A comprehensive assessment of the applicability of semi-analytical models of vortex characterization for gravitational water vortex hydropower plants

Predicting and analyzing vortexes’ characteristics (shape, size, circulation, pressure, velocity, etc.) is crucial for designing gravitational water vortex hydropower plants (GWVHP’s). Despite fluid dynamic simulations become valuable for this, they demand high computational cost, and semi-analytical models of vortex characterization could be useful in early design stages. In this work, a compressive assessment of the ability of these models to predict the vortex’s free-surface profile, as well as a physically consistent behavior of some field variables, under geometrical and operating conditions of GWVHP´s, is carried out using a calibration strategy proposed here, which is applicable for both strong and weak vortexes. This strategy is aimed to minimizing the L ² relative error norm between the free-surface profiles obtained analytically and those measured from experiments undergone in GWVHP’s at several inlet flow rates. Moreover, this strategy enforces the fulfillment of some vortex’s dimensions and of the mass conservation law between the inlet and outlet of the basin, assuming a far-field circulation equal to such of basin inlet. In general, convergent solutions of the calibration parameters were achieved, resulting in models that exactly reproduced the total vortex height, the air core radius at discharge for strong vortexes, and the submergence depth for weak vortexes; however, these models usually underestimated the vortex heights for radial coordinates corresponding to the air core zone. The calibrated models were compared in terms of the velocity components (radial, azimuthal and axial), axial vorticity, and axial and radial Rossby numbers, obtaining physically coherent results for some of them.