Impulsive impact of a submerged body

TL;DR

This paper derives an analytical solution for the impulsive impact of a submerged cylindrical body with arbitrary cross-section shape, using complex potential methods and integral equations, applicable to various depths and shapes.

Contribution

It introduces a novel analytical approach employing the integral hodograph method to solve free boundary problems for submerged bodies with arbitrary cross-sections.

Findings

Derived velocity field and impulsive pressure distributions.

Calculated added mass for different shapes and depths.

Validated the method across various geometries.

Abstract

An analytical solution of the impulsive impact of a cylindrical body submerged below a calm water surface is obtained by solving a free boundary problem. The shape of the cross section of the body is arbitrary. The integral hodograph method is applied to derive the complex velocity potential defined in a parameter plane. The boundary-value problem is reduced to a Fredholm integral equation of the first kind in the velocity magnitude on the free surface. The velocity field, the impulsive pressure on the body surface, and the added mass are determined in a wide range of depths of submergence for various cross-sectional shapes, such as a flat plate, a circular cylinder, and a rectangle.