Model for Vortex Rope Dynamics in Francis Turbine Outlet

Abstract

The present communication deals with the simulation of the vortex rope present in the outlet of a Francis turbine when operating at partial load regimes This approach is not devoted to the analysis of a complete turbomachinery system but rather to develop a rigorous mathematical analysis for a local phenomenon of practical relevance, We synthesise the problem calculating the three-dimensional unsteady motion of a vortex filament confined inside a cylindrical wall. In this first analysis we ignore cavitation effects in order to detect those phenomena which can be explained in teams of incompressible vortex dynamics The system rope-diffuser is assumed as isolated and we neglect any direct interaction with the turbine blades or the diffuser outlet.

Pressure fluctuations at the outlet of a Francis turbine operating at partial load regimes are evaluated with a computational method based on three-dimensional vortex dynamics. The fundamental frequencies and their dependence on the mean swirl-rate show a good agreement with measured data. Results also indicate the birth of aperiodic regimes.