Dynamics of a partially confined, discharging, cantilever pipe with reverse external flow Kyriakos Moditis a , Michael Paidoussis a,n , Joe Ratigan b a Department of Mechanical Engineering, McGill University, 817 Sherbrooke Street West, Montreal, Canada QC H3A 0C3 b Ratigan Engineering & Consulting LLC, 3824 Jet Drive, Rapid City SD 57703, USA article info Article history: Received 22 July 2015 Accepted 4 March 2016 Keywords: Brine-string Instability Tubular cantilever Flutter Counterflow abstract The potential for fluid-elastic instability of hanging cantilevered pipes subjected to simul- taneous 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 cri- tical flow-velocity and associated frequency reaching limiting values. Sufficiently long sys- tems lose stability by divergence rather than flutter. & 2016 Elsevier Ltd. All rights reserved. 1. Introduction This investigation is concerned with flow-induced vibrations of a flexible tubular cantilever, hanging concentrically within a shorter rigid outer tube, thus forming an annular channel between the two, as shown in Fig. 1. The whole system is immersed in incompressible fluid and is contained within an otherwise closed cavity, with the exception of one inlet into the cantilever, and one outlet to the annular space between the cantilever and the rigid tube. Fluid is directed as internal flow from the clamped towards the free end of the cantilever and exits as a free jet in stagnant fluid. Because of conservation of mass, initially stagnant fluid is then forced through the annular region, as a bounded reverse external flow, over only the upper portion of the cantilever. Contents lists available at ScienceDirect journal homepage: www.elsevier.com/locate/jfs Journal of Fluids and Structures http://dx.doi.org/10.1016/j.jfluidstructs.2016.03.002 0889-9746/& 2016 Elsevier Ltd. All rights reserved. n Corresponding author. Tel.: +514 398 6294. E-mail addresses: kyriakos.moditis@mail.mcgill.ca (K. Moditis), michael.paidoussis@mcgill.ca (M. Paidoussis), Joe@ratiganeandc.com (J. Ratigan). Journal of Fluids and Structures 63 (2016) 120–139