Flow-induced vibrations of four circular cylinders with square arrangement at low Reynolds numbers

Flow-induced vibrations (FIV) of four identical circular cylinders placed in a square arrangement are numerically investigated. Modeled as a spring-damping system subjected to uniform flows, each cylinder is allowed to freely oscillate with equal natural frequencies in the inline and transverse directions. The spacing ratio, LID, remains 5, where L is the central distance of any two adjacent cylinders and D the cylinder diameter. The Reynolds numbers are chosen as Re=80 and 160. The incidence angle of the incoming uniform flow is alpha=0 degrees. The mass ratio for each cylinder is M-r=6.0 and the reduce velocity, U-r, varies from 3 to 14. The coupled system is numerically resolved by a semi-implicit characteristics-based split (CBS) finite element algorithm under the arbitrary Lagrangian-Eulerian description. The calculated results are analyzed in detail. In particular, some intrinsic mechanisms are interpreted on the cylinder responses and the wake patterns. The unsymmetrical figures of 8 and O, and other irregular figures are observed in the cylinders' X-Y trajectories. Besides the 4S wake pattern, the 2P+2S pattern is discovered herein. The dual-resonance phenomenon, which indicates the cylinders' synchronizations occurring in both the inline and transverse directions, is detected in this work. (C) 2014 Elsevier Ltd. All rights reserved.