Space and time reconstruction of the precessing vortex core in Francis turbine draft tube by 2D-PIV

Francis turbines operating at part load conditions experience the development of a high swirling flow at the runner outlet, giving rise to the development of a cavitation precessing vortex rope in the draft tube. The latter acts as an excitation source for the hydro-mechanical system and may jeopardize the system stability if resonance conditions are met. Although many aspects of the part load issue have been widely studied in the past, the accurate stability analysis of hydropower plants remains challenging. A better understanding of the vortex rope dynamics in a wide range of operating conditions is an important step towards the prediction and the transposition of the pressure fluctuations from reduced to prototype scale. For this purpose, an investigation of the flow velocity fields at the outlet of a Francis turbine reduced scale physical model operating at part load conditions is performed by means of 2D-PIV in three different horizontal cross-sections of the draft tube cone. The measurements are performed in cavitation-free conditions for three values of discharge factor, comprised between 60% and 81% of the value at the Best Efficiency Point. The present article describes a detailed methodology to properly recover the evolution of the velocity fields during one precession cycle by means of phase averaging. The vortex circulation is computed and the vortex trajectory over one typical precession period is finally recovered for each operating point. It is notably shown that below a given value of the discharge factor, the vortex dynamics abruptly change and loose its periodicity and coherence