Nonlinear vortex-induced vibrations of slightly curved pipes conveying fluid in steady and oscillatory flows

Abstract

An effective nonlinear dynamic model is developed to investigate vortex-induced vibration (VIV) characteristics of a slightly curved pipe conveying fluid in steady and oscillatory flows. Initial displacement caused by geometric imperfection of the slightly curved pipe is considered. Interaction between the pipe and external flow is evaluated by the van der Pol equation. Based on Hamilton's principle and the Galerkin method, the nonlinear equations of motion of the pipe system taking into account the fluid-structure interaction are established, and solved by the fourth-order Runge-Kutta method. Typical vibration features in oscillatory flows such as build-up-lock-in-die-out cycle are studied and compared with the existing experimental results to validate the accuracy of the present model. The influences of some parameters on the VIV responses of the slightly curved pipe are examined and discussed. It is found that for steady external flow, there are obvious lock-in regions for the first three mode resonances of cross-flow vibration while the displacement amplitudes of in-line vibration increase monotonically with the increase of the reduced external fluid velocity. For oscillatory external flow, the VIV dynamical behaviors are more complicated and the lock-in regions are influenced by more factors, which are distinctly different from those of the steady flow.