# Flow-Induced Strength Analysis of Large Francis Turbine Under Extended Load Range
###### Abstract
Experimental and numerical studies of swirling flow and flow instability in Francis turbines under different loads have been carried out to capture the transient rotating flow characteristics in the draft tube [19]. Through the Francis turbine model test, it is possible to directly observe the complex flow characteristics of the draft tube vortex ropes under different operating conditions [20]. The physical mechanisms of unsteady flow and flow-induced structural vibration and stress in Francis turbine units under different operating conditions can be further elucidated by performing field measurements of pressure pulsation and stress on a prototype Francis runner [19; 21; 22]. To gain a deeper understanding of the prototype unit's vibration mechanism underwater, the vibration measurements of a simplified hydraulic turbine model have been carried out using novel distributed fiber optic sensing technology to monitor vibrations and stresses [23]. The underwater structural vibrations of Francis turbine runners were measured and simulated to evaluate the model behavior of the runners considering the added-mass effects of the surrounding water [24]. Studies involving field measurements and numerical simulations have shown that unsteady flow-induced stresses in Francis runners are closely related to pressure pulsation levels, rotational speed, and the geometric configuration of the turbine [25]. According to the results of a study into the runner blade breakdown of a 200 MW Francis turbine, cavitation damage from operations at low part loads combined with severe high-cycle fatigue caused the blade to crack [26]. Another investigation discovered that cracks on the runner blades of a prototype Francis turbine were produced by operating load conditions deviating from the rated condition [10]. Some Francis units may also be damaged as a result of excessive dynamic stresses within the runner and flow-induced structural resonance under off-design conditions [8]. According to some experts, the Francis runner's blades cracked because of the uneven weld surface, which was exacerbated by the weld filler material's hydrogen embrittlement [9]. The development of cracks in Francis turbine runners is a complicated issue that is impacted by several variables. One of the most frequent conclusions is that turbulence, particularly in off-design operating conditions, is a major factor in causing these cracks, even though the precise causes may differ. Many researchers have studied the flow dynamics and structural vibration of Francis turbine runners by computational fluid dynamics (CFD), finite element method (FEM) and field measurements, respectively. However, the research for the comprehensive analysis of large prototype Francis turbines with full three-dimensional fluid-structure interaction (FSI) methods is still relatively limited [27]. In order to capture the flow-induced dynamic behavior more accurately and to avoid serious flow-induced damage in Francis turbines, the flow-induced strength analysis of a 183 MW prototype Francis turbine is carried out in this study following the workflow shown in Figure 2.  
First, a geometrical model of the Francis turbine unit's fluid and structural domains is created. Second, three operating loads are chosen to perform the CFD analysis of the Francis turbine unit's entire flow passage in order to thoroughly examine the pressure distribution and the flow distribution characteristics: 33.3%, 66.6%, and 100% of the rated power. Ultimately, the finite element model of the Francis runner is mapped with the pressure data calculated from the CFD analysis, and an in-depth investigation of the runner's stress distribution is conducted.