1. Introduction
In recent years, due to the excessive exploitation of non-renewable energy, environmental pollution has become increasingly serious, leading to the great development of the renewable energy technology. As the main device for converting wind energy into electrical energy, wind turbines have turned from onshore to offshore, and their sizes have become larger and larger, and the inflow conditions have become more and more complex [
1]. The aerodynamic characteristics of wind rotors can be correctly estimated in the presence of different inflow conditions, which is of great significance to the aerodynamic and structural design of wind turbines.
Wind shear (WS) represents the most representative inflow conditions. Kim et al. [
2] examined the effects of atmospheric stability, turbulence intensity, and wind shear index on wind turbine power and annual power generation. Dimitrov et al. [
3] proposed a suitable wind shear model for flat terrain, reducing the inaccuracy of the fatigue load prediction of large wind turbines. Additionally, as a common inflow condition, extreme winds, such as gusts, tropical cyclones, and low-level jets (LLJ), often occur depending on geographic and climatic conditions. Lyu [
4] investigated the coupled response of wind rotors due to the extreme shear wind, extreme gust, extreme wind direction, and extreme turbulent wind. By performing an experimental study, Wang [
5] examined the wake characteristics of wind turbines under tropical cyclone conditions. Walter et al. [
6] studied the structural response of wind turbines due to the LLJ conditions. Na et al. [
7] explored the flow field characteristics of wind turbines in the presence of the LLJ conditions by the large-eddy simulation method. Among them, the influence of the LLJ on the aerodynamic characteristics of the wind rotor is the most noticeable with the increase in the hub height [
8,
9]. When the LLJ occurs, the inflow condition becomes very complicated, characterized by strong winds at the height of the LLJ and strong wind shear. Gutierrez et al. [
10] found that the wind speed would significantly grow, and the turbulence intensity would lessen under the LLJ condition, affecting the wind turbine for more than 40 m from the ground. Wilczak et al. [
11] found that the wind capacity factor magnifies by more than 60% due to the LLJ condition. Therefore, it is necessary to explore the influence of the LLJ on the aerodynamic characteristics of the wind rotor. Generally, the LLJ can be characterized by the LLJ height, LLJ strength, and wind speed profile shape [
12,
13]. Few studies have been carried out on the aerodynamic characteristics of wind turbines based on the LLJ structural parameters, such as LLJ intensity, LLJ height, and wind speed profile shape.
The calculation methods of aerodynamic characteristics of wind turbine rotors include the blade-element momentum (BEM) method [
14,
15], vortex wake (VW) method [
16,
17], and computational fluid dynamics (CFD) method. Generally, the BEM is affected by Reynolds number, three-dimensional rotation effect, tip losses, and root losses, and its predicted results are not very accurate. Therefore, it is necessary to correct the BEM via an appropriate approach, such as three-dimensional rotation correction, and tip and root losses correction. Due to the advantages of the BEM in computational efficiency, this methodology has been extensively employed in the design of wind turbine aerodynamics. The well-known GH-Bladed commercial software [
1] and OpenFAST [
2] open-source software basically exploited this approach. The CFD is a calculation method developed with the rise of computer technology. This method can directly and accurately analyze the complex flow field with high calculation accuracy, and, in addition, to calculating the aerodynamic force of the wind turbine, the details of the flow field can be readily extracted. However, the CFD method needs to solve a large number of Navier–Stokes equations, indicating huge computational resources and time. Furthermore, its accuracy relies on the selection of the turbulence model, the discrete format of equations in time and space, and the quality of the grid to a certain extent. Regodeseves [
18] scrutinized the unsteady flow of a horizontal axis wind turbine with the CFD method, focusing on the influence of the engine compartment, tower, and blade rotation on the induced zone and near wake. Frederik [
19] calculated the unsteady aerodynamic force of the wind turbine and carried out numerical calculations on the wind wheel and tower in the presence of the shear inflow condition. The VW method assumes blade and wind turbine wake as a series of vortices, which can be divided into the rigid vortex wake, predetermined vortex wake, and free VW method. The calculation accuracy of this approach is lower than that of the CFD, and its calculation efficiency is lower than that of the BEM. The model also requires to be modified like the BEM method. Therefore, it is not broadly implemented in the examination of the aerodynamic characteristics of the wind turbine. The advantages and disadvantages of different methods have been shown in
Table 1. However, irrespective of the calculation method exploited for calculating the aerodynamic characteristics of wind rotors, the wind speed, the rotor speed, and the blade-pitch angle are all known input parameters [
20,
21,
22]. Hence, when the wind speed profile is non-uniform or very complex, the rotor speed and blade-pitch angle depend on the equivalent uniform wind speed corresponding to the wind speed profile. There are usually two methodologies for evaluating the equivalent wind speed (EWS) [
23,
24], one based on the kinetic energy theory and the other based on the equivalent torque. Nevertheless, it is difficult and troublesome to calculate the equivalent wind speed, and the relevant established model is not universal [
23]. Irrespective of the used method, only the accuracy of the average value of aerodynamic characteristics can be guaranteed over one rotation cycle. As a general rule, the greater the difference between the equivalent wind speed and the inflow wind speed on the blade element is, the greater the aerodynamic characteristic error calculated using the rotor speed and blade-pitch angle corresponding to the equivalent wind speed is.
In summary, the previous studies mainly focused on the aerodynamic characteristics of wind turbines under different inflow conditions. In terms of content, the influence of the LLJ on the aerodynamic characteristics of wind turbines is increasing; however, few investigations have been devoted to this issue. In the present research method, the wind speed, the rotor speed, and the blade-pitch angle of blades are all known input parameters, but the present method has particular shortcomings that clearly mentioned above. Therefore, in this paper, firstly, in order to solve that the difficulty of the unknown rotor speed and blade-pitch angle under non-uniform inflow or complex inflow conditions, the BEM theory would be coupled with the generator-torque controller and blade-pitch controller when calculating the aerodynamic characteristics of the rotor, and a C++ program will be developed for implementing the proposed method. The chief reason for employing the BEM is that the iterative solution of the rotor speed and blade-pitch angle requires more calculation steps. Secondly, the influence of the LLJ intensity on the aerodynamic characteristics of the wind turbine can be examined and compared with the WS inflow. Finally, the impact of the LLJ height on the aerodynamic characteristics of the wind turbine is going to be explored as well. The LLJ intensity represents the local maximum of the wind speed on the wind speed profile, and the LLJ height indicates the vertical height of the LLJ intensity.
5. Conclusions
In the present paper, the BEM theory was coupled with the generator-torque controller and blade-pitch controller, and a C++ code was developed to implement the method. The influence of the LLJ strength on the aerodynamic characteristics of the wind rotor and the influence of different LLJ heights on the aerodynamic characteristics of the wind rotor were examined in some detail. The following crucial results are achieved.
Firstly, the difficulty of the unknown rotor speed and blade-pitch angle under non-uniform inflow or complex inflow conditions can be solved by coupling the control system with the aerodynamic characteristic calculation method. Secondly, when the wind speed is the same at the hub, the effect of the LLJ on the aerodynamic characteristics of the wind rotor is greater than that of the WS. The average aerodynamic loads of the wind rotor are less than those of the WS, and the amplitudes of the aerodynamic loads of the blade are greater than those of the WS. Finally, the influence of the LLJ should be considered in the aerodynamic and structural design of wind turbines. When the LLJ height is placed within the swept area of the wind rotor, the change curve of the aerodynamic loads of the blade in terms of the azimuth angle exhibits two local maximums and two local minimums. When the LLJ height is above the hub, local maximums are detectable in the first and second quadrants. For the case of the LLJ height lower than the hub height, maximums appear in the third and fourth quadrants. Further, two local minimums are observed at 0° and 180° azimuth angles. In addition, the closer the LLJ height is to the hub height, the greater the average aerodynamic loads of the wind rotor and the smaller the amplitude of the blade relative to the average value. The closer the LLJ height is to the tip, the smaller the average aerodynamic loads of the wind rotor are and the greater amplitudes of the blade are relative to the average value. When the LLJ height is placed outside the swept area of the rotor, the change law of aerodynamic loads of the blade is similar to a very strong WS inflow.