A new time-domain drag description and its influence on the dynamic behaviour of a cantilever pipe conveying fluid

Studying dynamic stability of a vertically suspended, fully submerged pipe conveying fluid upwards, researchers have found a contradiction between theoretical predictions and experiments. Experiments did not show any instability, while theory predicts instability at infinitesimally low fluid velocities for a pipe without dissipation mechanisms. To explain this contradiction, in 2005 Païdoussis and co-workers postulated a new description of the boundary condition at the free end of the pipe. Subject to this boundary condition the pipe is predicted to become unstable by divergence (stable node to saddle bifurcation) at a velocity higher than yet achieved in experiments. In this paper, it is shown that a realistic description of hydrodynamic drag in combination with conventional boundary conditions might result in even higher critical velocity, and hence, this could also be an explanation of the contradiction. The description of the hydrodynamic drag is based on experimental data available in literature. This data has been obtained by experimenting with submerged rigid cylinders. To make it applicable to flexible pipes, a key step is undertaken in this paper to translate the data from the frequency domain to the time domain. Using the time-domain description of the hydrodynamic drag in combination with the conventional boundary conditions at the free end, it is shown that the pipe becomes unstable by flutter (stable focus to unstable focus bifurcation) at a critical velocity, which is much higher than that attainable in small-scale experiments. For fluid velocities exceeding the critical one, the pipe motion reaches a steady oscillation of finite amplitude, i.e. a stable limit cycle.