## 6 Comparative Results and Analysis
### Pressure Pulsations
When comparing the pressure pulsation characteristics between the blunt impeller and sharp impeller, we can find differences on both the peak-peak values and the frequency values. Even though the instantaneous flow patterns in the blunt and sharp impellers were similar, the slight change of leading-edge shape can strongly influence the pressure pulsation that represented the subtle change of flow field. Figure 17 shows the pressure pulsations in the ellipse leading-edge impeller. Based on the waveform, it was observed that the pressure pulsation peak-peak values became much higher than in the blunt and sharp impellers. The peak-peak values were especially high on \(\mathrm{P}_{\mathrm{Bin}}\) and \(\mathrm{P}_{\mathrm{Bmid}}\), as they were about \(1.2\times 10^{-2}\) Pa and \(1.0\times 10^{-2}\) Pa, respectively. The peak-peak values on the other points were about \(3\times 10^{-3}\) Pa\(\sim 5\times 10^{-3}\) Pa, which were also higher than in the blunt and sharp impellers. Figure 17: Pressure pulsation in the ellipse leading-edge impeller: (**a**) time-domain plot (three revolutions); (**b**) frequency-domain plot, monitor points (1) \(\mathrm{P}_{\mathrm{Ain}}\), (2) \(\mathrm{P}_{\mathrm{Amid}}\), (3) \(\mathrm{P}_{\mathrm{Aout}}\), (4) \(\mathrm{P}_{\mathrm{Bin}}\), (5) \(\mathrm{P}_{\mathrm{Bmid}}\), and (6) \(\mathrm{P}_{\mathrm{Bout}}\). As in the sharp leading-edge impeller, there were also three obvious frequencies. Firstly, the main frequency was \(f_{me}=2.41\) Hz, which was approximately 1/5 rotating frequency. The second and third dominant frequencies were 2 and \(3f_{me}\), which are also indicated on Figure 17. Another low-frequency band can be observed on all the points, especially on P\({}_{\rm Amid}\), P\({}_{\rm Bin}\), and P\({}_{\rm Bmid}\). This low-frequency band covered about 0.2-1.4 Hz. Figure 18 shows the pressure pulsations in the round leading-edge impeller. The peak-peak value on P\({}_{\rm Amid}\) was around \(1.8\times 10^{-2}\) Pa, which was the highest among the six points. The peak-peak value was around \(1.0\times 10^{-2}\) Pa on P\({}_{\rm Bin}\) and much smaller on the other four points. Generally, in the A passage, pressure pulsation was high in the middle of the passage. In the B passage, pressure pulsation was high in the inlet and decreased gradually from the inlet to middle-passage to outlet. According to the frequency-domain plot, the main frequency on all six points was \(f_{mr}=1.00\) Hz, which was 0.083 rotating frequency. However, a wide frequency band covered around the main frequency. The band was approximately from 0.33 to 1.35 Hz. Another peak, 3.33 Hz, can be found on the frequency-domain plot. Figure 18: Pressure pulsation in the round 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\({}_{\rm Bout}\). The instantaneous flow patterns in the ellipse and round leading-edge impellers were similar. However, the frequency of pressure pulsation characteristics was different. The main frequencies were also different, as listed in Table 2. Comparing among all the four types of impellers, the blunt leading-edge impeller had the smallest amplitude of pressure pulsation but a noisier frequency pattern. On the contrary, the ellipse and round had the strongest pulsation amplitudes, but the frequency pattern is relatively pure. Table 3 shows the obvious frequencies or frequency bands on the frequency-domain plots of all the four leading-edge types of impellers. These obvious frequencies and frequency bands are denoted by their main frequency values: \(f_{mb},f_{ms},f_{me}\), and \(f_{mr}\). As shown in Table 3, the obvious frequencies or bands are complex, with five parts in the blunt leading-edge impeller. The 5 parts are \(f_{mb}\), 3\(f_{mb}\), 5\(f_{mb}\), 14.5\(\sim\)20.7\(f_{mb}\) and 36.2\(\sim\)39.3\(f_{mb}\).