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The Vortex-Induced Vibration on an elastically mounted circular cylinder is investigated by the numerical solution of the two-dimensional Reynolds Averaged Navier-Stokes equations and results are compared with experimental data. The upwind TVD scheme of Roe – Sweby is used to solve the governing equations and the k-ε turbulence model is used to simulate the turbulent flow in the wake of the cylinder. The cylinder is laterally supported by a spring and a damper and is free to oscillate in the transverse direction. Results for the lift coefficient amplitude, displacement amplitude, frequency, phase angle, and power absorbed by the system are presented and compared to experimental data. The code was tested for the fixed cylinder case, and for the moving cylinder. The comparison with experimental data obtained from the literature showed the good quality of the numerical results and validated the code for simulations of vortex-induced vibration.

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The hysteresis effect on the vortex induced vibration (VIV) on a circular cylinder is investigated by the numerical solution of the two-dimensional Reynolds averaged NavierStokes equations. An upwind and total variation diminishing (TVD) conservative scheme is used to solve the governing equations written in curvilinear coordinates and the k-e turbulence model is used to simulate the turbulent flow in the wake of the body. The cylinder is supported by a spring and a damper and free to vibrate in the transverse direction. In previous work, numerical results for the amplitude of oscillation and vortex shedding frequency were compared to experimental data obtained from the literature to validate the code for VIV simulations. In the present work, results of practical interest are presented for the power absorbed by the system, phase angle, amplitude, frequency, and lift coefficient. The numerical results indicate that the hysteresis effect is observed only when the frequency of vortex shedding gets closer to the natural frequency of the structure in air.