## 4 Results and Discussions
### Pressure Fluctuation Analysis of Draft Tube  
As an inflow component, the rotor-stator interaction and flow instability of the draft tube were mainly near the outlet of the draft tube. Figure 24 shows the distributions of the standard deviation coefficient of pressure fluctuation at the outlet of the draft tube under different flow rates within five rotation cycles. It can be seen that pressure fluctuation distributions under different flow rates at the outlet were similar. The pressure fluctuation intensity near the center was small and increased continuously along the radial direction. The pressure fluctuation intensity at the tube wall was about \(10^{2}\) times that at the center. In addition, the fluctuation intensity was the highest at 0.75 Q\({}_{\mathrm{d}}\) and the lowest at 1.0 Q\({}_{\mathrm{d}}\), indicating that deviated working conditions, especially at a small flow rate, will aggravate the pressure fluctuation at the outlet of the draft tube, which damages the stable operation of the unit.  
In order to further analyze the time and frequency domain characteristics of the pressure fluctuation of the draft tube under different flow rates, Figure 25 shows the time and frequency domain of pressure fluctuation at the outlet of the draft tube at monitoring points DT01, DT02, and DT03 within a rotational cycle. The results show that the pressure fluctuation distributions of DT01 and DT03 at the tube wall were similar. There are five peaks and valleys in a rotation period, which are affected by the rotor-stator interaction between the long blade and the outlet of the draft tube. In the time domain figures, the main frequency is 5 f\({}_{\mathrm{n}}\), and the secondary main frequency is 10 f\({}_{\mathrm{n}}\). The fluctuation amplitude under a rated flow rate at 1.0 Q\({}_{\mathrm{d}}\) was relatively small, while the negative amplitude under a small flow rate at 0.75 Q\({}_{\mathrm{d}}\) was relatively large, resulting in large pressure fluctuations under this working condition. In addition, by comparing the time domain figure of each flow rate, it can be found that the change of flow rate also has an obvious influence on the phase of pressure fluctuation. For the central monitoring point DT02, the time domain distribution showed an irregular periodic fluctuation, and the fluctuation amplitude under 1.25 Q\({}_{\mathrm{d}}\) was large, but the fluctuation amplitude was about two orders of magnitude lower than that of the monitoring point at the tube wall. In the frequency domain figures, it is shown that the main frequencies are axis-doubling frequencies, the main frequency is 5 f\({}_{\mathrm{n}}\), and the amplitude at 1.25 Q\({}_{\mathrm{d}}\) is relatively large, indicating that the influence of rotor-stator interaction between the runner and the draft tube on the middle position of the interface is relatively significant at a large flow rate.  
Figure 24: Pressure fluctuation distributions at the outlet of the draft tube.  
Figure 25: Time and frequency domain of pressure fluctuation at the outlet of the draft tube.  
Figure 26 shows the frequency domain of pressure fluctuation of DT04-DT12 under different flow rates. The results show that the main frequencies of pressure fluctuation at these positions were axis-doubling frequencies, in which 10 f\({}_{\rm n}\), 16 f\({}_{\rm n}\), and 20 f\({}_{\rm n}\) were caused by the upstream transmission of the rotor-stator interaction between the blackeless region and the runner. Overall, with the increase of the flow rate, the pressure fluctuation amplitude increased gradually from the inlet of the draft tube to the straight taper tube, and the amplitude at monitoring points DT04-DT09, which were near the elbow position and outer wall of the draft tube, was larger. Moreover, the amplitude of the outer wall of the tube was slightly larger than that of the inner wall, which was mainly due to the rotor-stator interaction between the runner and the draft tube, as well as the strong impact of the water flowing through the elbow tube on the outer wall.