Large-eddy simulations of Francis turbine flow control by radial jets

Francis turbine operation often experiences part load conditions, at which precessing vortex core (PVC) and double-helix structures can occur, limiting the stable operation range. The study investigates the mitigation of these flow instabilities in a Francis turbine air model by implementing radial jet injection. This approach is based on linear stability analysis and its adjoint formulation, revealing sensitive flow areas. Manipulating these zones can significantly impact instability dynamics. We perform large-eddy simulation of turbulent swirling flow in the Francis turbine model and employ radial injection through 12 circularly distributed holes on the runner crown tip with an injection flow rate of 2% of the inlet flow rate. A comparison with experimental data and a convergence study demonstrated good agreement in velocity fields and pulsation characteristics. Flow control was conducted for a wide range of hole positions and different angles between radial jets and the base flow. Spectral analysis of wall-pressure fluctuations revealed an optimal hole position, coinciding with the experimental results. However, flow control in simulations was less effective, reducing pressure pulsations of azimuthal flow modes m = 0, 1, 2 × 64, 33, and 17%, accordingly. Variation of the jet angle orientation demonstrated the highest pressure variance suppression for 90°. In pressure variance contours, PVC diminishing was observed near the runner crown, but that was amplified downstream.