Computer Analysis of Three-Dimensional Turbulent Flows around Ships' Hulls

Abstract

This paper describes a general solution method for three-dimensional, steady, turbulent flows around long, smoothly-shaped bodies, of arbitrary and varying cross-sectional shape. The particular example considered here concerns the flow around the hull of a ship, but the method can equally well be applied to other, similarly shaped bodies such as an aircraft fuselage, or a submarine. Moreover, the basic non-orthogonal grid method described can also be applied to internal flows in irregular shaped passages, or to the prediction of flows around bodies in ducts.

The mathematical model consists of the partial differential equations for continuity and three components of momentum, along with a two-equation model of turbulence, and proper modelling of the ship's hull.

The solution method utilizes a non-orthogonal coordinate system in the plane normal to the axis of the body, which has one coordinate surface coinciding with the hull surface. This coordinate system is flexible and is easily modified to enable the calculation procedure to handle bulbous ships' hulls, which are of great importance in modern ship design.

The differential equations involved are solved numerically after provision of the proper boundary and initial conditions. The solution procedure is a unique one, called ‘partially-parabolic’, as first used by Pratap and Spalding (1). Solutions are presented for flow around ships' hulls, which demonstrate the physical realism of the achieved results and the potential of the present method.