor of the entire wind turbine, the wind energy utilization factor of each blade section must be maximized, where the objective function is:

The constraints for this objective function is:

After obtaining the induced factors

In the above formulas, _{P} is the wind energy utilization coefficient, _{L} is the lift coefficient, ^{-5} m^{2}/s.

Firstly, according to the blade element theory, the wind turbine blade is divided into three parts along the spreading direction, which are blade root, blade middle and blade tip. The spacing between the blade elements at the root is 1.2 m, divided into two equal parts; the spacing between the blade elements at the middle of the blade is 0.3 m, divided into nine equal parts; the spacing between the blade elements at the tip is 0.9 divided into one equal part; each blade element is a separate airfoil that needs to be calculated.

For each blade element, the optimization problem is solved using

A fitting function is employed to fit the best lift coefficients for different Reynolds numbers to a curve. Using the initial Reynolds number, the initial lift coefficient and chord length are calculated based on

The fitting function is called to fit the best angle of attack corresponding to different Reynolds numbers to a curve, and according to

The obtained chord lengths and twist angles are ideal, so it is necessary to make linear corrections to the obtained chord lengths and twist angles in order to make the blades meet the requirements of machining, structure, etc.

Obtain the 3D coordinates of the airfoil sections of each blade element and import the 3D coordinates into Solidworks for modeling.

The program is developed using the Wilson optimization design method, and the optimization flowchart is presented in

In the programming, it is important to divide it into three parts: blade root, blade middle, and blade tip. Within the entire loop, if statements are inserted. After calculating the blade root, the various parameters are iterated to calculate the blade middle to prevent inaccurate results due to re-iteration. Similarly, after calculating the blade middle, the parameters are iterated to calculate the blade tip. This process continues until the calculation for the entire blade element is completed.

The ideal wind energy utilization coefficient for each cross-section of the blade element is presented in _{P} (coefficient of power) at the middle position of the blade exceeds 0.5, and _{Pmax} (maximum coefficient of power) is almost above 0.55, which is very close to the Baez limit. Meanwhile, the program output, which characterizes whether the Fmincon function finds the optimal value under the given constraint, indicates successful program execution after computing the optimal value.

The iterative calculations result in optimized chord lengths and twist angles for each blade element, maximizing the utilization of wind energy. However, in this ideal state, the chord length and twist angle exhibit a nonlinear relationship along the length of the blade, posing challenges in production and processing. To meet the design requirements for production and processing, it is necessary to utilize the curve-fitting function Polyfit in Matlab to perform fitting operations on the optimized chord lengths and twist angles. If the fitting iterations are too low, it may result in a significant deviation from the optimized parameters, reducing wind energy utilization. On the other hand, higher fitting iterations may approach theoretical data, but they might not achieve the desired correction effect, making installation and manufacturing more inconvenient. After comprehensive consideration and practical analysis, a third-degree polynomial fitting is applied to correct both the chord length and twist angle in this project. Due to the lower wind energy utilization at the blade root and tip, the chord length and twist angle of each blade element section within the range of 0.4 R–0.9 R are subjected to fitting correction. Moreover, at 0.4 R–0.9 R, the blade elements are positioned in the middle of the blade with small spacing, leading to a better fitting effect. The curves in

Fitting polynomial for the chord length:

Fitting polynomial for the twist angle:

The optimized values of each prime surface parameter for the blades are presented in

Radius/m | Twist angle/° | Fitting twist angle/° | Chord length/m | Fitting chord length/m | ||||
---|---|---|---|---|---|---|---|---|

1.2 | 0.3351 | 0.1422 | 18.88 | 16.10 | 0.5990 | 0.5862 | 0.9593 | 790613 |

2.4 | 0.3393 | 0.0387 | 7.84 | 7.77 | 0.3924 | 0.3893 | 0.9810 | 876708 |

2.7 | 0.3398 | 0.0308 | 6.34 | 6.33 | 0.3547 | 0.3546 | 0.9822 | 878994 |

3 | 0.3405 | 0.0251 | 5.10 | 5.10 | 0.3246 | 0.3246 | 0.9822 | 884600 |

3.3 | 0.3414 | 0.0209 | 4.06 | 4.06 | 0.2988 | 0.2987 | 0.9811 | 888609 |

3.6 | 0.3427 | 0.0177 | 3.17 | 3.16 | 0.2765 | 0.2764 | 0.9787 | 891745 |

3.9 | 0.3446 | 0.0152 | 2.40 | 2.39 | 0.2572 | 0.2570 | 0.9744 | 894175 |

4.2 | 0.3473 | 0.0133 | 1.72 | 1.71 | 0.2402 | 0.2401 | 0.9673 | 895912 |

4.5 | 0.3513 | 0.0118 | 1.11 | 1.10 | 0.2250 | 0.2250 | 0.9554 | 896697 |

4.8 | 0.3574 | 0.0107 | 0.55 | 0.54 | 0.2113 | 0.2111 | 0.9351 | 895710 |

5.1 | 0.3669 | 0.0099 | 0.01 | 0.00 | 0.1981 | 0.1980 | 0.8989 | 890634 |

6 | 0.1419 | 0.0039 | 1.11 | −1.82 | 0.0000 | 0.1570 | 0.0000 | 0 |

The wind turbine blade is a vital component of the wind turbine, and its complex shape poses challenges in achieving accurate modeling. The accuracy of the modeling directly impacts the efficiency of wind energy utilization.

By using the method of coordinate transformation, we first export the two-dimensional coordinates of each blade element section in Profili software, and then use the formula for spatial coordinate transformation to calculate the three-dimensional spatial coordinates of each blade element section. Finally, we import the three-dimensional coordinates of each blade element section into the modeling software to complete the modeling process. The basic process of coordinate transformation and the specific steps for solving three-dimensional coordinates are as follows:

(1) Obtain the raw airfoil coordinates (_{0}, _{0}) using Profili software.

(2) The acquired cross-section will be translated to the aerodynamic center, enabling the determination of two-dimensional coordinates (_{1}, _{1}). The coordinates of the aerodynamic center are assumed to be (0.25_{1}, _{1}) = (_{0}, _{0}) − (0.25

(3) Through the implementation of a three-dimensional coordinate transformation, the resulting coordinates are (

The calculated coordinates of each airfoil section are saved, and then imported into SolidWorks for the purpose of modeling. The resulting 3D model of the wind turbine is presented in

Aerodynamic performance calculation plays a crucial role in blade design and verification processes. Verifying its aerodynamic performance becomes an essential step to evaluate the design outcomes. Conversely, the results obtained from aerodynamic performance calculations offer valuable feedback for refining the aerodynamic shape of the blade.

In this study, the aerodynamic performance parameters are computed using the fitting formulas for chord length and twist angle obtained through the non-uniformly sampled blade element method. Additionally, a comparison is performed using the uniformly sampled blade element method for analysis. Both methods utilize twelve cross-sectional blade elements to calculate each parameter, with chord length and twist angle corrections made at 0.4 R–0.9 R. The chord length and twist angle functions obtained through fitting using two methods are used to calculate the aerodynamic performance parameters, including the wind energy utilization coefficient (_{P}), torque coefficient (_{M}), and thrust coefficient (_{T}). The curve depicting the variation of _{P} with tip speed ratio is shown in _{M} with tip speed ratio is shown in _{T} with tip speed ratio is shown in

_{P}) reaches maximum values of 0.4614 and 0.4516 when designing wind turbine blades using the non-uniform and uniform blade element methods, respectively, at a tip speed ratio of 6. Similarly, the torque coefficient (_{M}) reaches values of 0.0769 and 0.0752, while the thrust coefficient (_{T}) reaches values of 0.801 and 0.755. The wind energy utilization coefficient (_{P}) holds utmost significance for assessing the aerodynamic performance of wind turbine blades, reflecting their efficiency in capturing wind energy. Within the tip speed ratio range of 5 to 10, the wind energy utilization coefficient calculated using the non-uniform blade element method consistently surpasses that of the uniform blade element method. Additionally, it aligns with the tip speed ratio at the design point, attaining its peak value when the tip speed ratio is 6. Consequently, designing blades using the non-uniform blade element method leads to enhanced aerodynamic performance.

This study utilized two distinct methods for conducting calculations and analysis in wind turbine design. Specifically, 10, 15, 20, and 30 blade elements were employed, and the resulting outcomes are presented in

Number of blade elements | 10 | 12 | 15 | 20 | 30 |
---|---|---|---|---|---|

Wind energy utilization coefficient obtained through non-uniform design method | 0.4588 | 0.4614 | 0.4621 | 0.4622 | 0.4623 |

Wind energy utilization coefficient obtained through uniform design method | 0.4472 | 0.4516 | 0.4596 | 0.4617 | 0.4621 |

In this study, we extracted an airfoil inspired by the eagle and employed it in conjunction with the non-uniform blade element method to enhance the design of wind turbine blades. The resulting conclusions are outlined below:

(1) Using biomimicry, the airfoil of an eagle was extracted and compared with the aerodynamic characteristics of the NACA2412 airfoil. Through the analysis, it was determined that the eagle airfoil demonstrated superior aerodynamic performance.

(2) The blade was designed using the non-uniform blade element method and then compared with the same method itself. The analysis showed that the blades designed using this approach demonstrated superior aerodynamic performance, while effectively mitigating the challenge of increased complexity in calculations and modeling arising from a higher number of blade elements.

(3) When a smaller number of blade elements is used, the non-uniform blade element method outperforms the uniform blade element method.

None.

This study was supported by the National Natural Science Foundation Projects (Grant Number 51966018), the Chongqing Natural Science Foundation of China (Grant Number cstc2020jcyj-msxmX0314), the Key Research & Development Program of Xinjiang (Grant Number 2022B01003), Ningxia Key Research and Development Program of Foreign Science and Technology Cooperation Projects (202204), and the Key Scientific Research Project in Higher Education Institution from the Ningxia Education Department (2022115).

The authors confirm contribution to the paper as follows: supervision, project administration, funding acquisition and writing-review & editing: Yuanjun Dai, Dong Wang, Xiongfei Liu, Weimin Wu; study conception and design: Yuanjun Dai, Dong Wang; data collection: Dong Wang; analysis and interpretation of results: Dong Wang; draft manuscript preparation: Dong Wang. All authors reviewed the results and approved the final version of the manuscript.

The authors confirm that the data supporting the findings of this study are available within the article.

The authors declare that they have no conflicts of interest to report regarding the present study.