Vortex Evolution and Energy Production in the Blade Channel of a Francis Turbine Operating at Deep Part Load Conditions

The blade vortex evaluation in Francis Turbine under deep part load conditions generates severe pressure fluctuations in the runner. The complex flow in a model turbine is numerically investigated based on a modified Partially Averaged Navier-Stokes method. The main emphasis is focused on revealing the correlation mechanism of blade vortex evolution and energy production. The results indicate that the modified PANS method shows significant advantages in hydro turbine's simulation than the traditional RANS method. At deep part load conditions, the vorticity formed at the leading edge of the suction surface and the trailing edge of the pressure surface in the blade channels. The stretching term provides the most vorticity increments while the dilation term inhibiting part which only provides a decrement of the vorticity evolution. Based on the entropy production theory, the total entropy production distribution is consisting with the distribution of vorticity. At deep part load condition, direct dissipation and turbulent dissipation provide the most entropy, while at part load condition the proportion of these twopart decreased.