## 4 Results and Discussion  
### Comparative Analysis of Internal Flow Characteristics  
The flow pressure and total pressure efficiency curves of the impeller before and after modification, obtained through CFD simulations, are shown in Figure 11. Compared to the original impeller, the modified impeller demonstrates an improvement in total pressure efficiency across all flow conditions, with the highest efficiency of the modified impeller showing an increase of 11.7% over the original. The total pressure efficiency \(\eta\) is calculated using the following formula:  
\[\eta=\frac{Q\times p_{s}}{P} \tag{9}\]  
In the formula, \(Q\) represents the flow rate, \(p_{s}\) is the static pressure at the outlet, and \(P\) is the power. Figure 11: Comparison of pressure and efficiency at different flow rates before and after modification. Figure 10: Comparison of impeller models before and after modification: (**a**) original model and (**b**) modified model. Figure 9: Distribution of the impeller flow area along the streamline: (**a**) arc section position, (**b**) chord length of each section. To analyze the impact of incoming flow distortion on the inlet parameters of large high-speed centrifugal fans and the transmission of the distorted flow field along the axial direction, this study takes the design operating point as an example. The circumferential distribution of aerodynamic parameters at three cross-sections of the upstream collector ring, as shown in Figure 12, is analyzed for the centrifugal impeller. As shown in Figure 13, the circumferential distribution of axial velocity \(V_{z}\) and swirl angle \(\alpha\) at 0.6 times the radius of the three cross-sections is presented. From the figure, it can be observed that the circumferential distribution of the swirl angle from Section 1 to Section 3 is similar. The relative swirl distortion intensity \(SI_{rel}\) from Section 1 to Section 3 are \(3.83^{\circ},2.04^{\circ}\), and \(2.23^{\circ}\), respectively, indicating a reduction of 41%. This suggests that the swirl distortion significantly attenuates during downstream development due to mixing effects. The expression for the above circumferential relative distortion intensity \(SI_{rel}\) is as follows:  
\[SI_{rel}=\frac{\int\limits_{\theta}|\alpha(\theta)-\alpha_{av}|d\theta}{360} \tag{10}\]  
Simultaneously influenced by the distorted flow field, the axial velocity at the impeller inlet cross-section also exhibits distortion, showing a quasi-sinusoidal distribution in the circumferential direction. The maximum swirl angle occurs near the \(60^{\circ}\) circumferential position, while the minimum swirl angle appears near \(300^{\circ}\). To further analyze the impact of inlet distortion on the internal flow field of the impeller, flow passages A and B, corresponding to the \(60^{\circ}\) and \(300^{\circ}\) circumferential positions, respectively, are selected for analysis. The 3D tip leakage flow streamline diagrams for flow passages A and B in both the original and modified designs are shown in Figures 14 and 15, respectively. Figure 12: Axial position distribution of monitoring cross-sections in the centrifugal fan flow passage. Figure 13: Circumferential distribution of axial velocity and swirl angle at the monitoring cross-sections. Figure 14a illustrates the streamline distribution at the 0.9 blade height section of the original impeller. Within the original flow passage, various complex vortex structures of different scales are present. As shown in Figure 14b, under the impact of the high-speed mainstream, the leakage flow at the front of the blade tip moves downstream along the suction surface in the direction of the mainstream. The rim leakage flow in the middle section of the impeller is influenced by the vortex, converging along the suction surface and eventually mixing with the vortex. This interaction further leads to the formation of a large-scale vortex, known as a stall cell, in the downstream region of the flow passage.