## 4 Results and Discussion
### Analysis Results of Pressure Fluctuation Signal without Division Pier  
We selected the first four sub-bands--0-31.25 Hz, 31.25-62.50 Hz, 62.50-93.72 Hz and 93.72\(\sim\)125 Hz--after the fourth layer wavelet packet decomposition to analyze the relationship between the energy and flow of each sub-band, as shown in Figure 16. The energy value of each monitoring point in the sub-band 0-31.25 Hz was the largest, accounting for more than 99% of the total energy, indicating that the energy of the straight outlet conduit test section was mainly concentrated in the sub-band, and the energy fluctuation in the low-frequency band easily had a great impact on the safe and stable operation of the pump device. With the increase of the flow rate, the total energy value of the pressure in the test section of the straight outlet conduit decreased gradually and the average energy value of each monitoring point at 0.6 \(Q_{top}\) in the low flow rate condition was 3.76 times that at the optimal flow rate condition and 24.73 times that at the high flow rate condition; furthermore, the rotational intensity of the spiral flow in the straight outlet conduit was larger and the turbulent irregular motion increased the kinetic energy of the flow. However, the velocity circulation at the outlet of the guide vane became smaller under the condition of a high flow rate, and the intensity of the spiral flow in the straight outlet conduit was relatively weak. Under the same working condition, the energy values of different monitoring points in the same sub-band were different, which was mainly due to the inconsistency of the distribution of water pressure and velocity when the flow at the outlet of the guide vane spiraled into the straight outlet conduit.  
Figure 15: Vortex structure of the straight outlet conduit under different flow rate conditions (\(Q\) = 300 s\({}^{-2}\)).  
To analyze the energy difference of each monitoring point, the energy proportion was defined as the percentage of the total energy value of each monitoring point and the sum of the total energy values of four monitoring points. The results show that the difference in the energy ratios of P1 and P3 was small, and the difference as less than 1%. The energy ratio difference of P2 and P4 at the top and bottom of the straight outlet conduit was larger than 2%. Under the optimal flow rate condition, the energy proportion difference between P1 and P3 was the largest, and the energy proportion difference between P1 and P3 was 0.97%. Under the condition of a high flow rate, the energy proportion difference of P2 and P4 at the top and bottom of the straight outlet conduit was the largest, and the energy proportion difference of P2 and P4 was 6.95%. Under the same flow rate condition, the energy values of P1 and P3 on both sides of the straight outlet conduit along the flow direction showed little difference, and the energy values of P2 and P4 on the top and bottom of the straight outlet conduit showed the great difference; the total energy value of P4 at the bottom of the straight outlet conduit test section was the largest, and the total energy value of P2 at the left side of the straight outlet conduit along the flow direction was the smallest.  
The energy value of each monitoring point in the sub-band 0-31.25 Hz was the largest; thus, we selected this sub-band for power spectrum analysis, and the results are shown in Figure 17. Under low flow rate conditions, the dominant frequency of the power spectrum of each monitoring point in the sub-band 0-31.25 Hz was 1.46 Hz. Under the optimal flow rate condition, the dominant frequency of the power spectrum of P1 was 1.95 Hz, while that of P2 and P3 was 0.98 Hz and that of P4 was 2.93 Hz. Under high flow rate conditions,  
Figure 16: Energy value of each sub-band decomposed by wavelet packets at different monitoring points.  
the dominant frequencies of the power spectrum of P1, P2, P3 and P4 were 1.46 Hz, 3.42 Hz, 8.30 Hz and 4.88 Hz, respectively.