Prediction of hydro-acoustic resonances in hydropower plants by a new approach based on the concept of swirl number

Hydropower plant units operating in off-design conditions are subject to cavitation flow instabilities, potentially inducing hydro-acoustic resonances under certain conditions. They can be predicted by using one-dimensional numerical models of hydropower plants that rely on a proper modelling of the draft tube cavitation flow in off-design conditions. The latter is based on hydro-acoustic parameters that can be identified experimentally on the reduced scale physical model of the prototype on its complete operating range, which however requires an important number of measurements during model testing to consider the influence of both the head and the discharge. This article proposes a new methodology enabling the prediction of resonance conditions excited by a draft tube cavitation vortex on the complete head range of a hydropower plant unit. The methodology relies on the experimental identification at the model scale of the hydro-acoustic parameters and their transposition from the model to the prototype scale. By expressing the precession frequency of the vortex and the hydro-acoustic parameters of the draft tube cavitation flow as a function of the runner outlet flow swirl number, their value can be predicted on the complete part load operating range of the prototype whatever the value of both the head and discharge. The computation of the first natural frequency with a 1D numerical modelling of the hydropower plant enables finally the prediction of resonance conditions, which are compared with those identified by measurements on the full-scale machine.