Onset of flow separation for the oblique water impact of a wedge

For the oblique impact of a wedge on a liquid half space, the limiting angles of the entry velocity and the wedge orientation corresponding to flow separation from the wedge vertex during the initial stage of the impact are investigated on the basis of an analytical solution of the problem. The liquid is assumed to be ideal and incompressible; gravity, surface tension, and air cushioning effects are ignored. The flow generated by the impact is two dimensional and potential. The solution is presented in terms of two governing expressions, which are the complex velocity and the derivative of the complex potential defined in a parameter region. These expressions are obtained using generalized integral formulas for solving mixed and uniform boundary-value problems for the first quadrant. They include two unknown functions, which are the velocity magnitude and angle to the free surface determined from the dynamic and kinematic boundary conditions. The obtained system of integral equations is solved by using the method of successive approximations. The effect of the horizontal component of the entry velocity is studied for various wedge orientations. The analysis of the computations revealed configurations of the impact such that the pressure along the whole length of one side of the wedge becomes less than the pressure on the free surface. Although air effects are not included in the analysis, such a pressure distribution provides conditions for the ventilation of the wedge side, which, in the presence of the air, starts from the contact point on the free surface and extends suddenly along the whole length of the wedge side, thus leading to flow separation from the wedge vertex. The theoretical predictions of flow separation and the experimental data on flow separation by Judge et al. [“Initial water impact of a wedge at vertical and oblique angles,” J. Eng. Math. 48, 279 (2004)] are remarkably close to each other.