Hydraulics of swirling flows along vortex drop shafts

The vortex drop shaft is a benchmark structure in hydraulic engineering. It is often used in sewers and hydropower systems, given that a significant energy dissipation combined with a reduced space occupation is achieved. Conversely, the flow pattern establishing along the structure may lead to the occurrence of unstable phenomena as vibrations, abrasion and choking, particularly if the operational conditions are different from the standard design regime. It is advantageous to study the overall hydraulic efficiency of the structure, and particularly to derive the hydraulic conditions of the swirling flow along the vertical shaft. At this regard, the paper describes a physically based approach, based on the momentum conservation, to derive the rotational angle and the velocity profiles along the shaft. The method requires the calibration of an empirical parameter accounting for the increase of the wall friction stress due to the centrifugal force. The outcomes of the application of the proposed procedure are presented with reference to the operation of two physical models of supercritical vortex drop shafts, with a tangential or a spiral inlet at the shaft top. It is shown that the application of the empirically-modified momentum approach is necessary for accounting for the significant angular momentum imparted to the swirling flow by the spiral inlet and for modelling the rotational flow distribution along the vertical shaft accurately