# Flow-Induced Strength Analysis of Large Francis Turbine Under Extended Load Range
## 3 Specifications of the Francis Turbine Unit and Investigated Operating Conditions  
The hydropower plant of this study has six large-scale Francis turbine generation units, each rated at 183 MW. The turbine units' rated head and maximum head are 68 m and 80 m. The rated discharge and the rotating speed of the turbine are 294 m\({}^{3}\)s\({}^{-1}\) and 100 rpm, respectively. The Francis turbine unit has 20 stay vanes and 20 guide vanes, and the turbine runner has 13 blades. The rotating direction of the turbine runner is clockwise in the top view. The parameter specifications of the Francis turbine unit are listed in Table 1.  
The three-dimensional geometrical model of the water passage of the Francis turbine prototype is shown in Figure 3. The inlet and outlet of the turbine flow passages are also illustrated in the figure. The spiral case is the Francis turbine unit's flow intake structure, and its spiral design helps to maintain an even distribution of flow velocity and pressure, thereby minimizing energy loss as the water enters the stay vane flow passage. Stay vaneswithin the stay ring, positioned radially between the spiral case and the guide vanes, provide structural support to the spiral case and other structures of the turbine unit. The guide vanes can be adjusted in their opening angle to regulate water flow and finely control the power output on the turbine. The Francis runner is the core component of the turbine. When the water flows through the Francis runner, its potential and kinetic energy are converted into the mechanical energy of the rotor system. The draft tube, located at the outlet of the runner, discharges water from the runner to the downstream and converts the remaining kinetic energy of water exiting the runner into pressure energy. This increases the overall efficiency of the turbine by reducing energy losses. The water in the crown chamber and band chamber between the runner and the surrounding stationary structures balances the pressure and thrust of the runner. Labyrinth seals in the crown and belt chambers help to reduce water leakage of the runner passage. The power plant operation statistics show that the Francis turbine units often operate at 74 m, close to the maximum head. To meet the requirements of the grid load regulation, the turbine units of the power plant have to operate under off-design operating conditions for a long period and even extend their operation to the low load zone. In this study, three operating conditions of 33.3%, 66.6%, and 100% of the rated power are adopted for the CFD simulation and subsequent flow-induced strength analysis. The operating parameters of the selected operating conditions are analyzed based on site measurements (Table 2). To perform the CFD simulation of the turbine unit, the fluid domain computational model of the Francis turbine is generated with high-quality tetrahedral and hexahedral meshes. The meshes near the structure wall surfaces of key flow domains such as runner blades and guide vanes are refined. There are five mesh layers near the wall surfaces, with \begin{table}
\begin{tabular}{c c c} \hline \hline
**Specification** & **Value** & **Unit** \\ \hline Rated power & 183 & MW \\ Rated head & 68 & m \\ Maximum head & 80 & m \\ Rated discharge & 294 & m\({}^{3}\)s\({}^{-1}\) \\ Rotating speed & 100 & rpm \\ Stay vane number & 20 & - \\ Guide vane number & 20 & - \\ Runner blade number & 13 & - \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The specifications of the Francis turbine unit. Figure 3: The geometrical model of the water passage of the Francis runner unit. the first mesh height of 0.1 mm and an expansion ratio of 1.2. Three groups of meshes are generated for the fluid domain of the Francis turbine unit, with 7.3 million, 14.2 million, and 25.8 million elements, respectively, and the mesh sensitivity assessment is performed to ensure the reliability and convergence of the calculation results.