Three-dimensional dynamics of vortex-induced vibration of a pipe with internal flow in the subcritical and supercritical regimes

Abstract

The Three-dimensional (3-D) dynamical behaviors of a fluid-conveying pipe subjected to vortex-induced vibration are investigated with different internal flow velocity v. The values of the internal flow velocity are considered in both subcritical and supercritical regimes. During the study, the 3-D nonlinear equations are discretized by the Galerkin method and solved by a fourth-order Runge-Kutta method. The results indicate that for a constant internal flow velocity v in the subcritical regime, the peak Cross-flow (CF) amplitude increases firstly and then decrease accompanied by amplitude jumps with the increase of the external reduced velocity. While two response bands are observed in the In-line (IL) direction. For the dynamics in the lock-in condition, 3-D periodic, quasi-periodic and chaotic vibrations are observed. A variety of CF and IL responses can be detected for different modes with the increase of v. For the cases studied in the supercritical regime, the dynamics shows a great diversity with that in the subcritical regime. Various dynamical responses, which include 3-D periodic, quasi-periodic as well as chaotic motions, are found while both CF and IL responses are coupled while v is beyond the critical value. Besides, the responses corresponding to different couples of μ1 and μ2 are obviously distinct from each other. Keywords: Vortex-Induced Vibration (VIV), Three Dimension (3-D), Internal flow, Wake oscillator, Bifurcation diagram