Flow induced vibration of two rigidly coupled circular cylinders in tandem and side-by-side arrangements at a low Reynolds number of 150

Flow induced vibration of two rigidly coupled identical circular cylinders in tandem and side-by-side arrangements at a low Reynolds number of 150 is studied numerically. The two cylinders vibrate in the cross-flow direction and have the same displacement. The Navier-Stokes equations are solved by the finite element method and the equation of motion of the cylinders is solved by the fourth-order Runge-Kutta algorithm. Simulations are conducted for a constant mass ratio of 2 and the gap ratios (defined as the ratio of the centre-to-centre distance between the two cylinders L to the cylinder diameter D) of 1.5, 2, 4, and 6. The reduced velocities range from 0.5 to 15 with an increment of 0.5 for the tandem arrangement and from 0.5 to 30 with an increment of 0.5 for the side-by-side arrangement. It is found that the gap between the two cylinders has significant effect on the response. For a tandem arrangement, the lock-in regime of the reduced velocity is narrower than that of a single cylinder for L/D = 1.5 and 2 and wider than later for L/D = 4 and 6. If the two cylinders are allowed to vibrate in the cross-flow direction, the vortex shedding from the upstream cylinder occurs at L/D as small as 2. The most interesting phenomenon found in the side-by-side arrangement is the combination of vortex-induced vibration (VIV) and galloping at L/D = 1.5 and 2. For L/D = 1.5 and 2, the response is dominated by VIV as Vr<15 and by galloping as Vr>15. At reduced velocities close to 15, the response is a combination of VIV and galloping.