## 4 Numerical Results and Discussion
### Comparison of the Performances of the Original and Optimized Models  
Figure 11 shows the performance comparison between the original model and the optimized model. Both the static pressure and the static efficiency of the optimized model were improved compared with those of the original model. The highest efficiency of the optimized model was 78.1% at the point with a flow coefficient of 0.675, which was an improvement of more than 6.3% compared with the original model. \begin{table}
\begin{tabular}{c c c} \hline
**No.** & **Mesh** & **Static Pressure (Pa)** \\ \hline
1 & 7,432,111 & 418 \\ \hline
2 & 8,184,320 & 415 \\ \hline
3 & 8,954,841 & 410 \\ \hline
4 & 9,461,970 & 398 \\ \hline
5 & 9,806,594 & 397 \\ \hline \end{tabular}
\end{table} 
Table 4: Mesh independence verification of the optimized model. Figure 11: Comparison of performances between the original and optimized models (at 1100 rpm). Figure 10: Geometric shape of the blades of the original and optimized models: (**a**) Original model; (**b**) Optimized model. To verify the simulation results, two prototype fans made of ABS (Acrylonitrile Butadiene Styrene) were produced. Figure 12 shows an image of the prototype fan and the comparison between the simulation and experiment. It can be seen that the experimental results of the two prototype fans agreed well with the simulation results, within 3.1%. Figure 13 shows the static pressure distribution in the middle section of the original and models. In the optimized model, the static pressure in the channel increased uniformly and stably. By contrast, the original model showed a relatively large loss at the blade outlet. Figure 14 shows the relative velocity distributions in the middle section of the original and optimized models. There was a low-velocity region on the suction surface of the original model, and there was a high-velocity region on the blade's outlet surface. In the optimized model, homogeneous velocity distributions on the suction surface and the channel could be observed. The inhomogeneous velocity distribution on the suction surface or outlet surface was the main cause of flow separation, which caused fluid flow friction, resulting in large losses and performance degradation. Figure 15 shows the velocity streamline at the blade and the channel. In the original model, the fluid flow on the suction and outlet surfaces did not flow along the blade airfoil, and separation occurred. In the optimized model, on the other hand, some flow separation occurred at the blade tip, but the overall flow was stable along the blade airfoil. This stable flow reduced the fluid flow friction in the impeller to increase the performance and reduce noise. Figure 16 shows the turbulence eddy frequencies of the original and optimized models. In the original model, turbulence increased because of flow separation from the leading edge. On the other hand, in the optimized model, the flow separation at the leading edge was significantly reduced, making the flow stable. Additionally, the loss in the impeller outlet was significantly reduced in the  
Figure 12: Prototype test results: **(a)** Prototype fan image; **(b)** Comparison of performance between simulation and experimental results of the prototype fan (at 1100 rpm). Figure 13: Static pressure distribution (at 1100 rpm): **(a)** Original model; **(b)** Optimized model. 1. The smooth, curved surface of the three-dimensional blade of the optimized model stabilized the flow and reduced the flow friction by restraining the flow separation as much as possible. The results show that both static pressure and static efficiency were improved in the optimized model compared with the original model. The static efficiency of the optimized model was improved by more than 6.3% compared with that of the original model at its peak. 2. In the original model, a relatively large loss occurred at the blade outlet. Additionally, in the original model, it was confirmed that turbulence grew because of flow separation from the leading edge.