An Integral Method for Predicting Behaviors of Three-Dimensional Turbulent Boundary Layers on Ship Hull Surfaces

Abstract

A new integral method for predicting the development of the three-dimensional turbulent boundary layer on ship hull surfaces is presented. The effect of the cross flow on the momentum equations is exactly taken into account so that the integral form of the boundary layer equations is reduced to a set of partial differential equations. The auxiliary equation consists of the moment of momentum integral in the stream-wise direction, where the eddy viscosity is assumed to be a scalar, and a probable form of distribution is derived as an extension of the two-dimensional case. Coles' wall-wake law in three dimensions is used both for the assumption of the velocity profiles and as the skin friction formula. The potential flow outside the boundary layer is calculated using Hess and Smith's method. The results of the boundary layer calculations applied to three ship forms show fairly good agreement with the experiments. Also, it is confirmed that a considerable difference exists between potential and viscous stream lines, and that a vortex-like cross flow occurs near the bilge and the bottom of the fore body with a tendency to decrease as the Reynolds number increases.