The Effect of a Longitudinal Gravity Field on the Supercavitating Flow Over a Wedge

Abstract

In recent years a number of papers treating linearized free streamline problems have appeared subsequent to Tulin's introductory paper on this subject (1).* Among these may be mentioned Wu's extension of Tulin's method for supercavitating hydrofoils with arbitrary shape and cavitation number (2), hydrofoils with cavitation only near the leading edge (3), supercavitating hydrofoils in cascade (4) and Cohen's work on wall interference effects (5). In all of the above works the hydrfoil is assumed to be in a force-free field. However, Parkin recently has estimated the effect of a gravity field normal to the direction of the flow by means of a simplified representation of the gravity effect on the cavity boundary condition (6). As yet the problem of the longitudinal gravity field does not seem to have been discussed. Fully cavitated flows are known to occur in axial gravitational fields. The cavity associated with vertical water entry or exit is one example. An effect similar to that of axial gravity occurs when fully cavitating flow takes place in a large water tunnel with slightly diverging walls. The longitudinal pressure gradient that results from the variable cross section plays a role much like that of a force field. It appears then, that to have an understanding of free streamline problems in all cases of possible technical interest, the effect of an axial or longitudinal gravitational field must be examined.