The quasi-cylindrical (QC) approximation of the Navier-Stokes equations has been used to investigate the downstream evolution of vortex jets at two different situations: unconfined flows and vortices through straight pipes.
Unlike to the case of incompressible flows for which is
broadly accepted that the failure of the QC approximation
can be related to vortex breakdown, in the case of
compressible flows there are neither numerical nor
experimental evidence for such a relationship. Therefore,
for comparison, we have solved numerically the full
axi-symmetric Navier Stokes equations for compressible
swirling flows through straight pipes. The results of both
QC and full NS computations are in very good agreement.
[GM.002] Convective and absolute nature of the Crow and the elliptic instability
David Fabre (ONERA), Carlo Cossu (LadHyX, Ecole Polytechnique), Laurent Jacquin (ONERA)
We consider the spatio-temporal development of the Crow
(long-wave) and elliptic (short-wave) instabilities in a
pair of counter-rotating vortices in the presence of a
uniform axial advection velocity. The stability properties
depend upon the aspect ratio a/b of the vortex pair, where
a is the core radius of the vortices and b their
separation, and upon W_0/U_0 the ratio between the
self-induced velocity of the pair and the axial advection
velocity. For sufficiently small W_0/U_0, the
instabilities are convective, but an increase of W_0/U_0
may lead to an absolute instability. Near the absolute
instability threshold, spatial growth rates are larger than
those predicted by temporal stability theory. Considering
aeronautical applications, it is shown that instabilities of
the type considered cannot become absolute in farfield wakes
of high aspect ratio wings.
[GM.003] Spatial Correlation Function as a Tool to Detetect Streamwise Vortices
Hongzhou Xu, Ming De Zhou, Israel Wygnanski (Deptartment of Aerospace and Mechanical Engineering, University of Arizona)
The two-point, velocity fluctuation, spatial correlation
function is often used to examine the existence of spatial
structures and their evolution in time. The definition that
is based on velocity fluctuations worked fine in most
naturally developing turbulent flows, whenever one is
interested in the random component of the motion. However,
it can not detect the existence of the steady vortices in
general, or the steady component of undulating streamwise
vortices in particuar. For revealing these quantities, the
temporal fluctuations in the traditional definition of
correlation should be replaced by spatial fluctuations. This
leads to a new correlation function where the entire
instantaneous signal ( steady and time dependent) is
involved. Experiments were carried out in the two- as well
as three-dimensional flows. One of the experiments was a two
dimensional wall jet while the others were carried out in
boundary layers with vortex generators arranged in various
ways. The results reveal that both definitions of spatial
correltaions are valid whenever the steady components of the
streamwise vortices vanish. Once a steady component exists,
the new definition reveals clearly its existence while the
classical correlation function fails to do so.
[GM.004] Vortex Shedding from a Torsionally Oscillating Sphere
Richard Wiener (Pacific University), Rainer Hollerbach (University of Glasgow), Russell Donnelly (University of Oregon), Carlo Barenghi (University of Newcastle)
We investigate, experimentally and numerically, the flow
around a torsionally oscillating sphere enclosed within a
second, stationary sphere, with a radius ratio of 0.187. We
consider oscillation frequencies for which the inner radius
to penetration depth ratio is between 15 and 60, and
amplitudes less than \pi. The flow consists of a radial
jet of periodically fluctuating thickness emanating from the
equator of the oscillating sphere. As the oscillation
amplitude is increased, these fluctuations gradually become
more pronounced, until the faster portions of the jet
overtake the slower ones, causing them to curl back on
themselves to form vortex pairs. The experimental results
show that even after the appearance of the vortices the flow
remains predominantly axisymmetric, and also equatorially
symmetric, for a distance considerably greater than an inner
sphere radius from the inner sphere. A 2D numerical code is
therefore used to elucidate the precise details of the flow,
with excellent agreement on the range of amplitudes over
which the vortices gradually emerge, and on the variation of
that range with freqency.
[GM.005] Vortical flow past a sphere
Trent Mattner, Min Chong, Peter Joubert (The University of Melbourne)
Vortical flow past a sphere in a constant diameter pipe was
studied experimentally in a guide vane apparatus similar to
those used in fundamental experimental studies of vortex
breakdown. The initial effect of swirl was to shorten the
downstream separation bubble. For a small range of the swirl
intensity, an almost stagnant upstream separation bubble
formed. As the swirl intensity was increased, the bubble
became unstable and an unsteady spiral formed. At high swirl
intensity there was a mean recirculation region which
penetrated far upstream while the flow on the downstream
hemisphere was attached. Measurements of the velocity field
were obtained using laser Doppler velocimetry. Analysis of
these results suggests that the onset of upstream separation
is associated with the formation of a negative azimuthal
vorticity component which slows the axial flow near the axis
of symmetry. This is consistent with inviscid distortion of
the vortex filaments in the diverging flow approaching the
sphere.
[GM.006] Vortex Dynamics, Complexity and Symmetry in the Sphere Wake
Rajat Mittal (Department of Mechanical Engineering, University of Florida), Fady M. Najjar (Center for Simulation of Advanced Rocket, University of Illinois,), James J. Wilson (Department of Mechanical Engineering, University of Florida)
Direct numerical simulations have been used to study the
vortex dynamics and structure of the sphere wake in the
Reynolds number range from 500 to 1000. The numerical solver
employs a highly accurate Fourier-Chebyshev spectral
collocation method in space and a fractional-step method in
time. Our simulations indicate that the sphere wake at these
Reynolds numbers is dominated by vortex loops and rings, and
the formation and evolution of these vortex structures is
described. Simulations also indicate a clear path to
increasing complexity with Reynolds number which is
associated with the variability in the azimuthal orientation
of the vortex loops formed in the wake. The time-mean
structure of the wake is also described with particular
emphasis on the effect that the vortex loops in the near
wake have on the symmetry properties of the time-mean wake.
[GM.007] Wake of a Non-Parallel Pair of Circular Cylinders
Riho Hiramoto, Hiroshi Higuchi (Tohoku University)
It is known that state of vortex wake behind parallel pair of circular cylinders varies from biased shedding with multiple frequencies to synchronized shedding with a frequency corresponding to a diameter of the cylinder as the gap spacing between circular cylinders is increased. In this study, the vortex shedding from \underlinenon-parallel pair of circular cylinders placed side-by-side in a uniform flow is experimentally investigated. The gap size varies continuously along the span and wake patterns also changes from narrow gap spacing to wide spacing with varying frequency along the span. Flow is somewhat analogous to that behind a tapered cylinder where the shedding frequency is characterized by a local diameter of the tapered cylinder but varies discretely along the span. In this study, the three-dimensional vortex sheddings and their interactions are investigated by flow visualizations, PIV measurements and multi-point hot-wire measurements. Aspect ratio of each cylinder is 68 with the gap varying from almost 0 to 3 diameters, and the Reynolds number based on a diameter is 360. The results show that the discrete variation of the frequency along the span is caused by cell-like structure accompanied by vortex linking. Formations of vortex street, both in-phase and anti-phase, and vortex interactions with frequency jittering and phase shifting are analyzed and discussed.
[GM.008] Variational Principle for V-states
E.G. Evstatiev, P.J. Morrison (University of Texas at Austin)
The two-dimensional Euler equation governs the evolution of special finite regions of uniformly distributed vorticity called V-states. The conserved energy of that system serves as a Hamiltonian functional depending on the stream function, from which an equation of motion for the boundary of the V-state is obtained. In our approach, we approximate the stream function of a system by a trial stream function containing a certain number of parameters, and with its help construct an approximate Hamiltonian. Upon variation of the Hamiltonian with respect to the parameters of the trial stream function, we determine the time evolution of the V-state. In this way we find approximate, as well as exact (Kirchoff's ellipse), solutions to the two-dimensional Euler equation. We examine some properties of these solutions and, in particular, establish a relation between the rate of rotation of a V-state and the single parameter (aspect ratio) which determines its geometrical shape. We also establish the existence of critical V-states, previously a numerically known fact.