## 2 Design and Modeling of Helical-Axial Multiphase Pump
### Mesh Generation  
The mesh generator ICEM-CFD (education column) is used in the research, which is a comprehensive mesh generation tool. It is one of the most widely used mesh generator in recent years. It can also complete the mesh generation of models with complex geometric structure, because this mesh generator has the features such as model repair and mesh editing, so the high-quality mesh can be obtained. The impeller of the helical axial multiphase pump has complex structure with square channel and large curvature radius, so the mesh generator ICEM-CFD is employed to divide the unstructured mesh of the computational domain. The unstructured grid, with more flexibility and adaptability to the complex model, was used to divide the hydraulic parts of the multiphase pump. This kind of grids has no regular topological structure and no concept of layers. The distribution of grid nodes is arbitrary, so it has the property of flexibility and the distribution of the divided grids is reasonable. The rationality of grid distribution also affects the accuracy of numerical simulation, the unstructured grids has the reasonable distribution of grids, in addition, the grids near the blade are locally encrypted because the flow condition of this area changes dramatically. In order to ensure the accuracy of the numerical calculation and save the calculation time, the denser grids are distributed in the area where the flow field changes greatly, so the flow condition near this area can be described in more detail. The structured grid was used to divide the inlet and outlet sections using a simple structure. The overall grids were of high-quality at above 0.35, so the grids can be used in numerical simulations. The value 0.35 represents the quality of the grids. The criterion of grids quality generally includes orthogonality and smoothness of the grids [31]. Orthogonality of the grids means that the lines or faces of the grids should be as orthogonal as possible, the better the orthogonality, the higher the grids quality. The smoothness of the grids is usually represented by the dimensional change ratio between adjacent grids. The dimensional change ratio between adjacent grids should not exceed 2, which means the transition of grids is gradual, not a sudden change. The mesh smoothing function can be used if the smoothness of the grids is poor. There are certain requirements for the grids that can be used in numerical simulation calculations, such as the grids need to be checked and the quality of the grids needs to be higher than a certain value. The unstructured grids will be checked for errors after dividing, such as if there are duplicate element or missing internal faces. It must be guaranteed that there are no errors of grids, so the grids will meet the requirement for numerical simulation. According to the professional literature [32], the minimum quality of the grids used for numerical simulation is at least 0.2. The quality of grids can affect the accuracy of numerical simulation. If the quality of grids is less than 0.2, the accuracy of the numerical simulation will be reduced. The quality of grids in the manuscript has been checked and is higher than 0.35, which is above the minimum requirement for grids quality, the grids can be used in numerical simulations. To reduce the influence of the grid density on the numerical simulation results, all five sets of mesh are employed to conduct the independence test of mesh number under the design condition with an inlet gas volume fraction of 30%. Table 4 shows the predicted results of the hydraulic head and efficiency of the multiphase pump with different mesh schemes; it can be seen that the differences  
Figure 1: The model of the impeller and diffuser. of the hydraulic head and efficiency in schemes 3, 4 and 5 were relatively small. Therefore, the total number of cells was finally selected as 7.541 million for numerical simulation to reduce the required computing resources.