Finite element study of vortex‐induced cross‐flow and in‐line oscillations of a circular cylinder at low Reynolds numbers

Vortex-induced vibrations of a circular cylinder placed in a uniform flow at Reynolds number 325 are investigated using a stabilized space–time finite element formulation. The Navier–Stokes equations for incompressible fluid flow are solved for a two-dimensional case along with the equations of motion of the cylinder that is mounted on lightly damped spring supports. The cylinder is allowed to vibrate, both in the in-line and in the cross-flow directions. Results of the computations are presented for various values of the structural frequency of the oscillator, including those that are sub and superharmonics of the vortex-shedding frequency for a stationary cylinder. In most of the cases, the trajectory of the cylinder corresponds to a Lissajou figure of 8. Lock-in is observed for a range of values of the structural frequency. Over a certain range of structural frequency (Fs), the vortex-shedding frequency of the oscillating cylinder does not match Fs exactly; there is a slight detuning. This phenomenon is referred to as soft-lock-in. Computations show that this detuning disappears when the mass of the cylinder is significantly larger than the mass of the surrounding fluid it displaces. A self-limiting nature of the oscillator with respect to cross-flow vibration amplitude is observed. It is believed that the detuning of the vortex-shedding frequency from the structural frequency is a mechanism of the oscillator to self-limit its vibration amplitude. The dependence of the unsteady solution on the spatial resolution of the finite element mesh is also investigated. Copyright © 1999 John Wiley & Sons, Ltd.

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