On the Shape and Dimensions of Three-Dimensional Cavities in Supercavitating Flows

Abstract

The shape of long, trailing cavities behind three-dimensional headforms is discussed. The case of a flat elliptic wing is specifically treated. Three distinct shape regimes are found: quasi-planar, long-flat, spheroidal. These appear in successively higher speed ranges (lower cavitation numbers, σ). It is argued that the cavities may be replaced by surrogates in the form of slender ellipsoids. The pressures on these are almost constant and correspond to a cavitation number equal to twice their longitudinal added mass coefficient, k ₁. A heuristic theory based on kinetic energy fields is given, relating k ₁ to the product of headform drag and cavity length. This theory correlates with an exact theory in the same form given by Garabedian for axi-symmetric cones and also with its extension to planar flows. Results are given here for the shape of the cavity behind an elliptic wing of any aspect ratio, given drag, and cavitation number. Specific formulae are given in the form, ó = f(C_D/AR), for the transition between the quasi-planar and long-flat regime, and the long-flat and spheroidal regime.