Asymmetric impact between liquid and solid wedges

Abstract

The hydrodynamic problem of impact between a solid wedge and a liquid wedge is analysed. The liquid is assumed to be ideal and incompressible; gravity and surface tension effects are ignored. The flow generated by the impact is assumed to be irrotational and therefore can be described by the velocity potential theory. The solution procedure is based on the analytical derivation of the complexvelocity potential in a parameter plane and the function mapping conformally the parameter plane onto the similarity plane. The mapping function is found as a combination of the derivatives of the complex potential in the similarity and parameter planes, through the integral equations for mixed and homogeneous boundary-value problems in terms of the velocity modulus and the velocity angle with the fluid boundary, together with the dynamic and kinematic boundary conditions. These equations are solved through a numerical method. The procedure is first verified through comparisons with some known results. Simulations are then made for a variety of cases, and detailed results are presented in terms of the free surface shape, streamlines, pressure distribution on the wetted solid surface, and contact angles between the free surface and the body surface.

Cratering of a solid body due to liquid impact

“…The numerical approach employed in the present study is based on the method of successive approximations, which is similar to that used by Semenov and Wu [15], for solving self-similar impacts between an impermeable solid body and a liquid wedge. Let us consider two sets of points distributed along the part of the real axis, 0 < ξ j < 1, j = 1, .…”

“…(20), K is obtained with using Eqs. (10), (15) and (16), respectively to obtain dw/dζ and w(ζ ), while Eq. (17) is used to obtain dz/dζ .…”

“…(15) in the ζ -plane allows us to obtain the function w(ζ ) which conformally maps the first quadrant of the ζ -plane onto the corresponding region in the complex potential plane:…”

“…It enables the original boundary-value problem for the complex potential in the fluid domain to be converted into a system of integrodifferential equations along the straight lines. The method has been successfully used in a variety of impact problems [8,15,16]. However, the present problem has some new challenges.…”

Water entry of a wedge with rolled-up vortex sheet

“…Chekin (1989) generalized Dobrovol'skaya's approach to the problems of the oblique water entry of a wedge and an inclined flat plate. More recently, this problem was considered by Semenov & Iafrati (2006) and Semenov & Yoon (2009), Semenov & Wu (2012) using integral hodograph method (IHM), and by Iafrati (2000) and Xu, Duan & Wu (2008, 2010 using a numerical method. In all these works, the streamline from the tip is attached to the wedge surface and no vortex shedding is taken into account.…”