## 4 Conclusions  
The swirling flow, backflow, and vortex strip in the draft tube are the main factors responsible for causing hydraulic loss. The section before RSS produces a hydraulic loss of more than 70% of the total hydraulic loss, with a length of about 30% of the draft tube. Therefore, the flow pattern before RSS is more important to the performance of the draft tube. The effect of the locking nut downstream of the runner on both the hydraulic performance and internal flow characteristics of the draft tube cannot be ignored.  
The small locking nut results in less hydraulic losses both overall and in each section. The proportion of rotational momentum flux and circumferential velocity at the inlet is significantly reduced, and the attenuation rate of swirling flow is accelerated. The low-pressure generation near the axis is suppressed, the range of high and low-pressure zones is significantly reduced, and the pressure gradient is reduced. The backflow zone is obviously shortened, and the backflow velocity and area are reduced. The vortex strip shape is long conical, and the tail is more inclined to the wall. The whole and each section of the vortex surface area are decreased, the vortex intensity experiences one more set of peak and trough, and the minimum value increases.  
The extended lock nut resulted in greater overall hydraulic losses but less hydraulic losses in the second half of the MES. The proportion of rotational momentum flux at the inlet of the draft tube is significantly reduced; however, the circumferential velocity value at the inlet is larger, and the attenuation rate of the swirling flow is the largest. The low-pressure generation near the axis is suppressed with almost no large low-pressure zone, but the increased range of the high-pressure zone increases the pressure gradient. The backflow zone is extended and the backflow velocity increases significantly, but the backflow area decreases in the first half of FSS and MES. The vortex strip shape is cloudy, and the overall surface area of the vortex increases; however, only the surface area in MES increases. The vortex intensity experiences one more set of peaks and troughs, and the minimum value is smaller.  
In the future design of the water turbine, the diameter of the locking nut can be preferably selected in the range from 0.3 d to 0.55 d. If the flow requirement before the middle of the MES is higher, it is biased towards 0.3 d; if the flow requirement after the middle of the MES is higher, it is biased towards 0.55 d.  
Figure 23: Vortex intensity of draft tube cross-section along the flow direction.  
**Author Contributions:** Conceptualization, L.T.; methodology, Z.W.; software, W.W.; validation, C.Z.; investigation, Z.W.; resources, L.T. and S.Y.; data curation, W.W.; writing--original draft preparation, L.T. and Z.W.; writing--review and editing, L.T. and S.Y.; supervision, S.Y.; project administration, S.Y.; funding acquisition, L.T. All authors have read and agreed to the published version of the manuscript.  
**Funding:** This research was funded by the National Natural Science Foundation of China, grant number 52109105, the Jiangsu Association for Science and Technology Young Science and Technology Talent Support Project, grant number JSTJ-2023-XH029, the National Key Research and Development Program of China, grant number 2023 YFD1900704-02, and the Scientific and Technological Breakthrough Foundation of Henan Province, grant number 232102110286.  
**Institutional Review Board Statement:** Not applicable.  
**Informed Consent Statement:** Not applicable.  
**Data Availability Statement:** The data that support the findings of this study are available on request from the corresponding author upon reasonable request.  
**Conflicts of Interest:** The authors declare no conflicts of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript; or in the decision to publish the results.