Numerical simulation of the unsteady cavitating flow in a Francis turbine draft tube at Upper-Part-Load (UPL) conditions

At part-load conditions, Francis turbines experience the development of a precessing vortex rope in their draft tube (DT), rotating with a frequency between 0.2 and 0.5 times the runner frequency. It induces pressure pulsations at the precession frequency in the whole hydraulic system, undesirable vibrations and noise putting at risk the stability of the system and the lifetime of the machine components. In specific machines, a dramatic amplification of the noise and vibrations can be observed between 70% and 85% of the design conditions. In these cases, synchronous pressure pulsations with a high frequency, typically between 2 and 4 times the runner frequency, are observed, referred to as the so-called Upper-Part-Load (UPL) pulsations. These pulsations are induced by a self-excitation of the entire hydraulic system including the cavitation vortex rope at one of its high order eigenmodes. Besides, the cavitation vortex rope features an elliptical cross-section rotating around the vortex axis at a high frequency. In this manuscript, unsteady two-phase flow simulations using a Scaled-Adaptive-Simulation (SAS) turbulence model and ZGB cavitation model of a Francis turbine draft tube at 80% of the design condition are performed to clarify the mechanisms responsible for the formation of the elliptical shape of the vortex and the UPL pulsations. However, the numerical simulation with a constant inlet boundary condition cannot reproduce the UPL pulsation phenomenon since it is a self-excited oscillation at one eigenmode of the complete system, which is not considered. Therefore, the UPL pulsations component is extracted from the measured pressure fluctuations data by applying a band-pass filter and is then set as the inlet boundary condition in the numerical simulation. The flow field is therefore artificially excited which aims to confirm whether the same phenomenon can be observed and to compare with the flow field obtained with constant inlet boundary condition. The numerical simulations are validated by experimental results, and the wave propagation in the DT is clarified.