Nonlinear characteristics analysis of vortex-induced vibration for a three-dimensional flexible tube

• A three-dimensional numerical model for flexible tube vibration induced by cross flow is proposed.
• The dynamic behavior and response characteristic of the tube are investigated. Meanwhile, the limit cycle and bifurcation of lift coefficient and displacement are analyzed.
• Amplitude response, trajectory, phase difference, fluid force coefficient and vortex shedding frequency are investigated.
• A quasi-upper branch occurs in the fluid–structure interaction system, and there is no bifurcation of lift coefficient and lateral displacement occurred in three dimensional flexible tube submitted to uniform turbulent flow.

Vortex-induced vibration of a three-dimensional flexible tube is one of the key problems to be considered in many engineering situations. This paper aims to investigate the nonlinear dynamic behaviors and response characteristics of a three-dimensional tube under turbulent flow. The three-dimensional unsteady, viscous, incompressible Navier–Stokes equation and LES turbulence model are solved with the finite volume approach, and the dynamic equilibrium equations are discretized by the finite element theory. A three-dimensional fully coupled numerical model for vortex-induced vibration of flexible tube is proposed. The model realized the fluid–structure interaction with solving the fluid flow and the structure vibration simultaneously. Based on this model, Response regimes, trajectory, phase difference, fluid force coefficient and vortex shedding frequency are obtained. The nonlinear phenomena of lock-in, phase-switch are captured successfully. Meanwhile, the limit cycle, bifurcation of lift coefficient and displacement are analyzed using phase portrait and Poincare section. The results reveal that, a quasi-upper branch occurs in the present fluid-flexible tube coupling system with high mass-damping and low mass ratio. There is no bifurcation of lift coefficient and lateral displacement occurred in the three-dimensional flexible tube submitted to uniform turbulent flow.