Von Karman vortex induced vibration in a Francis turbine: a simplified numerical model for estimating the shedding frequency

Authors

Giacomo Zanetti  - University of Padua, Italy; 45 Engineering S.r.l, Italy
Giovanna Cavazzini - University of Padua, Italy
Alberto Santolin - 45 Engineering S.r.l, Italy

Abstract

Despite many types of vibration can occur in hydraulic turbines, the most common vibrational phenomenon is represented by the Von Karman vortex shedding from the trailing edge of both runner and guide vanes. This causes the onset of severe pulsations and noise with potential damages to blade trailing edges. Moreover, if it excites the natural frequencies of the impeller, the intensity of vibrations and noise significantly increases, leading to potential machine failures. In standard design approaches, the vortex shedding frequency is estimated from suggested values of the Strouhal number. To avoid lock-in condition and vortex induced resonances, this frequency has to be smaller than the natural frequencies of the machine components. However, it is a matter of fact that, despite this design strategy, vortex induced vibrations still occur in hydraulic turbines due to the uncertainties in the evaluation of both the vortex shedding frequency and of the natural frequencies. In this study, the case study of a Francis turbine, characterized by the onset of severe vibration and noise at full load, was experimentally and numerically analyzed to properly characterize the phenomena and to test the effectiveness of an active control strategy. In particular, assuming the cavitation as the noise source, air was injected through a pressure tap, located downstream of the spiral case inlet. This air injection at full load immediately damped the machine vibrations, confirming that they were induced by cavitation phenomena. As regards the experimental analysis, the performance of the machine and the emitted noise, in terms of acoustic pressure signals, were monitored and acquired with and without the vibration control strategy. Numerically, in order simulate the conditions leading to the vibration onset and to evaluate the influence of the air injection, an in-depth numerical simulation was performed on the entire machine fluid domain. A CFD commercial software was used to solve the incompressible unsteady Reynolds-Averaged Navier-Stokes equations. The Scale Adaptive Simulation fluid model (SAS-SST), a hybrid RANS-LES turbulence model, was adopted. To validate the numerical results, a comparison with the experimental results in terms of characteristic curves and pressure signals was performed. A spectral analysis was also performed on the numerical pressure signals, with and without air injection, in order to characterize the shedding frequency and the pressure pulsations induced by the Von Karman vortices at the trailing edge of both runner blade and guide vanes. The comparison between the experimental acoustic frequency and the numerical ones obtained from the numerical pressure signals, made it possible to confirm the nature of the vibrations. As consequence of the air injection, an amplitude decrement of the pressure pulsation associate to the Von Karman vortices was achieved.