Effect of length on the instability of hanging pipes

The flutter instability of a hanging fluid-conveying pipe is investigated, as its length is increased. Experiments show that there exists a critical length above which the flow velocity necessary to cause flutter becomes independent of the pipe length. The fluid-structure interaction is thus modelled by following the work of Bourrières and of Païdoussis. Computations using a standard Galerkin method confirm this evolution. A short pipe model is then considered, where gravity plays a negligible role. Transition between this short length model and the asymptotic situation is found to occur where a local stability criterion is satisfied at the upstream end of the pipe. For longer pipes, a model is proposed where the zone of stable waves is totally disregarded. Comparison of these models with experiments and computations show a good agreement over all ranges of mass ratios between the flowing fluid and the pipe.