## 3 Results and Discussion
### Performance Comparison of Airfoil Fan and Single-Arc Fan  
#### 3.2.1 Velocity Flow Fields  
As mentioned above, the fan designed with A airfoil has excellent aerodynamic performance under common flow conditions. Therefore, the fan designed with A airfoil will be compared with the single-arc fan to analyze the internal flow field information of the fan. The velocity flow field and the velocity vector of the A airfoil fan and the single-arc fan under different working conditions (Cases 2-4) are presented in Figure 16.  
As shown in Figure 16a,b, these are the velocity cloud diagrams of the fan section under different flow rates. In the case of a small flow rate (Case 2), the flow condition of the single-arc model is poor, and the velocity distribution in the impeller region is more uneven than that of the A airfoil model, which is more obvious in the red box area shown in Figure 16a,b. It should be noted that a severe blocking effect occurs in both models at the rotating surface, which is caused by the too-small gap between the motor and the impeller blades. However, at \(90^{\circ}<0<180^{\circ}\), the high-speed region of the A airfoil model in the impeller-volute gap is significantly higher than that of the single-arc model and the jet-wake is weaker in the tail region of the runner. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & **Flow (m3/h)** & **Rotating Speed (rpm)** & **Inlet Speed (m/s)** \\ \hline Case 1 & 58.60 & 1466 & 0.29 \\ \hline Case 2 & 242.10 & 1449 & 1.19 \\ \hline Case 3 & 398.00 & 1429 & 1.95 \\ \hline Case 4 & 506.70 & 1410 & 2.49 \\ \hline Case 5 & 578.10 & 1389 & 2.84 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Parameter conditions under various working conditions. Figure 15: Aerodynamic performance of four airfoil blades: (**a**) efficiency and (**b**) total pressure. The wake structure of the A airfoil model is obviously weakened in Case 3, especially in the black box selection region of \(270^{\circ}<\theta<15^{\circ}\) at the design flow point of velocity distribution nephogram, and the jet-wake structure is also suppressed compared to that of the single-arc model. With the increase in rotational speed, the jet-wake structure of the two models is suppressed, the vortex area is reduced, and the suppression degree of the A airfoil model is better. By comparing the velocity distribution of different sections, the velocity distribution of the A airfoil model in the impeller region is more uniform and the high-speed region is larger, indicating that the A airfoil model has a stronger working capability. Under the condition of a large flow (Case 4), the jet-wake structure of the single-arc model is obviously more serious than that of the A airfoil model, and the velocity distribution is more uneven. This was particularly evident in the blue boxed area in Figure 16. Under large flow, the flow state of the two models is improved due to the increase in flow, but the velocity distribution in the impeller is uneven due to the structural problem of the single-arc model, and the vortex is obvious. As shown in Figure 16c,d, under the low flow rate condition of Case 2, the two calculated models have different degrees of vortices. Especially in the region of \(0^{\circ}<\theta<180^{\circ}\), the pressure distribution in this region is uneven due to the existence of the volute tongue. In addition, the surface is also the most serious of all surfaces. This is because the gap between the motor and the impeller in this section is too narrow, resulting in the fluid's attack angle here being close to \(90^{\circ}\), which thickens the boundary layer of the suction surface. Due to the rotation, a large number of vortices appear. The difference between the two models is  
Figure 16: The velocity flow field and the velocity vector of the models: (**a**) the velocity flow field of the single-arc model, (**b**) the velocity flow field of the A airfoil model, (**c**) the velocity vector of the single-arc model, and (**d**) the velocity vector of the A airfoil model.