## 5 SNL Results
Figure 8: (a) Time history of the discharge factor \(Q_{ED}\), Speed-No-Load (SNL). (b) Time history of the speed factor \(n_{ED}\), SNL. CC, Curvature Correction; Plim, Production limiter; OES, Organised Eddy Simulation; SAS, Scale-Adaptive Simulation; BSL-EARSM, Baseline Explicit Algebraic Reynodlts Stress Model. Figure 9: Contours of the dimensionless mean axial velocity \(U_{x\,mean}^{*}\) on the meridional plane, SNL. (**a**) SST \(k-\omega\). (**b**) SST-CC-Plim \(k-\omega\). (**c**) SST-OES \(k-\omega\). (**d**) SST-SAS \(k-\omega\). (**e**) BSL-EARSM \(k-\omega\). Figure 10: Contours of the dimensionless mean pressure \(p_{mean}^{*}\) on the meridional plane, SNL. (**a**) SST \(k-\omega\). (**b**) SST-CC-Plim \(k-\omega\). (**c**) SST-OES \(k-\omega\). (**d**) SST-SAS \(k-\omega\). (**e**) BSL-EARSM \(k-\omega\). The instantaneous iso-surface of the Q-criterion in the runner (downstream view) is shown on Figure 12. The SST model predicted a large spanwise vortex close to the trailing edge of the runner blade. Downstream of the vortex, a high pressure region was observed. The vortex was stable in time and identical in each blade channel. The SST-CC-Plim and BSL-EARSM models provided the same pattern, but the vortex was less expanded in the spanwise direction. Moreover, some small vortex shedding was observed with the SST-CC-Plim model. Regarding the SST-OES model, no vortices were present, and the high pressure region disappeared. Finally, the SST-SAS model provided a more chaotic pattern of vortices in the blade channel, with still the presence of a high pressure region in the vicinity of the hub and the blade trailing edge. Figure 11: Instantaneous contours of the dimensionless eddy viscosity \(\
u_{t}^{*}\) on the meridional plane, SNL. (**a**) SST \(k-\omega\). (**b**) SST-CC-Plim \(k-\omega\). (**c**) SST-OES \(k-\omega\). (**d**) SST-SAS \(k-\omega\). (**e**) BSL-EARSM \(k-\omega\). Several probes have been located in one guide vane and blade channel (see Figure 13). The probe GV1 was located upstream of the passage reduction due to the low opening of the guide vanes, whereas the probe GV3 was located just downstream of the passage reduction. The probes Ru1 and Ru19 were located in the middle of the blade channel, whereas the probes Ru26 (close to the trailing edge of the blade) and Ru35 (close to the hub) were located on the suction side downstream of the large spanwise vortex described previously. Figure 12: Instantaneous iso-surface of the Q-criterion and contours of the dimensionless pressure on the hub and one runner blade (downstream view), SNL. (**a**) SST \(k-\omega\). (**b**) SST-CC-Plim \(k-\omega\). (**c**) SST-OES \(k-\omega\). (**d**) SST-SAS \(k-\omega\). (**e**) BSL-EARSM \(k-\omega\). The time history of the dimensionless pressure and velocity magnitude in the guide vane channel is shown on Figure 14. At position GV1, the turbulence model influenced the pressure level, which was higher for the SST-OES model and lower for the SST-SAS and BSL-EARSM models compared with the SST model. The SST-CC-Plim model did not change the pressure level compared to the SST model. At position GV3, the pressure level was the same for all the models, even if the fluctuations were damped by the SST-OES model. Therefore, the pressure drop at the guide vane passage differed between the different models, explaining the differences in the predicted speed and discharge factors. Indeed, since the SST-OES model predicted a higher pressure drop at the guide vanes, then the predicted specific energy was higher, and the speed and discharge factors were lower. Regarding the velocity magnitude, at position GV1, all the models provided the same behavior characterized by a positive slope compared to the SST model. This feature was absent at position GV3, where large velocity fluctuations were observed compared to position GV1, except for the SST-OES model.