Structural Parametric Study of an Ultra-High-Head Pump–Turbine Runner for Enhanced Frequency Safety Margin

Structural optimization focusing on the root fillet radius and the crown and band thicknesses was implemented to prevent rotor–stator interaction-induced resonance, with the objective of enhancing the frequency safety margin for the 4-nodal-diameter mode shape. An ultra-high-head pump–turbine runner is analyzed using an acoustic fluid–structure coupling method to investigate modal characteristics and identify effective design improvements. The results show that increasing the root fillet radius from 0 to 50 mm raises the frequency safety margin from 3.7% to 8.5%, thereby significantly reducing the resonance risk. Likewise, increasing the thickness of the crown, the band, or both leads to higher frequency safety margins, with simultaneous thickening of both components delivering the most improvement. Frequency safety margins continue to rise as the degree of thickening increases. When a runner’s natural frequency is only slightly higher than the corresponding excitation frequency, design measures such as enlarging the root fillet radius and jointly thickening the crown and band effectively expand the frequency safety margin. These findings can provide designers with both qualitative and quantitative references when modifying these structural parameters to mitigate resonance risk.