Vortex induced vibrations of a square cylinder at subcritical Reynolds numbers

Vortex induced vibration (VIV) of an elastically mounted square cylinder of low non-dimensional mass is simulated at subcritical Reynolds numbers (Re), i.e., Re ≤ 50 . The cylinder is allowed to vibrate in the transverse direction to the incoming flow. Four cases are considered for understanding the behavior of VIV of the square cylinder at subcritical Re. In the first case, the non-dimensional frequency varies as 3.1875/Re. In the second case, the non-dimensional frequency is kept constant at 0.1333. In both the cases, Re is varied. In third and fourth cases, studies are conducted for Re=25, 30 and 35, and Re=80, respectively. In the third and fourth cases, the non-dimensional velocity, U⁎, is varied. It is found that maximum transverse displacement is approximately 0.15D when the non-dimensional frequency, Fn, varies with Re. The maximum transverse displacement is 0.25D when the non-dimensional frequency is constant. For the first case, VIV starts at Re as low as 23.9 and it ceases at Re ∼ 33.5 . In all these cases, it is observed that the phase difference between the lift coefficient and the transverse displacement depends upon non-dimensional mass, Re, and non-dimensional velocity. In all the cases, the lock-in phenomenon is observed. In the fourth case of supercritical Re, hysteresis is also observed and it is seen that its extent depends upon non-dimensional mass. Stabilized finite-element space–time formulations (SUPG and PSPG) are utilized to solve the two-dimensional incompressible Navier–Stokes equations together with the equations of motion of the body.