Numerical simulation and analysis at partial load in Francis turbines: Three-dimensional topology and frequency signature of inter-blade vortices

Hydraulic machines are designed to operate in flow conditions close to the best efficiency point. However, to respond to the increasing demand for flexibility mainly due to the integration of renewable energy in the electric grid, the operating range of Francis turbines has to be extended towards smaller discharge levels without restriction. When Francis turbines are operated typically between 30% and 60% of the rated output power, the flow field is characterized by the appearance of inter-blade vortices in the runner. In these off-design operating conditions and due to these phenomena, dynamic stresses level can increase, and potentially lead to fatigue damage of the mechanical structure of the machine. The objective of this paper is to present investigations on the dynamic behaviour of the inter-blade vortices and their impact on the runner by using numerical simulations. Computations were performed with different turbulence modelling approaches to assess their relevance and reliability: Reynolds-Averaged Navier-Stokes (RANS) and Large-Eddy Simulation (LES). Computations aimed to better understand the emergence condition of the inter-blade vortices. The analysis showed that vortices can be generated due to poor inlet adaptation at part load, however other vortices can also be due to a local backflow in the runner. The competition between these both phenomena leads to various topologies of the inter-blade vortices. The numerical results were compared to experimental visualizations performed on scaled model as well as to previous numerical studies results. The impact of these inter-blade vortices on the runner were also investigated by considering the pressure fluctuations induced on the blades. The dynamic loading on the blade has to be known in order to evaluate the lifetime of the runner by mechanical analysis. A previous experimental study [S. Bouajila et al., TOP Conf. Ser.: Earth Environ. Sci., 2016] has shown that the appearance of the inter-blade vortices can be correlated with a large-band frequency signature in the pressure fluctuations measured on the blades. The numerical simulations presented in this paper focused on the prediction of this frequency signature as well as on the analysis of its origin.