## 6 Comparative Results and Analysis
### Pressure Pulsations  
Considering the cite-fixed alternating stall and its different performances in different blade passages of these different impellers, the pressure pulsations were monitored and analyzed. As shown in Figure 14, three monitoring points were set in an A passage: P\({}_{\rm{Ain}}\), P\({}_{\rm{Amid}}\), and P\({}_{\rm{Aout}}\). At the same time, three monitoring points were set in the neighbor B passage: P\({}_{\rm{Bin}}\), P\({}_{\rm{Bmid}}\), and P\({}_{\rm{Bout}}\). The pressure pulsations were monitored for more than 10 revolutions, as they became stable or rotating-periodic in changing. The time-domain data were handled by the fast Fourier transform (FFT) method with Hanning window. The time-domain and frequency-domain plots are shown below. Figure 15 shows the pressure pulsations in the blunt leading-edge impeller. Periodic variation was obvious on the time-domain plot. In the A passage, the pressure pulsation amplitude is relatively high, with peak-peak values of about \(5\times 10^{-6}\) Pa, on P\({}_{\rm{Ain}}\) and P\({}_{\rm{Amid}}\). On P\({}_{\rm{Aout}}\), the pressure pulsation amplitude decreased to a lower level. In the B passage, the pressure pulsation amplitude is relatively high, with peak-peak values larger than \(6\times 10^{-6}\) Pa, on P\({}_{\rm{Bin}}\). Because of the blockage and strong backflow, the pressure pulsation amplitude on P\({}_{\rm{Bmid}}\) and P\({}_{\rm{Bout}}\) became much lower. Figure 13: Contour of the sound power level, \(L_{sp}\): (**a**) blunt, (**b**) sharp, (**c**) round, and (**d**) ellipse. Figure 14: Monitoring points for pressure pulsations. Figure 15: Pressure pulsation in the blunt leading-edge impeller: (**a**) time-domain plot (three revolutions); (**b**) frequency-domain plot, monitor points (1) \(\mathrm{P_{Ain}}\), (2) \(\mathrm{P_{Amid}}\), (3) \(\mathrm{P_{Aout}}\), (4) \(\mathrm{P_{Bin}}\), (5) \(\mathrm{P_{Bmid}}\), and (6) \(\mathrm{P_{Bout}}\). The frequency-domain plot shows the frequencies on each point. These points were all dominated by frequency \(f_{mb}\), which is 9.67 Hz. This frequency was about 4/5 rotating frequency. Frequency 5 \(f_{mb}\) can be found in the A passage. Another frequency of 370 Hz was obvious on P\({}_{\rm Amid}\) and was widened to a band of 350\(\sim\)380 Hz. Frequencies 3 and 5 \(f_{mb}\) can be found in the B passage. On P\({}_{\rm Bin}\) and P\({}_{\rm Bmid}\), 3 and 5 \(f_{mb}\) frequencies were both obvious. On P\({}_{\rm Bout}\), 5 \(f_{mb}\) was obvious. Another frequency band of 140-200 Hz was found on P\({}_{\rm Bin}\). It disappeared on P\({}_{\rm Bmid}\) and P\({}_{\rm Bout}\). Figure 16 shows the pressure pulsations in the sharp leading-edge impeller. The waveform of the pressure pulsations was also periodic. The peak-peak value on P\({}_{\rm Bin}\) was the largest among the six monitoring points. It was about \(1.2\times 10^{-3}\) Pa. The peak-peak values on the other five points were about \(4\times 10^{-4}\) Pa-\(5\times 10^{-4}\) Pa. Generally, the pressure pulsation intensity in the sharp leading-edge impeller was approximately 100 times that of the blunt leading-edge impeller. As shown in Figure 16, the frequency of pressure pulsation in the sharp leading-edge impeller was dominated by three frequencies. Firstly, the main frequency (with the highest amplitude) was  
Figure 16: Pressure pulsation in the sharp leading-edge impeller: (**a**) time-domain plot (three revolutions); (**b**) frequency-domain plot, monitor points (1) P\({}_{\rm Aim}\), (2) P\({}_{\rm Amid}\), (3) P\({}_{\rm Aout}\), (4) P\({}_{\rm Bin}\), (5) P\({}_{\rm Bmid}\), and (6) P\({}_{\rm Bout}\). \(f_{ms}=0.81\) Hz on all six points. Moreover, \(f_{ms}\) is about 0.067 rotating frequency. Secondly, there was a vice frequency of about \(2f_{ms}\). Thirdly, the frequency of about \(3f_{ms}\) was also obvious in the A passage. The frequency of about \(3f_{ms}\) was widened to a band of 3.2-4.9 Hz, which was about 4-6\(f_{ms}\) in the B passage.