Hydraulic loss mechanisms in Francis turbines induced by guide vane opening based on entropy generation theory

Francis turbines are central to hydropower systems, yet their hydraulic loss mechanisms under variable guide vane openings remain insufficiently characterized. This study employs entropy generation theory and the shear stress transport k–ω turbulence model to investigate a medium specific-speed Francis turbine, analyzing guide vane openings from 26.5% to 66.3% of the maximum opening (α0max) under three heads (145, 160, 175 m). Results reveal that increasing the guide vane opening reduces guide vane entropy generation by 58.3% but induces a nonlinear redistribution of losses: the draft tube's contribution drops from 70.6% to 26.3%, while the runner's rises from 18.2% to 42.3%. This nonlinearity stems from a transition in dominant dissipation mechanisms—viscous effects (e.g., trailing-edge jet–wake interactions) prevail at low openings, while turbulent dissipation (e.g., runner secondary flows) dominates at high openings. In the draft tube, discrete wall-attached vortices at low openings evolve into helical vortex bands at high openings, transforming high-entropy zones from a circumferentially arranged annular pattern (low openings) to a helical vortex-dominated core (high openings). Concurrently, the runner exhibits amplified suction-side flow separation and mid-span secondary flows as the opening expands, elevating turbulent losses. These findings establish a direct link between flow evolution and entropy production, proposing actionable strategies: (1) avoiding prolonged operation in transitional opening ranges (α* = 0.4–0.6) where loss mechanisms compound and (2) optimizing blade geometry to mitigate secondary flows. This work advances Francis turbine design by integrating entropy-driven diagnostics with practical operational guidelines.