## 4 BEP Results

Table 4: List of the computations performed at the BEP. \begin{table}
\begin{tabular}{l c c c c} \hline \hline
**Reference** & \(Q_{ED}\) & \(n_{ED}\) & \(P_{ED}\) & \(\eta^{*}\) \\ \hline CFD1 & 0.187 & 0.268 & 0.175 & 1.00 \\ CFD2 & 0.190 & 0.271 & 0.177 & 1.00 \\ CFD3 & 0.188 & 0.269 & 0.177 & 1.01 \\ CFD4 & 0.187 & 0.267 & 0.174 & 0.99 \\ CFD5 & 0.186 & 0.275 & 0.174 & 1.00 \\ CFD6 & 0.187 & 0.268 & 0.178 & 1.01 \\ \hline EXP & 0.183 & 0.271 & 0.171 & 1.00 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: CFD results at the BEP compared with the measurements. The \(y^{+}\) contours on one of the blades are displayed in Figure 5 for both simulations CFD1 and CFD2. The refined mesh led to a reduction of the \(y^{+}\) by a factor of three. The \(y^{+}\) were very high in two regions: one on the pressure side at the trailing edge close to the shroud and one on the suction side at the leading edge close to the shroud. In order to investigate the influence of the \(y^{+}\) values on the flow in the turbine, the contours of the dimensionless magnitude of the relative velocity, pressure, eddy viscosity, and wall shear stress on the suction side of one blade are shown in Figure 6 for both meshes. For each quantity, the pattern of the contours was the same. The differences between the two meshes were observed mainly for the dimensionless eddy viscosity, which is lower on the refined mesh, as expected. The wall shear stress was slightly higher on the refined mesh at the shroud close to the leading edge. The relative velocity differed along the shroud with a lower value predicted by the refined mesh, which is in agreement with the refinement of the mesh at the walls. Finally, the contours of the dimensionless magnitude of the vorticity and eddy viscosity in a cross-section of a blade channel are displayed in Figure 7. The pattern for the two quantities was rather the same for the two meshes, even if close to the hub, the simulation CFD1 made a region with a low magnitude of the vorticity appear, which is not observed on the refined mesh (simulation CFD2). Figure 4: (**a**) Dimensionless pressure contours on the meridional plane, CFD1 structured mesh, BEP. (**b**) Dimensionless pressure contours on the meridional plane, CFD2 refined structured mesh, BEP. (**c**) Dimensionless axial velocity contours on the meridional plane, CFD1 structured mesh, BEP. (**d**) Dimensionless axial velocity contours on the meridional plane, CFD2 refined structured mesh, BEP. Figure 5: Contours of the \(y^{+}\) quantity, BEP. (**a**) Pressure side of a blade, CFD1 structured mesh. (**b**) Pressure side of a blade, CFD2 refined structured mesh. (**c**) Suction side of a blade, CFD1 structured mesh. (**d**) Suction side of a blade, CFD2 refined structured mesh. Figure 6: (**a**) Contours of the dimensionless magnitude of the relative velocity \(u^{*}\) on the suction side of a blade, CFD1 structured mesh, BEP. (**b**) Contours of the dimensionless magnitude of the relative velocity \(u^{*}\) on the suction side of a blade, CFD2 refined structured mesh, BEP. (**c**) Contours of the dimensionless pressure \(p^{*}\) on the suction side of a blade, CFD1 structured mesh, BEP. (**d**) Contours of the dimensionless pressure \(p^{*}\) on the suction side of a blade, CFD2 refined structured mesh, BEP. (**e**) Contours of the dimensionless eddy viscosity \(v_{t}^{*}\) on the suction side of a blade, CFD1 structured mesh, BEP. (**f**) Contours of the dimensionless eddy viscosity \(v_{t}^{*}\) on the suction side of a blade, CFD2 refined structured mesh, BEP. (**g**) Contours of the dimensionless wall shear \(\tau_{w}^{*}\) on the suction side of a blade, CFD1 structured mesh, BEP. (**h**) Contours of the dimensionless wall shear \(\tau_{w}^{*}\) on the suction side of a blade, CFD2 refined structured mesh, BEP. From the above analysis of the flow, it can be concluded that the simulation CFD1, with a slightly coarse mesh at the walls, allowed capturing the main features of the flow with an acceptable accuracy.