## 3 Numerical Methodology and Experimental Verification
### Experimental Verification  
The experimental system platform of the multistage mixed-transport pumps is shown in Figure 5. This platform was used to check the reliability of the numerical calculation results through the external characteristic test of the mixed-transport pump under different IGVFs. The experimental equipment and instruments met the level 2 accuracy requirements of GB/T 3216-2016. The liquid flow rate was controlled at a certain constant value, and the gas flow rate into the main pipeline was controlled using a regulating valve. Thus, the gas-liquid mixed medium with different gas contents was achieved. The external performance of the multistage mixed-transport pump under diverse gas contents was measured via the multiphase flow test. The main components and measuring elements of the experimental system are presented in the figure as well. The gas-liquid mixer 9 ensured that the mixture medium entering the inlet of the mixing pump was sufficiently mixed to form a bubble inflow condition, thereby ensuring the accuracy of the experiment.  
Figure 6 shows the comparison between the numerical simulation results and the experimental results under different flow conditions of pure water at 3500 rpm. The numerical calculation results  
Figure 4: Mesh validation.  
Figure 5: Experimental system schematic diagram of the multiphase pump. Labels: P—Pressure sensor; DP—Differential pressure sensor, 1—Tank; 2—Pressure pump; 3,4—Valves; 5—Mass flowmeter; 6—Check valve; 7—Air compressor; 8—Gasholder; 9—Air dryer; 10—Filter; 11—Mass flowmeter; 12—Commingler; 13—Multiphase pump test section.  
were very consistent with the data from the experiment. Thus, the numerical simulation method and calculation accuracy had a high reliability and accuracy. Under the pure liquid condition, the head decreased gradually with an increased flow rate, and a hump appeared at 0.32\(Qd\). When the volume flow rate was larger than 0.37\(Qd\), the efficiency growth rate of this pump increased slowly. As such, with an increased flow rate, the effects of the flow rate on efficiency were limited. The deviation between the experimental and numerical results may have been caused by not considering the roughness of the wall surface and ignoring the leakage loss at the impeller inlet, the loss along the pipeline, and the local loss. Furthermore, the differential pressure sensor used for measurement was a certain distance from the inlet position and outlet side of the mixed-transport pump, while the flow velocity in the pipeline increased with an increasing flow rate, the resistance loss along the pipeline and the local loss increased. Therefore, the larger the flow rate, the greater the error of the experimental and numerical results.  
Table 3 shows the head values comparison between the numerical simulation and the experiment of the multiphase mixed-transport pump at the rated flow rate under different air content conditions. With increasing IGVFs, the head value of the mixed-transport pump decreased continuously. Moreover, the error value between the numerical simulation and experiment increased, thereby indicating that the gas content had a considerable influence on the characteristics of the mixed-transport pump. When the inlet gas content was less than 20%, the numerical results were good agreed with the experimental results, and the relative deviations were within the allowable region. When the IGVF was greater than 20%, the numerical simulation result deviated remarkably from the experimental value. Thus, the numerical calculation method was suitable for the numerical simulation when the IGVF was less than 20%. The numerical calculation method under a high gas content should be further studied.