Energy loss analysis of a multi-stage pump as turbine based on a wall entropy production model

This study focuses on revealing the mechanisms of energy dissipation in the internal flow field of a multi-stage centrifugal pump as a turbine (PAT). Traditional entropy production approaches often struggle to accurately characterize near-wall flow losses, especially in narrow clearance and gap regions. To overcome this limitation, an enhanced wall entropy production model (WEPM) was presented and applied in the numerical investigation of the multi-stage PAT. The reliability of the proposed method was confirmed through experimental validation. Based on this framework, the contributions of different entropy production components were quantified under multiple operating conditions, while both the spatial distribution and transient evolution of entropy-related losses were carefully explored. The results indicate that turbulent entropy production is the predominant source of energy dissipation throughout the investigated operating range, contributing as much as 57.11% of the total loss, whereas viscous entropy production represents the smallest proportion, reaching a minimum of only 6.12%. In terms of flow passage components, the pump cavity, impeller, and guide vane were identified as the principal regions responsible for energy loss, contributing approximately 32%, 28%, and 34%, respectively, under design conditions. These findings provide deeper understanding of the energy loss characteristics in multi-stage PATs and offer valuable guidance for the optimization and design of critical hydraulic components.