# On the Vaneless Space Vortex Structures in a Kaplan Turbine Model Operating at Speed No Load
## 3 Results
### Cavitation Effects on 2V and 3V Structures  
Figure 9 permits to compare the TGV, PVS\({}_{\text{A}}\), SB\({}_{\text{R}}\), S\({}_{\text{T}}\) and A0y spectra when the turbine is operated under non-cavitation and cavitation conditions. A first observation is that the frequencies of the 2V and the 3V under non-cavitation conditions are approximately equal to those measured under cavitation conditions. For instance, the 2V peaks show exactly the same frequency for all SNL conditions and the 3V peaks only present a slight frequency decrease of less than 0.25% at 7.35\({}^{\circ}\). The VSV structures originate at the vaneless space and thus above the runner blades, at the high-pressure side of the turbine. However, cavitation usually occurs at the low-pressure side, below the runner blades. The frequency of the VSV structures may not be altered under cavitation condition because the amount of cavitation generated at the vaneless space might be low.  
Figure 8: _Cont._  
\begin{table}
\begin{tabular}{c c c c c} \hline  & & \multicolumn{2}{c}{\(\boldsymbol{\alpha}\) [\({}^{\circ}\)]} & \\ \cline{2-5}  & \(\boldsymbol{2.6}^{\circ}\) & \(\boldsymbol{3.98}^{\circ}\) & \(\boldsymbol{6.8}^{\circ}\) & \(\boldsymbol{7.35}^{\circ}\) \\ \hline
2V & 2.72 Hz & 2.27 Hz & 1.78 Hz & 1.66 Hz \\
3V & 2.96 Hz & 2.57 Hz & 2.16 Hz & 2.08 Hz \\ \hline \end{tabular}
\end{table}
Table 3: Reduced frequencies calculated with Equation (11) that should be detected from an off-board sensor measuring the vibrations transmitted from the rotor for 2V and 3V.  
The amplitudes of the 2V peaks at 3.98\({}^{\circ}\) under cavitation conditions are approximately equal to those found under non-cavitation conditions. However, the 2V induced amplitudes under cavitation conditions are consistently lower than those under non-cavitation conditions at 8.13\({}^{\circ}\). Similarly, the amplitudes of the 3V peaks at 3.98\({}^{\circ}\) and 7.35\({}^{\circ}\) under cavitation are also consistently lower than those under non-cavitation for most of the signals. Although there is a low degree of cavitation generated in the vaneless space, the intensity of the VSV structures decrease when the turbine is operated under cavitation conditions.  
Exceptionally, A0y shows similar 3V amplitudes under cavitation and non-cavitation conditions at 3.98\({}^{\circ}\) and a 3V amplitude increase with cavitation at 7.35\({}^{\circ}\). This amplitude increase cannot be explained considering a lineal transmission from the hydraulic excitation in the vaneless space to the turbine supporting structure. A0y is mounted on the walls of the draft tube cone and thus at the low-pressure side of the turbine. In this part, the amount of cavitation generated is high and thus it probably has a significant impact on the modal and dynamic response of the draft tube cone. This unexpected amplitude increase could happen due to a change in the natural frequency of the draft tube cone, resulting in a resonance with the 3V excitation, or of the modal properties of the draft tube cone, increasing the dynamic response at the 3V frequency.  
Figure 8: (**a**) Spectra and (**b**) induced amplitudes of draft tube cone vibration velocity (A0y) at \(\alpha\) equal to 2.6\({}^{\circ}\), 3.98\({}^{\circ}\), 6.8\({}^{\circ}\) and 7.35\({}^{\circ}\).