**5. Conclusions**

This study performed unsteady-state RANS analyses to investigate the e ffects of anti-cavity fins in the DT of a Francis turbine model on unsteady internal flow and pressure characteristics under low flow rate conditions. Reductions of around 0.5%–1.0% in hydraulic performance within the range of observed GV angles were observed, and the head losses of each component in the Francis turbine model were compared via the application of anti-cavity fins. Furthermore, the magnitudes and locations of the vortex ropes in the DT were verified via iso-surface distributions both with and without anti-cavity fins according to varying flow rate conditions. The existence of low-pressure regions due to flow resistance at the prominent air injection outlet on the anti-cavity fins was also confirmed.

The causes of the complicated flow phenomena in the DT respective to varying flow rates were confirmed via an analysis of the velocity triangles at the runner outlet. Furthermore, quantitative and qualitative investigations were conducted using the flow angle distributions at the runner outlet and the streamline distributions in the DT. A comparison of velocity distributions on the observed line confirmed the e ffects of the anti-cavity fins on the axial and circumferential velocity components in the DT. Furthermore, FFT analyses confirmed that the largest magnitudes of unsteady pressure were observed under low flow rate conditions with developed vortex ropes. There was a tendency for these magnitudes to gradually increase along the flow direction in the DT. Additionally, an approximate 41% reduction in the maximum unsteady pressure was confirmed with the application of anti-cavity fins.

Therefore, the use of anti-cavity fins was confirmed to a ffect the degradation of hydraulic performance under conditions of low flow rate, including BEP; however, the e ffects of reducing the unsteady pressure in the low-frequency regions were confirmed in the DT, which induced operational instability in the Francis turbine model. Thus, the anti-cavity fins can be presented as one alternative to suppress unsteady pressure fluctuations with vortex rope in the DT. Furthermore, by minimizing the loss induced by the anti-cavity fins through the optimization of the shape and length of the anti-cavity fins, it can be expected to improve the hydraulic performance with suppressing pressure fluctuation effectively. In the addition, based on the results of this research, the unsteady flow and pressure phenomena in the DT will be investigated in a future study by injecting air into the DT.

**Author Contributions:** Conceptualization, validation, investigation, data curation, S.-J.K.; Y.-S.C.; Y.C.; J.-W.C.; J.-J.H.; W.-G.J. and J.-H.K.; resources, Y.-S.C.; Y.C.; J.-W.C.; J.-J.H. and J.-H.K.; writing—original draft preparation, S.-J.K.; Y.-S.C. and J.-H.K.; writing—review and editing, supervision, project administration, J.-H.K.; funding acquisition, Y.C.; J.-W.C. and J.-J.H. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by the Korea Agency for Infrastructure Technology Advancement under the Ministry of Land, Infrastructure, and Transport [grant number 20IFIP-B128593-04].

**Conflicts of Interest:** The authors declare no conflict of interest.
