Analysis and Prevention of Vortex Breakdown in the Simplified Discharge Cone of a Francis Turbine

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Abstract
We perform a numerical analysis of the decelerated swirling flow into the discharge cone of a model Francis turbine operated at variable discharge and constant head, using an axisymmetric turbulent swirling flow model and a corresponding simplified computational domain. Inlet boundary conditions correspond to velocity and turbulent kinetic energy profiles measured downstream the Francis runner. Our numerical results are validated against experimental data on a survey section further downstream in the cone, showing that the Reynolds stress turbulence model with a quadratic pressure-strain term correctly captures the flow field. It is shown that the diffuser performance quickly deteriorates as the turbine discharge decreases, due to the occurrence and development of vortex breakdown, with a central quasistagnant region. We investigate a novel flow control technique, which uses a water jet injected from the runner crown tip along the axis. It is shown that the jet discharge can be optimized for minimum overall losses, while the vortex breakdown is eliminated. This flow control method is useful for mitigating the Francis turbine flow instabilities when operating at partial discharge.

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