# Optimization Design of Centrifugal Fan Blades Based on Bezier Curve Method
## 4 Result and Discussion
### Flow-Field Analysis  
Figure 13 provides a more intuitive demonstration of the changes in the blade profile. The original blade profile was an arc, so its curvature was the same at different chord lengths. Due to a decrease in \(\beta_{1}\) and \(r_{1}\), the optimized blade profile became more pronounced at the inlet section, with increased curvature; meanwhile, the range of \(r_{1}\), \(r_{2}\), and \(r_{3}\) reduced along with a decrease in h making the mid-to-rear section of the optimized blade profile smoother, with reduced curvature. Under the influence of \(\beta_{2}\), the optimized blade profile exhibited decreased curvature at the outlet section, even showing curvature opposite to that in the mid-to-anterior section, and changes in \(\beta_{3}\) lead to an increased chord length. The outlet angles of AM, BM, and CM increased sequentially, resulting in a corresponding increase in \(p_{st}\), which was consistent with the conclusions in Figure 12 and Table 4.  
Figure 14 shows the comparison of the external performance characteristics of the prototype fan and the three optimized fans, with the overall trends of the performance curves remaining essentially consistent. The \(\eta_{s}\) of the optimized fan had been improved \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Case** & \(p_{\text{st}}\) **(N)/Pa** & \(p_{\text{st}}\) **(R)/Pa** & \(\eta_{s}\) **(N)/\%** & \(\eta_{s}\) **(R)/\%** \\ \hline Prototype (PM) & 870.30 & & 63.01 & \\ A model (AM) & 882.98 & 881.20 & 66.25 & 66.28 \\ B model (BM) & 916.61 & 913.44 & 65.31 & 65.14 \\ C model (CM) & 929.72 & 936.91 & 63.43 & 63.50 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Comparison of RBFNN result (R) and numerical result (N) at design point. Figure 12: Pareto front solutions. Figure 13: Profiles of the prototype blade and three optimized blades. in both the operating and low flow conditions, while its efficiency decreased at high flow rates; additionally, the maximum efficiency operating condition has shifted towards low flow rates, which may have been caused by the decrease in the maximum flow rates of the optimized fan. Similarly, the \(p_{st}\) was improved in both operating and flow conditions, while the \(p_{st}\) was decreased at high flow rates, for the same reason as the decrease in efficiency. In practical applications, high-flow conditions are rarely used; therefore, the improvements in performance under the design and low-flow conditions--which are of greater engineering concern--make the optimization results quite reasonable. In this study, the origin of the coordinate system is located at the center of the back plate of the impeller. The impeller rotates along the Z-axis, and the airflow enters the impeller in the negative direction of the Z-axis. In order to better demonstrate and analyze the internal flow-field characteristics of the fan, the flow conditions at three heights of Z = 20 mm (near the rear plate of the impeller), Z = 45 mm (in the middle of the impeller), and Z = 70 mm (near the front plate of the impeller) were analyzed, as shown in Figure 15.  
Figure 16 shows the pressure distribution on the blade surface of fans. It can be seen that in PM, there is a high-pressure region near the front of the pressure side trailing edge, indicating that this area is the main work-performing region on the pressure surface. In contrast, the pressure near the trailing edge of the pressure surface is slightly lower, suggesting that this region performs less work compared to the high-pressure area. The high-pressure area near the trailing edge of the pressure surface increases in AM, implying that the effective work area of the blade has expanded after optimization, resulting in improved performance, while the performance of BM and CM deteriorates in the same area.