## 5 Conclusions  
The aerodynamic characteristics of the Invelox system were studied through numerical simulation. The flow passes through the Invelox system from the top to the bottom through funnels and pipes and the wind energy is extracted. When the airflow accelerates in the Venturi tube, it pushes the wind turbine to do work to generate electricity. However, because the Venturi tube is arranged horizontally, the system outlet may be affected by incoming flow. When the angle between the incoming flow and the Venturi tube axis exceeds 90\({}^{\circ}\), the speed ratio of the system begins to deteriorate. When the included angle exceeds 120\({}^{\circ}\), the incoming flow flows backward into the system from the outlet, and the system can no longer operate normally.  
In order to improve the inverted irrigation of the Invelox system, a new design is proposed, which consists of placing the Venturi tube vertically under the funnel. This design can capture wind energy from any direction. On this basis, the annular windshield is installed near the exit to improve the aerodynamic performance. According to the results, the average speed ratio increased by about 42% after installing the windshield, which is higher than the original Invelox system. The improved design can maintain the wind direction independence, being able to provide a high-speed ratio under any wind conditions.  
The influence of the atmospheric boundary layer wind profile velocity distribution on the Invelox system is also studied. The results show that the overall performance of the system is smaller than that of the uniform inflow after considering the non-uniform velocity inlet. The system outlet is greatly affected by wind speed. The flow field characteristics at the exit of the system have great influence on the system. If the external air flow at the exit dredges and accelerates the internal air flow, the lower the environmental wind speed at the exit is, the smaller the system speed ratio is. On the contrary, if the external air flow obstructs the internal air flow, the lower the environmental wind speed at the exit, the greater the system speed ratio. This presents a very interesting feature.  
In addition, the original Invelox system has a horizontal rotating axis due to the Venturi being laid out horizontally. In the process of wind turbine rotation, the blades will bear alternating loads under the influence of gravity, which puts forward a test for the fatigue performance of the blades. In the improved system, since the axis of the Venturi is consistent with the direction of gravity, the blades will not bear alternating loads.  
Both authors carried out data analysis, discussed the results and contributed to writing the paper. Both authors have read and agreed to the published version of the manuscript.  
This work was supported by the National Natural Science Foundation of China (Grant No. 11872212, 41873016), Natural Science Foundation of Jiangsu Province (Grant No. BK20190386), Science and Technology of China ENERGY (Grant No. GJNY-20-110) and is a project funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions.  
The authors declare no conflict of interest.