Three-Dimensional simulation of unsteady flow in a model francis hydraulic turbine

For Francis hydraulic turbines, unsteady flow caused by vortex ropes in the draft tube leads to a problem of stability in operation. The unsteady flow field of a model Francis hydraulic turbine was simulated under part-load operation. A sliding mesh model was used to calculate a time-accurate solution for the strong rotor-stator interactions between the runner and guide vanes, and the draft tube. Based on three-dimensional incompressible Reynolds averaged Navier-Stokes equations and on a renormalization group k-∊ turbulence model, spatial discretization was obtained by using the finite volume method with unstructured grid elements, and a second order fully implicit scheme was applied for time. Pressure fluctuations in the draft tube were recorded and analyzed via a fast Fourier transform calculation. The results were compared with the experimental data, and show that the vortex rope in the draft tube and the induced pressure fluctuations are well simulated.