scholarly journals Short-wave instabilities on a vortex pair of unequal strength circulation ratio

2011 ◽  
Vol 35 (4) ◽  
pp. 1581-1590 ◽  
Author(s):  
Joine So ◽  
Kris Ryan ◽  
Gregory J. Sheard
Keyword(s):  
Vortex Pair ◽  
Short Wave ◽  
Circulation Ratio ◽  
Wave Instabilities

Flow/Acoustic Mechanisms in Three-Dimensional Vortices Undergoing Sinusoidal-Wave Instabilities

2007 ◽  
Author(s):  
Wenhua Li ◽  
Z. C. Zheng ◽  
Ying Xu
Keyword(s):  
Flow Field ◽  
Three Dimensional ◽  
Vortex Pair ◽  
Particle Method ◽  
Acoustic Signals ◽  
Short Wave ◽  
Vortical Flow ◽  
Vortex Particle Method ◽  
Structure Changes ◽  
Wave Instabilities

It has been identified that vorticity in a vortex core directly relates to the frequency of a significant sound peak from an aircraft wake vortex pair where each of the vortices is modeled as an elliptic core Kirchhoff vortex. In three-dimensional vortices, sinusoidal instabilities at various length scales result in significant flow structure changes in these vortices, and thus influence their radiated acoustic signals. In this study, a three-dimensional vortex particle method is used to simulate the incompressible vortical flow. The flow field, in the form of vorticity, is employed as the source in the far-field acoustic calculation using a vortex sound formula that enables computation of acoustic signals radiated from an approximated incompressible flow field. Cases of vortex rings and a pair of counter-rotating vortices are studied when they are undergoing both long- and short-wave instabilities. Both inviscid and viscous interactions are considered and effects of turbulence are simulated using sub-grid-scale models.

Stability characteristics of a counter-rotating unequal-strength Batchelor vortex pair

2012 ◽  
Vol 696 ◽  
pp. 374-401 ◽  
Author(s):  
Kris Ryan ◽  
Christopher J. Butler ◽  
Gregory J. Sheard
Keyword(s):  
Stokes Equations ◽  
Vortex Pair ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Mode Amplitude ◽  
Nonlinear Growth ◽  
Circulation Ratio ◽  
Secondary Stage ◽  
Aircraft Wake ◽  
Crow Instability

AbstractA Batchelor vortex represents the asymptotic solution of a trailing vortex in an aircraft wake. In this study, an unequal-strength, counter-rotating Batchelor vortex pair is employed as a model of the wake emanating from one side of an aircraft wing; this model is a direct extension of several prior investigations that have considered unequal-strength Lamb–Oseen vortices as representations of the aircraft wake problem. Both solution of the linearized Navier–Stokes equations and direct numerical simulations are employed to study the linear and nonlinear development of a vortex pair with a circulation ratio of$\Lambda = \ensuremath{-} 0. 5$. In contrast to prior investigations considering a Lamb–Oseen vortex pair, we note strong growth of the Kelvin mode$[\ensuremath{-} 2, 0] $coupled with an almost equal growth rate of the Crow instability. Three stages of nonlinear instability development are defined. In the initial stage, the Kelvin mode amplitude becomes sufficiently large that oscillations within the core of the weaker vortex are easily observable and significantly affect the profile of the weaker vortex. In the secondary stage, filaments of secondary vorticity emanate from the weaker vortex and are convected around the stronger vortex. In the tertiary stage, a transition in the dominant instability wavelength is observed from the short-wavelength Kelvin mode to the longer-wavelength Crow instability. Much of the instability growth is observed on the weaker vortex of the pair, although small perturbations in the stronger vortex are observed in the tertiary nonlinear growth phase.

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

2003 ◽  
Vol 474 ◽  
pp. 35-84 ◽  
Author(s):  
J. M. ORTEGA ◽  
R. L. BRISTOL ◽  
Ö. SAVAŞ
Keyword(s):  
Three Dimensional ◽  
Subsequent Development ◽  
Vortex Pair ◽  
Tip Vortex ◽  
Two Dimensional ◽  
Experimental Conditions ◽  
Vortex Pairs ◽  
Circulation Ratio ◽  
Counter Rotating Vortex Pair ◽  
Wing Tip

A rapidly growing instability is observed to develop between unequal-strength counter- rotating 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 chord- based and circulation-based Reynolds numbers are of O(105). 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.

scholarly journals Long- and short-wave instabilities in helical vortices

2014 ◽  
Vol 524 ◽  
pp. 012154 ◽  
Author(s):  
T Leweke ◽  
H U Quaranta ◽  
H Bolnot ◽  
F J Blanco-Rodríguez ◽  
S Le Dizès
Keyword(s):  
Short Wave ◽  
Helical Vortices ◽  
Wave Instabilities

The observation of the simultaneous development of a long- and a short-wave instability mode on a vortex pair

1994 ◽  
Vol 265 ◽  
pp. 289-302 ◽  
Author(s):  
P. J. Thomas ◽  
D. Auerbach
Keyword(s):  
Vortex Pair ◽  
Short Wave ◽  
Wave Mode ◽  
Core Diameter ◽  
Vortex Pairs ◽  
Long Wave ◽  
Instability Modes ◽  
Bending Mode ◽  
Theoretical Predictions ◽  
The Stability

Experiments on the stability of vortex pairs are described. The vortices (ratio of length to core diameter L/c of up to 300) were generated at the edge of a flat plate rotating about a horizontal axis in water. The vortex pairs were found to be unstable, displaying two distinct modes of instability. For the first time, as far as it is known to the authors, a long-wave as well as a short-wave mode of instability were observed to develop simultaneously on such a vortex pair. Experiments involving single vortices show that these do not develop any instability whatsoever. The wavelengths of the developing instability modes on the investigated vortex pairs are compared to theoretical predictions. Observed long wavelengths are in good agreement with the classic symmetric long-wave bending mode identified by Crow (1970). The developing short waves, on the other hand, appear to be less accurately described by the theoretical results predicted, for example, by Windnall, Bliss & Tsai (1974).

A Visual Study of Vortex Instabilities in the Wake of a Rotor in Hover

2012 ◽  
Vol 57 (4) ◽  
pp. 1-8 ◽  
Author(s):  
Christopher V. Ohanian ◽  
Gregory J. McCauley ◽  
Ömer Savaş
Keyword(s):  
Growth Rate ◽  
Exponential Growth ◽  
Linear Growth ◽  
Short Wave ◽  
Linear Growth Rate ◽  
Water Tank ◽  
Vortex Filaments ◽  
Visual Study ◽  
Helical Vortex ◽  
Wave Instabilities

A visual study of the instability characteristics of the helical vortex filaments trailing from the tips of a three-bladed lifting rotor in a water tank is presented. The rotor diameter was 25.4 cm, and its rotation rate ranged from 4 to 12 revolutions per second. Soon after their formation, the vortex filaments developed long- and short-wave instabilities. In the long-wave instability mode, two of the three vortices coming off the rotor orbited around each other and merged in about 0.4 of the theoretical orbit time of equistrength two-dimensional vortices, after which the third vortex joined the merger to form a single, apparently turbulent helical vortex filament. The wavelengths of the short-wave instabilities were about 0.4 of the wake radius, about 17 cycles over the circumference. The short waves exhibited a linear growth rate during the first half of their orbital motion and an exponential growth prior to merging. The linear growth rate was about 0.0034 D/rad. The e-folding time for the exponential growth rate was about 0.52 rad.

The instability of short waves on a vortex ring

1974 ◽  
Vol 66 (1) ◽  
pp. 35-47 ◽  
Author(s):  
Sheila E. Widnall ◽  
Donald B. Bliss ◽  
Chon-Yin Tsai
Keyword(s):  
Vortex Ring ◽  
Vortex Pair ◽  
Short Wave ◽  
The Self ◽  
Core Size ◽  
The Core ◽  
Bending Waves ◽  
Bending Mode ◽  
Radial Structure ◽  
Bending Modes

A simple model for the experimentally observed instability of the vortex ring to azimuthal bending waves of wavelength comparable with the core size is presented. Short-wave instabilities are discussed for both the vortex ring and the vortex pair. Instability for both the ring and the pair is predicted to occur whenever the self-induced rotation of waves on the filament passes through zero. Although this does not occur for the first radial bending mode of a vortex filament, it is shown to be possible for bending modes with a more complex radial structure with at least one node at some radius within the core. The previous work of Widnall & Sullivan (1973) is discussed and their experimental results are compared with the predictions of the analysis presented here.

scholarly journals Spatio-temporal development of the long and short-wave vortex-pair instabilities

2000 ◽  
Vol 12 (5) ◽  
pp. 1247-1250 ◽  
Author(s):  
David Fabre ◽  
Carlo Cossu ◽  
Laurent Jacquin
Keyword(s):  
Vortex Pair ◽  
Short Wave ◽  
Temporal Development ◽  
Spatio Temporal
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