Numerical analysis of energy loss in electric submersible pump under stall conditions based on entropy production theory

Studying the energy loss characteristics of the electrical submersible pump (ESP) under stalling conditions is beneficial for reducing the global carbon emissions. By combining steady and unsteady numerical simulations with entropy production (EP) theory, the evolution of internal vortices in the ESP under stalling conditions is analyzed, and a theoretical model for predicting energy loss based on EP is established. The results show that turbulent dissipation entropy production inside the ESP is the main component of total entropy production. Under critical stall conditions, the stability of vortices inside the impeller of a single-stage ESP is higher. However, in the first-stage impeller of a multi-stage ESP, the periodic shedding and breakdown of vortices lead to a turbulent flow field at the inlet of the diffuser, resulting in increased impact losses. Under deep stall conditions, the inlet recirculation vortices in the impeller of a single-stage ESP exhibit a symmetric distribution. In multi-stage pumps, the evolution period of inlet recirculation vortices is asynchronous with the impeller rotation period. There are differences in the shedding period of vortices in each flow channel, resulting in nonsymmetrical distributions of vortices in the circumferential and radial directions. The interaction between the outlet vortices of the diffuser and the passage vortices leads to the formation of multiple high-energy, small-scale vortex structures at the entrance to the next-stage impeller. It will further lead to fluid separation and cause the next-stage impeller to enter a stall condition. The research results offer valuable insights that can be utilized as references for optimizing design and field application of ESPs.