## 6 Pressure Fluctuation Results and Analysis
### Analysis of Pulsation Signal in the Frequency Domain  
At speed \(n=2200\) r/min, under the low flow condition (\(R_{\rm Q}=0.5\)), the mean pressure amplitude at the top of the hump section was 0.663 kPa and, at the bottom, was 0.697 kPa; under the optimum condition (\(R_{\rm Q}=1.0\)), the mean pressure amplitude at the top of the hump section was 0.482 kPa and that at the bottom was 0.477 kPa; under the high flow condition (\(R_{\rm Q}=1.20\)), at the top of the hump section, the mean pressure amplitude at each measuring point was 0.187 kPa, and at the bottom, the mean pressure amplitude at each measuring point was 0.172 kPa. Under the condition of a large flow, the mean value of the pressure amplitude at each measuring point was small, and the relative difference between  
Figure 21: Pulsation time–domain of the points under different operating conditions (\(n=2200\) r/min).  
the mean value of the pressure amplitude at the top and bottom of the hump section was the largest, with a relative difference of 8.36%. Under the optimum condition, the relative difference between the mean value of the pressure amplitude at the top and bottom of the hump section was the smallest, with a relative difference of 1.04%. With the decrease of the flow rate, the mean value of the pressure amplitude at each measuring point at the top and bottom of the hump section increased gradually. As the flow rate of the pump unit decreased, the residual circulation at the outlet of the guide vane increased gradually, and the transverse velocity played a leading role in the intensity of the helical flow. The pressure fluctuation of the water flow in the hump section was large.  
When the speed decreased from 2200 r/min to 1450 r/min, the pressure amplitude at the same measuring point in the hump section decreased gradually, and the pressure amplitude at each measuring point decreased the most under the best operating condition (\(R_{\text{Q}}=1.0\)). The pressure amplitude at the top measuring point P1-P3 of the hump section decreased by 69.63%, while the pressure amplitude at the bottom measuring point P4-P6 of the hump section decreased by 63.5%; under the high flow condition (\(R_{\text{Q}}=1.20\)), the pressure amplitude at each measuring point decreased the least, the mean value of the P1-P3 pressure amplitude at the top of the hump section decreased by 1.79% and the mean value of the P4-P6 pressure amplitude at the bottom of the hump section decreased by 4.97%. As the speed decreased, the residual circulation at the outlet of the guide vane decreased, and the influence of transverse velocity on the inside of the siphon outlet conduit decreased. The effect of pulsation depended mainly on the flow rate.  
The collected pulsation time-domain data were analyzed by using short-time Fourier transform of the window-added Hanning function. The frequency was expressed as a multiple of the frequency conversion \(N_{F}\). The multiple of frequency conversion NF was calculated using the calculation method in Reference [32]:  
\[N_{F}=\frac{60F}{n} \tag{22}\]  
where \(F\) is the corresponding frequency value after short-time Fourier transform, and \(n\) is the speed.  
The pulsation spectrum of each monitoring point is shown in Figure 22. At 2200 r/min, the main frequency of the pulsation at each measuring point in the hump section is twice that of the frequency conversion under various calculation conditions.  
Figure 22: Cont.