Dynamics of the cavitation precessing vortex rope for Francis turbines at part load operating conditions

The massive penetration of the existing electrical grid by renewable energy sources requires a continuous extension of the operating range of hydroelectric powerplants, which can lead to cavitation flow instabilities inducing undesirable mechanical vibrations and large fluctuations of pressure and output power, putting at risk the structural integrity of the machine and ultimately the grid stability. A typical example is the development of a cavitation precessing vortex rope at the outlet of a Francis turbine runner operating at part load conditions. It acts as an excitation source for the hydraulic system, leading to the propagation of pressure fluctuations in the hydraulic circuit which are greatly amplified in case of resonance. Therefore, the assessment of the stability of hydropower plants operating at part load is crucial in order to ensure the safe extension of their operating range. The accurate prediction and transposition of pressure fluctuations from the model scale to the prototype scale by means of one-dimensional hydro-acoustic models represents a major challenge, as the physical mechanisms driving the excitation source and its interaction with the hydraulic system remain partially unclear. The main objective of this research work is to experimentally investigate the influence of the operating conditions on the dynamics of the cavitation precessing vortex rope and the excitation source it induces, as well as the interaction with the system. The test-case is a reduced scale physical model of a Francis turbine, accurately reproducing the behaviour of a real size machine. Experimental investigations include study of the flow field in the draft tube cone by means of Particle Image Velocimetry (PIV) and Laser Doppler Velocimetry (LDV), high-speed visualizations of the cavitation vortex and pressure measurements performed at various part load operating conditions, including cavitation-free and cavitation conditions. PIV measurements of the tangential flow field in the draft tube cone in cavitation-free conditions highlight the influence of the flow discharge on the vortex characteristics in terms of trajectory, circulation and structure, as well as the link between the vortex dynamics and the intensity of the excitation source. The effect of cavitation on the vortex rope dynamics and its interaction with the surrounding system is also studied, with a particular focus on resonance conditions. Flow velocity measurements performed for different values of the Thoma number reveal that the axial and tangential velocity fields in the draft tube cone are not impacted by the propagation of large synchronous pressure fluctuations. Among the other observations is a phenomenon of frequency lock-in between the excitation source and the system's oscillations occurring for low values of the Froude number. This phenomenon is assumed to be a consequence of the non-linear coupling taking place in resonance conditions between the excitation source and the oscillation of the cavitation volume. Finally, it is shown that the convective component of the pressure fluctuations at the precession frequency represents the main source of mechanical excitation for the runner.