## 3 Numerical Simulation and Results Analysis
### Analysis of Simulation and Experimental Results
The accumulation of the gas phase in the flow passage partly occurred near the hub of the impeller; when the gas phase accumulated to a certain extent, it was more likely to cause the unstable operation condition under the 0.6 \(Q_{0}\) condition than other conditions. The entrainment effect of the liquid phase on the gas phase decreased with the decrease of flow rates. The density of the gas phase was lower than that of the liquid phase, so the centrifugal force acted less in the gas phase than the liquid phase, and the pressure from the liquid phase to the gas phase was larger. Therefore, the gas was concentrated near the hub of the impeller outlet. With the increase in flow rate, the gas accumulation decreased, but the accumulation area was still near the hub area, which was mainly caused by the expelling effect due to the density difference of the gas and liquid phases. The expelling effect means the effect of the gas phase moving with liquid phase. The energy of the fluid increases with the increasing of the flow rate, so the ability of the low-density phase to follow the high-density phase increased. The larger the flow rate, the more obvious the expelling effect. The increase of the expelling effect, the difference in density and pressure in the gas-liquid two-phase caused the gas phase accumulated to the outlet area near the hub of the impeller passage more easily. Figure 4: Hydraulic performance curves of a multiphase pump with different flow rates. (**a**) Inlet gas volume fraction (IGVF) = 30% and (**b**) IGVF = 50%. The hydraulic performance of the multiphase pump with inlet gas volume fractions of 0.3, 0.4, 0.5, 0.6, and 0.7 under the design working condition are shown in Figure 6. The dimensionless head coefficient, defined in Equation (12), was used to describe the change in head with increasing inlet gas volume fraction. The head coefficient and efficiency of the multiphase pump both decreased with the increasing inlet gas volume fraction. In other words, the boosting capacity of the impeller and the performance of the multiphase pump decreased with the increasing inlet gas volume fraction. The head coefficient \(\Psi\) is defined as  
\[\Psi=\frac{2\text{g}H}{u_{2}}, \tag{12}\]  
where \(u_{2}\) is the circumferential velocity of the impeller shroud and \(g\) is the local gravity acceleration; their units are m/s and m/s\({}^{-2}\), respectively. Figure 5: Gas volume fraction (GVF) distribution of the meridional surface in the impeller passage at different flow rates. Figure 6: Hydraulic performance of a multiphase pump with different inlet gas volume fractions. The gas distributions at 10% of the blade height with inlet gas volume fractions of 0.3, 0.4, 0.5, 0.6 and 0.7 in the flow passage of impeller and diffuser were determined as shown in Figure 7. With the increasing of inlet gas volume fraction, the gas and liquid phases near the pressure side of the impeller blade mixed well. However, the gas accumulation phenomenon became more serious and the accumulation area increased accordingly in the region close to the suction side of blade, but the location of gas accumulation was basically maintained, which was concentrated on the suction side of the impeller near the hub. This was the position at which the pressure gradient was the largest in the impeller passage. Coupled with the influence of centrifugal force and pressure, the gas is more susceptible to gathering in areas of lower pressure and a small radius. With the increase in the gas volume fraction, the gas gradually diffused from the outlet of the backside to the inlet along the hub. Figure 7 also shows that the rotor-stator interaction between the impeller and diffuser strongly influenced the distribution of the gas phase in the diffuser flow passage. It is found in the figure that there is a certain rule in the distribution of gas phase. The main manifestation is that there were obvious changes between the interference region and the non-interference region of the stator and rotor cascades.