On the Flow Instabilities and Turbulent Kinetic Energy of Large-Scale Francis Hydroturbine Model at Low Flow Rate Conditions

This paper is to make a better understanding of the flow instabilities and turbulent kinetic energy (TKE) features in a large-scale Francis hydroturbine model. The flow instability with aspect of pressure oscillation and pressure-velocity correlation was investigated using large eddy simulation (LES) method along with two-phase cavitation model. The numerical simulation procedures were validated by the existing experimental result, and further the TKE evolution was analyzed in a curvilinear coordinates. By monitoring the fluctuating pressure and velocities in the vanes’ wake region, the local pressure and velocity variations were proven to have a phase difference approaching π/2, with a reasonable cross-correlation coefficient. Also the simultaneous evolution of pressure fluctuations at the opposite locations possessed a clear phase difference of π, indicating the stresses variations on the runner induced by pressure oscillation were in an odd number of nodal diameter. Considering the TKE generation, the streamwise velocity component u s ′ 2 contributed the most to the TKE, and thus the normal stress production term and shear stress production term imparted more instability to the flow than other production terms.