# On the Vaneless Space Vortex Structures in a Kaplan Turbine Model Operating at Speed No Load
## 4 Conclusions  
Five simultaneous VSV structures with different number of vortices and inducing torsional rotor vibrations were found in a reduced-scale Kaplan turbine model operating at SNL. Each structure precessed at a particular frequency in the turbine rotation direction, which depended on the turbine discharge factor, its number of vortices and its location. More specifically, the precession frequencies decreased with an increasing number of vortices and increased for closer distances of the structures to the runner blades. Among all the VSV structures observed, those formed by two and three vortices presented the highest pressure fluctuations, strains and torques. The similarities observed in the frequency evolutions and in the induced rotor vibrations among the five different VSV structures suggest that there is some interrelation among them.  
Figure 9: Spectra of (**a**) TGV, (**b**) PVSA, (**c**) SB\({}_{R}\), (**d**) SS\({}_{T}\) and (**e**) A0y, under non-cavitation (black) and cavitation (blue) conditions for \(\alpha\) equal to 3.98\({}^{\circ}\), 7.35\({}^{\circ}\) and 8.13\({}^{\circ}\).  
When the turbine was operated under cavitation conditions, the precession frequencies of the dominant VSV structures were not significantly altered. Their induced responses at different parts of the turbine test stand slightly decreased with the exception of the draft tube cone where they increased significantly.  
Then, the runner and the whole rotor should be designed having their natural frequencies far away from the VSV excitation frequencies and their harmonics to avoid dangerous resonances at SNL. Additionally, the machine should operate in the SNL condition presenting the less intense VSV structures in order to minimize the wear and tear generated at this operating point.  
As a future work, numerical simulations replicating the experimental tests should be performed for a better understanding of this particular flow field. The numerical results will help to understand the morphology of these structures and the mechanism driving the change in precession frequency and intensity observed experimentally.  
Conceptualization, R.R. and X.E.; methodology, R.R. and X.E.; software, X.S.-B; validation, R.R., X.S.-B. and X.E.; formal analysis, R.R.; investigation, R.R. and X.E.; resources, C.-M.H. and X.E.; data curation, R.R. and X.S.-B.; writing--original draft preparation, R.R.; writing--review and editing, R.R., X.S.-B., B.M., C.-M.H. and X.E.; visualization, R.R. and X.S.-B.; supervision, B.M., C.-M.H. and X.E.; project administration, C.-M.H. and X.E.; funding acquisition, C.-M.H. and X.E. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the European Union's Horizon H2020 research and innovation program under grant number 814958.  
Not applicable.  
Data Availability StatementData are contained within the article.  
The authors would like to acknowledge the technical support received from Vattenfall AB.  
Author [PERSON] and [PERSON] was employed by the company Vattenfall AB, R&D A lvkarleby. The remaining authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.