# Experimental Flow Performance Investigation of Francis Turbines from Model to Prototype
## 3 Experimental Results and Discussions
### Cavitation Development and Effects on Hydraulic Performance  
This study aims to predict performance and the impact of cavitation characteristics on the entire turbine domain, focusing on their impact on efficiency. [PERSON] [26] suggests the use of the cavitation number or sigma (\(\sigma\)) to determine the occurrence of cavitation in a turbine. A decreasing sigma (\(\sigma\)) significantly impacts component wear and material loss, resulting in reduced efficiency. The critical cavitation factor, or sigma (\(\sigma_{c}\)), varies depending on the turbine's specific speed. Figure 7 illustrates the cavitation formation and vortex rope of the model runner with a head of 38.50 m. At 50% partial load, the critical cavitation coefficient (\(\sigma_{c}\)) was measured, and initial cavitation began at the blade outlet due to low-pressure phenomena forming a vortex rope at the runner outlet that could be seen at the draft tube cone. When the turbine model load was changed from 70% to 80% and the guide vane opening was changed from 5.56\({}^{\circ}\) to 7.10\({}^{\circ}\), it can be seen that the efficiency fluctuated slightly, but  
Figure 6: Performance hill chart. (**a**) Model turbine. (**b**) Prototype turbine. there was no low-pressure phenomenon; the vortex rope still extended smoothly to the draft tube elbow, and the cavitation number (\(\sigma\)) was still larger than the critical cavitation number (\(\sigma_{c}\)). However, these cavitation bubbles rapidly disappeared when the working conditions changed. No cavitation or bubble formation was observed at the blade outlet when the turbine operated at 100% load. When the turbine model reached 100% load, with all other parameters including flow rates, speed, head, and guide vane opening angle at their maximum values, the turbine efficiency achieved 93.66%. Additionally, the observed cavitation number (\(\sigma\)) remained the same or higher than the critical cavitation number (\(\sigma_{c}\)). However, no cavitation or bubble formation was observed at the blade outlet and draft tube cone when the turbine operated at 100% load. Figure 8a,b illustrates the turbine operating conditions at both minimum (38.10 m) and maximum (37.10 m) head levels. When the model turbine operated at a minimum head of 38.10 m under 50% load and the minimum speed of the runner, it was observed that the vortex rope at the draft tube cone collapsed, with initial bubble formation being more visible than under design head-level operating conditions. This phenomenon was attributed to the low pressure, the low runner speed, and the guide vane opening angle. When the turbine model operated at 100% load, the vortex rope ran smoothly from the runner outlet towards the draft tube elbow. It was observed that the critical cavitation factor (\(\sigma_{c}\)) was lower than the cavitation coefficient (\(\sigma\)) or the plant's cavitation number. Initial bubble formation was noted at the hub and blade outlet, but these bubbles rapidly disappeared as working conditions changed. The vortex rope rotations indicated that initial cavitation bubble formation occurred at the draft tube cone and elbow. We the Francis turbine model was operating at 50% load with the maximum head (37.50 m), it can be seen that the efficiency was slightly higher than the minimum and design head-level working conditions, but when the turbine model operated at 100% load, maximum efficiency was slightly lower than the minimum head-level operating conditions. However, the cavitation factor (\(\sigma\)) remained the same, that is, bigger than the critical cavitation factor (\(\sigma_{c}\)). As the turbine model operated under all load conditions, vortex rope rotation was smooth, and the initial bubble formation rapidly disappeared at 100% load. The model Francis turbine achieved a maximum efficiency of 93.66%, and the cavitation factor (\(\sigma\)) was measured at 0.0429. [PERSON] et al. [21] investigated cavitation phenomena in a Francis turbine, varying the runner's rotation speed from 413.5 rpm to 649.7 rpm.