Global linear stability analysis of the flow inside a conical draft tube

Abstract

The paper presents the numerical simulations of the flow inside the draft tube of Francis-99 turbine at the part load (PL) operating condition. The rotating vortex rope (RVR) is a phenomenon that occurs during the PL operating regime inside the draft tube of hydraulic turbines. To reduce the computational cost, the numerical simulations are carried out in two steps. Firstly, steady state numerical simulations are performed in a reduced geometry of the runner which is made of a runner passage and part of the draft tube. The velocity profiles from the steady state simulation are used as a boundary condition for unsteady numerical simulation on the inlet of the full draft tube geometry. The velocities from the numerical simulations are time-averaged over a period of 5 RVR rotations and validated with the experimental velocities averaged over the same period. Further, a two-dimensional (2D) linear global stability analysis is performed on a plane extracted from the cone of the draft tube using the time-averaged flow. The frequency of three-dimensional (3D) flow simulation and of the 2D stability analysis are found to be in good agreement with the experimental frequency.