**4. Conclusions**

(1) The entire self-priming process of the self-priming centrifugal pump can be divided into three stages: gas-suction stage due to the impeller's rotating role in the initial self-priming stage, gas-suction stage due to the role of gas-water mixture and gas-water separation in the middle self-priming stage, and gas-suction stage due to the water flowing from the inlet section into the pump in the final

self-priming stage. Moreover, the self-priming time of the initial and final self-priming stages accounts for a small percentage of the entire self-priming process. The middle self-priming stage is the main stage in the self-priming process and determines the length of self-priming time.

(2) In the initial self-priming stage, the self-priming centrifugal pump is mainly based on drainage, and the gas is mixed with water before going outside the pump; it takes a certain amount of time for the gas to move from the inlet section to the outlet section. With the increase in the void fraction of the impeller, the drainage capacity of the self-priming pump is weakened, and the gas-exhausting rate is fast then slow. After entering the middle self-priming stage, due to the formation of a large negative pressure at the impeller inlet, the decreasing rate of the pressure continues to slow down on this basis, and the gas-suction rate of the self-priming centrifugal pump also slows down. In the final self-priming stage, the water in the inlet section goes into the impeller, whose power capability is enhanced obviously. The water mixed with the gas goes to the outlet section, so the gas-suction rate of the self-priming pump increased and reached the maximum value at a certain time. Afterward, the gas-suction rate decreased and finally approaches 0, due to the fact that the amount of gas in the pump decreases continuously.

(3) In the initial self-priming stage, the region near the suction surface of the impeller blade (low-pressure region) is easily occupied by gas. In the final self-priming stage, the region near the pressure surface of the impeller blade (high-pressure region) is easily occupied by water. In the middle self-priming stage, the impeller void fraction is high and a small amount of gas-water mixture exists in a small region close to the pressure surface of the impeller blade and impeller outlet. The key to successful self-priming is that the impeller's rotation forces a small amount of water mixed with some gas to flow along the pressure side of the impeller blade from the impeller inlet to the impeller outlet. Then, the mixture goes into the outward diffuser and flows along the pressure surface of the return diffuser, which shows that the gas-water mixture always flows along the high-pressure side of the pump in the self-priming process. The diffuser void fraction varies like the impeller void fraction, but its overall amplitude is lower.

(4) In the whole self-priming process, the backflow function of the backflow channel is the key to self-priming, and the pressure difference at both ends of the backflow channel is the main reason for the backflow function.

**Author Contributions:** B.H. and Y.Z. conceived and designed the experiments; X.W. performed the experiments; C.L. analyzed the data; C.W. and L.C. wrote the paper.

**Acknowledgments:** This research was funded by National Natural Science Foundation of China (Grant No.51609105), Jiangsu Province Science Foundation for Youth (Grant No. BK20170507), China Postdoctoral Science Foundation (Grant No.2016M601738 and 2018T110458). And the APC was funded by Priority Academic Program Development of Jiangsu Higher Education Institutions(PAPD).

**Conflicts of Interest:** The authors declare no conflict of interest.
