Dynamics of a cantilevered pipe discharging fluid, fitted with a stabilizing end-piece

In this communication, the dynamics of a flexible cantilevered pipe fitted with a special end-piece is considered, both theoretically and experimentally. This end-piece can be configured in two ways: (i) with the flow going straight through, unimpeded, and emerging at the free end as a jet, and (ii) with the straight-through path blocked, so that the flow is discharged radially from a number of holes perpendicular to the pipe. The dynamics in the first case is similar to that of a pipe with no end-piece: the system loses stability by flutter via a Hopf bifurcation, though the dynamics becomes more complex at higher flow velocities. The dynamics in the second case is entirely different: the system remains stable over the full range of flow velocities considered. This study provides insight into the mechanism of flutter of cantilevered pipes conveying fluid and the key role played by the mathematically obvious but physically counter-intuitive compressive follower force generated by the straight-through discharging jet.