## 3 Results: Analysis of the Non-Steady-State Wear
### Low Flow Rate Condition  
The model pump impeller has three blades, which are evenly arranged in the circumferential direction. Therefore, the flow process of one third of a cycle correctly reflects the wear characteristics of an entire impeller rotation cycle. Using a low flow rate (0.68 \(Q_{d}\)), the evolution process of the surface wear rate of the impellers and guide vanes was analyzed during one third of a rotation cycle (120\({}^{\circ}\)) of the impellers.  
Figures 4-7 show the evolution process of the surface wear rate of the first- and second-stage impellers, as well as that of the first- and second-stage guide vanes during one third of the rotation cycle (120\({}^{\circ}\)) of the impeller with a low flow rate (0.68 \(Q_{d}\)).  
\begin{table}
\begin{tabular}{c c c c c c} \hline \(b\) & \(c\) & \(x\) & \(y\) & \(w\) & \(z\) \\ \hline \(-\)13.3 & 7.85 & 1.09 & 0.125 & 1 & 1 \\ \hline \end{tabular} \(b\), \(c\), \(x\), \(y\), \(w\), and \(z\) are empirical constants in the impact angle function equation.  
\end{table}
Table 1: Values of parameters in the impact angle equation.  
Figure 5: Surface wear rate evolution of the second-stage impeller. (**a**) 0\({}^{\circ}\), (**b**) 24\({}^{\circ}\), (**c**) 48\({}^{\circ}\), (**d**) 72\({}^{\circ}\), (**e**) 96\({}^{\circ}\), (**f**) 120\({}^{\circ}\).  
Figure 6: Surface wear rate evolution of the first-stage guide vane. (**a**) 0\({}^{\circ}\), (**b**) 24\({}^{\circ}\), (**c**) 48\({}^{\circ}\), (**d**) 72\({}^{\circ}\), (**e**) 96\({}^{\circ}\), (**f**) 120\({}^{\circ}\).  
The surface wear of the impellers in Figures 4 and 5 reveals that during the rotation of the impeller, the relative position of the surface damage due to the wear of the solid particles on the impeller does not change, and the wear rate also remains stable. The wear damage is concentrated in the middle of each flow channel on the front shroud of the impeller, the blade inlet, and the hub near the blade inlet. Moreover, the area of the wear damage on the front shroud increases as the area of the front shroud for each flow channel increases. Unlike for the second-stage impeller, the wear damage on the surface of the first-stage impeller is more dispersed as the turbulent flow in the first-stage impeller with a low flow rate caused multiple collisions between particles and the surface of the impeller.  
The surface wear of the guide vanes shown in Figures 6 and 7 reveals that the wear due to particles on the surface of the guide vanes changes exhibits a pattern resembling bands, similar to that observed on the second-stage impeller, but the wear damage is more serious overall. After the particles are thrown out of the impeller outlet, their circular motion will continue over a certain distance until the particles finally collide with the surface of the blade in the middle of the guide vane. At this point, the wear rate reaches its maximum, and wear damage is relatively more concentrated in this area. In addition, these figures indicate that although the relative position between the impeller and guide vane changes over time, this change is periodical, resulting in interference between the dynamic impeller and static guide vane. Nevertheless, the wear on the surface of the guide vanes does not change significantly during this process.