Fluid-dynamic forces acting on the rotating inner cylinder in a concentric annulus

The fluid-dynamic forces acting on the rotating inner cylinder in a concentric annulus has been investigated. The rotating inner cylinder executes a periodic translational motion while the outer one is stationary. The hydrodynamic forces are of interest to study of flow-induced vibrations and related instabilities. In the present work, the governing equations for the confined now are expressed as Navier-Stokes equations, including the steady and unsteady terms. The fluid parameters for steady flow generated by the rotating cylinder are determined analytically while the unsteady ones by the oscillatory motion are evaluated by a numerical method based on the spectral collocation method. The numerical results are validated, as compared with the existing analytical ones for simple cases where both approaches are applicable. It is found the effects of the Reynolds number, defined by the rotating velocity, on the hydrodynamic forces are important for the case of a relatively low oscillatory Reynolds number, defined by circular frequency; Re-w/Re-s.