Part-Load Vortex-Rope-Dominated Cumulative Fatigue Damage in a Francis Turbine Runner: Transient Fluid–Structure Interaction and Excitation-Source-Separated Load Spectrum

Grid decarbonization forces Francis turbine runners into frequent start–stop and part-load duty, where vortex rope and repeated transients accumulate high-cycle fatigue damage; existing studies isolate conditions and rarely attribute damage to a specific excitation source. This paper builds a transparent chain from dynamic stress load spectrum to excitation-source-resolved damage: a transient one-way fluid–structure interaction model yields critical-point stress histories; four-peak-valley rainflow counting gives (Sa, Sm, n) cycle spectra; a two-parameter Weibull distribution and a Gaussian mixture model decompose the amplitude population; Smith–Watson–Topper correction with Miner accumulation then gives source-attributed damage. Four findings emerge: part-load cyclic stress far exceeds rated operation, its low-frequency vortex rope component dominating cumulative damage; a single distribution cannot describe the multi-source spectrum, whereas the mixture model is decisively preferred by information criteria; and cycle-level source separation shows that vortex rope cycles, though few, contribute most part-load damage, while transients give high per-event but rare damage; suppressing the vortex rope improves runner life more than trimming the low-amplitude BPF load. The contribution is a transparent, replaceable-input method chain and a source-resolved damage-attribution paradigm for dispatch and life extension.