Two-Dimensional Coupled Vortex-Induced Vibration of Circular Cylinder: Prediction and Extraction of Hydrodynamics Properties

An advanced model for predicting a two-dimensional coupled cross-flow and in-line vortex-induced vibration (VIV) of a flexibly-mounted circular cylinder in a uniform flow is proposed and investigated. Attention is placed on a systematic extraction of variable hydrodynamics properties associated with a bi-directional fluid-structure interaction system. The governing equations of motion are based on double Duffing-van der Pol (structural-wake) oscillators with the two structural equations containing cubic and quadratic nonlinear terms. The cubic nonlinearities capture the geometrical coupling of cross-flow/in-line displacements excited by hydrodynamic lift/drag forces whereas the quadratic nonlinearities allow fluid-structure interactions. The combined analytical and numerical solutions of the proposed model are established. By varying flow velocities in numerical simulations, the derived low-order model qualitatively captures several key VIV characteristics of coupled in-line/cross-flow oscillations. By making use of a newly-derived empirical formula, the predicted maximum cross-flow/in-line VIV amplitudes and associated lock-in ranges compare well with several experimental results for cylinders with low/high mass or damping ratios. Moreover, such important hydrodynamic properties as VIV-induced mean drag, added mass, excitation and damping terms can be systematically determined via the proposed model and compared well with some experimental results in the literature.