On the High-partial-load Pulsation in Francis Turbines

Abstract

Francis turbines with high specific speed may produce intense pulsations of system pressure when operating at approximately 70-85% of best-efficiency discharge. Frequencies between 1 and 4 times runner rotation are typical. The paper recalls and explains the particular set of properties. The pulsation is due to instability of the second-lowest eigenmode of the hydraulic system containing a cavitating draft tube vortex. A 1D model in frequency domain is used - with emphasis on the crucial role of the finite velocity of swirl propagation - to show how this mode can become unstable and give rise to a strong ‘breathing’ pulsation. A parameter study shows the well-known influence of draft tube pressure and why the behavior of prototype turbines is often different from the reduced-scale model. Some of the phase properties are explained by a 2D acoustic model. The phase reversal between upstream and downstream pressures is a consequence of the mode shape, with roughly two quarter waves of pressure along the cavitating vortex rope. The stability is quite sensitive to 2D effects; therefore the present 1D model, while useful for understanding the phenomena, is not likely to permit reliable predictions.