Computation of Total Forces and Moments of Bodies of Revolution Moving Beneath the free Surface

Abstract

The accurate prediction of the total forces and moments of a body of revolution which is moving beneath the free surface with and without an angle of attack is one of the important areas in ship hydrodynamics. The experiments to measure these forces and moments were undertaken in the past by several researchers. The experimental results of forces and moments for a body of revolution near the free surface were reported in Reference 1 for various angles of attack and depths. Those of deep submergence were given in References 2, 3, and 4 for different angles of attack. Although there are many other published papers on the measurement of forces and moments, only the results of References 1-4 are used in this paper to compare with the predicted results. The total forces and moments consist of two parts in the present method; namely the inviscid part and the viscous part. The inviscid part of the forces and moments is computed using three-dimensional potential theory. The body boundary condition is exact and the free-surface condition is linearized. The body surface is discretized with many surface elements and the unknown strengths of the source and sink at each surface element are assumed to be constant. The velocities at surface elements are computed and saved for later computation of the viscous forces and moments. The viscous part of the forces and moments is computed with the application of the boundary layer theory for laminar and turbulent flows. The method developed by Young (Reference 5) is used to compute the total drag of bodies of revolution. It is assumed in this method that there is no flow separation. The axial force is computed with this method. The lateral force and pitching moment are computed under the assumption that there is separation in the two-dimensional cross flow. The boundary layer equation is solved to the separation point and the friction force is integrated to compute frictional drag. Furthermore, it is assumed that a constant pressure is acting on the two-dimensional section beyond the separation point.