## 4 Optimization Design Scheme and Results Analysis
### Results Analysis  
Figure 11 shows the changes trend of the head coefficient \(\Psi\) and efficiency \(\eta\) with different thickness schemes under the designed working condition when the inlet gas volume fraction was 0.5. Figure 11 shows that when \(\delta_{\text{{hmax}}}\) remained unchanged and \(\delta_{\text{{smax}}}\) increased--i.e., reducing the thickness ratio coefficient \(\xi\)--the head coefficient and efficiency increase accordingly in every scheme. The data of the four schemes show the same trend, which is helpful for summarizing the relationship between the hydraulic performance of the multiphase pump and the thickness ratio coefficient. We concluded that the reduction in the thickness ratio coefficient \(\xi\) with the same \(\delta_{\text{{hmax}}}\) was conducive to improving the boosting capability and efficiency of multiphase pumps. 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. Figure 10: Thick airfoil schemes. Figure 12 shows the main area of gas accumulation in the flow passage, which is the outlet of the impeller suction side near the hub; the mixing of the gas-liquid two-phase in the other regions of the impeller was better than the accumulation area. Therefore, 10% of the blade height surface was selected to analyze the distribution of the gas-liquid two-phase in the flow passage. Figure 11: The relationship of the (**a**) head coefficient and (**b**) efficiency with different thickness schemes. Figure 13 shows the distribution of gas at 10% of the blade height with different thickness schemes when the inlet gas volume fraction was 0.5. Since too many figures will occupy a large space in the article, we selected only the distribution of gas with scheme 1 and scheme 4 in Figure 13. As the gas phase mainly accumulates at the hub and gradually decreased from the hub to the shroud, the volume distribution of gas phase at 10% of the blade height near the hub was selected for analysis. Figure 13 shows that, when keeping \(\delta_{hmax}\) unchanged and increasing \(\delta_{smax}\), which was equivalent to the process of decreasing the thickness ratio coefficient \(\xi\), the accumulation phenomenon of gas also improved. The gas mainly accumulated at the blade outlet of the suction side near the hub. The gas-liquid two-phase flow near the pressure side was always well mixed, and thus no significant separation phenomenon occurred. Figure 12: The accumulation of gas in the flow passage. With the linear thickening of the blade from hub to shroud, different values of the thickness ratio coefficient \(\xi\) corresponded to different profile lines of the blade; the profile of the pressure side was the same when the thickness ratio coefficient \(\xi\) changes. The changes in the airfoil thickness impacted the inclination degree of the blade backside. During the rotation of the impeller, the pressure side and the suction side of the blade acted with force on the two-phase medium. The force will change due to the changes in the inclination degree following the change in thickness. The larger the thickness ratio coefficient \(\xi\), the more inclined the backside of the blade is toward the shroud. Under the coupling action of centrifugal force and the force acted by the suction side of the blade, the high-density liquid phase becomes closer to the area near the shroud and the low-density gas phase moves closer to the hub. When the thickness ratio coefficient \(\xi\geq 1\), the radial component direction of the force points to the shroud along the hub, which was exerted on the gas-liquid two-phase medium by the suction side of the blade. This is consistent with the direction of the centrifugal force and provides an additional promotion of the separation of the gas-liquid two-phase flow. Thus, the separation of gas-liquid two-phase flow is more serious and causes the hydraulic head of the multiphase pump to decrease.