Predicting pump-turbine axial hydraulic thrust with the PMAT model: A coupled pressure-integration and momentum-theorem approach

Pumped-storage hydropower is the pivotal large-scale energy storage technology that enables stable, flexible, and low-carbon power grids. However, pump-turbines, as the core component of such systems, are prone to vibration and lift-off events caused by imbalances in axial hydraulic thrust acting on the runner. To address the limited adaptability and predictive accuracy of existing models under varying operating conditions, this study proposes a pressure–momentum axial thrust (PMAT) model for efficient and accurate prediction of axial hydraulic thrust. The model derives the pressure distribution within the gap chambers and establishes a quantitative relationship between the pressure differential and the leakage flow rate. The axial thrust induced by gap flow is determined through pressure integration over the acting surfaces, while that generated by the mainstream is obtained using the momentum theorem with the runner as the control volume. The total axial thrust is then evaluated as the sum of these two components. Validation against high-fidelity numerical simulations and experimental measurements demonstrates that the PMAT model predicts pressure differential, leakage flow rate, and axial thrust with an average relative error below 5%, confirming its high accuracy, computational efficiency, and cost-effectiveness. Moreover, parametric analyses quantify the effects of inlet width and seal-ring geometry on leakage behavior and thrust characteristics, providing valuable guidance for the optimized design and stable operation of pump-turbines. The PMAT model thus offers a reliable and rapid tool for axial thrust prediction in pumped-storage hydropower applications.