A canonical study is developed to investigate the unsteady interactions of a streamwise-oriented vortex impinging upon a finite surface using high-fidelity simulation. As a model problem, an analytically defined vortex superimposed on a free stream is convected towards an aspect-ratio-six ( ) plate oriented at an angle of and Reynolds number of in order to characterize the unsteady modes of interaction resulting from different spanwise positions of the incoming vortex. Outboard, tip-aligned and inboard positioning are shown to produce three distinct flow regimes: when the vortex is positioned outboard of, but in close proximity to, the wingtip, it pairs with the tip vortex to form a dipole that propels itself away from the plate through mutual induction, and also leads to an enhancement of the tip vortex. When the incoming vortex is aligned with the wingtip, the tip vortex is initially strengthened by the proximity of the incident vortex, but both structures attenuate into the wake as instabilities arise in the pair’s feeding sheets from the entrainment of opposite-signed vorticity into either structure. Finally, when the incident vortex is positioned inboard of the wingtip, the vortex bifurcates in the time-mean sense with portions convecting above and below the wing, and the tip vortex is mostly suppressed. The time-mean bifurcation is actually a result of an unsteady spiralling instability in the vortex core that reorients the vortex as it impacts the leading edge, pinches off, and alternately attaches to either side of the wing. The increased effective angle of attack inboard of impingement enhances the three-dimensional recirculation region created by the separated boundary layer off the leading edge which draws fluid from the incident vortex inboard and diminishes its impact on the outboard section of the wing. The slight but remaining downwash present outboard of impingement reduces the effective angle of attack in that region, resulting in a small separation bubble on either side of the wing in the time-mean solution, effectively unloading the tip outboard of impingement and suppressing the tip vortex. All incident vortex positions provide substantial increases in the wing’s lift-to-drag ratio; however, significant sustained rolling moments also result. As the vortex is brought inboard, the rolling moment diminishes and eventually switches sign as the reduced outboard loading balances the augmented sectional lift inboard of impingement.

Interactions of a streamwise-oriented vortex with a finite wing

This investigation addresses the impingement of the trailing vortex provided by a leader-wing upon a follower-wing operating in close proximity. Exploration of the relative spacing between the two wings reveals several distinct flow regimes occur within a small range of lateral positions of the incident vortex. These changes effectively alter the evolution of the follower-wing wake via mutual induction between the incident and trailing vortices. Several unsteady mechanisms impact the general flow field in each regime. The incident vortex for an inboard impingement rapidly decays over the wing due to transition to turbulence. A tip-aligned vortex results in a highly unsteady interaction and generates enhanced surface pressure fluctuations beneath the tip vortex. Placing the incident vortex outboard elicits mutual instability between the leader and follower-wing trailing vortices. While lift-enhancement was found to be dominated by an inviscid increase in effective angle of attack, viscous effects in the near-tip region alter the local surface force distribution and influence the rolling moment coefficient. These flow variations which occur over a small range of lateral positions could generate buffeting loads in the presence of a wandering streamwise vortex.

Analysis of streamwise-oriented vortex interactions for two wings in close proximity

Unsteady interactions of a wandering streamwise-oriented vortex with a wing

The interaction of meandering tip vortices shed from a leading wing with a downstream wing was investigated experimentally in a water tunnel using flow visualization, particle image velocimetry measurements, and volumetric velocity measurements. Counter-rotating upstream vortices may exhibit sudden variations of the vortex core location when the wing-tip separation is within approximately twice the vortex core radius. This is caused by the formation of vortex dipoles near the wing tip. In contrast, co-rotating upstream vortices do not exhibit such sensitivity. Large spanwise displacement of the trajectory due to the image vortex is possible when the incident vortex is further inboard. For both co-rotating and counter-rotating vortices, as long as there is no direct impingement upon the wing, there is a little change in the structure of the time-averaged vortex past the wing, even though the tip vortex shed from the downstream wing may be substantially weakened or strengthened. In the absence of the downstream wing, as well as for weak interactions, the most energetic unsteady modes represent the first helical mode |m| = 1, which is estimated from the three-dimensional Proper Orthogonal Decomposition modes and has a very large wavelength, on the order of 102 times the vortex core radius, λ/a = O(102). Instantaneous vorticity measurements as well as flow visualization suggest the existence of a smaller wavelength, λ/a = 5–6, which is not among the most energetic modes. These two-orders of magnitude different wavelengths are in agreement with the previous measurements of tip vortices and also exhibit qualitative agreement with the transient energy growth analysis. The very long wavelength mode in the upstream vortex may persist during the interaction, and reveal coupling with the trailing vortex as well as increased meandering.

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Experiments on tip vortices interacting with downstream wings

Impingement of a streamwise-oriented vortex upon a fin, tail, blade or wing represents a fundamental class of flow–structure interaction that extends across a range of applications. It can give rise to unsteady loading known as buffeting and to changes of the lift to drag ratio. These consequences are sensitive to parameters of the incident vortex as well as the location of vortex impingement on the downstream aerodynamic surface, generically designated as a wing. Particle image velocimetry is employed to determine patterns of velocity and vorticity on successive cross-flow planes along the vortex, which lead to volume representations and thereby characterization of the streamwise evolution of the vortex structure as it approaches the downstream wing. This evolution of the incident vortex is affected by the upstream influence of the downstream wing, and is highly dependent on the spanwise location of vortex impingement. Even at spanwise locations of impingement well outboard of the wing tip, a substantial influence on the structure of the incident vortex at locations significantly upstream of the leading edge of the wing was observed. For spanwise locations close to or intersecting the vortex core, the effects of upstream influence of the wing on the vortex are to: decrease the swirl ratio; increase the streamwise velocity deficit; decrease the streamwise vorticity; increase the azimuthal vorticity; increase the upwash; decrease the downwash; and increase the root-mean-square fluctuations of both streamwise velocity and vorticity. The interrelationship between these effects is addressed, including the rapid attenuation of axial vorticity in presence of an enhanced defect of axial velocity in the central region of the vortex. When the incident vortex is aligned with, or inboard of, the tip of the wing, the swirl ratio decreases to values associated with instability of the vortex, thereby giving rise to enhanced values of azimuthal vorticity relative to the streamwise (axial) vorticity, as well as relatively large root-mean-square values of streamwise velocity and vorticity.

Structure of a streamwise-oriented vortex incident upon a wing

The interactions of wingtip vortices in close-formation flight of two wings were examined experimentally. Both wings consisting of a NACA 23012 airfoil section and a rectangular planform of an aspect ratio of 5 were set in echelon formation in a wind tunnel. The lift-to-drag ratio increased the most effectively when the two wings were overlapped with each other by 5% of the wingspan with zero vertical offset for the present wing configuration. Flow visualizations and particle image velocimetry measurements showed that the trailing vortex of the lead wing collided at a slightly inboard point of the trail wing and was divided into two streamwise vortices in the most effective overlap condition. It was also observed that the tip vortices of the lead and trail wings interacted closely with each other to form a pair of counter-rotating vortices for smaller overlap conditions less than 5 % with zero vertical offset. For such small overlap cases, circulation of the trailing vortex of the trail wing was reduced markedly by influences of the trailing vortex of the lead wing.

Fumihide Mori

Papers

Detailed Observations of Interactions of Wingtip Vortices in Close-Formation Flight