Journal of Fluid Mechanics



High-frequency self-excited oscillations in a collapsible-channel flow


OLIVER E. JENSEN a1 and MATTHIAS HEIL a2
a1 Division of Applied Mathematics, School of Mathematical Sciences, University of Nottingham, University Park, Nottingham, NG7 2RD, UK
a2 Department of Mathematics, University of Manchester, Oxford Road, Manchester M13 9PL, UK

Abstract

High-Reynolds-number asymptotics and numerical simulations are used to describe two-dimensional, unsteady, pressure-driven flow in a finite-length channel, one wall of which contains a section of membrane under longitudinal tension. Asymptotic predictions of stability boundaries for small-amplitude, high-frequency, self-excited oscillations are derived in the limit of large membrane tension. The oscillations are closely related to normal modes of the system, which have a frequency set by a balance between membrane tension and the inertia of the fluid in the entire channel. Oscillations can grow by extracting kinetic energy from the mean Poiseuille flow faster than it is lost to viscous dissipation. Direct numerical simulations, based on a fully coupled finite-element discretization of the equations of large-displacement elasticity and the Navier–Stokes equations, support the predicted stability boundaries, and are used to explore larger-amplitude oscillations at lower tensions. These are characterized by vigorous axial sloshing motions superimposed on the mean flow, with transient secondary instabilities being generated both upstream and downstream of the collapsible segment.

(Received May 15 2002)
(Revised October 9 2002)



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