Numerical solutions for cavitating flow of a fluid with surface tension past a curved obstacle

The problem of cavitating flow past a two-dimensional curved obstacle is considered. Surface tension is included in the dynamic boundary condition. The problem is solved numerically by series truncation. Explicit solutions are presented for the flow past a circle. It is shown that for each value of the surface tension different from zero, there exists a unique solution which leaves the obstacle tangentially. As the surface tension approaches zero, this solution tends to the classical solution satisfying the Brillouin - Villat condition. Vander-Broeck considered the effect of surface tension on the cavitating flow past a flat plate and on the shape of a jet emerging from a reservoir. His results indicate that the velocity is infinite at the separation points. It is shown that these unbounded values of the velocity are removed when the thickness and finite curvature of the ends of the plate and of the ends of the walls of the reservoir are taken into account.