Theoretical and numerical analysis of wake vortices (original) (raw)
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Large-Eddy Simulations of Two Disturbed Counter-Rotating Vortex Pairs
Introduction In order to increase airport capacities whilst at least maintaining safety levels, the knowledge of wake vortex characterization and control achieves considerable significance. The possibility that constructive measures at the wings and flaps of aircraft may alleviate the strength of the shed vortices and result in their quicker decay is of utmost importance, especially when designing new very large aircraft. Recent numerical and experimental studies nourish the idea that a system of at least two co-or counterrotating vortex pairs is required across the symmetry line of the aircraft in the early mid field of the wake to favour the quick growth of unstable modes of the primary vortices [1]. Once sufficiently disturbed, the coherent vortices may decay quickly into incoherent turbulence in the late mid to early far field. In this study we investigate the temporal evolution of two counter-rotating and trailing vortex pairs which are subject to long-wave, short wave or random turbulence initial perturbations.
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.
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.
Wake-Vortex Topology, Circulation, and Turbulent Exchange Processes
AIAA Atmospheric and Space Environments Conference, 2010
Large eddy simulations (LES) of aircraft wake vortex evolution in various turbulent and stably stratified atmospheric environments have been conducted with two different LES codes. Passive tracers are used to investigate exchange processes between the vortex cores, the vortex oval and its environment as well as redistribution processes along the vortex tubes. A post processing method is employed to identify the vortex center lines even in progressed states of vortex decay where the coherent vortex structure is getting lost. This method allows, for example, analyzing the circulation evolution of vortex rings, establishing statistics of vortex deformation, and revealing the mechanisms of the vortex bursting phenomenon. Vortex bursting is related to the collision of secondary vorticity structures propagating along the vortex lines. In neutrally and weakly stratified environments long-living vortex rings are observed where circulation decay proceeds in three phases. During the initial diffusion phase vortex decay may depend on integral turbulence length scales. On average, the detrainment of a passive tracer from the primary vortices is correlated with circulation decay.
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.
Journal of Fluid Mechanics, 1998
The absolute/convective instability properties of the Batchelor vortex are determined by direct numerical simulation of the linear impulse response. A novel decomposition procedure is applied to the computed wavepacket in order to retrieve the complex wavenumber and frequency prevailing along each spatio-temporal ray. In particular, the absolute wavenumber and frequency observed in the laboratory frame are determined as a function of swirl parameter and external flow. The introduction of a moderate amount of swirl is found to strongly promote absolute instability. In the case of wakes, the transitional helical mode that first undergoes a switch-over to absolute instability is found to be m=−1 without requiring any external counterflow. In the case of jets, the transitional helical mode is very sensitive to swirl and varies in the range −5[les ]m[les ]−1. Only a slight amount of external counterflow (1.5% of centreline velocity) is then necessary to trigger absolute instability. The ...
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.