# Numerical Simulation of the Tip Leakage Vortex Characteristics in a Semi-Open Centrifugal Pump
## 4 Conclusions  
In this paper, the numerical simulation of a semi-open centrifugal pump was conducted to investigate the characteristics and the initiation, development, and dissipation mechanism of the tip leakage vortex in the tip clearance region. Some findings are summarized as follows.  
1. The numerical data and experiment results agreed well. Leakage vortex formed in the tip clearance led to a decrease in head and efficiency, which, respectively, decreased by 18.7% and 14.4% under the design condition. This decline became increasingly serious with the flow rate.  
Figure 16: Distribution of viscous diffusion term on different span planes.  
Figure 15: Distribution of Coriolis force term on different span planes.  
The large negative attack angle at the blade inlet was formed and led to the appearance of the low-speed region. The static pressure distribution law near the leading edge was changed, and the static pressure coefficient of the blade was reduced.
2. The structure of tip leakage vortex in the impeller mainly comprised TLV A formed at the leading edge, TLV B formed at the middle of the blade, and the tip leakage flow near the trailing edge. TLV A broke at approximately 35% M. The core region of TLV B extended to the leading edge of the adjacent blade. Most of the fluid was blocked by the wall; thus, fluid moved in the opposite direction and broke at approximately 60% M. The passage vortex was generated due to the deterioration of the flow field by tip leakage vortex. The entrainment effect was formed between the tip leakage flow and mainstream, and the secondary leakage flow emerged at the trailing edge of the adjacent blade.
3. The relative vorticity transport equation was adapted to analyze the movement mechanism of the tip leakage flow. High RVS was the main reason for the formation and development of tip leakage vortex. CORF could reflect changes in vorticity due to tip leakage flow. The relative motion with different velocities was formed between micro-jet and rotating impeller and fixed shroud, so VISD became vorticity source. All terms decreased with the blade span.
4. The change of the structure, trajectory, and breakdown position of the tip leakage vortex would affect the performance and stability of the semi-open centrifugal pump. This provided a reference for the design of the high-performance semi-open centrifugal pump and provided ideas for the research and development of efficient and stable flow control technology. We would study the influence mechanism of other parameters, such as the strength and initial position of tip leakage vortex on the centrifugal pump, and work on reducing and restraining the effect of tip leakage vortex by flow control technology in our future research.  
[PERSON] carried out the numerical simulations, analyzed data, conducted the experiment, and wrote the first draft of the manuscript. [PERSON] and [PERSON] conceived and supervised the study and edited the manuscript. [PERSON] and [PERSON] wrote the manuscript. All authors reviewed the manuscript.  
This research was funded by the National Natural Science Foundation of China, grant number 51679196 and the National Natural Science Foundation of China, grant number 51879216.  
The authors declare no conflict of interest.