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

Designing a Green Roof for Ireland

A model is presented for the gravity-driven flow of rainwater descending through the soil layer of a green roof, treated as a porous medium on a at permeable surface representing an efficient drainage layer. A fully saturated zone is shown to occur. It is typically a thin layer, relative to the total soil thickness, and lies at the bottom of the soil layer. This provides a bottom boundary condition for the partially saturated upper zone. It is shown that after the onset of rainfall, well-defined fronts of water can descend through the soil layer. Also the rainwater flow is relatively quick compared with the moisture uptake by the roots of the plants in the roof. In a separate model the exchanges of water are described between the (smaller-scale) porous granules of soil, the roots and the rainwater in the inter-granule pores

Water entry of a flat elastic plate at high horizontal speed

The two-dimensional problem of an elastic-plate impact onto an undisturbed surface of water of infinite depth is analysed. The plate is forced to move with a constant horizontal velocity component which is much larger than the vertical velocity component of penetration. The small angle of attack of the plate and its vertical velocity vary in time, and are determined as part of the solution, together with the elastic deflection of the plate and the hydrodynamic loads within the potential flow theory. The boundary conditions on the free surface and on the wetted part of the plate are linearized and imposed on the initial equilibrium position of the liquid surface. The wetted part of the plate depends on the plate motion and its elastic deflection. To determine the length of the wetted part we assume that the spray jet in front of the advancing plate is negligible. A smooth separation of the free-surface flow from the trailing edge is imposed. The wake behind the moving body is included in the model. The plate deflection is governed by Euler’s beam equation, subject to free–free boundary conditions. Four different regimes of plate motion are distinguished depending on the impact conditions: (a) the plate becomes fully wetted; (b) the leading edge of the plate touches the water surface and traps an air cavity; (c) the free surface at the forward contact point starts to separate from the plate; (d) the plate exits the water. We could not detect any impact conditions which lead to steady planing of the free plate after the impact. It is shown that a large part of the total energy in the fluid–plate interaction leaves the main bulk of the liquid with the spray jet. It is demonstrated that the flexibility of the plate may increase the hydrodynamic loads acting on it. The impact loads can cause large bending stresses, which may exceed the yield stress of the plate material. The elastic vibrations of the plate are shown to have a significant effect on the fluid flow in the wake

Particle Impact Analysis of Bulk Powder During Pneumatic Conveyance

Fragmentation of powders during transportation is a common problem for manufacturers of food and pharmaceutical products. We illustrate that the primary cause of breakage is due to inter-particle collisions, rather than particle-wall impacts, and provide a statistical mechanics model giving the number of collisions resulting in fragmentation

The impact of a deep-water plunging breaker on a wall with its bottom edge close to the mean water surface

The impact of a deep-water plunging breaker on a finite height two-dimensional structure with a vertical front face is studied experimentally. The structure is located at a fixed horizontal position relative to a wave maker and the structure’s bottom surface is located at a range of vertical positions close to the undisturbed water surface. Measurements of the water surface profile history and the pressure distribution on the front surface of the structure are performed. As the vertical position, (the axis is positive up and is the mean water level), of the structure’s bottom surface is varied from one experimental run to another, the water surface evolution during impact can be categorized into three classes of behaviour. In class I, with in a range of values near , where is the nominal wavelength of the breaker, the behaviour of the water surface is similar to the flip-through phenomena first described in studies with shallow water and a structure mounted on the sea bed. In the present work, it is found that the water surface between the front face of the structure and the wave crest is well fitted by arcs of circles with a decreasing radius and downward moving centre as the impact proceeds. A spatially and temporally localized high-pressure region was found on the impact surface of the structure and existing theory is used to explore the physics of this phenomenon. In class II, with in a range of values near the mean water level, the bottom of the structure exits and re-enters the water phase at least once during the impact process. These air–water transitions generate large-amplitude ripple packets that propagate to the wave crest and modify its behaviour significantly. At , all sensors submerged during the impact record a nearly in-phase high-frequency pressure oscillation indicating possible air entrainment. In class III, with in a range of values near , the bottom of the structure remains in air before the main crest hits the bottom corner of the structure. The subsequent free surface behaviour is strongly influenced by the instantaneous momentum of the local flow just before impact and the highest wall pressures of all experimental conditions are found