Verification of alternative mathematical model for design of vortex dropshafts

The alternative mathematical model presented for the vortex dropshaft design is based on theoretical considerations and suitable experimental parameters. Such a model is different from the previous ones because it considers the possible existence of negative pressure p(r) at the dropshaft inlet. The hypothesis of negative pressure, obtained through experimental tests, allows to overcome some uncertainties of the previous models. In particular: the experimental data of Viparelli (1950) show that, in the inlet section, pressure is zero, in accordance with equation p(r)/ = 0; while the experimental data of Binnie and Hookings (1948a), Ackers and Crump (1960) and Adami (1967) show positive pressure in accordance with equation p(r)/ = (A2/2g)(1/ro2-1/r2), in which  is the specific gravity, g is the gravitational acceleration, r is generic radius of the vortex in inlet section, ro is internal radius of the vortex in inlet section (vortex core) and A is a kinetic constant; in present paper, contrary to the other Researchers, on the basis of the experimental observations, it is assumed that the values of pressure in section can be negative in accordance with equation p(r)/ = (B2/2g)(1/r2-1/ro2), where B is a constant value that has to be determined. In effect the flow trajectories are curved both in plane of inlet section (horizontal) and in vertical planes: the two curvatures determine centrifugal forces which are opposing and, therefore, they affect in opposite way the value of pressure in the section. The interpretation of experimental data is that the influence of curvatures in vertical planes can be prevalent and, therefore, negative pressure can be verified. The estimation of experimental parameters has been carried out by means of the elaboration of tests concerning a large number of working dropshafts. In the final part of the present paper two procedures for design and verification of vortex dropshaft have been shown.