Time-domain prediction of the coupled cross-flow and in-line vortex-induced vibrations of a flexible cylinder using a wake oscillator model

A numerical study, based on a wake oscillator model, has been performed to determine the three-dimensional vortex-induced vibration (VIV) responses of a flexible cylinder subjected to uniform and non-uniform flows. The coupling equations of the structural oscillator and wake oscillator models in the cross-flow (CF) and in-line (IL) directions, have been solved by employing a standard central finite difference method. The structural displacement, structural frequency, response wave pattern, response trajectory for three different aspect ratios, and four different flow profiles have been compared. As the shear parameter beta increases, the maximum RMS values for a certain aspect ratio, in both CF and IL directions, display apparent decreasing tendencies. However, for a certain beta, the maximum RMS values in CF and IL directions vary slightly with the increased aspect ratio. The VIV displacements in both CF and IL directions exhibit standing wave and traveling wave behaviors, simultaneously. Further, as the shear parameter beta increases, the traveling wave behaviors becomes increasingly dominant. The value of dominant frequency of the CF displacement is always half of that of the IL displacement. The dominant frequency participates in the VIV process at all times, whereas, the other peak frequencies intermittently participate in the VIV process.