# 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  
According to the normal working conditions, the numerical simulation of the internal flow field of the turbine was carried out. By analyzing the flow characteristics of the fluid inside the turbine runner, the flow velocity distribution and sediment concentration distribution results of the internal flow field of the turbine runner were obtained. Based on these results, the wear area inside the turbine runner was determined. It can be seen in Figure 4 that the water flow passes through the inside of the runner, and the flow velocity first decreases and then increases from the entrance to the exit of the runner. The closer to the lower ring, the higher the flow velocity at the corresponding position. In addition, the fluid velocity around the long blade increases as it gets closer to the outlet of the runner, and the overall flow velocity on the back of the blade is greater than that on the working surface of the blade; especially when the back of the blade is near the water edge at the tail, the velocity reaches the maximum. Therefore, wear is more likely to occur at the back of the blade near the water edge than at other parts of the runner. Analyzing the sediment volume fraction distribution on the runner blade surface reveals that the sediment content is higher on the back of the blade near the lower ring compared to other areas. The degree of wear on the runner blade is influenced by the flow velocity of sand and the sediment concentration. Following the velocity distribution pattern of the flow field on the blade surface, it is evident that the area with the highest sediment flow velocity and concentration is on the back of the blade near the lower ring. Consequently, it can be deduced that the most severe wear occurs on the back of the blade near the lower ring, with the wear degree increasing as it approaches the water edge of the runner. Figure 4: Velocity field and sediment volume fraction distribution cloud map of the turbine runner internal flow. (**a**) Turbine runner velocity field cloud map; (**b**) velocity distribution cloud map of the turbine runner blades; (**c**) sediment volume fraction on the turbine runner blades; (**d**) sediment volume fraction on the back side of the blade. Figure 5 shows a runner that has been in service for some time. It can be seen intuitively that the worn area of the runner blade is at the water edge, with the most severe wear occurring at the junction between the blade's water edge and the runner's lower ring. This observation aligns with the wear positions and trends predicted by the numerical analysis of the runner's internal flow field. After identifying the worn areas on the runner blade, the next step is to measure the extent of wear at these locations. This is followed by establishing a general formula to calculate the wear rate for the turbine's flow components [20]:  
\[E=K\cdot k_{s}\cdot S^{M}\cdot W^{N} \tag{1}\]  
Here, \(K\) represents the influence coefficient for material properties and a comprehensive influence coefficient for other factors. \(k_{s}\) denotes the influence coefficient of sediment characteristics. \(S\) stands for sediment concentration, \(M\) represents an index, \(W\) indicates the relative water flow velocity, and \(N\) is the index. Ensure that the sediment content is consistent with the actual hydropower station. Therefore, the influence coefficient \(k_{s}=1.0\), the sediment concentration index \(M=1.0\), and the sediment concentration about \(S=1.93\) kg/m\({}^{3}\) were determined to obtain the relationship between the material wear amount of the runner blade and time [21]. \[\Delta H=0.65\times 10^{-9}S\cdot W^{3.7}\cdot T \tag{2}\]  
Considering the actual operating conditions of hydropower turbines, the wear on runner blades predominantly occurs during the flood season, a period that typically spans approximately four months, from May to September annually.