Exotic vortex wakes—point vortex solutions (original) (raw)

Theoretical and numerical analysis of wake vortices

ESAIM: Proceedings, 1999

The first part of the paper analyses the linear dynamics of a vortex pair thanks to a normal mode analysis. The basic flow is a superposition of two Lamb-Oseen vortices of radius a and distance b. The long-wave Crow instability and the short-wave Widnall instabilities are fully characterized for different aspect ratios a/b of the vortex pair. In particular, as a/b increases, it is shown that the antisymmetric Widnall instabilities are favoured for short-wave perturbations. This constitutes an explanation for the results obtained by . The second part of the paper deals with turbulence in the Batchelor vortex. A 3D Large Eddy Simulation (LES) shows that, starting from a linearly unstable wake-type vortex, high levels of turbulence can be obtained. But, the mean-flow then rapidly evolves towards a stable state. These results are in accordance with those of .

A mathematical model of 2P and 2C vortex wakes

Journal of Fluids and Structures, 2011

We present a mathematical model of the vortex wake modes that appear behind neighboring and/or oscillating, flapping, and swimming bodies in which there are four vortices generated in an anti-symmetric pattern during each shedding cycle. The twodimensional potential flow model consists of four point vortices with strengths 7 G in a spatially periodic domain. The relative vortex positions are restricted by a discrete symmetry that is motivated by the spatial symmetry observed in experimental wakes. The strength restriction and the imposed symmetry result in the model system being an integrable Hamiltonian dynamical system. We find that the point vortex motion can be one of four distinct types based on the values of linear impulse and Hamiltonian. Two of these types correspond to 2P wakes and consist of two oppositely signed, counterrotating vortex pairs. One of these types corresponds to 2C wakes and consists of two like-signed, co-rotating vortex pairs. The fourth type is an exchanging mode in which the two vortices near the wake centerline translate faster than the outer two vortices. Scaled comparisons of the model with both a 2P and a 2C experimental wake show good representation of the experimentally observed vortex dynamics and lead to estimates of the experimental vortex strengths.

2004 - On instability characteristics of isolated vortices and models of trailing-vortex systems

This paper demonstrates the applicability of a two-dimensional eigenvalue problem approach to the study of linear instability of analytically constructed and numerically calculated models of trailing-vortex systems. Chebyshev collocation is used in the 2D eigenvalue problem solution in order to discretize two spatial directions on which non-axisymmetric vorticity distributions are defined, while the third, axial spatial direction is taken to be homogeneous and is resolved by a Fourier expansion. The leading eigenvalues of the matrix discretizing the equations which govern small-amplitude perturbations superimposed upon such a vorticity distribution are obtained by Arnoldi iteration. The present approach has been validated by comparison of its results on the problem of instability of an isolated Batchelor vortex. Here benchmark computations exist, employing classic instability analysis, in which the azimuthal direction is also treated as homogeneous. Subsequently, the proposed methodology has been shown to be able to recover the classic long-(Crow) and short-wavelength instabilities of a counter-rotating vortex-pair basic flow obtained by direct numerical simulation. Finally, the effect on the eigenspectrum of the isolated Batchelor vortex is documented, when the basic flow consists of a linear superposition of such vortices. The modifications of the eigenspectrum of a single vortex point to the potential pitfalls of drawing conclusions on the instability characteristics of a trailing-vortex system by monitoring the constituent vortices in isolation.

Vortex Wakes of Conventional Aircraft

1975

X see Eq (5.48) a) circular frequency Q angular rate of rotation TABLE OF CONTENTS Introduction The Roll-Up of Trailed Vorticity 1.1 Point Vortex Computations of the Roll-Up Phenomenon 1.2 The Methods of Prandtl and Betz 1.3 Comparison with Experimental Measurements Aircraft Wake Geometry 2.1 Lumped Vorticity and the Approximations Involved 2.2 The Wake Geometry of Multiple Pair Wakes Sinusoidal Instability and Vortex Breakdown 3.

BiGlobal and Point Vortex Methods for the Instability Analysis of Wakes

31st AIAA Applied Aerodynamics Conference, 2013

To better understand destruction mechanisms of wake-vortices behind aircraft, the point vortex method for stability (inviscid) used by Crow is here compared with viscous modal global stability analysis of the linearized Navier-Stokes equations acting on a two-dimensional basic flow, i.e. BiGlobal stability analysis. The fact that the BiGlobal method is viscous, and uses a flnite área vortex model, gives rise to results somewhat different from the point vortex model. It adds more parameters to the problem, but is more realistic. I. Introduction T HE problem of aircraft wakes and how long they last before some mechanism destroys them has been widely studied. The importance of the problem aróse a long time ago, with the appearance of the Boeing 747, and was again of importance when Airbus 380 carne into service. However, in the present days, not only the hazard due to such big aircraft is important, also, as the air trafñc increases, the air space becomes more and more saturated and it is of major importance to reduce the distances between aircraft to be able to increase the density of them in saturated air spaces. Consequently, the acceleration of the destruction of wake vórtices, although studied for a long time, is still an open problem. In the way to eliminate that hazard, the stability of the wake needs to be studied in depth as a previous stage, to be able to distinguish which configurations can last for longer and to understand the mechanism of its destruction. An isolated vortex is known to last for very long, but, in general, aircraft wake destruction mechanisms use to involve various vórtices, so this dissipation occurs faster. A very good example of that statement is the very well known Crow instability for a counter-rotating vortex pair. Crouch also found some other mechanisms of destruction that act faster for two vortex pairs as it will be the configuration of a plañe with deployed flaps. Following this line, many other studies can be found that analyze vortex interaction for wake destruction.

Absolute/Convective Instabilities and Spatial Growth in a Vortex Pair

Lecture Notes in Physics, 2000

Airplane trailing vortices have a destabilizing e ect on ensuing aircrafts. Security spacings, related to the trailing vortices \lifetime" are actually enforced between take-o s and landings. This spacing limits the maximum take-o and landing frequency in saturated airports 19]. A number of studies have been devoted to the understanding of vortex wake dynamics, usually modeled by a pair of counterrotating vortices. Two types of vortex pair three-dimensional instabilities have been identi ed in the past: a long-wave instability (of the order of the spacing b between the two vortices) and a short-wave instability (of the order of the vortex core radius a) have been rst considered respectively by Crow 4] and by Moore & Sa man 15] and Tsai & Widnall 20]. These two mechanisms, which are thought to participate in the vortex wake dissipation, have been observed in recent experiments 12]. One possible technique to accelerate the dissipation of aircraft wakes is to force these instabilities by on-board control devices 2,21,22]. Until now only temporal vortex pair instability analyses are available. If one wants to force these instabilities, however, it would be more appropriate to analyze their spatial stability in the airplane reference frame. As the spatial analysis makes sense only when the instabilities are convective, an absolute/convective stability analysis is required. The results presented consist of the absolute/convective and spatial stability analyses of both long{ and short{wave instabilities.

Experimental study of the instability of unequal-strength counter-rotating vortex pairs

Journal of Fluid Mechanics, 2003

A rapidly growing instability is observed to develop between unequal-strength counterrotating vortex pairs. The vortex pairs are generated in a towing tank in the wakes of wings with outboard triangular flaps. The vortices from the wing tip and the inboard tip of the flap form the counter-rotating vortex pair on each side of the wing. The flow fields are studied using flow visualization and particle image velocimetry. Both chordbased and circulation-based Reynolds numbers are of O(10 5). The circulation strength ratios of the flap-to tip-vortex pairs range from −0.4 to −0.7. The initial sinuous stage of the instability of the weaker flap vortex has a wavelength of order one wing span and becomes observable in about 15 wing spans downstream of the wing. The nearly straight vortex filaments first form loops around the stronger wing-tip vortices. The loops soon detach and form rings and move in the wake under self-induction. These vortex rings can move to the other side of the wake. The subsequent development of the instability makes the nearly quasi-steady and two-dimensional wakes unsteady and three-dimensional over a distance of 50 to 100 wing spans. A rectangular wing is also used to generate the classical wake vortex pair with the circulation ratio of −1.0, which serves as a reference flow. This counter-rotating vortex pair, under similar experimental conditions, takes over 200 spans to develop visible deformations. Velocity, vorticity and enstrophy measurements in a fixed plane, in conjuction with the flow observations, are used to quantify the behaviour of the vortex pairs. The vortices in a pair initially orbit around their vorticity centroid, which takes the pair out of the path of the wing. Once the three-dimensional interactions develop, two-dimensional kinetic energy and enstrophy drop, and enstrophy dispersion radius increases sharply. This rapid transformation of the wake into a highly three-dimensional one offers a possible way of alleviating the hazard posed by the vortex wake of transport aircraft.

2015 - On vortex filament methods for linear instability analysis of aircraft wakes

Linear stability analysis of vortical systems is discussed in a systematic manner using the classic inviscid vortex filament method. Well-known results are recovered as special cases of a unified linearization procedure. The symmetries of the vortex systems analyzed are exploited to obtain an analytical picture of different classes of growing and decaying eigenmodes. Finally, comparisons with viscous global linear theory reveal the limits of applicability of the vortex filament method for the instability analysis of realistic vortex systems.

Meandering dynamics of streamwise vortex pairs in afterbody wakes

2020

Wakes of upswept afterbodies are often characterized by a counter-rotating streamwise vortex pair. The unsteady dynamics of these vortices are examined with a spatiotemporally resolved Large-Eddy Simulation (LES) dataset on a representative configuration consisting of a cylinder with upswept basal surface. Emphasis is placed on understanding the meandering motion of the vortices in the pair, including vortex core displacement, spectral content, stability mechanisms and overall rank-behavior. The first two energy-ranked modes obtained through Proper orthogonal decomposition (POD) of the time-resolved vorticity field reveals a pair of vortex dipoles aligned relatively perpendicularly to each other. The dynamics is successfully mapped to a matched Batchelor vortex pair whose spatial and temporal stability analyses indicate similar dipole structures associated with an |m| = 1 elliptic mode pair. This short-wave elliptic instability dominates the meandering motion, with strain due to axi...