Computation of the Hydrodynamic Forces and Moments Developed on a Body of Revolution at Combined Angles of Attack and Angles of Drift and Yawing Angular Velocities

The accurate prediction of the hydrodynamic forces and moments developed on the hull and appendages of a submerged vehicle is required for determining its stability, control, and maneuvering characteristics. Various analytical methods have been developed to make these predictions, including those of computational fluid dynamics, but none of them have been totally successful. This is because it is particularly difficult to accurately determine both the distribution of the velocity over the surface of the hull and the location of the separation lines. The location of the lines of separation has an important effect on the magnitude of the hydrodynamic forces and moments developed on the hull. The present method is an extension of the technique discussed in Reference 1. It is assumed that the total hydrodynamic force and moment can be divided into inviscid and viscous parts. The inviscid part of the forces and moments is computed using three dimensional potential theory. 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 axial force is computed with the method of developed by Young (2). The lateral forces and its moments 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 frictional drag is integrated to compute frictional force. Furthermore, it is assumed that a constant pressure is acting on the two dimensional section beyond the separation point.