Proper orthogonal decomposition of turbulent swirling flow of a draft tube at part load

Abstract

A large scale vortical structure, i.e., rotating vortex rope (RVR), generally forms at part load (PL) operation of a reaction turbine due to the combined effect of swirling flow at the runner outlet and the adverse pressure gradient in the draft tube. Even with the data analysis through advanced measurement techniques like Laser Doppler velocimetry (LDV) and Particle Image Velocimetry (PIV), the information available about the flow instabilities developed due to RVR is still incomplete. This paper presents an application of the proper orthogonal decomposition (POD) method to analyze the flow field inside the draft tube cone at PL operation of a high-head model Francis turbine. The POD analysis is performed on 250 PIV snapshots containing the axial and radial velocities. The results show that the first eight modes contain more than 95% of the total kinetic energy (KE) of the flow field and are associated with the organized motion of the flow. The first mode contains more than 50% of the total energy, and the axial velocity profile reconstructed with the first mode is identical to the mean axial velocity flow field. The maximum dissipation of the turbulent kinetic energy (TKE) occurs through unorganized motion.