A comparison of pre-impact gas cushioning and Wagner theory for liquid-solid impacts

ACKNOWLEDGEMENTS Snizhana Ross was supported by the Development Trust of the University of Aberdeen.Peer reviewedPostprintPublisher PD

A theory for the impact of a wave breaking onto a permeable barrier with jet generation

We model a water wave impact onto a porous breakwater. The breakwater surface is modelled as a thin barrier composed of solid matter pierced by channels through which water can flow freely. The water in the wave is modelled as a finite-length volume of inviscid, incompressible fluid in quasi-one-dimensional flow during its impact and flow through a typical hole in the barrier. The fluid volume moves at normal incidence to the barrier. After the initial impact the wave water starts to slow down as it passes through holes in the barrier. Each hole is the source of a free jet along whose length the fluid velocity and width vary in such a way as to conserve volume and momentum at zero pressure. We find there are two types of flow, depending on the porosity, ß , of the barrier. If ß : 0 = ß < 0.5774 then the barrier is a strong impediment to the flow, in that the fluid velocity tends to zero as time tends to infinity. But if ß : 0.5774 = ß = 1 then the barrier only temporarily holds up the flow, and the decelerating wave water passes through in a finite time. We report results for the velocity and impact pressure due to the incident wave water, and for the evolving shape of the jet, with examples from both types of impact. We account for the impulse on the barrier and the conserved kinetic energy of the flow. Consideration of small ß gives insight into the sudden changes in flow and the high pressures that occur when a wave impacts a nearly impermeable seawall

Cavity formation on the surface of a body entering water with deceleration

The two-dimensional water entry of a rigid symmetric body with account for cavity formation on the body surface is studied. Initially the liquid is at rest and occupies the lower half plane. The rigid symmetric body touches the liquid free surface at a single point and then starts suddenly to penetrate the liquid vertically with a time-varying speed. We study the effect of the body deceleration on the pressure distribution in the flow region. It is shown that, in addition to the high pressures expected from the theory of impact, the pressure on the body surface can later decrease to sub-atmospheric levels. The creation of a cavity due to such low pressures is considered. The cavity starts at the lowest point of the body and spreads along the body surface forming a thin space between a new free surface and the body. Within the linearised hydrodynamic problem, the positions of the two turnover points at the periphery of the wetted area are determined by Wagner’s condition. The ends of the cavity’s free surface are modelled by the Brillouin–Villat condition. The pressure in the cavity is assumed to be a prescribed constant, which is a parameter of the model. The hydrodynamic problem is reduced to a system of integral and differential equations with respect to several functions of time. Results are presented for constant deceleration of two body shapes: a parabola and a wedge. The general formulation made also embraces conditions where the body is free to decelerate under the total fluid force. Contrasts are drawn between results from the present model and a simpler model in which the cavity formation is suppressed. It is shown that the expansion of the cavity can be significantly slower than the expansion of the corresponding zone of sub-atmospheric pressure in the simpler model. For forced motion and cavity pressure close to atmospheric, the cavity grows until almost complete detachment of the fluid from the body. In the problem of free motion of the body, cavitation with vapour pressure in the cavity is achievable only for extremely large impact velocities

Three-dimensional steep wave impact on a vertical cylinder

In the present study we investigate the 3-D hydrodynamic slamming problem on a vertical cylinder due to the impact of a steep wave that is moving with a steady velocity. The linear theory of the velocity potential is employed by assuming inviscid, incompressible fluid and irrotational flow. As the problem is set in 3-D space, the employment of the Wagner condition is essential. The set of equations we pose, is presented as a mixed boundary value problem for Laplace's equation in 3-D. Apart from the mixed-type of boundary conditions, the problem is complicated by considering that the region of wetted surface of the cylinder is a set whose boundary depends on the vertical coordinate on the cylinder up to the free-surface. We make some simple assumptions at the start but otherwise we proceed analytically. We find closed-form relations for the hydrodynamic variables, namely the time dependent potential, the pressure impulse, the shape of the wave front (from the contact point to beyond the cylinder) and the slamming force