# Flow-Induced Strength Analysis of Large Francis Turbine Under Extended Load Range
###### Abstract  
To meet the load requirements of the power grid, the hydroelectric power plants need to extend the operational load range of the turbine units, which are often operated under off-design operating conditions. This new challenge significantly changes the flow characteristics of the hydro turbine units. Strong vibrations and high stresses caused by pressure pulsations at various loads directly lead to severe damage to the runner blades, threatening the safe operation of the hydropower unit. In this study, the detailed flow dynamics analysis under three loading conditions of a large-scale Francis turbine, i.e., 33.3%, 66.6%, and 100% of the Francis turbine's rated power, is investigated with computational fluid dynamics (CFD) calculations. The pressure files at different operating conditions are adopted to carry out the corresponding flow-induced strength analysis of the Francis runner prototype. The pressure distributions and flow velocity distributions at these three typical operating conditions are studied, and the maximum stress of the runner gradually increases with the power output of the turbine, but it is only around one-third of the yield stress of the runner material. It reveals that the runner is safe to operate in the extended operation range from a 33.3% to 100% of the rated power load. The analysis approach in this work can be applied to other hydraulic machinery including Francis turbines, pumps and pump-turbines. Francis turbine; extended load range; multiple operating conditions; flow dynamics; flow-induced strength; CFD and FEM 2020  
changes in weather and time. The instability of photovoltaic and wind power requires large hydropower units as a regulating power source to balance the grid and ensure the stability and reliability of the power supply. In order to cope with load fluctuations after a huge amount of photovoltaic and wind power is connected to the grid, hydropower units, especially large Francis turbines, are required to operate in the load range to balance the grid and ensure the stability and reliability of the power supply. Changes in electricity consumption lead to continuous fluctuations in the load demand on the grid for hydroelectric power plants throughout the day. The hydropower units in the power plants must operate frequently under a broad range of loads under off-design operating conditions in order to meet the power grid's requirements for absorbing new energy sources, such as photovoltaic and wind power. This has resulted in severe issues with the turbine runners and has drastically altered the operating characteristics of the units [4; 5]. Francis turbine runners are susceptible to unstable flow when they operate under off-design conditions for an extended period. This can result in intense vibrations in the runner blades and a reduction in power generation efficiency [6; 7]. Francis turbines can experience flow-induced cracks and damage in severe instances [8; 9; 10]. Figure 1 shows damage to the runner blade of a large prototype Francis turbine. Scholars worldwide have conducted a large number of in-depth studies on the unsteady flow characteristics of Francis turbines when they are operated outside of their rated operating conditions. The flow distribution in the Francis runner flow channel under partial loads is irregular, causing cavitation on the runner blades. Cavitation erosion decreases turbine performance, increases hydraulic losses, and causes material loss on the runner blades [12; 13]. The runner blades of Francis turbines may develop pits and cracks as a result of prolonged cavitation erosion [14; 15]. The time- and frequency-domain properties in the vaneless region of Francis units under various load conditions were monitored and simulated [16]. At part-load conditions, the Francis turbine unit can experience draft tube pressure pulsations, leading to severe hydraulic vibrations in the Francis turbine unit and threatening  
Figure 1: Flow-induced damage of the runner blade of a large Francis turbine [11]. its stability [17; 18].