Global linear stability analysis of flow inside an axial swirl generator with a rotating vortex rope

Abstract

In hydraulic turbines, either Francis or axial turbines, a high swirling flow is generated at PL conditions at the inlet of the draft tube resulting in the formation of a rotating vortex rope (RVR). This leads to pressure fluctuations which limit the operating range of single regulated turbines. In the present study, an axial hydraulic turbine has been numerically simulated by the k−ϵ and SST-based Scale-Adaptive Simulation model (SST SAS) turbulent models to capture helical RVR. Considering the formation of the RVR as the result of a global instability, linear global stability analysis of the time-averaged turbulent flow field has been conducted. For the first time in axial hydraulic turbines, how boundary conditions affect the unstable mode and which frequency, plunging or rotating, is related to the vortex rope instability have been studied. It is found that the flow inside the draft tube is sensitive to the asymmetrical disturbances with a frequency close to the rotational component.