Analysis of the Francis turbine upper-part-load pulsation Part I - Experimental results vs. hydro-acoustic model

An acoustical model for wave propagation on a cavitating vortex flow bounded by a cylindrical wall is applied to the upper-part-load pressure pulsation of some Francis turbines with high specific speed. Due to the high frequency, the pressure amplitude has an important radial gradient. Together with the precession of the eccentric vortex axis, this gradient entails a modulation of pressure amplitude at each point of the draft tube wall; this causes the asynchronous side bands in the pressure spectra. Experiments confirm that the oscillation is synchronous within one cross section. Oval deformation of the cavity, occasionally observed, does not show in the phase of wall pressure; it is not relevant for the oscillation mechanism. The typical amplitude and phase relationships upstream and downstream of the turbine are also properly described by the simplified model. The upper-part-load pulsation occurs only in presence of a cavitating part-load vortex to which it is superimposed. Like the full-load surge, it occurs in a load range with relatively high absolute mass-flow gain. The frequency is always much higher than the precession and lowest natural frequency. Model tests reproduced the pulsation and its relative frequency in a wide range of the test head, which means it does not depend very much on the response of the test installation. The pressure at the upper and lower end of the vortex has roughly opposite phase. In some tests the pressure amplitude in the draft tube cone was smaller than upstream and downstream. Like the reversal of phase, this is a consequence of the mode shape. All these facts suggest this pulsation is self-excited and based on a half-wavelength standing wave on the cavitating flow region. The mechanism of self-excitation is analyzed in Part II of the study.