Single- and double-spiral-vortex models for a supercavitating non-symmetric wedge in a jet

Abstract

The problem of determining the free surface of a jet incident on a rigid wedge and the boundary of a cavity behind the wedge is considered. The single- and double-spiral-vortex models by Tulin are used to describe the flow at the rear part of the cavity. The location of the wedge in the jet and the sides lengths are arbitrary. This circumstance makes the flow domain doubly connected for the single-vortex model while it is simply connected for the double-vortex model. Both models are solved in closed form by the method of conformal mappings. The maps are expressed through the solutions to certain Riemann–Hilbert problems. For the former model, this problem is formulated on a genus-1 Riemann surface. The double-vortex model requires the solution to a standard Riemann–Hilbert problem on a plane. By comparative analysis of the numerical results for the two models, it is found that the drag and lift are practically the same while the jet surface, the cavity boundary at the rear part and the deflection angle of the jet at infinity are different. Also, the problem of determining the parameters for the conformal mapping in the single-vortex model has two solutions. It is shown that one of the solutions leads to a non-physical shape of the cavity and needs to be disregarded.