The inclined entry of a thin wedge into an incompressible fluid

Abstract

The self-similar problem of the inclined entry of a thin wedge into a half-space filled with an ideal incompressible fluid is considered in a linear formulation. The different modes of fluid motion whose existence has been previously demonstrated [1]are investigated. A criterion for non-separated flow is obtained in the form of a relation between three angles, defining the angle of the wedge, the direction of the entry velocity and the angle of attack. If this relation is not satisfied, modes of motion are possible in which a cavity is adjacent to one of the faces of the wedge. If the pressure in the cavity is less than the pressure at the surface of the fluid half-space, then only two of these modes exist and both faces are always wetted by the fluid, even in the case when the angle of the wedge is zero. If the pressure in the cavity is equal to the pressure at the surface of the half-space, another mode of motion exists: one of the faces of the wedge is not wetted by the fluid A criterion is obtained for the transition from this mode to the mode with a cavity. The dependence of the size of the cavity and the force acting on the faces of the wedge on the parameters of the problem is investigated numerically.