Hydrodynamic Impact of a Falling Body upon a Viscous Incompressible Fluid

Abstract

The hydrodynamic impact of a falling body upon a viscous incompressible fluid is investigated by the development and solution of a mathematical model which simulates the impact of a rigid flat-bottomed body upon the quiescent free surface of viscous incompressible water. A one-dimensional compressible air layer exists between the falling body and the water free surface. Velocity and pressure distributions within the air layer are calculated using the continuity equation and the one-dimensional momentum equation derived from the Navier-Stokes equations. The water free surface is allowed to deform as the air pressures acting on it increase. The two-dimensional rectangular coordinate form of the Navier-Stokes equations for an incompressible fluid is applied to the water. A normalization scheme is used which causes the water free surface to appear straight and simplifies the application of free-surface boundary conditions. Water velocities are calculated from the momentum and continuity equations. Pressures are calculated using the pressure equation derived from the Navier-Stokes equations. Air-water interface velocities are obtained from boundary-layer relations. The governing equations of the air layer and water region are expressed in finite difference form and are solved on a high-speed digital computer. The behavior of the air layer before impact is discussed. Air layer velocity and pressure distributions are obtained. The influence of the air layer on the water is studied. Pressure and velocity distributions in the water are obtained before and at the instant of impact. Pressure distributions and pressure histories compare favorably with available experimental data. Corresponding plots of the moving free surface show the actual shape of the compressible air region. A slight variation in the body deadrise angle is found to significantly change impact pressures and the shape of the pressure distributions.