Numerical investigation of the upper part load vortex rope behaviour in a Francis turbine

Abstract

The vortex rope in the draft tube is considered as the source of the upper part load pressure pulsations, which is one of some unstable phenomena in a Francis turbine. In this study, the pressure pulsations and the vortex rope in the draft tube of a Francis turbine at upper part load operation are investigated by a three dimensional unsteady numerical method. Firstly, the main frequencies of the pressure fluctuations in three planes, which are z=0.2m, 0.4m and 0.6m, in the draft tube are obtained, which are 0.38fn, 0.67fn,1.04fn,1.33fn and 1.71fn (fn is the runner rotation frequency). The simulated main frequencies show a good agreement with the results from model tests, which are 0.34fn and 1.72fn. To simplify the problem in this study, the isopressuresurface of p=-25000Pa is considered as a vortex rope. It is found that the shape of the three vortex rope sections is almost elliptical. Then the motions of the elliptical shaped sections, which are decomposed into two components that are the motion of geometric center and alteration of the major or minor axis of the ellipse, are analyzed. Obviously, the geometric center motion represents the precession movement, and the time evolution of the major or minor axis corresponds to the self-rotation of the vortex rope, respectively. The results show that the first dominant frequency of the geometric center motion fp1 is 0.38fn, and the second dominant one fp2 is 1.71fn. And the first dominant frequency of the major(minor) axis alteration fs1is 0.67fn, and the second one fs2is 1.33fn. That is, the pressure fluctuation frequencies in the draft tube are combinations of the rope precession motion frequencies and self-rotation frequencies, namely fp1, fs1, fp1+fs1,fp2, fs2, etc. Based on the analysis, the upper part load pressure pulsations may be induced by the behavior of the elliptical vortex rope in the draft tube.