Analyses of a slender body moving near a curved ground

Abstract

The irrotational flow induced by a slender body moving near a curved ground is analyzed by extending the classical slender body theory. The flow far away from the body is shown to be a direct problem, represented by the line source distribution along the body long axis, whose strength is at the variation rate of the double cross-section areas of the body. The flow near the body is reduced to the two-dimensional flow problem of the deformation, vertical and lateral translations of double cylinders in a symmetrical manner. In particular, an analytical flow solution is obtained for a slender body of revolution at angles of attack and yaw, moving near an arbitrary curved ground. The attraction and side force, and pitching and yaw moments, acting on the body, are obtained in the form of the integrals along the body length by using the control volume method. Numerical analyses are then performed for the body moving near flat, convex, concave, and wavy grounds, respectively. The analyses reveal the orders of the attraction and side force, and pitching and yaw moments, as well as their variation trends in terms of the angles of attack and yaw of the body, the profile of the curved ground, and the clearance between them, etc. These irrotational dynamic features provide a basic understanding of the problem, which will be beneficial to further numerical and experimental studies involving more physical effects.