# Experimental Flow Performance Investigation of Francis Turbines from Model to Prototype
## 3 Experimental Results and Discussions
### Pressure Pulsation Impacts on Hydraulics Performance  
The analysis of pressure pulsations is crucial for validating prototype turbine designs, optimizing performance, and establishing a foundation for hydraulic stability, vibration, noise, and cavitation in Francis turbines. These pressure pulsations initiate from various sources, such as rotor-stator interactions, guide vane opening, and turbulent flows, which induce pressure fluctuations throughout the entire turbine domain. Parameters affected by pressure pulsations include discharge, head, and power output, all of which are critical to the turbine's overall efficiency. Figure 9 illustrates the peak-to-peak values and frequency spectra under design head with various working conditions from 50% to 100% load, and four points (\(P_{1}\) spiral inlet, \(P_{2}\) head cover, \(P_{3}\) draft tube cone, and \(P_{4}\) draft tube elbow) were selected to measure the magnitude of pressure changes across the entire turbine domain. Figure 8: Cavitation formation and vortex rope of the model runner at (**a**) 38.10 m and (**b**) 37.50 m.  
Table 3 presents the maximum peak-to-peak amplitude values and frequency amplitude spectra under conditions with and without air compensation in the draft tube. Without air injection, the highest amplitudes were consistently observed at the 50% load. At four points (\(P_{1}\) spiral inlet, \(P_{2}\) head cover, \(P_{3}\) draft tube cone, and \(P_{4}\) draft tube elbow) significant change in peak-to-peak amplitudes was noted as the working conditions changed from 50% to 100% load. Pressure pulsation amplitude data at 100% load indicated no low-pressure phenomena related to cavitation, vibration, or noise, and turbine performance reached its best efficiency. When the air was injected, only a slight changing amplitude was detected at sensor \(P_{1}\), causing a minor shift towards higher frequencies. The effect of air injection on damping was relatively minimal, with hydraulic performance remaining consistent under partial load conditions. The results, presented in Figures 10-12, were obtained through an experimental investigation of the flow field and opening guide vane angle. These Figures include time and frequency domain curves measured at four monitoring points: \(P_{1}\) spiral inlet, \(P_{2}\) head cover, \(P_{3}\) draft tube cone, \(P_{4}\) draft tube elbow. When the Francis turbine model operated at the minimum head of 38.10 m under 50% to 100% load, pressure fluctuation amplitudes at \(P_{1}\) (spiral inlet) were observed to be higher than those at the design head of 38.50 m and the maximum head of 37.50 m. The pressure pulse amplitude of \(P_{2}\) (head cover) was measured to be higher at the design head (38.50 m) compared to both the minimum head (38.10 m) and the maximum head (37.50 m). It was also observed that there were no vibrations or sounds when the guide vane opening angle was adjusted under various working conditions. At the design head of 38.50 m and 50-100% load working conditions, the pressure at the \(P_{3}\) (draft tube cone) was higher than the minimum and maximum head working conditions, though the pressure fluctuation amplitudes at the draft tube cone and \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Model** & **Suction** & **Air Compensation Coefficient** & **Air Compensation Coefficient** \\
**Head** & **Head** & \(\phi\) **= 0 (\%) (without Air)** & \(\phi\) **= 0 (\%) (with Air)** \\ \hline m & m & \(\triangle\)H/H(\%) and \(f/f_{n}\) & \(\triangle\)H/H(\%) and \(f/f_{n}\) \\ \hline
38.10 & \(-\)2.63 & 1.12 and 0.07 & 2.14 and 0.172 \\ \hline
38.50 & \(-\)2.58 & 1.01 and 0.284 & 0.58 and 0.03 \\ \hline
37.50 & \(-\)2.55 & 1.02 and 0.058 & 0.86 and 0.105 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Peak-to-peak \(\triangle\)H/H(%) values with and without air injection. Figure 9: Peak-to-peak values (\(\triangle\)H/Hm) within the inlet, head cover, draft tube cone, and elbow at different partial loads 50–100% at 38.50 m  
the flow exit to the draft elbow showed only minor differences.