# Fatigue Damage Assessment of Turbine Runner Blades Considering Sediment Wear
## 3 Numerical Calculation of Dynamic Stress on the Runner Blades of a Turbine
### Identification of Wear Locations and Quantification of Wear on Turbine Runner Blades
The extent of wear on the blades is assessed by examining the flow field velocity near the water edge of the upper runner blade's working surface and applying the wear rate formula specific to the blade material. Wear initially occurs on the back of the blade near the water edge, and as working time increases, this wear surface progressively thins. Once the wear reaches a certain degree, the material at the tail of the blade near the water edge is worn away. This advanced wear leads to structural changes in the blade's tail. By calculating the water flow velocity on the surface of the wear area after the blade has experienced different degrees of wear, it was found that the variation in water flow velocity is relatively small. Therefore, in this paper, the water flow velocity is taken as a constant value when calculating the wear amount of the blade, with the velocity magnitude set at 37.82 m/s. Figure 5: Actual turbine runner wear areas. In this paper, the flow velocity at the worn area of the runner blade's tail and the material wear rate formula were combined to determine the blade's wear amount under various working times. The results are presented in Table 3.  
Establishment of a Fluid-Structure Interaction Model for Runner Blades and Setting of Boundary Conditions  
Before conducting fluid-structure interaction analyses, 3D models of runner blades with varying degrees of wear are created using 3D modeling software. To ensure the accuracy of these analyses, it is essential that the blade models, regardless of their wear degree, are meshed to a high quality. The steps for modeling and meshing blades with different wear degrees are consistent. This section will provide a detailed introduction to the model of a blade at the wear degree T\({}_{0}\). Figure 6 displays the finite element model for a blade at wear degree T\({}_{0}\), which consists of 211,344 mesh elements and 386,134 nodes. In this paper, the calculation of fluid-structure interaction for the runner blade employs a one-way coupling method, necessitating only the transfer of dynamic pressures from the fluid to the blade surface. The fluid domain and solid domain data transfer method used in this study is the Conservative interpolation method in ANSYS's MFX multi-physics solver. When the fluid-structure interaction surface is perfectly matched, precise data transfer between the interfaces can be achieved. For this study, the interface between the fluid \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline Degree of Wear & T\({}_{0}\) & T\({}_{1}\) & T\({}_{2}\) & T\({}_{3}\) & T\({}_{4}\) & T\({}_{5}\) \\ \hline Time (month) & 0 & 2 & 4 & 6 & 8 & 10 \\ Wear amount (mm) & 0 & 1.1225 & 2.245 & 3.367 & 4.490 & 5.612 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Blade wear data. Figure 6: Turbine runner blade model and constraint loads. (**a**) Turbine runner blade model; (**b**) turbine runner blade mesh model; (**c**) imposition of constraints; (**d**) dynamic pressure data transfer. dynamics and finite element analysis modules facilitates the transmission of these dynamic pressure data. Prior to the transfer of dynamic stress data, the material for the runner blade must be specified, along with defining the material's elastic modulus, Poisson's ratio, density, and other relevant performance parameters. The runner blade is connected to the upper crown and lower ring of the runner via welding. To replicate the stress on the runner blade under actual operating conditions, constraints and fixed supports are applied to the interface between the runner blade and the upper crown and lower ring, as per the internal structural features of the runner. The runner operates at a rotational speed of 500 rad/min.