Computations are presented for the linearized force and moment acting on a submerged slender spheroid in regular waves, the resulting pitch and heave motions, and the second-order mean force and moment. These numerical results, which are based on the use of a three-dimensional panel code, are compared with the approximations based on slender-body theory. The accuracy of the slender-body approximation is relatively good for the first-order forces and body motions, but substantial errors are revealed for the second-order mean drift force and pitch moment. Unlike the approximate result, the more correct numerical prediction of the mean pitch moment is non-zero, and generally acts in the bow down direction in head seas. To explain this result it is shown that the wave elevation directly above the spheroid increases in amplitude from bow to stern, thus causing a greater upward force on the afterbody relative to the forebody.
Flow analysis in two-dimensional impeller of centrifugal pump by the surface singularity method combined with a flow-model of three-dimensional boundary layer.