## 4 Results and Discussion
### Analysis of Unstable Flow Structure
At different flow rates, the average vorticity intensity at the blade trailing edge of OBS30 is less than that of the average vortex intensity of OTE, and the average vorticity intensity of OBS15 is greater than the average vortex intensity of OTE. At 0.2\(Q_{\text{d}}\), the average vorticity intensity of the OBS15 scheme is 561.96 s\({}^{-1}\). The average vorticity intensity of the OBS30 scheme is 462.90 s\({}^{-1}\). Compared with the original impeller OTE, the average vortex intensity at the blade trailing edge of the OBS30 scheme is reduced by 46.57 s\({}^{-1}\). At 1.4\(Q_{\text{d}}\), the value of the OBS30  
Figure 12: Shedding vortex distribution in impeller outlet with different impellers (0.2\(Q_{\text{d}}\)): (**a**) OTE impeller; (**b**) OBS15 impeller; (**c**) OBS30 impeller. Figure 13: Shedding vortex distribution in impeller outlet with different impellers (1.4\(Q_{\text{d}}\)): (**a**) OTE impeller; (**b**) OBS15 impeller; (**c**) OBS30 impeller. impeller is 378.34 s\({}^{-1}\), and the value of the OBS15 impeller is 461.16 s\({}^{-1}\). These results show that OBS30 can improve the flow structure of blade trailing edge of the centrifugal pump at 0.2\(Q_{\text{d}}\) and 1.4\(Q_{\text{d}}\). Figure 15 shows the transient total pressure distribution in the midsection of the centrifugal pump with different impellers when the blades are in the tongue-separating position under part-load condition 0.2\(Q_{\text{d}}\). As shown in Figure 15, a low-pressure area appears at the tongue of the centrifugal pump and forms a large pressure gradient with the adjacent high-pressure area of the blade trailing edge. The low-pressure area at the tongue of the OBS15 impeller is significantly larger than that of the OTE impeller. The central pressures in the low-pressure region at the tongue of the OTE, OBS15 and OBS30 are 510, 495 and 660 kPa, respectively. The central pressures in the high-pressure region at the blade trailing edge of the OTE, OBS15 and OBS30 are 935, 990 and 1045 kPa, respectively. The pressure difference at the tongue of the OBS30 impeller is slightly smaller than that at the OTE impeller, and the reduction value is 40 kPa. The pressure distribution in the area far from the tongue is uniform, indicating that the internal flow of the pump is stable in other areas. The large pressure difference in the tongue region will lead to a large pressure gradient region, thereby resulting in the generation of an unstable flow structure in this region. Figure 16 shows the relative velocity streamline distribution at the tongues of the centrifugal pump with different impellers when the blades are in the tongue-separating position at 0.2\(Q_{\text{d}}\) flow rate. As shown in Figure 16, different degrees of backflow and vortex flow occur at the high-pressure gradient  
Figure 14: Comparison of the average vorticity intensity at the blade trailing edge of the different schemes: (**a**) part-load condition (0.2\(Q_{\text{d}}\)); (**b**) over-load condition (1.4\(Q_{\text{d}}\)). Figure 15: Pressure distribution in centrifugal pumps with different impellers (0.2\(Q_{\text{d}}\)): (**a**) OTE impeller; (**b**) OBS15 impeller; (**c**) OBS30 impeller. regions of the septum tongue of centrifugal pump with different blade trailing edges. Two unstable vortex structures appear at the tongue of the OTE impeller, and a certain distance is observed between the two vortex cores. Two vortex structures also appear at the tongue of the OBS15 impeller, where the area of the unstable vortex structure is larger than that of the OTE impeller, and the distance between the two vortex cores is short. The unstable vortex structure at the tongue of OBS30 impeller is weaker than that of the OTE impeller, and no obvious vortex core structure appears. This condition indicates that the OBS30 impeller has a certain improvement on the unstable vortex structure caused by backflow at the centrifugal pump tongue, thereby resulting in a significant decrease in the intensity of unstable pressure pulsations at the tongue.