## 4 Optimization Design Scheme and Results Analysis
### Results Analysis
Figure 17 shows the variation in the aggregation degree \(\lambda\) with different thickness schemes. When \(\delta_{hmax}\) is unchanged, the aggregation degree \(\lambda\) decreases with the decrease in thickness ratio coefficient \(\xi\), which indicates that the aggregation phenomenon of gas is improved in the flow passage with the reduction in thickness ratio coefficient \(\xi\). This is contrasting to the change trend of the hydraulic performance of the multiphase pump; i.e., the reduction of the hydraulic performance of the multiphase pump is directly related to the aggregation degree \(\lambda\) in the flow channel. The value of \(\lambda\) is inversely related to the hydraulic performance in every thickness scheme. The smaller the value of the aggregation degree \(\lambda\), the better the hydraulic performance of the multiphase pump. The gas accumulation in the flow passage of the multiphase pump can be improved by appropriately reducing the thickness ratio coefficient \(\xi\). The aggregation of the modification multiphase pump is 30.3% lower in comparison to the base pump, which means the aggregation phenomenon of gas phase in the impeller passage is improved after modification. If complete separation does not occur in 90% of the chord length area from the inlet to the outlet in the flow passage, the airfoil of the impeller can be regarded as a super-separated airfoil. The impeller model with scheme 1 of \(\xi\) = 0.8 can delay the completely separated area beyond the region with a chord length greater than 90%. This basically solves the problem of preventing the separation of the gas-liquid phase in the middle and rear parts of the flow passage. The airfoil of the multiphase pump in this scheme can be regarded as a super-separated airfoil. Figure 18 shows the turbulent kinetic energy of the meridional surface with different thickness schemes. We also selected the turbulent kinetic energy with scheme 1 and scheme 4 in Figure 18 to save space in the article. The gradient of the turbulent kinetic energy at the inlet of the impeller was relatively large, because the fluid entering the passage of the impeller impacted the surface of the blade, resulting in unstable flow at the inlet. The flow was more stable in the middle area of the runner. The turbulent kinetic energy and gradient near the hub at the outlet of the impeller were higher than  
Figure 11:1 The variation in the aggregation degree with different thickness schemes. in other regions, which was consistent with the gas accumulation areas in the passage of impeller. Combined with Figure 17, it can be seen that the change trend in the turbulent kinetic energy gradient at the impeller outlet and the aggregation degree \(\lambda\) of each scheme were consistent with the change in the thickness ratio coefficient \(\xi\). When the \(\delta_{lmax}\) was the same, the higher the thickness ratio coefficient \(\xi\) was, the larger the turbulent kinetic energy gradient and aggregation degree. The accumulation of gas caused additional energy loss in the flow passage with the increase of aggregation degree. This reveals why the head coefficient \(\Psi\) and efficiency \(\eta\) increase with the decreases of thickness ratio coefficient \(\xi\). The gas phase aggregation phenomenon in the flow passage of impeller improved and the energy loss decreased, while the thickness ratio coefficient \(\xi\) decreased, so the hydraulic performance of the multiphase pump improved. Considering the technological factors in the actual processing and the crowding-out effect of the blade, the thickness ratio coefficient in the present study could be set as low as 0.8.