## 5 Conclusions  
A single compression unit was designed to investigate the mixture transportation characteristics of the gas-liquid two-phase flow in a helical-axial pump. By comparing the numerical simulation  
Figure 18: Turbulent kinetic energy of meridional surface with different thickening schemes. (**a**) Scheme 1 with \(\delta_{lmax}\) = 7.5 mm and (**b**) scheme 4 with \(\delta_{lmax}\) = 9 mm.  
results and experimental results, the accuracy of the numerical simulation method with the Eulerian multiphase model and the shear stress transport (SST) _k-w_ turbulence model on helical-axial multiphase pumps was validated. The head coefficient and efficiency of a multiphase pump with different schemes were obtained and the flow characteristics were analyzed. The following conclusions could be drawn:  
1. As the head coefficient \(\Psi\) and efficiency \(\eta\) increase, the aggregation degree of gas \(\lambda\) decreased with the decreasing of the thickness ratio coefficient \(\xi\) while the hub thickness was maintained. The head coefficient of the modification multiphase pump was 5.8% higher in comparison to the base pump, while the efficiency was 3.1% higher than that of the base pump; the optimal model in the research was the model of scheme 1 with \(\xi\) = 0.8.
2. When the maximum thickness of the hub was unchanged, the reduction of the thickness ratio coefficient \(\xi\) decreased some of the separation inductive force of the gas-liquid two-phase flow, which is conducive to inhibiting the separation of the gas-liquid two-phase, thus improving the gas-liquid two-phase transportation performance of multiphase pumps.
3. A super-separated airfoil was defined and found to be \(\xi\) = 0.8 in scheme 1, which was able to delay the separation area of the gas and liquid two-phase flow beyond the region with a chord length greater than 90%. The aggregation degree of this model was the lowest, which was 30.3% lower in comparison with the base pump.
4. The change trend in the gradient of turbulent kinetic energy in the flow passage of the impeller was related to the distribution of gas. The gas accumulation region was similar to the area where the gradient of turbulent kinetic energy was large, and so the energy loss could be interpreted. The accumulation phenomenon of gas phase became more and more obvious along the hub side from the inlet to the outlet, especially at the outlet area.
5. The research on the influence of the thickness ratio coefficient on the multiphase pump provided some reference value for the modification design of impellers. In future work, visual observation techniques of the internal flow field can be adopted to provide visual evidence for the modification of the multiphase pump.  
[PERSON] conceived and designed the research, [PERSON] drafted the article, [PERSON] completed the English check, [PERSON] processed the data, [PERSON] was the leader of the research team, and [PERSON] organized the layout of the manuscript. All authors have read and agreed to the published version of the manuscript.  
This study was supported by the National Key R&D Program Projects of China [Grant no. 2018 YFB0606100], and the National Natural Science Foundation of China [Grant no. 51669012, 51966010].  
There are no known conflicts of interest.