How angular-momentum flux controls Francis turbine full-load surge

Abstract

Abstract Hydropower plants equipped with Francis turbines may enter unstable conditions at high turbine discharge [13], with strong pulsations of power output and internal pressure. The cause are oscillations of a vapor-filled cavity in the vortex flow downstream of the turbine runner, interacting with the draft tube and penstock pressure. The paper describes the structure and simulation results of a 1D distributed-parameter model for full-load surge, parametrized from results of a high-resolution unsteady two-phase CFD simulation study (Wack [14]) of high-load pulsations in the reduced-scale model of a medium-specific speed Francis turbine. In earlier research on the same model turbine, Müller [12] had suggested that runner blade cavitation could cause instability. To clarify this, variation of turbine intake flow was sup-pressed, and the influence of pressure variation via runner blade cavitation on the relative runner exit flow angle and angular-momentum flux was simulated. Due to the upstream boundary condition, the influence of mass-flow gain χ is replaced by a cavitation gain factor ψ, likewise delayed by the limited speed of swirl propagation. It is found that gain factors obtained from steady-state simulation cannot be directly used with a lumped-parameter model because the swirl effect is much reduced due to its phase changes along the vortex; using the steady-state gain factors would thus exaggerate the influence of swirl on cavity volume. Simulation in frequency domain with realistic swirl transport delay confirms that instability can occur because in some parts of the cavitation zone the swirl provides oscillation power.