Study on clearance flow distortion and associated force response in pump-turbines operating under S-characteristic conditions

This study numerically investigates the clearance flow dynamics and the associated hydraulic force response of a pump-turbine operating under S-shaped characteristic conditions, based on a model unit of a pumped storage power station. The unsteady flow structures within the upper crown and lower ring clearances and their coupling with runner loads are systematically examined. The results indicate that, as the operating point progresses into the S-characteristic region, the clearance flow evolves from a predominantly axial leakage pattern to a highly three-dimensional turbulent regime characterized by multiscale vortical structures. Correspondingly, pronounced velocity gradients develop within the clearance, with local amplification of up to approximately nine times relative to the initial stage. The interaction between shear layers and coherent vortical cores gives rise to alternating high- and low-pressure regions, which intensify unsteady hydraulic excitation. This process results in an increase of about 17% in the peak axial hydraulic thrust and an order-of-magnitude growth in the spectral amplitude of the radial force. Meanwhile, the dominant frequency content of the radial force response shifts from low-frequency components to broadband excitation extending to approximately 7.5 f n . Structural analysis reveals concentrated deformation near the runner lower ring and the adjacent stationary components, indicating an elevated sensitivity to clearance-induced loading asymmetry. The findings provide quantitative insight into the flow-force-structure coupling mechanisms governing pump-turbine stability under non-stationary operating conditions and offer guidance for structural safety assessment and clearance design in pumped storage applications.