A Simple Approach to Estimating Three-Dimensional Supercavitating Flow Fields

A simple method is formulated for predicting three-dimensional supercavitating flow behind cavitators subject to gravitational acceleration and motion of the cavitator. The method applies slenderbody theory in the context of matched asymptotic expansions to pose an inner problem for the cavity evolution downstream from the locus of cavity detachment. This inner problem is solved by means of a coupled set of equations for the Fourier coefficients characterizing the cavity radius and the velocity potential as a function of downstream location and circumferential location, thus resulting in a two-dimensional multipole solution at each station. For the lowest-order term in the Fourier expansion, it is necessary to match the parabolic inner solution to a fully elliptic outer solution. This step allows the application of any one of a number of methods to solve the axisymmetric problem, which serves as the base solution that is perturbed by the three-dimensional effects. The method is an attempt to formalize the Logvinovich principle of independent cavity section evolution. Results flow past a circular disk cavitator are presented for several values of the cavity Froude number.