Linear global stability analysis of a transient swirling flow leading to the formation of a helical precessing vortex breakdown in a straight diffuser

Abstract

Vortex breakdown occurs in highly swirling flows in various engineering applications, such as hydraulic turbines working in either high-load or part-load conditions, leading to pressure pulsations and performance degradation. In the present study, the formation of a helical vortex breakdown having rotational and plunging components (axial oscillation) in a straight diffuser is investigated with transient simulation from its columnar state to a helical vortex breakdown state. It is similar to the helical precessing vortex rope occurring in hydraulic turbines operating at part-load condition. In addition, considering vortex breakdown as a global instability, a linear global stability analysis of the time-averaged turbulent flow field is conducted for different flow states. The main objective is to understand the role of plunging mode in vortex rope formation in straight draft tubes and identify its differences with the one observed in hydraulic turbines with elbow draft tubes operating at part-load condition. Results showed that in contrast to the elbow draft tubes where the plunging mode appears earlier than the rotating mode, the transient simulation showed that the plunging mode appears after several vortex rope rotations in the straight draft tube. This is confirmed by the stability analysis showing that the flow is unstable to the asymmetrical disturbances with a frequency close to the rotating frequency not the plunging ones. Finally, the stability analysis showed a higher critical flow rate than the one obtained from the contour of local swirl number and time history of pressure and velocity.