Pressure Oscillations with Ultra-Low Frequency Induced by Vortical Flow Inside Francis Turbine Draft Tubes

Abstract

The present paper investigates the pressure oscillations with ultra-low frequency induced by the precessing vortex rope (PVR) whose frequency f PVR is one-fifth of runner frequency for a model Francis turbine operated at part-load condition. Numerical simulations based on the MSST PANS model are conducted to reveal the vortical flow and the DMD method is applied to analyze the modes for unstable flow inside the draft tubes. To make out the effect of draft tube structure on the PVR and pressure oscillation, both conventional elbow draft tube (EDT) and conical draft tube (CDT) are treated in the study. Two pressure oscillation components with ultra-low frequencies (near one third and two third of f PVR ) are captured in the EDT. The internal flow analysis depicts that the pressure oscillations with ultra-low frequency occur due to the strong interaction between the PVR and the backflow in the draft tube, and the elbow structure promotes the interaction and the swirling flow. It is noted that cavitation changes the dynamic characteristics of the vortex rope significantly. Cavitation alleviates the strong interaction between vortex rope and backflow, and suppresses the pressure oscillations with ultra-low frequency in the draft tube.