## 3 Results and Discussion
### Loss Mechanism of Tip Clearance Leakage Flow  
Figures 15 and 16 show the energy loss near the tip clearance of the front impeller and rear impeller, respectively. The figures provide the energy loss distribution at SPN = 0.99 surface. From Figure 15, there is a high-value region of energy loss near the suction surface at the 1.2 \(Q_{\rm BEP}\) flow rate. As the leakage flow moves downstream, this high-value region of  
energy loss gradually expands, mainly due to the expanding influence range of the leakage vortex. A certain degree of energy loss also occurs near the pressure side of the blade, but it is significantly lower than the energy loss near the suction surface. This is closely related to the leakage vortex starting from the suction surface and gradually propagating downstream to the vicinity of the pressure surface of the next stage blade. Compared to the large flow rate (1.2 \(Q_{\text{BEP}}\)), at 1.0 \(Q_{\text{BEP}}\), the energy loss near the blade tip will increase slightly, mainly manifested by an expansion of the high-value energy loss region near the blade suction surface, and the starting position of this high-value region moving closer to the leading edge of the blade. This is mainly due to the starting position of the tip clearance leakage vortex shifting towards the leading edge of the blade and its influence range gradually increasing. As the flow rate decreases to 0.8 \(Q_{\text{BEP}}\), high-energy-loss regions appear near the suction surface and leading edge of the blade, which are significantly higher than those under the flow rates of 1.0 \(Q_{\text{BEP}}\) to 1.2 \(Q_{\text{BEP}}\), and have a considerable impact on the impeller inlet region. Overflow at the blade leading edge, tip leakage flow, and backflow at the impeller inlet are the main causes of the increased energy loss. It is worth noting that significant energy loss occurs near the outlet of the impeller and covers the entire outlet region. This is mainly due to the backflow from the rear impeller to the outlet of the front impeller forming a circumferential vortex at the outlet of the impeller. This vortex prevents the fluid from effectively flowing out of the impeller outlet, thereby blocking the mainstream flow and ultimately causing a large amount of energy loss. From Figure 16, it can be observed that under large flow rates, a high-energy-loss region exists near the blade tip, mainly concentrated on the suction surface of the blade, starting from the leading edge of the impeller and gradually shifting towards the impeller outlet and the pressure surface of the next stage blade. This is primarily due to the tip clearance leakage vortex. At 1.0 \(Q_{\text{BEP}}\), the high-energy-loss region near the blade tip significantly increases, with a notable increase in energy loss on the suction side of the blade, surpassing the levels observed at 1.2 \(Q_{\text{BEP}}\). This increase is closely related to the increased intensity and expanded influence range of the tip leakage vortex. Overall, the spatial distribution pattern of energy loss near the blade tip for the rear impeller remains relatively consistent, but the loss is greater than that of the front impeller. As the flow rate further decreases to 0.8 \(Q_{\text{BEP}}\), the energy loss near the blade tip increases significantly, with most regions of the impeller experiencing high energy loss. Compared to the optimal flow condition, the high-energy-loss region becomes larger due to the tip leakage flow and the leading edge overflow entraining a large amount of mainstream fluid, resulting in larger spiral vortices and backflow. It is worth noting that no high-energy-loss region appears near the outlet of the rear impeller. This is because the region near the outlet of the rear impeller is not influenced by the tip leakage flow and backflow, which is a significant difference from the front impeller. Figure 14: Average backflow velocity in the impeller along the spanwise direction: (**a**) Front impeller; (**b**) Rear impeller.