Numerical simulation and experimental study on hydraulic instability of pump as turbine devices induced by thoma number based on scale-averaged wavelet spectrum

Low-head hydropower resources are widely distributed, water-rich, and readily exploitable clean renewable energy sources. However, low-head pumps as turbines (PAT) unit often encounter challenges such as flow instability, significant cavitation, and output power fluctuations when operating under off-design conditions, severely compromising their efficiency and operational stability. Although previous studies have explored the cavitation and vortex characteristics of PATs, there is a lack of systematic research on the physical mechanisms underlying these phenomena and their impact on dynamic output power under varying Thoma numbers. This study combines numerical simulations with experimental methods to investigate the relationship between internal flow characteristics and output power fluctuations in PATs under different Thoma numbers, utilising the normalised scale-averaged wavelet spectrum (NSAWS) as an analytical tool. The results reveal that a decrease in the Thoma number leads to pronounced cavitation concentrated on the blade suction surface (SS) and the formation of complex vortex structures in the draft tube (DT), causing nonlinear fluctuations in output power. For the first time, a dual-peak (DP) energy concentration phenomenon is observed, with energy evolution characterised by three distinct stages: focusing, expansion, and splitting. These stages significantly affect the operational stability of the equipment. This study proposes a novel approach to optimising the design and operation of PATs and provides theoretical support for enhancing the performance of low-head micro-hydropower systems.