Flow-induced vibrations of a light circular cylinder at Reynolds numbers 10³ to 10⁴

Abstract

Stabilized space-time finite-element methods are employed to investigate vortex-induced vibrations of a light circular cylinder placed in a uniform flow at Reynolds number in the range of 10³-10⁴. The governing equations for the fluid flow are the Navier-Stokes equations for incompressible flows. The cylinder is mounted on lightly damped, flexible supports and allowed to vibrate, both in the in-line and cross-flow directions under the action of aerodynamic forces. Results are presented for various values of the structural frequency of the oscillator including those that are super-harmonics of the vortex-shedding frequency for a stationary cylinder. In certain cases the effect of the mass of the oscillator is also examined. The motion of the cylinder alters the fluid flow significantly. To investigate the long-term dynamics of the non-linear oscillator, beyond the initial transient solution, long-time integration of the governing equations is carried out. For efficient utilization of the available computational resources the non-linear equation systems, resulting from the finite-element discretization of the flow equations, are solved using the preconditioned generalized minimal residual (GMRES) technique. Flows at lower Reynolds numbers are associated with organized wakes while disorganized wakes are observed at higher Reynolds numbers. In certain cases, competition is observed between various modes of vortex shedding. The fluid-structure interaction shows a significant dependence on the Reynolds number in the range that has been investigated in this article. In certain cases lock-in while in some other cases soft-lock-in is observed. The trajectory of the cylinder shows very interesting patterns including the well-known Lissajou figure of 8. Several mechanisms of the non-linear oscillator for self-limiting its vibration amplitude are observed.