## 4 Numerical Results and Analysis
### Gas Phase Distribution  
Figure 9 shows the air volume fraction distribution at different spans of the blade heights in the second stage impeller and diffuser of the mixed-transport pump with a 20% inlet gas content. The gas phase in the impeller flow channel was primarily gathered in the suction surface of the front cover plate at the impeller outlet. The air volume fraction near the front cover plate was greater than the back cover plate. Given the work done by the impeller, the bubbles were removed toward the exit direction and were influenced by the differential pressure between the front and rear of the blade. This phenomenon further promoted the gas movement toward the back surface of the blade. Given that the density of the gas and liquid phase was different, the water was higher than the air; therefore, it was subjected to a greater centrifugal force. This force pushed the water to the back cover plate. At the impeller blade outlet, the GVF of the local area was higher due to liquid phase flow separation, which also caused the increase in pressure fluctuation amplitude of the IMS1 monitoring point. In the diffuser channel, the gas phase primarily gathered at the front cover and gradually diffused to the main flow area along the flow orientation. The gas at the outlet of the impeller passage continued to flow into the diffuser passage due to an inertia effect. The centrifugal force effect disappeared in the diffuser passage, and the density of air was less than water. As such, the gas phase diffused to the main flow area and moved downstream in the guide vane passage.  
The distribution of the gas content on the surface of the second impeller under the conditions of GVF = 5%, 10%, 15%, and 20% is shown in Figure 10. With an increased IGVF, the air aggregation area on the suction surface of blades increased continuously within the four different IGVF situations. The gas phase primarily gathered in the suction surface of the blade head. The results of the GVF distribution show that the gas distribution at the blade head was relatively high, thereby affecting the  
Figure 8: Pressure fluctuation frequency domain diagrams for IMS1–IMS5 and DPS1–DPS5.  
Figure 9: GVF distribution at diverse spans in the second stage impeller and diffuser under IGVF = 20%.  
amplitude of the pressure pulsation at the blade head, and the values of the amplitude at blade head were the largest. This phenomenon was attributed to the mixed medium that entered the impeller and collided with the blade head. Another reason was the influence of the impeller rotation. The gas phase was primarily gathered close to the front cover of the impeller given that the water within a higher density is subjected to more centrifugal force than the gas phase; thus, the pressure on the rear cover plate was greater than that on the front cover. A pressure difference between the impeller shroud and hub was observed; thus, the gas content at the hub was greater than that at the shroud. With an enhanced gas content, the air in the impeller passage moved toward the outlet along the blade surface. Under a high GVF condition, the air accumulated in the first half of the impeller passage, and a large amount of air blocked a portion of the flow channel. The air was affected by the pressure gradient, which caused the air bubbles to flow in the opposite direction at the outlet position of impeller blade suction surface.