Effect of hydrodynamic drag on the stability of a cantilever pipe conveying fluid

摘要

When studying the stability of a vertically suspended, fully submerged pipe conveying water upwards, researchers found a contradiction between theoretical predictions and experiments. Experiments did not show any instability, while theory predicted instability at small fluid velocities. Recently, searching for a resolution of this contradiction, Paiedoussis et al. postulated a new description of the boundary conditions at the free end of the pipe. With these boundary conditions, the pipe becomes unstable by divergence (stable focus to saddle bifurcation) at a higher fluid velocity, than predicted earlier and than was reached in the experiments so far. Thus, it might seem that the reason for the contradiction has been found. However, in this paper another explanation is given why the experiments should not have shown any instability. This explanation is based on a realistic description of hydrodynamic drag, based on experimental data available in the literature. Using this drag description, it is shown that the pipe becomes unstable by flutter (stable focus to unstable focus bifurcation) at a much higher fluid velocity than predicted by Paiedoussis et al.