A spectral collocation method is formulated in this paper for the analysis of unsteady annular flows between eccentric cylinders, induced by transverse oscillations of one the cylinders. This method uses convenient spatial and temporal expansions for the unsteady flow parameters and a collocation approach to determine the a priori unknown complex coefficients in these spectral expansions.
The method is first used to solve the unsteady potential flow between long eccentric cylinders generated by small amplitude translational oscillations. For validation, the resulting solutions for the added mass coefficients are compared with the available ideal flow results for concentric and eccentric configurations.
Spectral solutions are then obtained with this method for the more complex problem of unsteady viscous flows. Solutions for the unsteady pressure and fluid-dynamic forces are obtained for oscillations either in the plane of symmetry of the eccentric annular configuration or normal to it; they are compared to existing analytical and finite element viscous flow solutions, for concentric and eccentric cylinders, respectively. A parametric investigation is conducted to expose the influence of the relative eccentricity, outer to inner radius ratio and the oscillatory Reynolds number on the added mass and viscous damping coefficients.