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

摘要

The Three-dimensional (3-D) dynamical behaviors of a fluid-conveying pipe subjected to vortex-induced vibration are investigated with different internal flow velocityv. 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 velocityvin 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 ofv. 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 whilevis beyond the critical value. Besides, the responses corresponding to different couples ofμ1andμ2are obviously distinct from each other.