## 4 BEP Results  
The simulations at the BEP aim at checking and validating the CFD setup using only the SST \(k-\omega\) turbulence model. Several simulations (see Table 4) have been performed in order to investigate the influence of the mesh, the size of the computational domain, the algorithm, and the inlet boundary conditions. Regarding the unsteady simulation CFD6, the time step was set to a \(0.9^{\circ}\) revolution per time step, and three runner revolutions have been computed. \begin{table}
\begin{tabular}{l c c c c c} \hline \hline
**Sub-Domain** & **Structured Mesh** & **Refined Structured Mesh** & **Unstructured Mesh** \\ \hline  & **Min Angle** & **Max Aspect** & **Min Angle** & **Max Aspect** & **Min Angle** & **Max Aspect** \\  & **(deg)** & **Ratio** & **(deg)** & **Ratio** & **(deg)** & **Ratio** \\ \hline Spiral Case & 20 & 2248 & 20 & 2248 & \\ Stay Vanes & 29 & 77 & 29 & 77 & 12 & 592 \\ Guide Vanes & 23 & 62 & 23 & 118 & & \\ \hline Runner & 7 & 75 & 3 & 212 & 30 & 147 \\ \hline Draft Tube & 20 & 171 & 20 & 774 & 20 & 329 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Minimum angle and aspect ratio for each mesh. \begin{table}
\begin{tabular}{l c c c} \hline \hline
**Sub-Domain** & **Structured Mesh** & **Refined Structured Mesh** & **Unstructured Mesh** \\ \hline Spiral Case & 720 & 720 & 90 \\ Stay Vanes & 550 & 550 & 160 \\ Guide Vanes & 850 & 285 & 300 \\ Runner & 2700 & 690 & 250 \\ Draft Tube & 330 & 310 & 90 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Average \(y^{+}\) value on solid walls. Best Efficiency Point (BEP). The results compare the discharge \(Q_{ED}\), the speed \(n_{ED}\), and power \(P_{ED}\) factors and the dimensionless efficiency (the dimensionless efficiency was computed as the ratio between the CFD and measured efficiencies) \(\eta^{*}\) with the measured values (see Table 5). Regarding the discharge factor \(Q_{ED}\), the discrepancy between the CFD and the measurements was between +1.4% for the computation CFD5 with the imposed total pressure at the inlet and +3.8% for the computation CFD2 using the refined structured mesh. For the speed factor \(n_{ED}\), the discrepancy was between \(-1.5\%\) for the computation CFD4 with the extended draft tube and +1.5% for the computation CFD5 with the imposed total pressure at the inlet. The power factor \(P_{ED}\) was overestimated at least by +1.8% and at most by +4%. Finally, the dimensionless efficiency was predicted with 1% of precision. Keeping in mind the uncertainties on the input and measured values and the fact that the leakage flow through the labyrinths is neglected in the CFD, the accuracy of the numerical results was good and not strongly influenced by the numerical setup or the mesh. Figure 4 shows the dimensionless pressure and axial velocity contours in the meridional plane provided by the simulations CFD1 (structured mesh) and CFD2 (refined structured mesh). No differences were observed on the pressure contours between the two meshes. Regarding the axial velocity contours, both simulations gave the same pattern, with spots of high magnitude at the trailing edge of the runner blades close to the shroud. The small differences in the draft tube cone can be related to the use of a frozen interface. \begin{table}
\begin{tabular}{l c c c c c} \hline \hline
**Reference** & **Algorithm** & \begin{tabular}{c} **Rotor/Stator** \\ **Interface** \\ \end{tabular} & \begin{tabular}{c} **Computational** \\ **Domain** \\ \end{tabular} & \
\begin{tabular}{c} **Mesh** \\ \end{tabular} &
\begin{tabular}{c} **Inlet Boundary** \\ **Condition** \\ \end{tabular} \\ \hline CFD1 & Steady & Frozen & standard & structured & mass flow rate \\ CFD2 & Steady & Frozen & standard & refined structured & mass flow rate \\ CFD3 & Steady & Frozen & standard & unstructured & mass flow rate \\ CFD4 & Steady & Frozen & extended & structured & mass flow rate \\ CFD5 & Steady & Frozen & standard & structured & total pressure \\ CFD6 & Unsteady & Transient & standard & structured & mass flow rate \\ \hline \hline \end{tabular}
\end{table}