Numerical Investigation of Response and Wake Characteristics of a Vortex-Excited Cylinder in a Uniform Stream

Abstract

The numerical solution of vortex-excited oscillations of a circular cylinder is described herein, at Reynolds numbers below 130, where the wake behind the cylinder is fully laminar. The mathematical model of the problem consists of the Navier-Stokes equations, in the formulation where the stream function and the vorticity are the field variables. The finite element technique was favoured for the numerical solution of the Navier-Stokes equations. The parameters of the cylinder-elastic support arrangement considered in the numerical computation were identical to those of an experimental investigation at similar conditions, for the sake of comparison of the results. From the numerical results, the cylinder oscillation frequency to be slightly lower than the cylinder natural frequency in air below the lock-in region, and slightly higher and above the lock-in region. Outside the lock-in region the cylinder displacement and the hydrodynamic forces are modulated, although the numerical model is two-dimensional. For all Reynolds numbers considered, the time history of the cylinder displacement and of the hydrodynamic forces acting on the cylinder were calculated. The time-dependent velocities of the fluid in the stream- and cross-flow directions were calculated at some nodal points downstream of the cylinder from the stream function values. The effect of cylinder oscillation on the vortex spacing was examined by plotting the equivorticity lines. The results of this investigation were found to be in good agreement with the experimental evidence, except at reduced velocities above the lock-in region.