On the nonlinear water entry problem of asymmetric wedges

Abstract

The self-similar solution that characterizes the water impact, with a constant vertical velocity, of a wedge entering the free surface with an arbitrary orientation is derived analytically. The study is carried out by assuming the fluid to be ideal, weightless and with negligible surface tension effects. The solution is based on the complex analysis of nonlinear two-dimensional problems of unsteady free boundary flows and is written in terms of two governing functions, which are the complex velocity and the derivative of the complex potential defined in a parameter domain. The boundary value problem is reduced to the system of an integral and an integro-differential equation in terms of the velocity modulus and of the velocity angle to the free surface, both written as functions of a parameter variable. The system of equations is solved through a numerical procedure which is validated in the case of symmetric wedges. Comparisons with data available in literature are established for this purpose. Results are presented in terms of free surface shape, contact angles at the intersection with the wedge boundary, pressure distribution, force and moment coefficients. For a given wedge angle, the changes induced by the heel angle on the above quantities are discussed. A criterion is proposed to determine the limit conditions beyond which flow separation from the wedge apex occurs. Comparisons with experimental results available in literature are presented.

Simulation of water entry of a wedge through free fall in three degrees of freedom

“…It means that 4 in equation (2.7) is no longer an explicit function of time and its dependence on time is through a and b. As discussed in the introduction, the similarity solutions based on these nondimensional variables have been obtained by Dobrovol'skaya (1969) for vertical entry of a symmetric wedge, Semenov & Iafrati (2006) for vertical entry of an asymmetric wedge and Xu et al (2008) for oblique entry of an asymmetric wedge. Here, we shall use the similarity solution of Xu et al (2008) as the initial solution and then use the time stepping method for the solution at the later stage.…”

“…In particular, they solved the Laplace equation using the boundary element method together with the time matching method. Semenov & Iafrati (2006) considered the problem of *Author for correspondence (gx_wu@meng.ucl.ac.uk). vertical water entry of an asymmetric wedge using a kind of mapping method for the complex potential, while Xu et al (2008) solved the problem of oblique water entry of an asymmetric wedge using the boundary element method for the complex potential. There are many other studies based on various simplified methods or asymptotic expansion, including those by Howison et al (1991), Fraenkel & McLeod (1997) and Mei et al (1999).…”

Asymmetric impact between liquid and solid wedges

“…By taking advantage of self-similarity of the flow defined in equation (2.1), and introducing the self-similar spatial coordinate of arc length defined previously, Semenov & Iafrati [10] reduced this equation to the following:…”

“…The kinematic boundary condition derived by Semenov & Iafrati [10] in terms of the velocity magnitude v and velocity angle θ with the free surface for any self-similar flow problem has the following form: 22) which is valid on both the left and right free surfaces OD ∞ and BD ∞ . This equation is obtained using the fact that the acceleration of the fluid particle is orthogonal to the free boundary if the pressure along the free surface is constant.…”

“…2N. The numerical approach used in the present study is based on the method of successive approximations used by recent studies [10,11] for solving self-similar water-entry problems. The solution at the intersection of the free surface and body surface is very challenging owing to the singularity occurring here [8].…”