Effect of blockage on free vibration of a circular cylinder at low Re

Abstract

The effect of the blockage on vortex-induced vibrations of a circular cylinder of low non-dimensional mass (m^∗ =10) in the laminar flow regime is investigated in detail. A stabilized space-time finite element formulation is utilized to solve the incompressible flow equations in primitive variables form in two dimensions. The transverse response of the cylinder is found to be hysteretic at both ends of synchronization/lock-in region for 5% blockage. However, for the 1% blockage hysteresis occurs only at the higher Re end of synchronization/lock-in region. Computations are carried out at other blockages to understand its effect on the hysteretic behavior. The hysteresis loop at the lower Re end of the synchronization decreases with decrease in blockage and is completely eliminated for blockage of 2.5% and less. On the other hand, hysteresis persists for all values of blockage at the higher Re end of synchronization/lock-in. Although the peak transverse oscillation amplitude is found to be same for all blockage (~0.6D), the peak value of the aerodynamic coefficients vary significantly with blockage. The r.m.s. values show lesser variation with blockage. The effect of streamwise extent of computational domain on hysteretic behavior is also studied. The phase between the lift force and transverse displacement shows a jump of almost 180° at, approximately, the middle of the synchronization region. This jump is not hysteretic and is independent of blockage.