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, L/D, 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 α=0°. The mass ratio for each cylinder is Mr=6.0 and the reduce velocity, Ur, 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.