Dynamics of a partially confined, discharging, cantilever pipe with reverse external flow

The potential for fluid-elastic instability of hanging cantilevered pipes subjected to simultaneous internal and external axial flows is investigated. Such systems may lose stability by amplified oscillations (flutter) or buckling (static divergence). The system of interest is a flexible tubular cantilever hanging concentrically within a rigid outer tube of larger diameter. Flow inside the cantilever is directed from the clamped end to the free end. Upon exiting the cantilever, the fluid flows in the opposite direction in the annular region between the outer tube and the cantilever. The rigid outer tube is of variable length and it can cover part of the length of the cantilever. This system has applications in brine production and salt-cavern hydrocarbon storage. A linear model is derived based on the work of Paidoussis, Luu and Prabhakar; the presence of the shorter outer rigid tube is taken into account in a simplified way. Series solutions are obtained using a Galerkin method with Euler-Bernoulli beam eigenfunctions as comparison functions. Experimental results are presented and compared with the theoretical model. Additional computations are performed to quantify the effect of confinement (i.e. the narrowness of the annular region) on the cantilever stability, as well as the effect of confined-flow length, for both the short laboratory-sized system and long brine-string-like systems. An increase in these parameters gives rise to flutter for short systems, or a succession of flutter and divergence for long systems. In addition, the effect of the system length is investigated. Increasing length results in asymptotic behaviour, with both the critical flow-velocity and associated frequency reaching limiting values. Sufficiently long systems lose stability by divergence rather than flutter.