Local wave speed and bulk flow viscosity in Francis turbines at part load operation

The operation of Francis turbines at off-design conditions may cause the development of a cavitation vortex rope in the draft tube cone, acting as a pressure excitation source. The interactions between this excitation source and the hydraulic system at the natural frequency may result in resonance phenomena, causing serious hydro-mechanical oscillations. One-dimensional draft tube models for the simulation and prediction of part load resonances require an accurate modelling of the wave speed and the bulk viscosity for the draft tube flow. This paper introduces a new methodology for determining these two hydroacoustic parameters in the draft tube of a reduced scale physical model of a Francis turbine, based on experimental identification of the hydraulic natural frequency of the test rig. Finally, dimensionless numbers are derived to define both the wave speed and bulk viscosity for different operating points of the turbine.