Francis hydraulic turbines are commonly used in hydropower plants and operate at a variety of different load conditions \[1\]. As the demand from the electrical grid fluctuates, hydraulic machines might operate at excessive flow rates. At excess load conditions, the flow instabilities can lead to high-pressure fluctuations in the unit. Flow-induced fluctuations are a structural threat and have undesirable effects on the operational stability of the unit \[2, 3\].

Large Eddy Simulations (LES) were conducted to characterize the turbulent flow structures in the Francis turbine unit operating at an excess load condition. 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. The incoming flow rate, 3 /s, was 120% of the optimal design point rate, 2.5 /s. The velocity, vorticity, and iso-surfaces of Q-criterion were acquired inside the draft tube. The pressure signals were obtained using probes placed at different downstream locations along the wall and centerline of the draft tube. Flow images and pressure signals were compared to the turbine operating at the design flow rate to highlight the differences in flow patterns and the impact on pressure fluctuations and power generation. Second-order discretization schemes were used to solve the filtered LES governing equations with WALE subgrid approximation. The spatial resolution of the mesh inside the runner and the draft tube will be discussed in terms of yplus value and the first layer thickness.

Results showed a straight vortex rope extending from the entrance of the draft tube to the middle of the tube. Small scale vortex filaments generated from the blade region are distributed uniformly inside the draft tube between the vortex rope and the wall. In the central region, low pressure is observed. The velocity is low at the core of the rope but is very high at the periphery of the vortex rope. High-pressure fluctuations are observed from the probe located along the centerline. The predicted power output at 120% flow rate was twice the power output of the design point, 1,805 versus 961 kW \[4\]. The amplitude of pressure fluctuations acquired at excess load, shown by the standard deviation of the pressure magnitude normalized by the total head of the water, was 14 times as much compared to that at the design point, or 26.80 versus 2.55 \[4\]. At the draft tube wall, the amplitude of pressure fluctuations at the excess and design condition are nearly the same. Mitigation strategies of flow-induced pressure fluctuations at various conditions, including excess load, should be considered as a future study.

References:

\[1\] Qian, Z.D., Li, W., Huai, W.X. and Wu, Y.L., 2012. The effect of runner cone design on pressure oscillation characteristics in a Francis hydraulic turbine. Proceedings of the Institution of Mechanical Engineers, Part A: Journal of Power and Energy, 226(1), pp.137-150.

\[2\] Qi, S., Shuhon, L., Yulin, W., Weizhang, W. and Xingming, T., 2004. Three-dimensional simulation of unsteady flow in a model Francis hydraulic turbine. Tsinghua Science and Technology, 9(6), pp.694-699.

\[3\] Qian, Z.D., Yang, J.D. and Huai, W.X., 2007. Numerical simulation and analysis of pressure pulsation in Francis hydraulic turbine with air admission. Journal of hydrodynamics, 19(4), pp.467-472.

\[4\] Altimemy, M., Attiya, B., Daskiran, C., Liu, I.H. and Oztekin, A., 2019. Mitigation of flow-induced pressure fluctuations in a Francis turbine operating at the design and partial load regimes—LES simulations. International Journal of Heat and Fluid Flow, 79, p.108444.


Performance of Francis Turbine Operating at Excess Load Condition

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