Anti-phase oscillations of an elliptical cavitation vortex in Francis turbine draft tube

Abstract

In this paper, the dynamic behavior of a precessing cavitation vortex featuring an elliptical cross section in Francis turbine draft tube is investigated. This phenomenon may occur for values of discharge coefficient within 70%–85% of the discharge coefficient at the best efficiency point, for which Francis turbines can experience the onset of the so-called upper-part load (UPL) instability. The latter is characterized by the propagation of high-amplitude synchronous pressure fluctuations through the complete hydraulic circuit. High-speed visualizations of the cavitation vortex are performed on a Francis turbine model by means of two cameras synchronized with pressure sensors arranged along the draft tube for different Thoma numbers at a given discharge coefficient. A simplified analytical model of the cavitation vortex is proposed. It enables the interpretation of the video post-processing results in the frequency domain and the estimation of both the vortex cross section dimensions and their oscillations with time. It is first demonstrated that both the vortex cross section ellipticity (given by the ratio between its semi-major and semi-minor axes) and the amplitude of its oscillations are directly correlated with the amplitude of UPL pressure fluctuations during intermittent UPL instability. Furthermore, the evolution along the draft tube of the dimensions of the elliptical vortex cross section and their oscillations during fully developed UPL instability is highlighted. The ellipticity of the vortex cross section increases as the vortex center position gets closer to the draft tube wall away from the turbine outlet. In addition, the vortex cross section dimensions oscillate with opposite phase from either side of a pressure node located along the draft tube. This results in low oscillations of the total void fraction in the draft tube, compared with results obtained locally. This effect should be considered in the one-dimensional modeling of the cavitation flow during UPL instability for further stability analysis. The new insights on UPL instability presented in this paper may potentially lead to a better theoretical understanding and modeling of this phenomenon in Francis turbines draft tube.