Airplane trailing vortices and their control

Crouch, J. D.

doi:10.1016/j.crhy.2005.05.006

Cited by 35 publications

(16 citation statements)

References 24 publications

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“…During the formation and evolution of the wake vortices, it is also possible to take into account the image vortices, linked to the presence of the wall and symmetrically located with respect to it. The near wake vortex pair and its image form a symmetric four-vortex system, a configuration analyzed previously in the context of aircraft trailing wakes (e.g., Crouch 2005;Winckelmans et al 2005;Jacquin et al 2005). The existence of short-wave (elliptic) and Crow-type long-wave instabilities was also found in these systems.…”

Section: Stability Of the Fully Developed 2d Periodic Wakementioning

confidence: 87%

Two- and three-dimensional wake transitions of an impulsively started uniformly rolling circular cylinder

et al. 2017

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This paper presents the characteristics of the different stages in the evolution of the wake of a circular cylinder rolling without slipping along a wall at constant speed, acquired through numerical stability analysis and two-and three-dimensional numerical simulations. Reynolds numbers between 30 and 300 are considered. Of importance in this study is the transition to three-dimensionality from the underlying two-dimensional periodic flow and, in particular, the way that the associated transitions influence the fluid forces exerted on the cylinder, and the development and the structure of the wake. It is found that the steady two-dimensional flow becomes unstable to threedimensional perturbations at Re c,3D = 37, and that the transition to unsteady twodimensional flow -or periodic vortex shedding -occurs at Re c,2D = 88, thus validating and refining the results of Stewart et al. (2010). The main focus here is for Reynolds numbers beyond the transition to unsteady flow at Re c,2D = 88. From impulsive start up, the wake almost immediately undergoes transition to a periodic two-dimensional wake state, which, in turn, is three-dimensionally unstable. Thus, the previous threedimensional stability analysis based on the two-dimensional steady flow provides only an element of the full story. Floquet analysis based on the periodic two-dimensional flow was undertaken and new three-dimensional instability modes were revealed. The results suggest that an impulsively started cylinder rolling along a surface at constant velocity for Re 90 will result in the rapid development of a periodic two-dimensional wake that will be maintained for a considerable time prior to the wake undergoing threedimensional transition. Of interest, the mean lift and drag coefficients obtained from full three-dimensional simulations match predictions from two-dimensional simulations to within a few percent.

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Section: Stability Of the Fully Developed 2d Periodic Wakementioning

confidence: 87%

Two- and three-dimensional wake transitions of an impulsively started uniformly rolling circular cylinder

et al. 2017

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“…With the help of stability theory, the underlying physical mechanisms of these innovative, albeit intuitive strategies can be further understood and potentially be harnessed for effective flow manipulation. Crouch (2005) summarizes recent control efforts that either excite three-dimensional instabilities using some form of active control or attempt to alter the structure of the vortices or the vortex wake. Our physics-based approach based on a parabolized stability analysis falls into the first category.…”

Section: Introductionmentioning

confidence: 99%

Active attenuation of a trailing vortex inspired by a parabolized stability analysis

Edstrand¹,

Sun²,

Schmid³

et al. 2018

J. Fluid Mech.

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Designing effective control for complex three-dimensional flow fields proves to be nontrivial. Oftentimes, intuitive control strategies lead to suboptimal control. To navigate the control space, we utilize a linear parabolized stability analysis to guide the design of a control scheme for a trailing vortex flow field aft of a NACA0012 half-wing at an angle of attack α = 5 • and a chord-based Reynolds number Re = 1000. The stability results show that the unstable mode with the smallest growth rate (fifth wake mode) provides a pathway to excite a vortex instability, whereas the principal unstable mode remains in the wake of the wing. Inspired by this finding, we perform direct numerical simulations that excite each mode with body forces matching the shape function from the stability analysis. Relative to the baseline uncontrolled case, the principal wake mode reduces the vortex length, while the fifth wake mode further shortens the tip vortex. Analogously, the streamwise circulation of the trailing vortex is found to be significantly reduced. From these results, we conclude that a rudimentary linear stability analysis can provide key insight into the underlying physics and help engineers design more effective control.

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“…In the near field, the trailing vortex sheet quickly rolls up and detaches from the wing tips and outer flap tips to form a set of discrete co-rotating vortices on each semi-span, which subsequently merge and form a pair of counter-rotating vortices downstream of the wing over a distance of 5-10 wing spans (Meunier, Le Dizès & Leweke 2005). These vortex systems may persist over long times before finally diffusing, and can impose potentially dangerous rolling moments on any following aircraft that encounters them (Crouch 2005). Airport safety regulations impose additional delays between aircraft movements in order to mitigate such events, and much of the motivation for studying dynamics and stability of trailing vortex wake systems stems from desire to increase airport utilization factors, especially for large aircraft.…”

Section: Introductionmentioning

confidence: 99%

Non-normal dynamics of time-evolving co-rotating vortex pairs

2012

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Transient energy growth of disturbances to co-rotating pairs of vortices with axial core flows is investigated in an analysis where vortex core expansion and vortex merging are included by adopting a time-evolving base flow. The dynamics of pairs are compared with those of individual vortices in order to highlight the effect of vortex interaction. Three typical vortex pair cases are studied, with the pairs comprised respectively of individually inviscidly unstable vortices at the streamwise wavenumber that maximizes the individual instabilities, viscously unstable vortices also at the streamwise wavenumber maximizing the individual instabilities and asymptotically stable vortices at streamwise wavenumber zero. For the inviscidly unstable case, the optimal perturbation takes the form of a superposition of two individual helical unstable modes and the optimal energy growth is similar to that predicted for an individual inviscid unstable vortex, while where the individual vortices are viscously unstable, the optimal disturbances within each core have similar spatial distributions to the individually stable case. For both of these cases, time horizons considered are much lower than those required for the merger of the undisturbed vortices. However, for the asymptotically stable case, large linear transient energy growth of optimal perturbations occurs for time horizons corresponding to vortex merging. Linear transient disturbance energy growth exhibited by pairs in this stable case is two to three orders of magnitude larger than that for a corresponding individual vortex. The superposition of the perturbation and the base flow shows that the perturbation has a displacement effect on the vortices in the base flow. Direct numerical simulations of stable pairs seeded by optimal initial perturbations have been carried out and acceleration/delay of vortex merging associated with a dual vortex meandering and vortex breakup related to axially periodic acceleration and delay of vortex merging are observed. For axially invariant cases, the sign of perturbation has an effect, as well as magnitude; the sign dependence relates to whether or not the perturbation adds to or subtracts from the swirl of the base flow. For a two-dimensional perturbation that adds to the swirl of the base flow, seeding with the linear optimal disturbance at a relative energy level $1\ensuremath{\times} 1{0}^{\ensuremath{-} 4} $ induces the pair to move towards each other and approximately halves the time required for merger. Direct numerical simulation shows that the optimal three-dimensional perturbation can induce the vortex system to break up before merging occurs, since the two-dimensional nature of vortex merging is broken by the development of axially periodic perturbations.

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Airplane trailing vortices and their control

Cited by 35 publications

References 24 publications

Two- and three-dimensional wake transitions of an impulsively started uniformly rolling circular cylinder

Two- and three-dimensional wake transitions of an impulsively started uniformly rolling circular cylinder

Active attenuation of a trailing vortex inspired by a parabolized stability analysis

Non-normal dynamics of time-evolving co-rotating vortex pairs

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