A numerical method for the determination of flow-induced damping in hydroelectric turbines

To estimate structural fatigue, vibrational response to realistic spectrum of excitations and associated equivalent damping are of paramount importance. In this paper, an approach to quantify flow-induced damping of a relatively heavy fluid on a vibrating hydraulic turbine blade using numerical simulations is presented. First, mode shapes and frequencies of the immersed structure are obtained by modal analysis using the finite element method. Then, forced oscillatory modal motion is prescribed on the structural boundary of unsteady Reynolds-averaged Navier-Stokes flow simulations. Damping is finally computed as the normalized work done by the resulting fluid load on the structure. Validation is achieved by comparing the numerical results with available experimental data for a steel hydrofoil oscillating in flowing water. For this case, the linear increase in the damping ratio with the flow velocity is reproduced within 10% of the experimental values. Application of the method to an actual hydroelectric propeller turbine blade yields a fluid damping value of around 15% of critical damping for its first vibration mode.