Generation of Twin Vortex Rope in the Draft-Tube Elbow of a Francis Turbine During Deep Part-Load Operation

This paper focuses on the generation of twin vortex rope in the draft-tube elbow of a Francis turbine at deep part-load operation through analyzing the results of model tests along with numerical simulations. Model tests, including pressure fluctuations measurements, are conducted over ten speed factors. By considering the frequency of the pressure fluctuations with respect to the swirl intensity at the runner outlet, the part-load operating range is divided into three regimes, with two clear transitions between each occurring at swirl numbers 0.4 and 1.7. For operating conditions with a swirl number S > 0.4, a linear correlation between the frequency of the precessing vortex core and the swirl number is established. During the deep part-load regime (S > 1.7), low-frequency pressure fluctuations appear. Their frequency features another linear correlation with the swirl number. Unsteady computational fluid dynamics simulation of the full domain is performed to elucidate the generation mechanisms of the low-frequency fluctuations. By tracking the center of the vortical structures along the draft-tube, generation of three vortices in the elbow responsible for the pressure fluctuations at the lowest frequency is highlighted: the main precessing vortex core (PVC) hits the draft-tube wall in the elbow resulting in its break down into three vortices rotating with half the rotational speed of the PVC. Two of the vortices rotate with opposite angular position, constituting a structure of twin vortices. The periodic rotation of these three vortices in the elbow induces low-frequency pressure fluctuations.