Numerical predictions and stability analysis of cavitating draft tube vortices at high head in a model Francis turbine

Draft tube vortex is one of the main causes of hydraulic instability in hydraulic reaction turbines, in particular Francis turbines. A method of cavitation calculations was proposed to predict the pressure fluctuations induced by draft tube vortices in a model Francis turbine, by solving RANS equations with RNG k-turbulence model and ZGB cavitation model, with modified turbulence viscosity. Three cases with different flow rates at high head were studied. In the study case of part load, two modes of revolutions with the same rotating direction, revolution around the axis of the draft tube cone, and revolution around the core of the vortex rope, can be recognized. The elliptical shaped vortex rope causes anisotropic characteristics of pressure fluctuations around the centerline of the draft tube cone. By analyzing the phase angles of the pressure fluctuations, the role of the vortex rope as an exciter in the oscillating case can be recognized. An analysis of Batchelor instability, i.e. instability in q-vortex like flow structure, has been carried out on the draft tube vortices in these three cases. It can be concluded that the trajectory for study case with part load lies in the region of absolute instability (AI), and it lies in the region of convective instability (CI) for study case with design flow rate. Trajectory for study case with over load lies in the AI region at the inlet of the draft tube, and enters CI region near the end of the elbow.