Abstract
The linear stability of the flow in the annular gap between
two infinitely long cylinders,
driven by the constant rotation and harmonic oscillation in the
axial direction of the
inner cylinder, is analysed using Floquet theory. Closed form solutions
for the basic
flow are derived, both with and without the presence of endwalls. Recent
experiments
and theory using the narrow gap approximation have shown that the axial
oscillations
significantly stabilize the flow with respect to centrifugal
instabilities. However, the
agreement has only been qualitative. The present analysis reproduces the
experimental
results to well within experimental uncertainty. We have identified
the major source of discrepency with the previous theory to be due to the
lack of
global endwall effects
enforcing a net zero axial mass flux. Analysis of the basic flow indicates
that the
stabilization is primarily due to waves of azimuthal vorticity propagating
inwards
from the cylinder boundary layers due to the axial oscillations.
Publisher
Cambridge University Press (CUP)
Subject
Mechanical Engineering,Mechanics of Materials,Condensed Matter Physics
Cited by
51 articles.
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