The Complex Dynamics of the Precessing Vortex Rope in a Straight Diffuser

Abstract

The decelerated swirling flow in the discharge cone of Francis turbines operated at partial discharge develops a self-induced instability with a precessing helical vortex (vortex rope). In an axisymmetric geometry, this phenomenon is expected to generate asynchronous pressure fluctuations as a result of the precessing motion. However, numerical and experimental data indicate that synchronous (plunging) fluctuations, with a frequency lower than the precessing frequency, also develops as a result of helical vortex filament dynamics. This paper presents a quantitative approach to describe the precessing vortex rope by properly fitting a three-dimensional logarithmic spiral model with the vortex filament computed from the velocity gradient tensor. We show that the slope coefficient of either curvature or torsion radii of the helix is a good indicator for the vortex rope dynamics, and it supports the stretching - breaking up - bouncing back mechanism that may explain the plunging oscillations.