Modelling Flow and Oscillations in Collapsible Tubes
Abstract
Laboratory experiments designed to shed light on fluid flow through collapsible tubes, a problem with several physiological applications, invariably give rise to a wide variety of selfexcited oscillations. The object of modelling is to provide scientific understanding of the complex dynamical system in question. This paper outlines some of the models that have been developed to describe the standard experiment, of flow along a finite length of elastic tube mounted at its ends on rigid tubes and contained in a chamber whose pressure can be independently varied. Lumped and onedimensional models have been developed for the study of steady flow and its instability, and a variety of oscillation types are indeed predicted. However, such models cannot be rationally derived from the full governing equations, relying as they do on several crude, ad hoc assumptions such as that concerning the energy loss associated with flow separation at the timedependent constriction during largeamplitude oscillations. A complete scientific description can be given, however, for a related twodimensional configuration, of flow in a parallelsided channel with a segment of one wall replaced by a membrane under longitudinal tension T. The flow and membrane displacement have been calculated successively by lubrication theory, Stokesflow computation, steady NavierStokes computation and unsteady NavierStokes computation. For a given Reynolds number, Re, steady flow becomes unstable when T falls below a critical value (equivalently, when Re exceeds a critical value for fixed T), and the consequent oscillations reveal at least one perioddoubling bifurcation as T is further reduced. The effect of wall inertia has also been investigated: it is negligible if the flowing fluid is water, but leads to an independent, high frequency flutter when it is air. The computations require very large computer resources, and a simpler model would be desirable. Investigation of the streamlines of the flow and the distribution of viscous energy dissipation reveals how the onedimensional model might be improved; but such improvement is as yet incomplete.
 Publication:

Theoretical and Computational Fluid Dynamics
 Pub Date:
 1998
 DOI:
 10.1007/s001620050064
 Bibcode:
 1998ThCFD..10..277P