Author(s): M. Fanelli
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Abstract: The phenomenon under consideration is represented as the superposition of two potential-flow motion fields, endowed with singularities ofhelicoidal shape. In the first field the singularity is a helicoidal vortex (i.e. the circulation around it is finite); in the second one the singularity is a uniform distribution line source, sinusoidally pulsating in time. If the draft tube is rectilinear, the solution pertaining to the first field adequately represents the "rotating perturbation field", devoid of any synchronous component: it is not necessary in this case to assign a finite amplitude to the second flow field. If the draft-tube rectilinear stretch is followed by an elbow, qualitative considerations show that a synchronous component must needs arise. If, moreover, the vortex rope is cavitated, the linear combination (with suitable amplitudes) of the two flow fields allow the total perturbation field to be represented (rotating+ synchronous components). Obviously, a certain number of compatibility conditions have to be satisfied. Those concern on one hand the flow coming out of the runner (and this allows the parameters of the first flow field to be defined), on the other hand the other parts of the hydraulic system (and this leads to determination of the parameters of the second flow field, i.e. of the dynamic amplification of the synchronous excitation tied to the elbow). The main characters of the proposed mathematical model are in qualitative agreement with what is known from tests on reduced scale model or from measurements performed on actual installations. The proposed model, after proper quantitative validation, could provide a useful tool in order to advance comprehension of the phenomena. Moreover, it could be used in order to carry out a correct, reliable transposition from reduced-scale model tests to full-size prototype (it is a well-known fact that such a transposition is nowadays fraught with uncertainties).
DOI: https://doi.org/10.1080/00221688909499108
Year: 1989