## 1 Introduction  
With the development of human society, energy shortage and environment pollution are very critical and need to be solved urgently in some regions of the world. With the increasing demand for energy, traditional non-renewable energy is becoming more and more urgent [1; 2; 3; 4]. In recent years, with the rapid development of global economy and the increasingly serious environmental problems, the contradiction between the power structure dominated by thermal power and fossil energy consumption has become more and more prominent [5; 6; 7; 8]. The traditional energy mainly consists of coal, oil, and natural gas, which not only have limited resource reserves, but also cause serious environmental pollution. Therefore, the development and utilization of renewable energy, especially wind energy, has been highly valued by all countries in the world. Wind power is a renewable, pollution-free, and promising energy. In order to curb the trend of environmental degradation and realize the sustainable development of energy, the development of wind energy has become the strategic choice [9; 10; 11; 12; 13]. The wind turbine is a device that converts wind energy into mechanical energy and then into electrical energy. According to the relative position between the rotating spindle of wind turbine and the ground, it can be divided into a horizontal axis wind turbine [14; 15; 16] and a vertical axis wind turbine [17; 18; 19]. The rotating axis of the horizontal axis wind turbine is parallel to the ground, and the wind energy utilization coefficient can reach 0.4, but the wind wheel needs to be adjusted with the change of wind direction. In contrast, the rotating axis of the vertical axis wind turbine is perpendicular to the ground, and the wind wheel does not need to adjust the direction with the change of wind direction, but the wind energy utilization coefficient is relatively low. Compared with the vertical axis wind turbine, the horizontal axis wind turbine has a larger capacity and a higher wind energy utilization coefficient, so it is widely used. However, due to the characteristics of its own structure, the horizontal axis wind turbine has many inevitable issues to be resolved. First, the horizontal axis wind turbine needs a yaw device to ensure that the wind turbine plane is directly opposite to the flow. Secondly, the horizontal axis wind turbine starts with high wind speed, which is not particularly suitable for areas with low wind density. What is more, high-speed blades can produce very strong low-frequency noise, which can cause great harm to people and wildlife. In order to overcome the defects in traditional horizontal axis wind turbines, a wind turbine system called Invelox [20,21] has been developed by SheerWind, as shown in Figure 1.  
The wind collector at the top can collect wind energy from all directions. The collected wind moves through the funnel to the Venturi section at the downstream to realize acceleration. The wind turbine arranged in the Venturi section converts the wind energy into electric energy under the optimal wind speed. Compared with the traditional horizontal axis wind turbine, the Invelox wind turbine system does not need a yaw device. SheerWind claims in its announcement that the system can produce electricity with wind speeds as low as 0.45 m/s. As inventors of the patent, [PERSON] et al. [20,21] conducted numerical and field studies of the Invelox system. They found that the Invelox system could deliver far more power than a conventional wind turbine of the same size. Moreover, the Invelox system does not require any wind regulation, and all rotating parts of the Invelox are located on the ground, making it easy to operate and maintain. [PERSON] et al. [22] studied the performance of the Invelox wind turbine system in low-wind areas of the Sistan plain through numerical simulations and field tests. They examined the energy output and noise characteristics of wind turbines at different heights.