Flow-induced vibration of two side-by-side square cylinders with combined translational motions

This paper presents a series of two-dimensional numerical simulations of flow-induced vibrations (FIV) and coupled wake flow behind two identical square cylinders in a side-by-side configuration at Re=200. The computational results of stationary configuration are firstly investigated and compared with the existing experimental observations as a function of gap ratio g*, which is the ratio of spacing between the inner cylinder surfaces to the diameter of the cylinder. Consistent with the experimental measurements, four distinct regimes have been observed namely: (i) the single bluff-body, (ii) the gap flow with narrow and wide streets, (iii) the coupled-vortex street regime, and (iv) the quasi-independent vortex shedding. We estimate the merging downstream distance of two vortex streets and compare it against the measurement trend for the gap ratio range 0.4 less than or similar to g* less than or similar to 2.0. We next investigate the configuration of two elastically mounted square cylinders, which are free to oscillate in both streamwise and transverse directions. Instead of independent vibrations due to the individual fluid forces, the two square cylinders are tied together as a single rigid body with a fixed relative position between them. The role of flow passing through the gap between two cylinders is examined by exploring interactions of shear layers with the gap flow in the near-wake region. Through controlled numerical experiments, we show that the gap flow mechanism has a profound role on both vortex-induced vibration and galloping regimes corresponding to low and high reduced velocities, respectively. The fluid-structure simulations are performed via a nonlinear partitioned iterative scheme for the variational coupled system based on the Navier-Stokes equations and rigid body dynamics. For the freely vibrating condition, all the 2D simulations are computed at Reynolds number Re = 200, mass ratio m* = 10, damping ratio zeta= 0 and reduced velocity Ur is an element of [1, 501 and the four regimes are considered based on the stationary analysis. The effects of reduced velocity on the force variation, the vibration amplitudes and the vorticity contours are analyzed systematically to understand the underlying FIV physics of side-by-side cylinders in the four regimes. For a fixed mass-damping parameter, we introduce simple correlations for the prediction of amplitudes for the vortex-induced vibration and galloping modes of freely vibrating side-by-side cylinders in the four regimes.