Origin of the synchronous pressure fluctuations in the draft tube of Francis turbines operating at part load conditions

Abstract

The synchronous pressure surge effect is a critical phenomenon occurring in Francis turbines operating at part load conditions. In this regime, pressure fluctuations are predominantly coming from the temporal rotation of a single helical vortex inside the turbine draft tube, called the part load vortex rope. However the combination of multi-physics interactions, geometry, cavitation, swirling flow and acoustic waves leads to a pressure amplification, called the synchronous pressure surge effect, which is more dangerous than the fluctuations resulting from the precessing vortex rope. While this subsequent amplification mechanism has been unraveled, the physical mechanism originating in the synchronous pressure wave remains poorly understood. We have therefore investigated the birth and the growth of the synchronous pressure wave in Francis turbines. By energy consideration of an azimuthal–temporal Fourier decomposition of the three dimensional numerical flow solutions in an axisymmetric draft tube geometry that is slightly disturbed at the wall, the source of the synchronous pressure and its amplification region are identified. In addition, the origin of this wave as the interaction of a wall disturbance with the part load vortex rope, is investigated using an asymptotic analysis and brings deeper comprehension of the synchronous wave generation mechanism.