The flow around stationary and elastically-mounted circular cylinders in tandem and staggered arrangements

A numerical study is presented of the flow around two circular cylinders in tandem and staggered arrangements in a freestream, examining the fluid forces and vortex-shedding behaviour, as well as the oscillation of both cylinders when allowed to move and vibrate in response to the flow. The streamwise distance between the cylinder centres is 1.5 diameters, while the crossstream offset is varied from 0.0 to 5.0. The Reynolds number, based on cylinder diameter, D, and freestream velocity, U, is 200. Reduced velocity, U = U over fND, where fN is the spring natural frequency, is varied from 0.0 to 14.0. Results are obtained using a sharp-interface immersed boundary finitedifference method. For the stationary cylinders a range of behaviours are observed over the cylinder offset range, including a difference in primary vortex-shedding frequency when the crossstream offset is greater than 1:5D. For the elasticmounting, in contrast to existing results in the literature, three modes of vortex-shedding and oscillation are observed over the U range for the tandem arrangement. These modes are distinct in the phase difference between the front and rear cylinder oscillation, as well as the number of vortices shed from each cylinder.