## 4 Results and Discussion  
### Performance of the Original Model  
The Invelox system is essentially a wind gathering-accelerating device, and the dimensionless coefficient Speed ratio (SR) is usually used to evaluate its aerodynamic performance, which is defined as  
\[\text{SR}=\frac{\text{Average air velocity in the Venturi tube}}{\text{Incoming wind velocity}} \tag{11}\]  
Figure 8 shows the variation of the average SR in the wind direction at the Venturi tube. Considering the symmetry of the model, only the range of 0-180\({}^{\circ}\) is calculated. When the angle between the wind direction and the axis of the Venturi tube axis \(\theta\) exceeds 90\({}^{\circ}\), the SR decreases rapidly. When \(\theta\) is larger than 120\({}^{\circ}\), the SR becomes negative, which means that the airflow is pouring back into the Venturi tube from the outlet. Thus, the Invelox system cannot really capture wind power from any wind direction. When the environmental wind direction changes, the system cannot supply effective wind energy consistently and stably. The results show that the aerodynamic performance of the system is very sensitive to wind direction, and the change in wind direction will have a great influence on the steadiness of the output power of the wind turbine. The streamline can visually observe the movement characteristics of the flow. Figure 9 shows the streamlines near the upstream entrance of the original Invelox model under different wind conditions. When \(\theta\) is less than 90\({}^{\circ}\), air from the upwind direction of the Invelox enters the wind collection device and part of the air escapes from the leeward side, and the rest of the air travels through the pipe to the Venturi tube. As \(\theta\) increases, the external flow forms a barrier at the Invelox exit, blocking the flow of the internal flow. When \(\theta\) reaches 120\({}^{\circ}\), almost all the airflow into the wind energy collection device \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Mesh** & **Coarse** & **Medium** & **Fine** \\ \hline Average velocity in the Venturi tube, \(\varphi\), m/s & 10.518 & 10.317 & 10.286 \\ Cell number, \(N\), million & 2.86 & 3.79 & 6.97 \\ Relative error, \(\delta\) & - & 0.019 & 0.003 \\ Grid refinement ratio, \(r\) & - & 1.10 & 1.23 \\ Order of convergence, \(e\) & - & 20 & - \\ GCL, \% & - & 0.36\% & 0.01\% \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Independence study. Figure 8: The effects of wind direction on the speed ratio of the original model. will flow out from the leeward side. In this case, the airflow speed in the Venturi tube is very small, and the wind turbine will not be able to work normally. Figure 10 is the velocity vector diagram at the exit of the system under different wind directions. It can be clearly seen that when the outlet normal direction is consistent with the incoming flow direction, that is, when \(\theta=0^{\circ}\), the directions of the velocity vector inside and outside the flow tube are basically consistent. As \(\theta\) increases, the external flow will form a barrier to the internal flow, which will hinder the movement of the latter. When \(\theta\) increases to \(120^{\circ}\), the external air flow moves almost along the exit plane near the exit, so the internal air flow is almost zero. As \(\theta\) increases further, the external flow flows into the system from the outlet, at which point the velocity ratio of the system becomes negative. The essence of motion is the drive of pressure difference. Figure 11 shows the total pressure contours in the vertical plane of the Invelox system at \(0^{\circ}\) and \(180^{\circ}\). Section A refers to the exit plane of the system, and section B is the section below the funnel. The diameters of both sections are 10 ft. When \(\theta=0^{\circ}\), the cross-section A is on the leeward side. The airflow enters the funnel from above, some escaping from the leeward side, the other into the Venturi, and then exits through the outlet.