A nonlinear model for a hanging cantilevered pipe discharging fluid with a partially-confined external flow

Abstract

In this paper, a nonlinear theoretical model is developed for the dynamics of a flexible cantilevered pipe that is simultaneously subjected to internal and partially-confined external axial flows. The pipe under consideration discharges fluid downwards, which accumulates in a relatively large tank, and then flows upwards through a generally shorter annular region surrounding the pipe. Thus, the internal and external flows are interdependent and in opposite directions. A practical application of this system may be found in solution mining processes for brine production, and in the subsequent usage of the salt-mined caverns for hydrocarbon storage. The equation of motion is derived using the extended Hamilton’s principle to third-order accuracy with a separate derivation of the fluid-related forces associated with the internal and external flows. The equation is discretized using Galerkin’s scheme and solved via the pseudo-arclength continuation method and a direct time integration technique. Two pipes of different dimensions and materials are considered in this study; the stability of these pipes is investigated with increasing flow velocity. Also, the influence of varying the length and tightness of the annular region on the dynamical behaviour of the pipes is explored theoretically. The predictions of the proposed model are compared to experimental observations from the literature for systems with the same parameters as those considered in this paper, as well as to predictions of an earlier linear theory. The results obtained are in excellent qualitative and good quantitative agreement with the experimental observations. Furthermore, this model predicts the frequencies of oscillation more accurately than linear theory.