Study of the two-dimensional spray formed near a discontinuity using the Helmholtz–Kirchoff theory of free jets

Abstract

The Helmholtz–Kirchoff theory of free jets is used to develop a linearized potential flow solution for the fluid flow near the leading edge of a two-dimensional flat surface. This flow region is important in fluid–structure interaction problems in which spray is formed at an air–water interface near a discontinuity such as an edge or a corner. Potential uses of the results include studies of the spray formed near the chines of planing boats, ship bow slamming, ventilated or cavitating hydrofoils and wave impacts on breakwaters. The conformal transformations using the Helmholtz–Kirchoff theory are shown to be identical to previously published expressions using the Chaplygin method. In the past, this solution has been used in matched asymptotic expansions for complex problems such as determining the lift on a planing flat plate with a spoiler or studying the flow about a curved flat plate. Here, the solution near the spray root is explored further and computations are made of the free surface profile and the pressure distribution as a function of the spray angle, demonstrating the primary characteristics of this flow. The results are qualitatively compared with photographs from towing tank model experiments and an example problem is given.