A rotating stall occurring in the reversible pump turbine operating within the S-shaped region significantly impairs hydrodynamic stability, leading to severe torque oscillations and pressure pulsations. Currently, theoretical frameworks and quantitative predictions for stall inception are still lacking. This study develops a theoretical model for rotating stall based on small-disturbance theory. The model analyzes the resonance conditions and stability characteristics of disturbance waves by coupling internal flow perturbation dynamics with the external characteristics of the pump-turbine system. Key stall parameters, including the onset point, rotational speed, and the number of stall cells, are predicted based on the finite-difference-based numerical implementation. The results show that single-cell stall patterns are more dominant than two-cell patterns, with the former exhibiting a clear critical stability threshold. Complementarily, an unsteady flow simulation approach is adopted to capture transient flow behavior from runaway to low-flow conditions under four guide-vane openings. Pressure fluctuations in the vaneless area are analyzed using wavelet transform to identify the onset of rotating stall. Comparison between the numerical simulation and theoretical predictions confirms the model's accuracy and utility in predicting stall onset.

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• Flow instability
• Vortex dynamics
• Complex fluids