Predicting pump-turbine characteristic curves by theoretical models based on runner geometry parameters

The characteristic curve of a pump-turbine is the essential data for calculating the hydraulic transient processes of a pumped storage power station. However, this curve is often unavailable during the preliminary design stage of pumped storage power stations. The shape of the characteristic curve directly influences the transient guarantee parameters. To date, adjusting the runner geometry to control the characteristic curve's shape for improving hydraulic transients remains a challenging issue. This paper proposes a model for predicting the characteristic curve that correlates its shape with the runner's geometric parameters. Considering the bidirectional flow in pump-turbines, two sets of governing equations are derived separately for the centripetal and centrifugal flow conditions. The governing equations for the unit discharge curve and the unit torque curve are constructed based on the energy equation and torque equation, respectively. Each term in these equations is subsequently organized into the expressions involving the runner's geometric parameters and unit parameters. To make the equations solvable, several sets of feature points are introduced. Based on the approach to obtain the feature points, an experiment/CFD (Computational Fluid Dynamics)-based prediction method and a statistics-based prediction method are proposed. Verifications using manufacturer-measured curves show that the experiment/CFD-based method is well-suited for model test acceleration and characteristic curve repair due to its higher prediction accuracy and availability, while the statistics-based method is more suitable for borrowing similar curve data during the power plant's preliminary design phase or rapidly predicting the corresponding characteristic curves during runner design. This work establishes a theoretical basis for improving hydraulic transient guarantee parameters by runner design optimization.