Simplified models to evaluate nonlinear dynamics in hydropower rotors

Abstract: In hydropower systems, it is essential to avoid catastrophic failures that lead to human and economic losses. Unfortunately, a hydropower rotor can behave abnormally since several nonlinear effects occur during start-up, shut-downs or when running at nominal speed. Weak nonlinear interaction in the bearings, electromagnetic interaction between the generator and rotor or fluid-structure interaction in turbines are typical nonlinear effects that may appear. Moreover, strong nonlinearities can also occur due to blade contacts and assembly errors. These types of nonlinearities can be dangerous in case of bad design of the rotor, and it could even lead to catastrophes in the worst case. In this thesis, simple models are used to describe the different types of nonlinearities, with focus on blade rubbing, bearings and electromagnetic interaction. These interactions are usually investigated on Jeffcott rotors or rigid rotors to reduce the dimension of the design space to a few important parameters only. The dynamics of the system are evaluated by using common tools such as Poincare sections, bifurcation diagrams, Maximum Lyapunov Exponent (MLE), Lyapunov spectrum and waterfall plots of the Fast Fourier Transform (FFT). The numerical results have been compared with experimental results to ensure that these models are satisfying in our range of study. Once these simple models have been verified, they can be used to simulate the full hydropower rotor by including all interaction types. A focus is made on the numerical methods to employ and reduction methods to gain computation time, as well as to know under which circumstances the nonlinear interactions have to be included in comparison with the linear analysis. As a result, this work intends to provide guidelines about the models to use to perform dynamic simulations on fullscale turbines and to know when a linear model can be sufficient to evaluate a machine at design stage or when changing any mechanical component in the hydropower rotor.