## 4 Computational-Experimental Result Verification  
Computational fluid dynamics (CFD) method was used for predicting the flow field in centrifugal pump impellers with different leading-edge shapes. To have an accurate computational result, a computational-experimental result verification was conducted at first. The relative velocity, \(V\), vectors on the spanwise 50% surface, the contour of turbulence kinetic energy (\(k_{2D}\)) on the spanwise 50% surface, and the relative radial velocity (\(V_{r}\)/\(U_{2}\)) distribution on the spanwise 50% surface at \(R=0.9\ R_{2}\) were compared. \(U_{2}\) denotes the rotational linear velocity at \(R=R_{2}\). Figure 4 shows the CFD predicted relative velocity (\(V\)) vectors on the spanwise 50% surface. It can be compared with the experimental data by [PERSON] et al. in Ref. [32]. The alternate stall pattern, which includes three well-behaved and three stalled passages, can be observed in the impeller. The symbols \"A\" and \"B\"--\"A\" denotes the well-behaved passage, and \"B\" denotes the stalled passage--were drawn on this figure. CFD simulation captured the flow separation at leading-edge on the blade suction side and the backflow near the outlet in the B passage. The large-scale \"vortex\" flow was also found in the middle of the B passage. These undesirable flow structures were also measured in the experiment. Figure 5 shows the CFD-predicted contour of turbulence kinetic energy (\(k_{2D}\)) on the spanwise 50% surface, compared with the experimental data in Ref. [32]. There were three high \(k_{2D}\) cites captured. Firstly, a high \(k_{2D}\) cite occurred at the leading-edge flow separation region in the B passage. Secondly, a high \(k_{2D}\) cite occurred on the blade suction side in the middle of the A passage. Thirdly, a high \(k_{2D}\) cite generated at the impeller outlet in the B passage. These three high \(k_{2D}\) cites were also captured in the experiment, which proved the CFD simulation to be relatively accurate. However, there is a deviation that shows the experimental \(k_{2D}\) value at the impeller outlet was stronger than CFD simulation. In this computational case, only the impeller domain was considered. In the experimental study of Reference [32], a vaned-diffuser was set downstream to the impeller. The intensity of \(k_{2D}\) would be influenced by the vaned-diffuser. In this study, the main target was to compare the internal flow among different leading-edge impellers. Thus, the CFD simulation can be considered correct and accurate. \begin{table}
\begin{tabular}{l c c} \hline \hline
**No.** & **Mesh Node Number of Initial Impeller** & **Residual of Hydraulic Efficiency** \\ \hline
1 & 159,836 & - \\
2 & 323,332 & 2.53\% \\
3 & 602,024 & 1.32\% \\
4 & 1,500,322 & 0.951\% \\
5 & 3,112,086 & 0.217\% \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Mesh independence check details. To have a better comparison near impeller outlet, the radial velocity, which represents the flow direction, was compared at \(R=0.9\ R_{2}\). Figure 6 compares the relative radial velocity, \(V_{r}/U_{2}\), distribution on the spanwise 50% surface at \(R=0.9\ R_{2}\). Generally, the distribution laws were similar between the CFD data and the experimental data. In detail, in the A passages, the radial velocity from the CFD simulation was larger than that from by experimental test. In the middle of the B passages, the CFD-predicted radial velocity was higher than that of the experimental data. These two differences might also be influenced by the downstream vaned-diffuser and may have changed the local velocity intensity. Figure 4: Relative velocity (\(V\)) vectors on the spanwise 50% surface by CFD, the experimental pattern can be found in Reference [32]. A: well-behaved passage, B: stalled passage. Figure 5: Contour of turbulence kinetic energy \(k_{\rm 2D}\) on the spanwise 50% surface by CFD, the experimental pattern can be found in Reference [32]. A: well-behaved passage, B: stalled passage.