Decay of Far-Flowfield in Trailing Vortices

Baldwin, B. S.; Chigiex, N.A.; Sheaffer, Y. S.

doi:10.2514/3.50654

Cited by 8 publications

(3 citation statements)

References 5 publications

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“…Decay then begins, the peak tangential velocity falling as the inverse square root of streamwise distance. Iversen attributes this behaviour to the action of a non-equilibrium turbulence structure, on the basis of earlier turbulence model calculations by Donaldson (1972) and Baldwin, Chigier & Sheaffer (1973). However, because of the large streamwise distance before decay begins, interaction between the vortices also seems a strong possibility.…”

Section: Introductionmentioning

confidence: 95%

The structure and development of a counter-rotating wing-tip vortex pair

1997

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Experiments have been performed to examine the turbulence structure and development of a pair of counter-rotating wing-tip vortices. The vortices were generated by two rectangular NACA 0012 half wings placed tip to tip, separated by 0.25 chordlengths. Preliminary studies showed the vortices to be insensitive to the introduction of a probe and subject only to small wandering motions. Meaningful measurements could therefore be made using hot-wire probes. Three-component velocity measurements were made 10 and 30 chordlengths downstream of the wing leading edges for a chord Reynolds number of 260000.At 10 chordlengths the vortex cores are laminar. True turbulence levels within them are low and vary little with radius. The turbulence that surrounds the cores is formed by the roll-up of and interaction of the wing wakes that spiral around them. This turbulence is stretched and organized but apparently not produced by the circulating mean velocity fields of the vortices.At 30 chordlengths the vortex cores have become turbulent. True turbulence levels within them are larger and increase rapidly with radius. The turbulent region surrounding the cores has doubled in size and turbulence levels have not diminished, apparently being sustained by outward diffusion from the core regions. The distribution of the turbulence has also changed, the wake spirals having been replaced by a much more core-centred turbulence field.This change in flow structure contrasts sharply with what is seen in the equivalent isolated tip vortex, produced when one of the wings is removed. Here the vortex core remains laminar and the turbulence surrounding it decays rapidly with downstream distance. This implies that the transition to turbulence in the cores of the vortex pair is stimulated by interaction between the vortices. Spectral measurements at 10 chordlengths suggest that short-wave instability may be the cause.

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Section: Introductionmentioning

confidence: 95%

The structure and development of a counter-rotating wing-tip vortex pair

1997

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“…It is significant, however, that despite increasing turbulence intensity, the equilibrium level was not reached within the lifespan of the vortex, since this would have resulted in a final dependence as t~1 /2 . Using the appropriate equations given in the papers of Baldwin et al 18 and Donaldson, 12 the equilibrium eddy-viscosity level was estimated to be (v r /v) equ « 150.…”

Section: Resultsmentioning

confidence: 99%

“…We are thus dealing with a nonequilibrium flow in which the nonequilibrium is constituted by the imbalance between turbulence production and dissipation. In the work of Baldwin et al, 18 for instance, nonequilibrium conditions were taken into account in order to calculate the downstream decay of turbulent trailing vortices. Significantly, the initial levels of turbulence used in these computations were comparable in their magnitude to values that are known from flight and wind-tunnel tests, and were considerably larger than those that can be sustained by a vortex flow.…”

Section: Effect Of Turbulent Viscosity On Vortex Decay Theoretical Comentioning

confidence: 99%

Water Tank Study of the Decay of Trailing Vortices

Lezius

1974

AIAA Journal

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Underwater towing experiments were carried out with a rectangular airfoil of aspect ratio 5.3 at 4° and 8°a ngles of attack and at chord-based Reynolds numbers between 2.2 x 10 5 and 7.5 x 10 5 . Tangential velocity measurements in the downstream region between 100 and 1000 chord lengths indicate rates of vortex decay proportional to r 7/8 at 8°, whereas previous flight tests show that the decay rate approaches £~1 /2 far downstream. The observed behavior is explained in terms of an analytical solution that includes time dependence of the turbulent eddy viscosity, V T ~ t m . It shows that, for m > 0, an isolated turbulent vortex decays faster than t~1 /2 . In this case, the decay is accompanied by increasing v r , or levels of turbulence, which corresponds to turbulent nonequilibrium flow. The special case of vortex decay with equilibrium flow (m = 0) leads to the well-known decay rate 2 . Since, in towing tank experiments at low Reynolds number, turbulent vortex decay may occur predominantly in nonequilibrium, it is doubtful that such tests correctly predict the late stage of decay of aircraft trailing vortices, when turbulence is the only dissipating mechanism. Nomenclaturea = core radius b = wing span c -wing chord AH = head loss in boundary layer p = pressure p m = fluid pressure as r -> oo p(0) = pressure on the vortex axis r = radius measured from vortex axis t = time At = time difference in velocity measurement T = time parameter, T -F^ t/c 2 U ^ -towing speed v = tangential velocity component v a = tangential velocity at r = a w = axial velocity component vv 0 = axial velocity on vortex axis z = downstream distance behind airfoil ex = angle of attack /? = constant of proportionality, Eq. (6) F = circulation F a = circulation at core radius F^ = circulation of wing 0, A0 = angle in velocity measurement v = kinematic viscosity V T = eddy viscosity (v T /v) a = eddy viscosity at core radius p = fluid density Superscripts m = exponent in expression for time-dependent V T , Eq. (7)Subscripts a = conditions at the core radius, r = a v e = effective viscosity (v T /v) 0 = eddy viscosity level after rollup 0 = conditions on the vortex axis, r -0 oo = conditions at r = GO

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Asymptotic behavior of the far region of turbulent wake vortices

Lugovtsov¹

1999

J Appl Mech Tech Phys

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Introduction. The problem of wake vortices has become especially pressing with the appearance of heavy airplane, behind which intense vortex lines extend over several kilometers and are a serious hazard to small airplanes falling in the region of these vortices [1].In this connection, it is.of interest to study the far region in a vortex wake, i.e., the region where the ordinary momentum-free wake (the drag force is compensated by the engine thrust) is no longer significant and, at the same time, the phenomena caused by the instability and breakup of a vortex pair into structures such as vortex rings, etc., are not yet manifested.Experimental studies and theoretical descriptions of this phenomenon involve solving complex problems of the dynamics of concentrated vortices. Under laboratory conditions, measurements in the far region are impossible because of the limited dimensions of experimental installations and the significant effect of the wake due to the body drag (under real conditions, it is compensated by engine operation). Full-scale experiments are technically difficult and axe complicated by many additional factors: atmospheric turbulence, wind, stratification of the atmosphere, etc. These circumstances lead to a wide spread of measurement results and, in some cases, to contradictory results.Under real conditions, the motion in such vortices is turbulent, as confirmed in experiments. The lack of a reliable, serviceable mathematical model for describing turbulent fluid flow hinders the development of an adequate mathematical model and a fairly comprehensive theoretical description of this phenomenon.The complexity of the problem is responsible for the considerable simplifications used in analytical studies. In a number of papers, one vortex line is considered, the flow in its vicinity is considered axisymmetric, and the effect of the second vortex line is ignored [2, 3]. This approach is justified on the initial segment after roll-up of the vortex wake shed from the wing (lifting surface) and as long as the variation in the total circulation due to turbulent diffusion of vorticity is negligible. It is clear that at a certain distance, the

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Decay of Far-Flowfield in Trailing Vortices

Cited by 8 publications

References 5 publications

The structure and development of a counter-rotating wing-tip vortex pair

The structure and development of a counter-rotating wing-tip vortex pair

Water Tank Study of the Decay of Trailing Vortices

Asymptotic behavior of the far region of turbulent wake vortices

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