Water entry of a flat elastic plate at high horizontal speed

Abstract

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: (<jats:italic>a</jats:italic>) the plate becomes fully wetted; (<jats:italic>b</jats:italic>) the leading edge of the plate touches the water surface and traps an air cavity; (<jats:italic>c</jats:italic>) the free surface at the forward contact point starts to separate from the plate; (<jats:italic>d</jats:italic>) 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.