Blunt-body impact on the free surface of a compressible liquid

Abstract

The present paper deals with the plane unsteady problem of the penetration of a blunt solid contour into an ideal compressible liquid. At the initial instant of time, the solid body touches the liquid free boundary at a single point. At the initial stage, the duration of which depends on the body geometry, the displacements of liquid particles are small and the disturbed fluid motion is described within the framework of the acoustic approximation. The main feature of the problem is the existence of a contact line between the free surface of the liquid and the solid-body surface. The position of this line is not known in advance and is to be determined together with the solution of the problem. A brief description of the method that provides a solution of complicated nonlinear problems such as this is given. The pressure distribution and the velocity field in the liquid are shown to be given in quadratures and in the case of a parabolic entering contour in an explicit form. For a parabolic entering contour the pressure at the top of the contour calculated using the model of an incompressible liquid is observed to deviate from a precise value by not more than 10% of the latter after the first expansion waves have passed the contact point. The solution analysis enabled us to distinguish the regions in which the acoustic approximation fails and the liquid flow becomes essentially nonlinear.