[PERSON]  
4 State Key Laboratory of Hydroscience and Engineering, Department of Energy and Power Engineering, Tsinghua University, Beijing 100084, China 4  
[PERSON]  
2 Baihetan Engineering Construction Department, China Three Gorges Construction Engineering Corporation, Chengdu 610041, China; [PERSON]AIL_ADDRESS] (K.J. ); [PERSON]AIL_ADDRESS]om.cn (F.G.); [PERSON]AIL_ADDRESS] (X.L.) [PERSON]  
4 State Key Laboratory of Hydroscience and Engineering, Department of Energy and Power Engineering, Tsinghua University, Beijing 100084, China 4  
[PERSON]  
2 Baihetan Engineering Construction Department, China Three Gorges Construction Engineering Corporation, Chengdu 610041, China; [PERSON]AIL_ADDRESS] (K.J. ); [PERSON]AIL_ADDRESS]om.cn (F.G.); [PERSON]AIL_ADDRESS] (X.L.) [PERSON]  
2 Baihetan Engineering Construction Department, China Three Gorges Construction Engineering Corporation, Chengdu 610041, China; [PERSON]AIL_ADDRESS] (K.J. ); [PERSON]AIL_ADDRESS] (F.G.); [PERSON]AIL_ADDRESS]n (X.L.) [PERSON]  
4 State Key Laboratory of Hydroscience and Engineering, Department of Energy and Power Engineering, Tsinghua University, Beijing 100084, China 4  
[PERSON]  
3S.C.I. Energy, Future Energy Research Institute, Seidengasse 17, 8706 Zurich, Switzerland; 3  
[PERSON]S] ([PERSON]ESS] ([PERSON]ESS] ([EMAIL_ADDRESS] ([PERSON]ESS] (X.  
characteristics of the vaneless zone. This connection has a profound impact on the hydraulic behaviors of the crown chamber and the bottom ring chamber ([3]). Variations in installation deviations result in changes in clearance dimensions, subsequently influencing the flow characteristics near the turbine runner ([4]). These alterations in flow patterns around the runner can lead to fluctuations in power output, increased structural vibrations, and fatigue failure. Collectively, these factors pose substantial risks to the safe and stable operation of power stations ([5]). [PERSON] et al. [6] conducted systematic investigations into turbine leakage and cavity pressure while varying seal clearance sizes and drain hole parameters. Their research provided valuable insights for determining seal clearance sizing and drain hole parameters. The work by [PERSON] et al. [7] delved into the structural vibration characteristics stemming from uneven clearances in the labyrinth ring of the turbine runner. Their research highlights the significant influence of uneven clearance distribution on the overall unit's vibration. [PERSON] et al. [8; 9] demonstrated that, under optimal unit speed conditions and accounting for disc loss, numerical simulations yielded turbine efficiency results consistent with model test outcomes. However, they observed that under non-optimal working conditions, the flow field exhibited numerous vortices and shedding phenomena, resulting in numerical simulation efficiency values falling below those observed in model tests. Fundamentally, the uneven flow within the clearance affects the runner and other components in two main ways: axial and radial forces. Axial forces in hydraulic machinery encompass several components, such as the rotating part's mass, water buoyancy on the runner, forces acting on the blades during hydraulic machinery operation, hydrostatic forces at the shaft end, and axial forces due to water pressure in the crown chamber and bottom ring chamber ([4]). On the other hand, radial water thrust can be categorized as frequency radial forces and other radial forces. Frequency radial forces stem from imbalances in the runner's mass, uneven water distribution within the runner's inner cavity, inconsistencies in blade profiles and installation angles, and dynamic blade deformations ([6]). These frequency radial forces primarily contribute to partial shaft wear and uniform bearing bush wear. Additionally, there are other factors, such as radial forces with fixed directions due to inlet and outlet flow asymmetry, resulting in uniform shaft wear and partial bearing bush wear. Regarding the study of axial forces, [PERSON] et al.