Calculation of Wave Resistance and Sinkage by Rankine-Source Method. Prediction of 2-D Near Wake Flow by Making Use of Time-Dependent Vorticity Transport Equation. Free Surface Boundary Layer and Necklace Vortex Formation

摘要

A. The flow about a wavemaking ship form is treated in terms of source distributions on the wetted hull and the free surface, with the simple source potential serving as the Green function. The free-surface boundary condition is linearized based on the double-hull flow, and the hull surface condition is approximately satisfied by the double hull potential. The equations are discretized by finite-difference methods and solved iteratively. Results are given for Inuid model M-21 and a Wigley parabolic ship form. B. The vorticity-transport equations is applied to predict near-wake flows of shiplike bodies, with initial or boundary values given by an upstream boundary-layer calculation. Vorticity transport is calculated by a finite-difference time-marching method. The k-e model is applied for closure of the turbulence equations. Near wakes of a flat plate and two elliptic cylinders are calculated. C. A shear layer, or free-surface boundary layer may develop under a free surface with significant curvature due to a zero-free-stress boundary condition. Equations for predicting this development are presented. A weak vorticity generated by this mechanism may be amplified by vortex stretching as the flow approaches a ship bow. This theory can explain the formation of the so-called necklace vortex around the bow. A simple calculation for the case of a vertical circular cylinder demonstrates that the formation of a necklace vortex can be prevented by a bulbous bow. (Author)