Modal Decomposition of the Precessing Vortex Core in a Hydro Turbine Model

Abstract

We report on the experimental study of a precessing vortex core (PVC) in an air model of a Francis turbine. The focus is placed on the modal decomposition of the PVC that occurs in the draft tube of the model turbine for a range of operation conditions. The turbulent flow fluctuations in the draft tube are assessed using stereo particle image velocimetry (PIV) measurements. Proper orthogonal decomposition (POD) is applied to the antisymmetric and symmetric components of the velocity fields to distinguish the dynamics of the azimuthal instabilities. The pressure pulsations induced by the PVC are measured by four pressure sensors mounted on the wall of the hydro turbine draft tube. Spatial Fourier decomposition is applied to the signals of the pressure sensors to identify the contributions of azimuthal modes, m=1 and m=2, to the total pressure fluctuations. The analysis based on velocity and pressure data shows similar results regarding the identification of the PVC. The contribution of the m=2 mode to the overall turbulent kinetic energy is significant for the part load regimes, where the flow rates are twice as low as at the best efficiency point (BEP). It is also shown that this mode is not the higher harmonic of the PVC, suggesting that it is driven by a different instability. Finally, we show a linear fit of the saturation amplitudes of the m=1 and m=2 oscillations to determine the critical bifurcation points of these modes. This yields critical swirl numbers of Scr=0.47 and 0.61, respectively. The fact that the PVC dynamics in hydro turbines are driven by two individual instabilities is relevant for the development of tailored active flow control of the PVC.