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The vortex-induced vibration (VIV) phenomenon has drawn the attention of researchers in Engineering for several decades. An example is the riser used for petroleum exploration, in which it is subjected to marine flows that may cause oscillations due to vortex shedding. In this paper, numerical analyses of the phenomena that occur in the interaction among flows at low Reynolds numbers and elastically mounted cylinders are presented. The simulation is carried out by using the numerical model Ifeinco that 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 rigid body motion description is calculated by using the Newmark method. Firstly, the characteristics of the vortex generation process for the fixed cylinder are analyzed. In this case, the Strouhal number, the mean drag and the RMS lift coefficients for Reynolds numbers ranging from 90 to 140 are shown. Afterwards, an analysis of a flexible supported cylinder (with a spring and a damper) in transverse direction subject to flows with Reynolds numbers ranging from 90 to 140 is carried out. The cylinder displacement and the vibration frequencies are studied; the synchronization between the vortex shedding and the vibration frequency (lock-in) is analyzed. Similar results to the experimental ones developed by Anagnostopoulos and Bearman (1992) were obtained in this study.

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