Unsteady potential and viscous flows between eccentric cylinders

This paper presents a newly developed spectral collocation method for the study of the unsteady annular flow between two eccentric cylinders. In order to predict the stability of a system in a confined flow, the formulae and results of added mass and fluid damping are provided in the present paper when a cylinder undergoes oscillatory motion in the plane of symmetry and normal to the plane of symmetry in an eccentric annulus. The potential flow theory has been developed to obtain the added mass for incompressible, inviscid and irrotational fluid. For the viscous fluid, the added mass and the viscous damping are presented. This method is validated by comparison with the available analytical solutions obtained for the unsteady potential flow in the eccentric annular space. Excellent agreement was found between the solutions obtained with the present spectral method and the available analytical solutions. In the present study, the viscous effect on the added mass can be evaluated, comparing the results obtained by potential flow theory with those obtained by the viscous flow theory, and viscous damping is investigated.