# On the Vaneless Space Vortex Structures in a Kaplan Turbine Model Operating at Speed No Load
## 1 Introduction
[25] investigated numerically a Kaplan prototype at SNL and compared the results with experimental measurements. The mean quantities were predicted more accurately in the pressure side of the runner blade than in the suction side. However, the amplitude of the torque fluctuations was underestimated by a factor of 30. Four vortex structures below the blades, which joined in pair of two further downstream, were observed. [PERSON] et al. [26] studied numerically the start-up and SNL operation of a bulb turbine and compared the results with experimental measurements. The largest discrepancies were found at SNL since most phenomena at this condition were a consequence of turbulence while the flow inertia effects dominated in the first stage of the start-up. [PERSON] et al. [27] studied the flow-induced excitations coupled to the shaft vibrations on an old and a refurbished Kaplan turbine at SNL. In order to investigate the origin of the vibrations, experimental measurements were performed on both the model and prototype turbines and on a twin unit with the old runner design. They concluded that the origin of the vibrations was a VSV structure whose frequency coincided with a natural frequency of the shaft line and a resonance occurred. It was also observed that the frequency of the flow disturbances depended on the runner blade opening. [PERSON] et al. [28] investigated experimentally and analytically the vortices occurring in the vaneless space of Kaplan turbines at SNL. Air injection was employed to visualize the VSV structures, which were formed by a particular number of vortices precessing at a particular frequency. They found that these VSV structures may cause strong vibrations. [PERSON] et al. [29; 30; 31] studied numerically the VSV structures occurring at SNL on an axial turbine. The vortices attached to the inner head cover were formed in the radial transition between the main flow and a backflow region, which was extended from the inner head cover into the draft tube. Additionally, the topology of these vortices was observed to be independent of the runner. [PERSON] et al. [32] performed measurements in a Kaplan turbine and carried out numerical simulations to investigate the VSV structures at DPL and SNL. Similarly, it was also concluded that the VSV structures were originated at the interface between the backflow region and the main flow. [PERSON] et al. [33] studied the VSV structures generated at DPL on a diagonal, a propeller and a Francis turbine through experiments and numerical simulations. Vortexwere confirmed to be generated due to mainly backflow. In the case of the propeller turbine, large VSV structures were found in the numerical simulations although vibrations on the turbine prototype were within acceptable levels. As introduced previously, the VSV structures are hydraulic phenomena of periodic nature and, consequently, they generate periodic pressure pulsations and they exert periodic forces on the turbine. Their analysis in the frequency domain is then appropriate. In the current work, the time domain signals were transformed to the frequency domain through Discrete Fourier Transforms (DFT) solved by means of Fast Fourier Transform (FFT) algorithms. The FFT is an appropriate and efficient approach to solve DFT reducing the computation effort significantly. For instance, the computation effort to solve DFT of signals with more than 512 discrete samples is reduced to a 1% using the FFT evaluation relative to the direct evaluation [34]. Most literature related to VSV structures in Kaplan turbines focused on their characterization when generated in a particular SNL condition. However, in order to deepen the insight on these hydraulic structures, there is the need to also study their induced structural responses on different components of the turbine as well as their dynamic evolution with the SNL condition and with the presence of cavitation.