Effect of spacing on a pair of naturally oscillating circular cylinders in tandem arrangements employing IB-LB methods: Crossflow-induced vibrations

Abstract

An efficient velocity-correction based immersed boundary-lattice Boltzmann method (IB-LBM) is employed and coupled with structural equations to investigate the vortex-induced vibration characteristics of two identical circular cylinders in various tandem arrangements at a low Reynolds number of 100 with 1.0 < Sx/D ≤ 12.0 and frequency ratio Fr=1.0; here, Sx is the streamwise displacement between the cylinder centers, D is the cylinder diameter, and Fr is the ratio of the vortex shedding frequency to the natural frequency of the oscillator. The cylinders are set to oscillate naturally in the transverse direction only, and a mass-spring system characterizes their motion. Considering a similar flow and structural parameters, a single cylinder is also studied for reference and comparison. Furthermore, a fixed cylinder and two stationary cylinders in tandem arrangements with same spacing ratios are also examined. Four distinct regimes of cylinder arrangements have been identified based on the cylinder maximum, gradual decrease to a minimum, persistence, and single cylinder response. At Sx/D=1.5, the cylinders vibrate violently with overall maximum amplitude. A critical spacing at (Sx/D)c=3.5 is observed both in the stationary and oscillated cylinders, where the forces and amplitude have the minimum values. The response amplitude and force coefficients remain constant over a range of spacing, i.e., Sx/D=4.0−8.0. The cylinders behave as single cylinders when placed more than eight-diameters apart as the interaction between the fluid and structure are decoupled. The interference and wake effects are diminished in this regime. The hydrodynamic force coefficients and flow physics of the oscillating tandem cylinders are also discussed. The results reveal that the flow in the gap between the cylinders and in the wake significantly affects the forces and hence, the dynamic response of the tandem structure.