Analysis of Hydraulic Losses in Vortex Rope Inside the Draft Tube of Francis Pump-Turbine Based on Entropy Production Theory

The existence of vortex ropes inside the draft tube significantly impacts hydraulic efficiency and operational stability, and few studies on the formation mechanism of vortex ropes and hydraulic loss problems have been explored. Hence, in this paper, we build an inherent correlation between the local entropy production rate (LEPR) in the draft tube and the dynamics of vortex motion, by incorporating the vortex identification method Omega(R) with entropy production theory, using the OpenFOAM-v2212 software. From the analysis of the entropy production theory, the entropy production rate caused by turbulence dissipation (EPTD) is responsible for the majority of energy loss in the form of entropy production rate, accounting for about 87% of the total entropy production rate (TEPR) in different load operations. Comparatively, the entropy production rate caused by wall shear stress (EPWS) can account for up to 12%, while the entropy production rate due to direct dissipation (EPDD) plays a minor role in TEPR. The rotating vortex rope movement of the unit at part load conditions leads to more intense LEPR. Therefore, to determine the hydraulic loss caused by the vortex rope, the TEPR at the cross-section can be used to assess the hydraulic characteristics of the draft tube.