Meandering dynamics of streamwise vortex pairs in afterbody wakes (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.
Three-dimensional vorticity patterns of cylinder wakes
Experiments in Fluids, 2009
The vortex organization of cylinder wakes is experimentally studied by time-resolved tomographic Particle Image Velocimetry at Reynolds numbers ranging from 180 to 5,540. Time resolved measurements are performed at Re = 180, 360 and 540, whereas the transitional (Re = 1,080) and turbulent regimes (Re = 5,540) are investigated by snapshots separated in phase by more than p/4. The vortex structure evolution is visualized by the 3D vorticity field, revealing a regular shedding at the lowest Reynolds, whereas at Re [ 500 the Bénard-Kármán vortex street exhibits counter-rotating stream-wise vortex pairs (characteristic of Mode B) dominating the 3D motion. The regime at Re = 360 produces a transitional pattern where the counter-rotating vortex pairs (Mode B), coexist with profoundly distorted shedding of oblique elements forming a chain of rhombus-like vortex cells. In the turbulent flow regime (Re = 5,540) a large increase in the range of flow scales is directly observed with the appearance of Kelvin-Helmholtz type vortices in the separated shear layer consistently with what is abundantly reported in literature. The statistical description of the secondary structures is inferred from a 3D autocorrelation analysis yielding two span-wise wavelengths for the counter-rotating pairs, an inner length given by (twice) the distance between counter-rotating elements and an outer one given by the distance between pairs. The uncertainty analysis of the present tomographic PIV experiments reveals that this approach is suited for the investigation of vortex wakes with a typical error of 2 and 10% on the velocity and vorticity vectors, respectively.
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 .
Physics of Fluids, 2007
In this paper, we focus on the three-dimensional growth of the vortical structures behind two square cylinders when placed in a side-by-side arrangement and examine different possible modes of flow bifurcation along their spanwise extended corelines. For this, unsteady three-dimensional flow simulations are conducted with five different values of gap/diameter ratios ͑g * ͒, namely, 2.1, 1.7, 0.7, 0.5, and 0.2, that cover important known phases, i.e., coshedding ͑g * = 2.1 and 1.7͒, asymmetric ͑g * = 0.7 and 0.5͒, and single-body type ͑g * = 0.2͒ of wake evolution. In order to exploit flow physics within the transition range, the Reynolds number of the flow is taken as 100. Notably, for all the investigated cases, parallel vortex shedding has been observed behind the two cylinders. However, with the decrease of gap ratio g * , the downstream flow gradually lost stability and the corelines of the shedded vortices appeared in a wavy fashion. While for g * = 2.1 and 1.7, the simulated streamwise flows exhibit antiphase and in-phase synchronization of the wake, respectively, there is also observed a notable difference in the structural growth of corresponding spanwise flows. For the antiphase flow ͑at g * = 2.1͒ the downstream wake evolved through a symmetry-breaking mode-I Hopf bifurcation along various spanwise extended vortex corelines. However, the presence of an additional mode-II Hopf bifurcation was detected in the wake of an in-phase flow ͑at g * = 1.7͒. The development of a number of local pressure maxima over different spanwise extended vortex corelines, and the gradual decrease of pressure along their left and right, respectively, are noted to be responsible for initiating such flow bifurcations. In the biased ͑asymmetric͒ regime, with g * = 0.7 and 0.5, the flow behind the cylinders showed visible signs of growing instability and there occurred significant spanwise pressure fluctuations, which in turn inflicted large three dimensionality into the downstream wake and local velocity irregularities. The corresponding wake evolution patterns are thereby noted to exhibit predominantly unsteady and transitional features. In this biased flow regime, the gap flow flip-flopped randomly and became deflected alternately towards the top and bottom cylinders. On the one hand, clear dominance of both mode-I and mode-II flow bifurcations was observed with both of these initially locked biased flows. However, due to increased flow asymmetry the spanwise length scales of such bifurcations changed significantly. On the other hand, for the single-body regime flow with g * = 0.2, the occurrence of only mode-I bifurcation was detected in the wake of the cylinders.
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.
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.
Streamwise evolution of an inclined cylinder wake
Experiments in Fluids, 2011
The streamwise evolution of an inclined circular cylinder wake was investigated by measuring all three velocity and vorticity components using an eighthotwire vorticity probe in a wind tunnel at a Reynolds number Re d of 7,200 based on free stream velocity (U ?) and cylinder diameter (d). The measurements were conducted at four different inclination angles (a), namely 0°, 15°, 30°, and 45°and at three downstream locations, i.e., x/d = 10, 20, and 40 from the cylinder. At x/d = 10, the effects of a on the three coherent vorticity components are negligibly small for a B 15°. When a increases further to 45°, the maximum of coherent spanwise vorticity reduces by about 50%, while that of the streamwise vorticity increases by about 70%. Similar results are found at x/d = 20, indicating the impaired spanwise vortices and the enhancement of the three-dimensionality of the wake with increasing a. The streamwise decay rate of the coherent spanwise vorticity is smaller for a larger a. This is because the streamwise spacing between the spanwise vortices is bigger for a larger a, resulting in a weak interaction between the vortices and hence slower decaying rate in the streamwise direction. For all tested a, the coherent contribution to v 2 is remarkable at x/d = 10 and 20 and significantly larger than that to u 2 and w 2 : This contribution to all three Reynolds normal stresses becomes negligibly small at x/d = 40. The coherent contribution to u 2 and v 2 decays slower as moving downstream for a larger a, consistent with the slow decay of the coherent spanwise vorticity for a larger a.
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.
Longitudinal vortex structures in a cylinder wake
Physics of Fluids, 1994
This paper presents the velocity field of the longitudinal vortices found in the wake of a circular cylinder, as measured using digital particle image velocimetry (PIV). Vorticity and circulation of the longitudinal vortices are presented, based on instantaneous velocity distributions in a transverse plane behind the cylinder. Recently, flow visualizations by Wei and Smith,' Williamson,' Welsh et a1.,3 and Bays-Muchmore and Ahmed4 have shown that three-dimensional (3-D) vertical structures develop in the wake of a bluff body. The 3-D vertical structures were found to include pairs of counterrotating longitudinal vortices superimposed on the nominally two-dimensional (2-D) Kirmin vortex street as speculated