## 1 Introduction  
Nowadays hydropower is perceived as a mature technology but it has to face to new requirements more challenging than ever: the stochastic nature of renewable energy sources (wind, solar), irregular market requirements for energy, climate changes, constraints and environmental concerns [1]. Therefore, the hydraulic turbines have to operate over a wide range [2; 3] under a fast change of the parameters to compensate the fluctuating part delivered in the electrical grid by the renewable energies. Several times, these requirements implied transient phenomena (e.g., load acceptance, load rejection, start-stop, emergency shutdown, spin no load, total load rejection) in operation [4; 5; 6; 7]. Along the upstream passage of the hydraulic turbine, the potential energy of the water available in the upper tank is converted into kinetic energy. Then, this hydraulic energy available at the runner inlet is converted by the mechanical energy at the turbine shaft. The flow energy which is not converted by the runner is ingested by the draft tube of the hydraulic turbines [8]. A fraction of this residual energy is converted back into potential energy along to the draft tube [9]. Over 50-75% of this residual energy is recovered in the first part of the draft tube, which is called the discharge cone. Therefore, the hydraulic efficiency of the medium-to-low head turbines is significantly affected by performing the draft tube on a wide range operation [10]. [PERSON] et al. (2019) have shown that the hydraulic losses in a Francis turbine draft tube can reach up to 10% from the turbine head, far away from the best efficiency point (BEP). The fixed blade turbines, i.e., Francis and propeller types, operated at far-away conditions from the BEP, leads to a high level of swirl at the draft tube inlet because of the mismatch between the swirl delivered by the wicket gates and the angular momentum extracted by the runner ([PERSON], 2019). Therefore, the decelerated swirling flow in the draft tube cone often results in the vortex breakdown (known as the vortex rope), which is the main cause of the pressure fluctuations generated in the hydraulic turbines at part load conditions ([PERSON], 2019). This phenomenon and the associated effects is known in the literature as a draft tube surge ([PERSON], 2019; [PERSON], 2019). One of the most harmful effects of operating hydraulic turbines at a part load are the following: the wear and fatigue of mechanical parts, cavitation and cracks of the runner blades ([PERSON], 2019; [PERSON], 2019; [PERSON], 2019). Over time, several techniques have been investigated to tame/eliminate the vortex rope. The various techniques that have been employed to mitigate vortex rope are intended either to produce an axisymmetric draft-tube flow or to diminish the swirl in the draft tube below the critical level, including pulsating axial jet, J-groove, air admission/injection, splitter plates, fins, runner crown extension and freely rotating runner cone extension (FRUCE) ([PERSON], 2019; [PERSON], 2019; [PERSON], 2020; [PERSON], 2020). These techniques bring improvements at part-load conditions. Notwithstanding, passive techniques cannot be moved to other regimes, which may add undesirable hydraulic losses. Our group has promoted the active water injection method through the runner crown along to the turbine axis to control the decelerated swirling flow from the conical diffuser of hydraulic turbines operating at part-load conditions ([PERSON] and [PERSON], 2019). Extensive experimental investigations were carried out by [PERSON] et al. (2019), showing that a jet discharge larger than 10-12% of the volumetric flow rate associated to the operating point is required to remove the vortex rope and its undesirable effects. From a practical point of view, these investigations have revealed a new issue regarding the control jet supply. Here, a significant fraction of the turbine discharge bypasses the runner leading to unacceptable volumetric losses.