## 4 Results
### Local Pressure  
Several pressure probes have been set in the computational domain as shown in Figure 7. Two probes are located in two different guide vane channels, six are located on a runner blade with three on the pressure side and three others on the suction side, two times four probes are distributed at ninety degrees on the wall in two sections of the draft tube cone (as in the experiment) and finally two probes are set in the draft tube elbow.  
For each probe, the fluctuations of the pressure coefficient are computed by subtracting the average pressure at the probe location and then by dividing the result by \(0.5\,\rho\,U_{\rm I}^{2}\) (with \(U_{\rm I}\) the peripheral velocity at the runner outlet). In addition, for the probes in the cone of the draft tube, a spatial averaging is also performed.  
The pressure signals on the pressure side of the runner at the leading edge (probe Ru1) and on the suction side of the trailing edge (probe Ru6) and in the two sections of the  
Figure 6: Magnitude of the Fourier transform of the efficiency (left) and volume of vapour (right) signals.  
Figure 7: Positions of pressure probe in the computational domain (left). Zoom on the runner probe locations (right).  
draft tube cone are displayed in Figure 8. In the draft tube cone, the experimental pressure signals are also added.  
At the leading edge of the runner, the pressure fluctuations captured by the three simulations are identical with a high frequency content. At the trailing edge, the fluctuations at high frequency alternate with a flat period corresponding to the period during which the probe is covered by a pure vapour sheet. No clear pattern can be observed. In the draft tube cone, compared to the experiment, the simulations _Case 2_ and _Case 3_ are smoother without a strong peak of pressure after the partial collapse of the vortex rope. Simulation _Case 1_ presents a strong pressure peak at the collapse of the vortex rope, which seems to follow qualitatively the trends of the experimental one. However, as already mentioned, the simulation diverges after the collapse.  
The Fourier transforms of the pressure signals in the runner and the draft tube are represented in Figure 9. At the leading edge of the runner, the guide vane passage frequency \(f_{gy}=20f_{n}\) and its harmonic until the fourth are clearly observed. At the trailing edge, only the fundamental is observed. In addition, a frequency around \(120f_{n}\) is captured by the simulations _Case 2_ and _Case 3_. This frequency is also observed in the cone of the draft tube but with an attenuation. The origin of this frequency is not clear.  
In the draft tube, the comparison of the simulation _Case 2_ with the experiment makes the presence of the low frequency appear around \(0.3f_{n}\) in the simulation instead of \(0.25f_{n}\) in the experiment. Obviously, the amplitude is low compared to the experiment due to the  
Figure 8: Time history of the pressure fluctuations in the runner and the draft tube cone. The zero of experimental signal has been set arbitrary.  
inability of the simulation to capture accurately the collapse of the vortex rope as shown in Figure 8.