A Numerical Calculation of Wake Distribution by Boundary Layer Approximation

Abstract

In this paper, authors present a numerical calculation method using boundary layer approximation to predict the velocity distribution of a ship wake which has ordinarily the complicated shape infulenced by the existence of bilge vortices. The procedure of this method for obtaining the velocity distribution consists of the following steps ; 1) The secondary flow velocity is evaluated by solving 3-D boundary layer equations using Okuno's integral method. 2) The shear stress in the boundary layer is assumed to obey Boussinesq's eddy viscosity conception, using the equivalent kinetic viscosity approximated by the quartic equation. 3) The differential equation for the streamwise flow velocity is derived by substituting these secondary flow velocity and shear stress for boundary layer equation. 4) Solving this differential equation numerically, the velocity distribution in the boundary layer is obtained. The wake distribution near the propeller disk of two ship models are calculated by this method and compared with the measured ones. The result is that the method adopted here to obtain the velocity distributions might to predict the wake distribution, the shape of which has the similarity to that of the measured wake distribution.