Hydroacoustic interaction between draft tube and penstock eigenmodes under Francis turbine full load instability

Abstract

At high load, Francis Turbines may experience self-sustained pressure surge leading to significant power swing and pressure fluctuations along the waterway. The physical mechanism initiating this instability phenomenon has been the subject of much research. The development of the axisymmetric cavitating vortex rope at the runner outlet modifies the hydroacoustic properties of the draft tube waterway. Very low wave speed due to high cavitation volume combined with a high swirling number initiates the unstable axial pulsations of the cavitating vortex rope which frequency corresponds to a penstock’s eigenfrequency. The 15 MW power plant of Monceaux-la-Virole in France, composed of two units fed by a single penstock, experiences such full-load surge. On-site tests have been carried out to analyze the envelope of pressure fluctuations along the penstock once instability occurs. Combined with a 1D SIMSEN model of the power plant, these measurements have allowed to enhance the understanding of this instability phenomenon. To achieve this, an advanced draft tube modelling taking into account distributed wave speed, convective terms and divergent geometry is used and frequency analysis is carried out. Unstable draft tube eigenmodes and stable penstock eigenmodes are predicted. The key draft tube model parameters such as wave speed and second viscosity are calibrated to set the draft tube eigenmode frequency to the unstable measured frequency for different operating points. This frequency analysis concludes that high load instability occurs when a matching between the draft tube and the penstock eigenfrequencies is experienced. Moreover, it is shown that the unstable draft tube eigenmode is able to interact with different order penstock eigenmodes as function of the operating point of the unit.