Dynamics of a long tubular cantilever conveying fluid downwards,which then flows upwards around the cantilever as a confined annular flow

A theoretical model is developed for the dynamics of a hanging tubular cantilever conveying fluid downwards; the fluid, after exiting from the free end, is pushed upwards in the outer annular region contained by the cantilever and a rigid cylindrical channel. This configuration thus resembles that of a drill-string with a floating fluid-powered drill-bit. The linear equation of motion is solved by means of a hybrid Galerkin–Fourier method, as well as by a conventional Galerkin method. Calculations are conducted for a very slender system with parameters appropriate for a drill-string, for different degrees of confinement of the outer annular channel; and also for another, bench-top-size experiment. For wide annuli, the dynamics is dominated by the internal flow and, for low flow velocities, the flow increases the damping associated with the presence of the annular fluid. For narrow annuli, however, the annular flow is dominant, tending to destabilize the system, giving rise to flutter at remarkably low flow velocities. The mechanisms underlying the dynamics are also considered, in terms of energy transfer from the fluid to the cantilever and vice versa, as are possible applications of this work.