## 3 Numerical Simulation and Results Analysis  
### Numerical Method  
With the pressure increase of the multiphase pump, the gas volume fraction changes with the work process. It is assumed that the gas-liquid two-phase flow is incompressible bubble flow. The compressibility of gas can be determined by the Mach number. The compressibility of gas is not considered when the Mach number is less than 0.3. Since the speed of the fluid in the helical-axial multiphase pump is far less than the local speed of sound, its Mach number is less than 0.3. Therefore, the compressibility of the gas phase is not considered in the numerical simulation of the article [33]. Considering the high-volume fraction of the gas phase and the stability and rationality of the simulation results, we selected the high-accuracy Eulerian multiphase model to conduct the steady-state calculation in the numerical simulation. The hydraulic performance of the multiphase pump with different thickness ratio coefficient schemes can be investigated by the numerical simulation method, the distribution of gas-phase can also be obtained by the steady-state simulation. The steady-state simulation has the characteristics of reliable results and easy convergence; therefore, the steady-state simulation is adopted in the research. The Eulerian multiphase model is suitable for mixed or separated flows. It has a good effect in simulating the aggregation and fragmentation of gas and is commonly used. The Eulerian multiphase  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline  & & & & \\ \hline
**Components** & **1** & **2** & **3** & **4** & **5** \\ \hline Inlet domain & 1,522,500 & 1,522,500 & 1,522,500 & 1,522,500 & 1,522,500 \\ Impeller & 625,907 & 1,193,245 & 2,761,281 & 3,618,690 & 4,780,106 \\ Diffuse & 772,633 & 1,417,004 & 1,735,270 & 2,458,466 & 3,177,553 \\ Outlet domain & 1,522,500 & 1,522,500 & 1,522,500 & 1,522,500 & 1,522,500 \\ Total meshes & 4,443,540 & 5,655,249 & 7,541,551 & 9,122,156 & 11,002,659 \\ Hydraulic head & 32.61 & 31.86 & 31.4 & 31.36 & 31.33 \\ Efficiency & 68.1\% & 67.3\% & 66.2\% & 66.17\% & 66.13\% \\ \hline \hline \end{tabular}
\end{table}
Table 4: Independence test of mesh number.  
Figure 2: Grids of a single compression unit.  
model establishes a momentum equation and continuity equation for each phase; the interaction between the two phases and the transfer of physical quantities on the phase interface are considered in the model, so the flow characteristics of the research object can be described more accurately [34]. The shear stress transport (SST) _k-w_ turbulence model, which is appropriate for the prediction of flow separation among two-equation linear eddy-viscosity models, was adopted [35]. This model combines the advantage of _k-w_ model in simulating the near-wall flow and that of the _k-\(\varepsilon\)_ model in simulating flow outside the boundary layer [36]. Thus, the SST _k-w_ turbulence model can be used to obtain a very high accuracy and stability of the solution. In addition, it has been found that SST _k-w_ turbulence model does a better job of predicting flow field in impeller than other turbulence models [37]; it is widely used in relevant studies on gas-liquid two-phase flow [38; 39]. The pressure-based solver can provide Eulerian multiphase model, which is adopted in the numerical simulation. The pressure-based solver is mainly used in the incompressible flow and has the feature of fast convergence, the gas-liquid two-phase flow in the research is incompressible, so the pressure-based solver is employed in the research. The phase-coupled SIMPLE scheme was used in the pressure-velocity coupling calculation.  
The applicability of different multiphase models and turbulence models [40] are shown in Tables 5 and 6.  
Combined with the application of different multiphase models and turbulence models, the Eulerian multiphase model and SST _k-w_ are the most suitable models that can be used to the numerical simulation of the gas-liquid two-phase flow in the research.