Dynamics of a confined pipe aspirating fluid and concurrently subjected to external axial flow: a theoretical investigation

Abstract A linear model is developed for a hanging pipe aspirating fluid with internal flow velocity U i , flowing up the pipe from its lower end, and also subjected to an external flow of velocity U o flowing down from the upper end of the annulus formed between the pipe and a relatively shorter rigid outer tube; both the tube and pipe are cantilevered from their top ends. In this model, the pipe is modelled as an Euler-Bernoulli beam, with the internal flow modelled as a plug flow and the external one by means of slender-body theory; flow over the unconfined portion of the pipe is also taken into account. This model is discretized and solved using the Galerkin method to obtain the eigenfrequencies of the pipe for a number of flow velocity ratios U o / U i . In all cases, the pipe loses stability, mostly via first-mode flutter, at sufficiently high values of U i . Subsequently, the theoretical results are compared with earlier theoretical results and also with all available experimental results. The present theoretical results are in reasonably good agreement with the experimental results. The system under consideration represents an idealized mode of operation of ‘salt-mined caverns’, which are large underground storage spaces created to store hydrocarbons, such as natural gas and oil.