Modal analysis of a spinning disk in a dense fluid as a model for high head hydraulic turbines*

In high head Francis turbines and pump-turbines in particular, RSI is an unavoidable source of excitation that needs to be predicted accurately. Precise knowledge of turbine dynamic characteristics, notably the variation of the rotor natural frequencies with rotation speed and added mass of the surrounding water, is essential to assess potential resonance and resulting amplification of vibrations. In these machines, the rotating disk-like structures of the runner crown and band as well as the head cover and bottom ring give rise to the emergence of diametrical modes and a mode split phenomenon for which no efficient prediction method exists to date. Fully coupled FSI methods are too computationally expensive; hence, a simplified method based on the modal force approach would be a powerful tool for the design and expected life prediction of these turbines. This work presents the development of an analytical model for a rotating disk in a dense fluid, which accurately predicts the natural frequency split as well as the natural frequency drift that are observed in experiments. Additionally, the analytical model gives an explanation on the physical origin of the mode split phenomenon.