Abstract
Time-dependent swirling flows inside an enclosed cylindrical rotor–stator cavity with
aspect ratio H/R = 4, larger than the ones usually considered in the literature,
are studied. Within a certain range of governing parameters, vortex breakdown
phenomena can arise along the axis. Very recent papers exhibiting some particular
three-dimensional effects have stimulated new interest in this topic. The study is carried
out by a numerical resolution of the three-dimensional Navier–Stokes equations, based
on high-order spectral approximations in order to ensure very high accuracy of the
solutions.The first transition to an oscillatory regime occurs through an axisymmetric bifurcation
(a supercritical Hopf bifurcation) at Re = 3500. The oscillatory regime is caused
by an axisymmetric mode of centrifugal instability of the vertical boundary layer and
the vortex breakdown is axisymmetric, being composed of two stationary bubbles.
For Reynolds numbers up to Re = 3500, different three-dimensional solutions are
identified. At Re = 4000, the flow supports the k = 5 mode of centrifugal instability.
By increasing the rotation speed to Re = 4500, the vortex breakdown evolves to
an S-shaped type after a long computational time. The structure is asymmetric and
gyrates around the axis inducing a new time-dependent regime. At Re = 5500, the
structure of the vortex breakdown is more complex: the upper part of the structure
takes a spiral form. The maximum rotation speed is reached at Re = 10000 and the
flow behaviour is now chaotic. The upper structure of the breakdown can be related
to the spiral-type. Asymmetric flow separation on the container wall in the form of
spiral arms of different angles is also prominent.
Publisher
Cambridge University Press (CUP)
Subject
Mechanical Engineering,Mechanics of Materials,Condensed Matter Physics
Cited by
66 articles.
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