Double cavity flow past a wedge

Abstract

A mathematical model of supercavitating flow past a wedge with sides of arbitrary length is proposed. The flow branches at a point on the lower side of the wedge. At the vertex of the wedge and at the ends of the wedge, the flow breaks away forming a nose bubble and a trailing cavity. The closure mechanism is described by the Tulin single-spiral-vortex model. The flow domain is mapped into a parametric plane cut along a unit segment. The conformal mapping function is reconstructed through the exact solution of two Riemann–Hilbert problems on a genus-zero Riemann surface. To complete the solution, one needs to determine five real parameters from a certain system of transcendental equations. Numerical results are presented for the case when a wedge can rotate about the vertex in the flow domain. In this case, the flow branches at the vertex and the number of the parameters to be determined is 3.