## 3 Analysis of Calculation Results
### Comparison of Inner Flow Field  
In order to clarify the variation of \(P_{\text{total}}\) with the backflow clearance, spatial distributions of total dissipation rate of the impeller, backflow clearance, rear guide vane and outlet passage under different \(R_{\text{b}}\) were compared and analyzed, as shown in the following section. Figure 10 shows the cylindrical section of the impeller and guide vane. In addition, the radial coefficient of the cylindrical section \(Span\) is defined as follows:  
\[Span=\frac{R-R_{h}}{R_{s}-R_{h}} \tag{14}\]  
where \(R\), \(R_{\text{h}}\), and \(R_{\text{s}}\) are the radius of the cylinder section, impeller hub, and impeller rim, respectively. Figure 11 shows the velocity distribution in cylindrical section of the impeller with different backflow clearance radii under \(1.0Q_{\text{des}}\). The velocity decreases gradually from the impeller inlet to the impeller outlet, and the highest velocity can be found near the leading edge. Since the impeller outflow returns to the impeller inlet through the backflow clearance, the velocity near the impeller outlet decreases with the increase of \(R_{\text{b}}\). In addition, the clearance backflow mixes with the impeller inflow, resulting in velocity loss, so the velocity near the impeller inlet also decreases with the increase of \(R_{\text{b}}\). Figure 10: Cylindrical section of (**a**) impeller and (**b**) rear guide vane. Figure 12 shows the distribution of total dissipation rate in the cylindrical section of the impeller with different backflow clearance radii under \(1.0Q_{\text{des}}\). Under \(R_{\text{b}}\) = 0 mm, the total dissipation rate in the cylinder section of the impeller is low; only the total dissipation rate near the suction side is high due to the flow separation. However, the backflow through the backflow clearance leads to velocity loss of the impeller inflow and outflow, so the total dissipation rate near the inlet and outlet increases with the increase of \(R_{\text{b}}\). Furthermore, the backflow aggravates flow separation near the suction side and, therefore, the total dissipation rate near the suction side also increases with the increase of \(R_{\text{b}}\). Figure 13 shows the distribution of total dissipation rate on the blade surface under different \(R_{\text{b}}\) at \(1.0Q_{\text{des}}\). The load of the pressure side mainly comes from the impact of the relative circumferential velocity, which gradually increases from hub to rim. Thus, the total dissipation rate near rim of pressure side is the highest, as indicated by the mark in the figure. The load of the suction side also comes from the relative velocity impact, and the relative velocity near the suction side gradually decreases from the leading edge to trailing edge according to Figure 11. Therefore, the total dissipation rate near the leading edge of suction side is the highest, as indicated by the mark in the figure. In addition, because of the velocity loss of the impeller inflow caused by clearance backflow, the total dissipation rate near the rim of pressure side decreases with the increase of \(R_{\text{b}}\). However, the suction side is not only impacted by the impeller inflow but also by the clearance backflow. Although there is a velocity loss of the impeller inflow, the total dissipation rate near the leading edge of the suction side increases with the increase of \(R_{\text{b}}\). Figure 14 shows the leakage flow rate of three backflow clearances under five operation flow rates. Because the flow resistance of the backflow clearance decreases with the increase of \(R_{\text{b}}\), the leakage flow rate rises with the increase of \(R_{\text{b}}\) at same operation flow rate. In addition, the leakage flow is driven by the pressure difference between the impeller inlet and outlet, which decreases with the increase of operation flow rate. Therefore, the leakage flow rate decreases with rise of the operation flow rate.