Multi-objective optimization design of a pump-turbine runner based on machine learning method

The optimization design of runner blades plays a crucial role in improving efficiency and stability of pumped storage units. In this study, a multi-objective optimization design system combining machine learning method is proposed for pump-turbine runners, including 3D inverse design, Computational Fluid Dynamics (CFD), Design of Experiment (DoE), and Response Surface Methodology (RSM). Blade loading distribution parameters and the blade lean angle at the high-pressure side are selected as design parameters, with multi-condition efficiency of the pump-turbine as the optimization goals. Two optimized runners with positive and negative blade lean are designed. The optimization results show that the optimized runners achieve higher efficiency, with the negative blade lean angle runner achieving a 1.02 % efficiency increase at turbine rated operating condition, a 1.28 % increase at 50 % turbine design load, and a 0.66 % increase at pump design condition. Pressure distribution on blade pressure side reveals that the runner with negative blade lean exhibits a more stable pressure difference along the span direction resulting in enhanced work capacity. Additionally, the pressure fluctuation magnitude within the runner and vaneless area is lower along the flow direction under three target conditions, indicating higher stability. Detailed hydraulic loss analysis shows that the optimized runner effectively reduces the hydraulic losses at runner inlet and the runner with negative blade lean can further reduce the hydraulic losses at locations such as the high-pressure side of the blade compared to the runner with positive blade lean. These findings provide valuable reference for the development of high-performance pump-turbine runners.