Numerical analysis of flow-induced vibration of two circular cylinders in tandem at low Reynolds numbers

Abstract

Uniform flows over circular cylinders in different arrangements appear in many practical situations. Analyses of side-by-side, tandem and staggered arrangements have shown significant differences among flow parameters and the interaction of the flow and the cylinder, by comparison with single cylinder parameters. This paper describes the study of two circular cylinders in tandem arrangement subject to bi-dimensional uniform laminar flows at low Reynolds numbers from 90 to 140. Cases with distance between cylinders equal to 5.25 diameter for both fixed cylinders and for a fixed upstream cylinder and a downstream one elastically mounted in transversal direction are analysed. The numerical model Ifeinco, which is based on the finite element method and uses a partitioned scheme that considers two-way interaction of fluid flow and structure, is employed in the analysis. The fluid flow model uses a semi-implicit two-step Taylor-Galerkin method to discretize the Navier-Stokes equations and the arbitrary Lagrangean-Eulerian formulation to follow the cylinder motion. The analysis of the cylinder movement is carried out by using one DOF dynamic equation for the transverse direction discretized in time by the implicit Newmark method. For both fixed cylinders, differences in terms of lift and drag coefficients and Strouhal number are found by comparison with the ones of the single cylinder. When the downstream cylinder is elastically mounted, a lock-in phenomenon is observed in a range of Reynolds numbers, characterized by the discontinuity of the lift and drag coefficients, vortex vibration and natural frequencies approximation and increase in vibration amplitude.