Potential flow over bodies of revolution in unsteady motion

Abstract

The problem of axisymmetric bodies performing rigid and bending oscillations in an incompressible flow has been investigated. A line source/doublet element method has been developed for computation of pressures, forces, and moments for bodies in steady and oscillatory motion. A new \L~ a rule is derived to relate the dipole strength to the local body geometry in the crossflow instead of extending the commonly used inset distance method. The bodies under consideration are required to be smooth in curvature and have closed ends. The method is otherwise general in body geometries, reduced frequencies, and mode shapes of oscillations. In the case of steady flow, good agreement is found with the results of Mess's surface panel method and Lamb's exact solution. For bodies in rigid oscillations, studies were carried out to investigate the effects of the body thickness and nose curvature on the unsteady pressures and stability derivatives. It is found that bodies with blunt noses are statically unstable and dynamically stable whereas those with sharp noses are statically and dynamically unstable. For elastic bodies in bending oscillations, unsteady pressures and local damping forces are obtained, including body thickness effects at high reduced frequencies. In all cases considered, the present results approach the slender-body-theory limit in a consistent manner.