The dynamics of cylinder in a confined swirling flow with constant vorticity

Abstract

In this work, we present a rigid body dynamics model that accounts for phenomena earlier studied both within hydrodynamic stability theory and the area of fluid-induced vibrations. The model captures the transverse dynamics of a rigid cylinder in a confined swirling flow. We show that a linear inviscid stability analysis of the whole system with respect to two-dimensional disturbances could be decomposed into a solution governing rotational disturbances with homogeneous boundary conditions and a solution governing irrotational disturbances with inhomogeneous boundary conditions. This implies that the continuous stable spectrum of rotational disturbances is unchanged by the supposition of a free boundary. Moreover, the time-dependence of irrotational disturbances is governed by the disturbance of the rigid cylinder. Consequently, a rigid body dynamics model suffices to determine the time evolution of irrotational disturbances. The model is based on the definition of a merged homogeneous state in which the solid mass of the rigid cylinder equals the displaced fluid mass and the flow is in solid body rotation. A departure from this merged homogeneous state yields an imbalance of the fictitious Coriolis and centrifugal force of the rigid cylinder and the counterbalancing motion-induced fluid forces. This imbalance makes the fluid flow support propagation of waves and may render a concentric position of the body unstable. A non-uniform distribution of the angular velocity delays the onset of instability so that the rigid cylinder can maintain a concentric position even though it is denser than the fluid.