Vortex-induced vibration on a two-dimensional circular cylinder with low Reynolds number and low mass-damping parameter

The vortex induced vibration (VIV) on a circular cylinder with low mass-damping parameter and low Reynolds number is investigated numerically as basis for applications on dynamics of risers used in the offshore oil and gas industry and as a first step before tackling the harder high Reynolds number problem. The cylinder is supported by a spring and a damper and free to vibrate in the transverse direction. The numerical solution of the Unsteady Reynolds-Averaged Navier-Stokes equations written in curvilinear coordinates is obtained using an upwind and Total Variation Diminishing conservative scheme and the k-ε turbulence model. Results were obtained for the phase angle, response amplitude, response frequency, and lift coefficient for reduced velocities from 2 to 12, for six different fixed Reynolds numbers, and for three different proportional variations of Reynolds number with reduced velocity, 2000-6000, 2000-12,000, and 2000-24,000. The results indicate the strong effect of the Reynolds number on the response amplitude, lift coefficient, and response frequency for a low mass-damping parameter. The upper branch of the response amplitude curve is only obtained when the Reynolds number varies proportionally to reduced velocity. For a fixed Reynolds number, only the initial and lower branches are captured.