## 4 Results and Discussions
### Pressure Fluctuation Analysis of Volute  
Figure 21 shows the pressure fluctuation distributions at the mid-span of the volute in five rotation cycles under different flow rates. It can be seen that the flow rate had a significant influence on the intensity and distribution characteristics of pressure fluctuation in the volute. At a low flow rate at 0.75 Q\({}_{\mathrm{d}}\), the pressure fluctuation at the tongue was the most violent, and the fluctuation intensity of the pressure surface decreased gradually with the increase of the section area, forming the pressure fluctuation gradient, which reached the minimum value at the farthest distance from the tongue and then maintained stability at the outlet direction. The pressure fluctuation intensity at a rated flow rate at 1.0 Q\({}_{\mathrm{d}}\) was small and uniformly distributed, and there was no gradient change. As the flow rate increased, compared with other positions, the pressure fluctuation of the flow passage with a small section near the tongue increased significantly, but it was still about 10\({}^{-1}\) times that of the same position with a small flow rate. This indicates that deviated conditions, especially low flow conditions, will lead to a significant increase in pressure fluctuation of the flow passage at a small cross-section near the tongue, which may seriously induce strong vibrations. In the pump working condition, as a downstream component, the unsteady pressure distribution of the volute is susceptible to the influence of rotor-stator interaction in the upstream, especially in the bladeless region. Figure 22 shows the distribution of 5 f\({}_{\mathrm{n}}\) and 10 f\({}_{\mathrm{n}}\) amplitudes for each monitoring point in the volute. As can be seen from the figure, the pressure fluctuation amplitude at the mid-span  
Figure 21: Pressure fluctuation distributions at the mid-span of the volute. Figure 20: Circumferential distribution of 10 f\({}_{\mathrm{n}}\) and 20 f\({}_{\mathrm{n}}\) amplitudes at different vane heights. of the volume at a low flow rate at 0.75 Q\({}_{\rm d}\) was strong at 7.8 f\({}_{\rm n}\), and the spectral feature was nonlinear, which is consistent with the fluctuation characteristic in the bladeless region. Monitoring point SC01, which was near the tongue, had the maximum amplitude, while monitoring point SC08 far from the tongue had the minimum amplitude. With the increase of flow, the pressure fluctuation at the mid-span of the volume was mainly concentrated in the rotor-stator interaction frequencies of 5 f\({}_{\rm n}\), 10 f\({}_{\rm n}\), 15 f\({}_{\rm n}\), and 20 f\({}_{\rm n}\), especially in the blade frequency of 10 f\({}_{\rm n}\) and the single-type blade passing frequency of 5 f\({}_{\rm n}\). In order to further analyze the distribution rules of these two frequencies at the mid-span of the volume, Figure 23 shows the distribution of 5 f\({}_{\rm n}\) and 10 f\({}_{\rm n}\) amplitudes in the volume at rated flow rates at 1.0 Q\({}_{\rm d}\) and 1.25 Q\({}_{\rm d}\). It can be seen that, for the blade frequency of 10 f\({}_{\rm n}\), the amplitude at 1.25 Q\({}_{\rm d}\) was higher than that at 1.0 Q\({}_{\rm d}\), and the distribution of the two in the volume were similar. From SC01 to SC05, 10f\({}_{\rm n}\) had a high attenuation rate, reached a minimum value at SC08-SC09 (far from the tongue), and was stable near the outlet of the volume. For a single-blade passing frequency of 5 f\({}_{\rm n}\), the amplitude of the blade from the small section to the large section gradually decreased at the rated flow rate at 1.0 Q\({}_{\rm d}\). While at the large flow rate at 1.25 Q\({}_{\rm d}\), the amplitude of SC01-SC06 at the small section near the tongue was less than the rated flow rate, but the amplitude of SC07-SC12 at the large section near the exit was significantly increased and higher than the rated flow rate. This indicates that the change of flow rate changes the propagation characteristic of 5 f\({}_{\rm n}\), thus changing the amplitude distribution rule corresponding to 5 f\({}_{\rm n}\).