Dynamic modal analysis during reduced scale model tests of hydraulic turbines for hydro-acoustic characterization of cavitation flows

Francis turbines operating at off-design conditions experience the development of unfavourable cavitation flows in the draft tube at the runner outlet, which induce pressure pulsations and hydro-acoustic resonances in the worst cases. The assessment of hydropower plant units at off-design conditions is possible by means of one-dimensional numerical simulation, which however requires a proper modelling of the draft tube cavitation flow. The corresponding hydro-acoustic parameters can be identified for a wide number of operating points on the reduced scale model of the machine by modal analysis of the hydraulic test rig. This identification approach is efficient but can however be time-consuming for an industrial project. The paper aims at proposing and validating a faster procedure to identify the eigenfrequencies and the corresponding eigenmodes of a hydraulic test rig featuring a reduced scale model of a Francis turbine operating in off-design conditions. The test rig is excited by injecting a periodical discharge with a rotating valve whose frequency linearly increases from 0 to 7 Hz. Based on the response of the test rig, measured by pressure sensors placed along the pipes, the eigenfrequencies and the corresponding eigenmodes are identified for several operating conditions. The hydro-acoustic parameters are then identified by using a one-dimensional numerical model of the test rig. The results are in very good agreement with those obtained with the standard procedure, i.e. with a stepwise increase of the excitation frequency. This new approach represents an important gain of time and might be applied to assess hydropower plant stability in an industrial context.