## 5 Conclusions  
The intensity and frequency distribution of pressure fluctuation under a low flow rate at 0.75 Q\({}_{\rm d}\), rated flow rate at 1.0 Q\({}_{\rm d}\), and high flow rate at 1.25 Q\({}_{\rm d}\) were analyzed. The influence of different flow rates on the rotor-stator interaction in the pump-turbine were analyzed in detail. The main results are as follows:  
1. The pressure fluctuation analysis of the runner concludes that, under the influence of rotor-stator interaction, the fluctuation near the trailing edge pressure surface of the long and short blades was the most violent. At 0.75 Q\({}_{\rm d}\), compared with 1.0 Q\({}_{\rm d}\) and 1.25 Q\({}_{\rm d}\), flow instability led to a greater pressure fluctuation intensity which, to some extent, intensified the rotor-stator interaction at the blade's trailing edge, and the amplitude of the nonlinear frequency exceeded the rotor-stator interaction frequency.  
2. The pressure fluctuation analysis of the blackeless region and double-row cascade concludes that, at 0.75 Q\({}_{\rm d}\), compared with 1.0 Q\({}_{\rm d}\) and 1.25 Q\({}_{\rm d}\), strong flow instability led to more nonlinear frequency components, and the flow rate would affect the energy distribution of rotor-stator interaction at different node-diameter numbers. From the blackeless region to the outlet of the stay vanes, the amplitude of the rotor-stator interaction frequency attenuated continuously, and the amplitude attenuation of each frequency was mainly concentrated in the area of the guide vanes. The amplitude attenuation rate of the stay vane region was small, indicating that the frequency passability of the guide vane region was low while the frequency passability of the stay vane region was high.  
3. The pressure fluctuation analysis of the volute concludes that the flow rate had a significant impact on the pressure fluctuation intensity and distribution characteristics in the volute. The pressure fluctuation intensity at the tongue was the most violent at 0.75 Q\({}_{\rm d}\). The pressure surface fluctuation intensity gradually decreased along the direction of the increase in the section area, forming a pressure fluctuation gradient and strong nonlinear spectral characteristics. In contrast, the pressure fluctuation intensity at 1.0 Q\({}_{\rm d}\) and 1.25 Q\({}_{\rm d}\) was small and evenly distributed. In addition, the flow difference at the outlet of the long and short blades had great influence on the pressure fluctuation at the large section of the volute.  
Figure 26: Frequency domain of pressure fluctuation of DT04–DT12.  
4. The analysis of the pressure fluctuation of the draft tube concludes that the pressure fluctuation near the outlet wall of the draft tube was more violent under the influence of rotor-stator interaction, especially in the working condition of the small flow. The protruding frequencies of pressure fluctuation at the inlet of the liner tube to the straight taper tube were all axial multiples, the amplitude of pressure fluctuation near the outlet and the elbow tube was larger, and the amplitude of pressure fluctuation outside the tube wall was slightly larger than that inside the tube wall.  
Conceptualization, J.Z. and Y.X.; methodology, H.C. and H.S.; formal analysis, P.H.; resources, J.Z.; writing--original draft preparation, Y.X. and H.C.; writing--review and editing, H.S.; supervision, J.Z. and P.H. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the National Natural Science Foundation of China: 51809121 and 51779107, Natural Science Foundation of Jiangsu Province: BK20170548, Special Supported Project of China Postdoctoral Science Foundation: 2019T120394, and the National Key R&D Program of China: 2017 YFC0806604.  
On behalf of all authors, the corresponding author states that there is no conflict of interest.