Effect of blockage on vortex-induced vibrations at low Reynolds numbers

There have been quite a few studies in the past to investigate the effect of blockage on flow past a stationary cylinder, but very few for the case when the cylinder is vibrating. Compared to a stationary cylinder, a vibrating cylinder is associated with a wider wake and therefore the blockage is expected to play an even more significant role. The effect of blockage on the vortex-induced vibrations of a cylinder at low Re (Re⩽150)(Re⩽150) is investigated numerically via a stabilized space–time finite element formulation. The cylinder of low nondimensional mass (m*=10)(m*=10) is free to vibrate in both transverse and in-line directions. Two sets of computations are carried out for each of the cases with 1% and 5% blockage. In the first set of computations the reduced velocity, U*(=U/fnD, where fnfn is the natural frequency of the oscillator, U the free-stream speed, and D   the cylinder diameter) is fixed to 4.92 and the effect of Re is studied. In the second set of computations, both Re and U*U* are varied. Lock-in is observed for a range of Re. A hysteretic behavior of the cylinder response close to the lower and upper limits of the synchronization/lock-in region is observed for the case with 5% blockage. The flow is associated with a different arrangement of vortices in the wake depending on whether one is on the “increasing Re” or “decreasing Re” branch. However, for the case with 1% blockage, the hysteretic behavior is completely eliminated near the lower Re range of the lock-in. The solutions for the decreasing as well as increasing Re branch are very similar. They are both associated with intermittent switching of the vortex shedding frequency between the structural frequency and the vortex shedding frequency for stationary cylinder. The hysteretic behavior for a range of Re close to the upper limit of the lock-in region is observed for both the low and high blockage.