Frequency and vibration amplitude prediction of rotating discs subject to mode splitting

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Modern hydroelectric turbines are designed to achieve near perfect efficiency while keeping production costsas low as possible. One way to accomplish such a goal is by reducing the thickness of turbine blades,consequently lowering their stiffness and increasing their propensity to experience critical vibration levels.Moreover, the end-users' growing need for power regulation due to the integration of intermittent renewablesources leads to more frequent off-design operations as well as machine starts and stops, for which dynamicmechanical stresses are significantly higher than at best efficiency point. In this context, precise knowledge ofthe turbine dynamic characteristics, notably the variation of the natural frequencies of the rotor with rotationrate, is essential to avoid problematic vibrations. In many publications, pump-turbine runners have beenmodelled using a rotating disk submerged in water, highlighting the phenomenon of frequency split: a forwardand a backward travelling waves emerge as the disk rotate. This phenomenon is linked to the variation of addedmass with rotational velocity. The project has two main objectives: understand better the mechanism offrequency split; and develop a simplified simulation strategy to evaluate the natural frequencies of a rotatingdisk. Understanding the frequency split of pump-turbine runners and its underlying mechanisms is critical toevaluate the resulting stresses and the expected life of the machine. This project will provide an accurate andfast tool to improve the design of high head Francis turbines and pump-turbines. This tool is essential todevelop new reliable turbines and provide detailed information about the fatigue life of the equipment.