Fluid deformation induced energy loss of pump-turbines based on the transport of mean kinetic energy

In-depth research into the energy loss characteristics of pump-turbines is crucial for their proper design and optimization. This paper presents a study of the energy loss in pump-turbines to highlight the mechanisms of energy loss in these machines and reveal the energy conversion process. The analysis of the mean kinetic energy transport equation, based on the Reynolds-averaged flow, shows that energy losses within a pump-turbine are transformed into heat and turbulent kinetic energy. This transformation occurs through two mechanisms: viscous dissipation and the generation of turbulent kinetic energy by the mean flow. The turbulent kinetic energy generation term dominates the energy loss, accounting for 50 %–67 % of the total loss. There is a strong connection between the energy loss in the deformation of the runner and fluid element. The turbulent kinetic energy generation correlates to a large extent with the fluid shear stress and stretching deformation (ρP is between 0.81 and 0.98). This shows that turbulent kinetic energy is mainly generated by fluid shear and stretching. Shear deformation contributes more, caused by backflow and flow separation on the blade. Stretching deformation is affected by the flow and also affects the shear. In the runner inlet, the fluid elements are stretched 66 % in the z-direction and sheared 66 % in the xy plane due to backflow and impact. This shows that a fluid element in a level goes through a certain degree of shear deformation, the fluid element is subject to stretching deformation in the normal direction of that plane. The findings of this study provide theoretical support for performance enhancement and hydraulic optimization of pump-turbines and provide significant practical engineering value.