Flow past a linearly-sprung, freely-rotatable circular cylinder with an eccentric center of mass

Previous work (Tumkur et al., J. Fluid Mech. 828, 196-235, 2017; Blanchard et al. Phys. Rev. Fluids, 4, 054401, 2019; Blanchard & Pearlstein, Phys. Rev. Fluids, 5, 023902, 2020) for crossflow past a linearly-sprung (nonrotatable) circular cylinder with an attached rotatable mass allows multiple unsteady, long-time solutions at Reynolds numbers (based on cylinder diameter) below 50, and that locking or releasing the attached mass can be used as an onn/off switch for vortex-induced vibration (VIV).  Here, we consider a similar case, but with a freely-rotatable cylinder whose center of mass lies off-axis, with no separate attached mass.  The cylinder is allowed to vibrate in the cross-stream direction, and to rotate about its geometric axis driven by torque due to the flow, and damped by shaft friction (with damping proportional to the angular velocity).  Computations over a range of dimensionless parameters characterizing the spring constant, the damping associated with rotation about the shaft, and the mass distrbution in the cylinder show that the stability properties of the steady, symmetric motionless-cylinder solution (with no VIV) are reasonably similar to those found previously, but that the dynamical behavior of the solutions arising from the instability is quite different.