Stability and Control of Spiral Vortex Breakdown

Journal of Fluid Mechanics, 2010

Physica D-nonlinear Phenomena, 2008

A simple -yet plausible -model for B-type vortex breakdown flows is postulated; one that is based on the immersion of a pair of slender coaxial vortex rings in a swirling flow of an ideal fluid rotating around the axis of symmetry of the rings. It is shown that this model exhibits in the advection of passive fluid particles (kinematics) just about all of the characteristics that have been observed in what is now a substantial body of published research on the phenomenon of vortex breakdown. Moreover, it is demonstrated how the very nature of the fluid dynamics in axisymmetric breakdown flows can be predicted and controlled by the choice of the initial ring configurations and their vortex strengths. The dynamic intricacies produced by the two ring + swirl model are illustrated with several numerical experiments.

Physics of Fluids, 2009

2000

Received: date / Accepted: date Abstract This work is focused to study the development and control of the laminar vortex breakdown of a flow en- closed in a cylinder. We show that vortex breakdown can be controlled by the introduction of a small fixed rod in the axis of the cylinder. Our method to control the onset of vortex breakdown

2001

The aim of this work is to identify current developments in the field of vortex breakdown modelling in order to initiate the development of a numerical model for the simulation of F/A-18 empennage buffet. Some attempts at using vortex models for prediction of vortex breakdown were found in the open literature. Their advantages and shortcomings are discussed, allowing the evaluation of their feasibility for the computation of LEX vortex burst. It was concluded that vortex methods are able to simulate an onset of breakdown in simple vortical flows. However, their predictive abilities require further improvement to provide accurate modelling of the temporal and spatial characteristics of the unsteady pressure field past a burst LEX vortex.

Journal of Fluid Mechanics, 2008

Vortex breakdown is a phenomenon inherent to many practical problems, such as leading-edge vortices on aircraft, atmospheric tornadoes, and flame-holders in combustion devices. The breakdown of these vortices is associated with the stagnation of the axial velocity on the vortex axis and the development of a near-axis recirculation zone. For large enough Reynolds number, the breakdown can be time-dependent. The unsteadiness can have serious consequences in some applications, such as tail-buffeting in aircraft flying at high angles of attack. There has been much interest in controlling the vortex breakdown phenomenon, but most efforts have focused on either shifting the threshold for the onset of steady breakdown or altering the spatial location of the recirculation zone. There has been much less attention paid to the problem of controlling unsteady vortex breakdown. Here we present results from a combined experimental and numerical investigation of vortex breakdown in an enclosed cyl...

Fluid Dynamics Conference, 1995

A mathematical model of vortex breakdown is developed for a free cylindrical vortex of radius "a" that passes through a region of non-cylindrid flow and regains the cylindrical flow structure of radius "b" downstream. The criterion of zero axial velocity within the free vortex, dowmtmm, yields a relationship between the radius ratio bla and the

Journal of Fluid Mechanics, 1994

Weakly nonlinear descriptions of axisymmetric cnoidal and solitary waves in vortices recently have been shown to have strongly nonlinear counterparts. The linear stability of these strongly nonlinear waves to three-dimensional perturbations is studied, motivated by the problem of vortex breakdown in open flows. The basic axisymmetric flow varies both radially and axially, and the linear stability problem is therefore nonseparable. To regularize the generalization of a critical layer, viscosity is introduced in the perturbation problem. In the absence of the waves, the vortex flows are linearly stable. As the amplitude of a wave constituting the basic flow increases owing to variation in the level of swirl, stability is first lost to non-axisymmetric 'bending' modes. This instability occurs when the wave amplitude exceeds a critical value, provided that the Reynolds number is larger enough. The critical wave amplitudes for instability typically are large, but not large enough to create regions of closed streamlines. Examination of the most-amplified eigenvectors shows that the perturbations tend to be concentrated downstream of the maximum streamline displacement in the wave, in a position consistent with the observed three-dimensional perturbations in the interior of a bubble type of vortex breakdown.

Journal of Fluid Mechanics, 2006

This paper is motivated by an observation: in the nascent state of vortex breakdown before it develops into a full-grown radial expansion, an initially straight vortex core first swells, and does so even in a straight pipe for no apparent reason. Although this initial swelling may be explained in many ways according to the perspectives chosen, we offer our own interpretation framed solely within vorticity dynamics: the radial swelling as well as the subsequent growth are induced by the azimuthal vorticity gradient decreasing downstream. The negative azimuthal vorticity gradient first appears at start-up and moves eventually into the region where the circulation reaches its steady-state value. The vorticity gradient can become negative without necessarily being accompanied by a sign-switch of the azimuthal vorticity itself. The key point-that the negative azimuthal vorticity gradient induces initial radial swelling and its growth-is demonstrated in two analyses. First, a kinematic analysis results in an equation for the radial velocity where the azimuthal vorticity gradient appears as a source term. Its solution shows, in general and explicitly, that the negative azimuthal vorticity gradient does induce radially outward velocity. Two heuristic examples serve to illustrate this point further. In the second analysis, using the equation of motion in the streamline coordinates, the negative azimuthal vorticity gradient is shown to diverge the meridional streamlines radially. A numerical simulation using a modified vortex filament method not only corroborates this role of the azimuthal vorticity gradient in initiating and promoting the radial expansion, but also adds details to track the formation process. Both analyses and simulation support our interpretation that the initial radial swelling and its subsequent growth are induced by the negative azimuthal vorticity gradient.

A method for predicting the outcome of vortex breakup in a rotating flow is introduced. The vortices dealt with here are subject to both centrifugal and barotropic instabilities. The prediction of the aftermath of the breakup relies on knowing how both centrifugal and barotropic instabilities would equilibrate separately. A theoretical model for non-linear equilibration in centrifugal instability is wedded to two-dimensional simulation of barotropic instability to predict the final vortices that emerge from the debris of the original vortex. This prediction method is tested against three-dimensional Navier-Stokes simulations. For vortices in which a rapid centrifugal instability triggers a slower barotropic instability, the method is successful both qualitatively and quantitatively. The skill of the prediction method decreases as the time scales of the two instabilities become comparable.