Jensen, O.E. & Heil, M. (2003) High-frequency self-excited
oscillations in a collapsible-channel flow.
Journal of Fluid Mechanics 481
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 discretisation 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
characterised by vigorous axial sloshing motions superimposed on the
mean flow, with transient secondary instabilities being generated both
upstream and downstream of the collapsible segment.
Page last modified: February 28, 2003
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