**5. Conclusions**

The transient processes of the four pump-turbines with different specific speeds from turbine mode were simulated, and the macro parameter variations, flow pattern evolutions, as well as pressure fluctuations were analyzed. The working conditions, the transitions of backflows at the runner inlet and outlet, and the pressure pulsations at different locations ware compared, and the following conclusions were drawn.

1. The lower specific speed of the pump-turbine, the easier the chance for pump-turbines to enter into the reverse pump mode, generating undamped runaway oscillations. During these runaway processes, backflows and violent pressure pulsations occur in all turbines, and similarities and differences are obvious.

2. The position where the backflows generate at the runner inlet is related to the blade lean angle, which can affect the distribution of pressure gradient. As a result, the water turns from the higher-pressure side to the lower one, then the backflows generate at the lower pressure side. In addition, because lower specific speed turbine has smaller inlet height, the backflows occupy relatively larger range at the runner inlet and are easier to have transitions.

3. The pressure pulsations at different locations are influenced by the relative runner inlet height, distance to runner blades and flow pattern transitions. The smaller the runner inlet height, the smaller the differences in the pressure signals at three locations. The smaller the distance to the runner blades, the larger the pressure pulsations. Furthermore, flow pattern transitions and the turbulent kinetic energy distribution are important and should be considered.

4. S-characteristics in different pump-turbines are quite different, therefore, besides the four pump-turbines in this paper, more pump-turbines should be chosen to investigate the evolutions of pressure pulsation and flow patterns during the runaway process. Also, more factors including water conveyance systems, inertia of rotating parts, and guide vane openings should be considered to study the flow patterns and pressure pulsations in practical power stations. In addition, control methods should be investigated in the design stage by 3D simulations of transient processes.

**Author Contributions:** Data curation, Z.L. and Z.Y.; formal analysis, Z.Y. and Z.L.; investigation, Z.Y. and L.X.; validation, X.Z.; writing—original draft, Z.Y. and Y.C.; writing—review & editing, K.L. and X.Z. All authors have read and agreed to the published version of the manuscript.

**Funding:** This work was supported by the National Natural Science Foundation of China (NSFC) (Grant Nos. 51839008 and 51579187), the Natural Science Foundation of Hubei Province (Grant No. 2018CFA010), the National Natural Science Foundation of China (Grant No. 51909226), and the Natural Science Foundation of Fujian Province, China (Grant No. 2018J01525).

**Acknowledgments:** The numerical simulations were conducted on the supercomputing system in the Supercomputing Center of Wuhan University.

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