Large Eddy Simulations of Francis Turbine Operating at Ultra-Low Loads

Large Eddy Simulations (LES) are conducted to characterize the turbulent flow structures in the Francis turbine unit operating at ultra-low load conditions. The incoming flow rate is 50 and 40% of the optimal design point rate, 2.5 /s. The runner rotates with a constant rotation speed of 1,000 rpm, or Reynolds number 2×10⁷ based on the runner reference diameter. Second-order discretization schemes are used to solve the filtered LES governing equations with a WALE subgrid scheme. The turbine consists of a runner and a draft tube. The runner domain consists of 15 blades with a diameter of D = 0.62m. It is connected to a diffuser-shaped draft tube length of L = 5D with a 5° angle of expansion. Contours of vorticity, velocity, and iso-surfaces of the Q-criterion will be presented to characterize the flow field in the draft tube. Plots of the frequency and the averaged amplitude of the pressure fluctuations, normalized by the turbine head, and power of the turbine will be presented. The pressure signals at various locations will be probed to assess the level of fluctuations.  The intensity of the vortex rope into the draft tube at different flow rate operation regimes will be determined and presented. By investigating the flow structure at ultra-low loads, more information on whether Francis Turbines should be operated at such conditions will be obtained.

A no-slip boundary condition is applied at the surfaces of the runner and the draft tube, a pressure outflow condition is imposed at the outlet of the draft tube, and a mass flow inlet with fixed turbulence intensity is imposed at the runner. The spatial resolution of the mesh inside the Francis turbine runner and the draft tube will be reported regarding y-plus values and first layer thicknesses. Pressure probes are utilized along the length of the draft tube to measure the pressure signal at various downstream locations.  There is a strong correlation between the amplitude and frequency of pressure fluctuations and the dynamics of the vortex rope. The dynamic behavior of the rope can lead to low-frequency, high amplitude, pressure fluctuations inside the draft tube. There could also be high-frequency pressure fluctuations typically caused by the interactions of small and large scale eddies from the runner blades.

Hydropower is a clean and renewable energy source widely used to generate electricity. Hydropower plants use Francis hydraulic turbines, which operate at high head and low flow rate conditions. Many adverse conditions make turbine operation very difficult, including partial load, high load, cavitation, and vortex-rope formation. Moreover, a buildup of vorticity inside the flow domain may damage the runner blades. Another big challenge is pressure fluctuations inside turbine units, especially in the draft tube. One of the leading solutions to mitigate pressure fluctuations is injecting water or air into the center of the draft tube.