Numerical prediction of vortex-induced vibrations of a long flexible cylinder in uniform and linear shear flows using a wake oscillator model

A numerical study based on a wake oscillator model was conducted to determine the response performance of vortex-induced vibration (VIV) on a long flexible cylinder with pinned-pinned boundary conditions subjected to uniform and linear shear flows. The coupling equations of a structural oscillator model and wake oscillator model were solved using a standard central finite difference method of the second order. The structural displacement, structural frequency, standing waves, travelling waves, lift force coefficient and transferred energy for uniform and linear shear flows were compared. The numerical results show that the VIV response is a combination of standing waves and travelling waves. In a uniform flow, the VIV response is dominated by the standing waves along the total cylinder span. In linear shear flows, standing waves and travelling waves dominate the VIV response near the cylinder ends and midpoint, respectively, and the VIV displacements display multi-frequency characteristics when monitoring their characteristics during a long time. However, for a given time, the displacements instantaneously exhibit mono-frequency characteristics. The variation of the transferred energy from a positive value to a negative value is due to the decrease of the phase lag between the structural displacement and the lift force coefficient.