## 5 SNL Results  
The SNL operating point was computed using the different turbulence models described in the governing equations subsection. The procedure for the computations was as follows: first, the SST model was used to compute a steady state simulation, then 6.25 runner revolutions with a time step set to \(0.9^{\circ}\) of revolution per time step were computed, and finally, 6.25 additional runner revolutions with a time step reduced to \(0.36^{\circ}\) of revolution per time step were computed. This last result was used as an initial guess to compute 6.25 additional runner revolutions simulated using: the SST model with the activation of the Curvature Correction and the Production limiter (SST-CC-Plim), the SST-OES model with a value of \(\beta^{*}=0.02\), the SST-SAS model, and the BSL-EARSM model. The CPU time required for 6.25 runner revolutions was around \(5\times 10^{7}\) s, which corresponds to approximately one month on 24 CPUs. The time history of the discharge and speed factors are displayed in Figure 8. A low frequency was observed on both factors for each turbulence model except for the SST-OES model, which seemed to converge to a stable operating point. The four other turbulence models presented a similar time evolution of the global parameters of the turbine. The time-averaged values of the \(Q_{ED}\) and \(n_{ED}\) over 6.25 runner revolutions are given in Table 6 for each simulation. However, for the SST-OES model, the final values of the \(Q_{ED}=0.0168\) and \(n_{ED}=0.269\) were more valuable. Comparing with the experimental data, the SST-OES model was the one that provided the closest values of the \(Q_{ED}\) and \(n_{ED}\) within an accuracy of 1%. The others turbulence models overestimated the \(Q_{ED}\) and \(n_{ED}\), whereas, for the BSL-EARSM model, a maximum overestimation of the \(Q_{ED}\) value by 4.7% and of the \(n_{ED}\) value by 5.2%. Figure 7: **(a)** Contours of the dimensionless eddy viscosity \(v_{t}^{*}\) in a cross-section of a blade channel, CFD1 structured mesh, BEP. **(b)** Contours of the dimensionless eddy viscosity \(v_{t}^{*}\) in a cross-section of a blade channel, CFD2 refined structured mesh, BEP. **(c)** Contours of the dimensionless vorticity \(\Omega^{*}\) in a cross-section of a blade channel, CFD1 structured mesh, BEP. **(d)** Contours of the dimensionless vorticity \(\Omega^{*}\) in a cross-section of a blade channel, CFD2 refined structured mesh, BEP. **(e)** Position of the cross-section in a blade channel. The contours of the dimensionless axial velocity (Figure 9) and pressure (Figure 10) on the meridional plane did not show any difference between the turbulence models. Comparing to the BEP, the pressure field was not strongly affected, whereas the axial flow was mainly concentrated close to the wall of the draft tube with a recirculation in the center of the draft tube around the tripod. Despite the weak influence of the turbulence model on the mean pressure and axial velocity, the turbulence field was strongly affected by the turbulence model, as shown in Figure 11, which displays the instantaneous contours of the dimensionless eddy viscosity on the meridional plane. Compared to the SST model, the BSL-EARSM and the SST-OES models led to an increase of the eddy viscosity in the runner and the draft tube, whereas the SST-CC-Plim and the SST-SAS models led to a decrease of the eddy viscosity. The large magnitude of the eddy viscosity predicted by the SST-OES model was the explanation for the stable behavior observed on the \(Q_{ED}\) and \(n_{ED}\) factors. \begin{table}
\begin{tabular}{l c c} \hline \hline
**Turbulence Model** & \(Q_{ED}\) & \(n_{ED}\) \\ \hline SST & 0.0176 & 0.280 \\ SST-CC-Plim & 0.0176 & 0.281 \\ SST-OES & 0.0170 & 0.272 \\ SST-SAS & 0.0177 & 0.283 \\ BSL-EARSM & 0.0178 & 0.284 \\ \hline EXP & 0.0170 & 0.270 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: CFD results at the SNL operating point compared with the measurements. Averaged values over 6.25 runner revolutions.