Sediment erosion poses a significant challenge for hydraulic turbines in sediment-laden rivers. This paper investigates the erosion patterns in high-head Francis turbines using numerical simulations. It analyzes how sediment concentration, particle size, and operating conditions affect wear on turbine components. The results identify the trailing edges of the guide vanes, the intersection of runner blade trailing edge, and runner band as primary erosion zones. Higher sediment concentrations increase erosion intensity and extend the erosion range upstream. Small particles uniformly affect both pressure and suction sides of the blades, while larger particles concentrate erosion near the runner band trailing edges. The flow rate has a greater impact on runner blade erosion than water head, with lower flow rates reducing pressure side erosion but initially increasing, then decreasing suction side erosion. Additionally, the study proposes a multi-objective, multi-condition optimization design method that balances erosion resistance and energy efficiency. The optimized runner reduces the maximum erosion rate by 23.91% while limiting the weighted efficiency loss to under 0.1%. The improved runner design reduces high erosion areas on both blade sides, particularly decreasing particle impact speeds near the trailing edges. Sensitivity analysis reveals a trade-off between minimizing erosion and maintaining hydraulic efficiency, highlighting the importance of span height at 75% for controlling erosion. Changes in blade circumference angle generally reduce erosion but may also lower efficiency. Overall, this research demonstrates a successful reduction in Francis turbine erosion while preserving hydraulic efficiency, offering valuable guidance for anti-erosion turbine design in sediment-heavy environments.
