## 3 Numerical Simulation and Results Analysis
### Analysis of Simulation and Experimental Results  
Figure 3 shows the schematic diagram and the picture of the gas-liquid two-phase flow pump performance test bench. Experiments were performed with a mixture of air and water. During the progress of the experiment, the speed of the pump was regulated by an electromotor; an air compressor was used to pressurize the gas. The flow rate of liquid was regulated by the liquid inlet valve and the electromagnetic flowmeter, and the gas flow rate into the pipeline was regulated by the air flowmeter and air inlet valve. Pressure gauges for the inlet and outlet were used to measure the differential pressure to calculate the hydraulic head of the multiphase pump. The torque was tested using a torque sensor to calculate the efficiency of the multiphase pump. The hydraulic head and efficiency of the multiphase pump under the condition of 0.6, 0.8, 1, 1.2, and 1.4 times the designed flow rate \(Q_{0}\) with the inlet gas volume fractions of 30% and 50% were predicted with the numerical simulation, respectively, as shown in Figure 4. The experimental results of different flow rates with inlet gas volume fractions of 30% and 50% are also shown in Figure 4. It can be seen that the simulation results were in good agreement with the experimental results. The numerical simulation hydraulic head (\(H\)) and efficiency (\(\eta\)) of the single compression unit of the inlet gas volume fraction of 30% were 31.4 m and 66.2% under the designed conditions, respectively. The experimental head was 29.2 m while the efficiency was 60% under the designed condition. It can also be seen from Figure 4 that the numerical simulation hydraulic head (\(H\)) and efficiency (\(\eta\)) of the single compression unit of the inlet gas volume fraction of 50% were 29.32 m and 65.96% under the designed conditions while the corresponding experimental values were 27.12 m and 57.89%, respectively. The error between the simulation results and experimental results of different inlet gas volume fractions was within 10% at the design point, which was reasonable because the gas-liquid two-phase flow had a certain loss in the actual progress of operation. The external characteristics can indirectly verify the accuracy of numerical simulation, and the internal flow characteristics can be inferred based on external characteristics. This proved that the method used in the numerical simulation is reliable, and indicated that we can use this method for the modification design of the impeller in the subsequent study. As the flow rate increased, the numerical and experimental hydraulic head decreased continually. The efficiency reached a maximum at 1.2 \(Q_{0}\), and the range of high efficiency was wide. Figure 3: Gas-liquid two-phase flow pump performance test bench. **(a)** The schematic diagram of the gas–liquid two-phase flow pump performance test bench. 1,4,15,16,18—Pressure gauge; 2—Electromagnetic flow meter; 3—Liquid inlet valve; 5—Low pressure bomb; 6—Gas valve; 7—Air compressor; 8—Air compressor control room; 9—Flowmeter; 10—Gas inlet valve; 11—Electromotor; 12—Coupling; 13—Torque sensor; 14—Model pump; 17—Medium pressure bomb. **(b)** Picture of the test bench. Figure 5 shows the gas volume fraction (GVF) distribution of the meridional surface in the impeller passage with different flow rates. The meridional surface with different flow rates had the same horizontal and vertical scales. With the increasing of the flow rate, the aggregation area of gas in the flow passage gradually moved from the inlet to the outlet of the impeller. The maximum gas volume fraction in the flow passage decreased with the increase in flow rate, which indicates that the increase in flow was conducive to the outflow of gas. The gas accumulation occurred near the middle area of the flow passage under the working condition of 0.6 \(Q_{0}\), and the gas aggregation was more serious than under other working conditions.