# Fatigue Damage Assessment of Turbine Runner Blades Considering Sediment Wear
## 1 Introduction  
As a renewable energy, hydropower is one of the pillars of China's electric power system, playing a crucial role in promoting economic development. As the core component of a hydropower station, the turbine's safety, stability, and reliability are paramount. In Southwest China, rivers feature substantial water flow, significant head variation, and high sediment content, which varies greatly with the seasons. This variability leads to severe wear on the turbine's internal structures and diminishes the fatigue strength of the runner blades. The causes of fatigue damage to the turbine's runner components are also complex. Ensuring the stable operation of hydropower units thus requires a detailed estimation of the fatigue damage and life of the turbine runner components. [PERSON] et al. [1] proposed a numerical method to understand critical operational areas and access fatigue damage, and compared the simulation results with measured data. The appropriate consistency between the measured data and simulation results indicates that the numerical simulation method is feasible for calculating fatigue damage in hydraulic turbines. [PERSON] et al. [2] compared the stress distribution and deformation of pump blades under positive and reverse power generation conditions. Theoretical and numerical calculations of fatigue strength were conducted, and a preliminary estimation of the runner's fatigue life was made to investigate how to extend the service life of the pump station. [PERSON] et al. [3] employed bidirectional fluid-structure coupling analysis on a Francis turbine to determine its stress characteristics, iteratively solving for the couplingcoefficients in both fluid and structural equations until convergence. Based on the structural analysis, the maximum stress, maximum displacement, and wear locations within the turbine were identified, providing valuable insights for the design and optimization of the turbine. [PERSON] [4] employed the finite element method to analyze the stress and strain of a turbine blade and calculated the blade's stress fatigue characteristics using specialized fatigue analysis software. The results of the analysis were in line with actual requirements and offered valuable data for the analysis of fatigue characteristics in turbine blades. [PERSON] et al. [5] conducted internal flow field analysis to determine the blade surface pressure under various startup conditions of a hydropower station's Francis turbine, and established the blade stress distribution for analyzing the turbine's fatigue performance. They also optimized the design of the blade's critical areas to enhance the blade's fatigue life. [PERSON] [6] performed a numerical simulation analysis on the hydrodynamic performance and structural characteristics of a hydraulic turbine using two-way fluid-structure coupling calculations. The analysis considered the effects of turbine speed and water depth variations and predicted the fatigue life of the blades. The accuracy of these computational results was validated through model testing. ALSTOM Company [7,8] used numerical simulation to analyze the pressure pulsations and equivalent stresses of the runner blades in a low-head Francis turbine, and, combining this with measured stresses, predicted the fatigue life of the runner under various operating conditions. [PERSON]. [9] analyzed the bucket blades of the Francis turbine and determined that fatigue failure of the runner blade was due to repeated alternating or cyclic stress, which, despite being lower than the normal yield strength, occurred over a long period. [PERSON] et al. [10] conducted fatigue life prediction research on the rotating blade of a generator set. The blade's stress was determined through transient dynamic analysis of the blade surface load. The blade's life was calculated using both the linear Miner criterion and a fuzzy life estimation method, and the results of the two methods were compared. It was determined that the fuzzy life estimation method proved more accurate for calculating blade life.