Vortex Rebound Research Articles

Vortex-dipole impingement with convex and concave boundaries

The vortex-dipole interactions with convex and concave boundaries in a two-dimensional domain are analyzed using the Bhatnagar–Gross–Krook (BGK) collision-based lattice Boltzmann method (LBM). The formation and detachment of the boundary layers at the flat wall creates new dipoles of non-identical vortices, following cyclic trajectories and exhibiting logarithmic variations in the production of maximum vorticity with Reynolds number (Re). The vortex-dipole interactions with concave boundaries produce a series of secondary dipoles, whose relative strength linearly decreases for the given Re in subsequent vortex-releasing events. Oblique interactions with cavity corners cause secondary dipoles to undergo head-on collisions at the domain center, influencing partner exchange and orthogonal propagation. Conversely, convex boundaries split the primary vortex-dipole upon impingement, intensifying the vorticity production and strain effects. Whereas, the larger ingestion of vorticity at the convex corners of the “T-shaped” cavity forms new dipoles, which deflect, rebound, and follow a parabolic trajectory for the vortex exchange. Normalized enstrophy, Ω(t), and palinstrophy, P(t), show distinct peaks during dipole interactions with boundary walls, influencing enhanced kinetic energy, E(t), decay. Moreover, the evolution of E(t) and Ω(t) satisfies the relation valid for no-slip boundaries. The collision behavior, vorticity production, and vortex rebound are functions of Re. The convex boundaries modify the scaling results of maximum Ω(t) and P(t) to higher exponent values than the dipole interactions with flat and concave boundaries.

A Fast Analysis of Pesticide Spray Dispersion by an Agricultural Aircraft Very near the Ground

This study provides a fast analysis of pesticide spray trails and dispersion influenced by crosswind, headwind, velocity field and the wake of an agricultural aircraft approaching the ground, to improve operational efficiency and reduce environmental impact. The lifting line-wingtip vortices mixture model is proposed to calculate induced velocity field around a monoplane far to 190 wingspans downstream, and N-vortex system based on point vortex dynamics is applied to simulate vortex rebound and vortex motion on considering extreme ground effect. The droplet trajectories governed by wake vortices and their induced velocity field are therefore determined under the Lagrangian framework. According to the ground deposition of typical droplets, the Gaussian mixture model is employed to predict droplet drift or dispersal for the whole spectrum of droplets in the spanwise direction. The fast analysis is compared to AGDISP and computational fluid dynamics (CFD) simulation for Thrush 510G aircraft, which runs on a common personal computer (CPU 2 GHz, memory 2 GB) within 3.2 s, faster than AGDISP and CFD, and does not rely on swath width input needed by AGDISP. The results suggest crosswind speed and droplet size are two leading factors affecting the drift and ground deposition. To increase droplet size or reduce the portion of fine droplets, the pesticide drift can be suppressed in some degrees.

Optimal growth of counter-rotating vortex pairs interacting with walls

Abstract

A vortex pair in ground effect, dynamics and optimal control

The dynamics and control of a vortex pair in ground effect are investigated in a planar, incompressible and laminar setting. The evolution of the vortices obtained numerically shows vortex rebound as a consequence of the separation of the boundary layer induced at the wall by the vortices. An optimal control approach is developed and employed for vortex Reynolds numbers of 200 and 1000 in order to identify the optimal Dirichlet boundary condition at the wall to counteract this rebound and allow for an increased lateral displacement of the vortex, similarly to the inviscid evolution of the flow, which features hyperbolic trajectories. The work is primarily a conceptual approach to deal with aircraft separation distances in airport airspace by moving the vortices laterally, away from the runway but may also apply to the control of coherent structures in wall bounded turbulence. The most efficient control is able to double the lateral position and yields mostly vertical in and outflow at the wall. An optimal horizon time is found, equal to 5 characteristic time units of the vortex system, beyond which control is not able to further displace the vortices. The control is shown to delay the separation of the boundary layer at the origin of vortex rebound by applying suction ahead of the vortex, and to generate a vorticity flux at the wall, leading to a pusher vortex of sign opposite to that of the primary vortex, that attenuates the effect of the no-slip boundary condition at the wall by pushing the vortex outward.

Experimental Study of Aerodynamics and Wingtip Vortex of a Rectangular Wing in Flat Ground Effect

The ground effect on the aerodynamics and tip vortex flow of a rectangular wing is investigated experimentally at Re = 2.71 × 105. The results show that there is a large lift increase with reducing ground distance. By contrast, only a small drag increase is observed in ground effect except in close ground proximity for which a great drag increase appears. The tip vortex also moves further outboard and upward with reducing ground distance. Near the ground, there is the presence of a corotating ground vortex (produced by the rolling up of the boundary layer developed on the ground surface), leading to an increased vortex strength. In extreme ground proximity, a counterrotating secondary vortex (SV) (induced by the crossflow of the tip vortex), relative to the tip vortex, appears which causes a reduced vortex strength and a lowered lift-induced drag, as well as a vortex rebound. The impact of ground effect on the vortex flow properties is also discussed. The lift-induced drag, computed based on the crossflow measurements via the Maskell wake integral method, in ground effect is also compared against the inviscid-flow predictions and wind tunnel total drag force measurements.

A ctenophore (comb jelly) employs vortex rebound dynamics and outperforms other gelatinous swimmers.

Gelatinous zooplankton exhibit a wide range of propulsive swimming modes. One of the most energetically efficient is the rowing behaviour exhibited by many species of schyphomedusae, which employ vortex interactions to achieve this result. Ctenophores (comb jellies) typically use a slow swimming, cilia-based mode of propulsion. However, species within the genus Ocyropsis have developed an additional propulsive strategy of rowing the lobes, which are normally used for feeding, in order to rapidly escape from predators. In this study, we used high-speed digital particle image velocimetry to examine the kinematics and fluid dynamics of this rarely studied propulsive mechanism. This mechanism allows Ocyropsis to achieve size-adjusted speeds that are nearly double those of other large gelatinous swimmers. The investigation of the fluid dynamic basis of this escape mode reveals novel vortex interactions that have not previously been described for other biological propulsion systems. The arrangement of vortices during escape swimming produces a similar configuration and impact as that of the well-studied ‘vortex rebound’ phenomenon which occurs when a vortex ring approaches a solid wall. These results extend our understanding of how animals use vortex–vortex interactions and provide important insights that can inform the bioinspired engineering of propulsion systems.

Experimental Investigations on the Interaction of the Single/Co-Rotating Vortex with the Ground

Experiments on the interactions between a single vortex/co-rotating vortices and the ground were conducted in a water channel using particle image velocimetry (PIV) measurements. Both the single vortex (SNV) and co-rotating vortex pair (CVP) were generated by using NACA0012 vortex generators to simulate the main flow features behind one side of the wings at the farfield and near field. The ground effect was achieved by allocating a flat plate downstream of the vortex generators. It has been found that the lower initial vortex height led to greater vortex rebound and lateral drift in both the SNV and CVP cases, whereas the development of a secondary vortex was also promoted with lower initial vortex height. In the CVP cases, the mutual rotation of the primary vortices led to variation of the close-to-wall velocity distribution. This effect added the disturbances to the formation and evolution of the secondary vortical structure, which eventually affected the height of the secondary vorticity and the rebound of the primary vortices.

Wind Impact on Single Vortices and Counterrotating Vortex Pairs in Ground Proximity

Wall-resolved large eddy simulations are employed to investigate the behaviour of wake vortices and single vortices in ground proximity at a variety of wind conditions. The six considered strengths of wind, ranging between 0.5 and 4 times the initial wake vortex descent speed, w 0, include practically and theoretically significant wind speeds. A crosswind of 0.5 w 0 may lead to windward stall posing a potential hazard to subsequently landing aircraft, whereas theoretical considerations predict that at 4 w 0 the rebound of the luff vortex is completely suppressed. The same range of wind speeds is also used to investigate the effects of headwind and diagonal wind in order to discriminate between effects of environmental turbulence increasing with wind speed and the direction of the wind shear. The study has been complemented by a number of single vortex computations in order to differentiate between effects related to the mutual interaction of the vortex pair and the individual vortices with the turbulent boundary layer flow. It is shown that vortex ascent, descent, rebound and decay characteristics are controlled by (i) the interaction of the vortices with secondary vorticity detaching from the ground, (ii) the redistribution of vorticity of the boundary layer which is altering the path of the primary vortices by mutual velocity induction, and (iii) the interaction of the vortices with the environmental turbulence.

Investigation of co-rotating vortex merger in ground proximity

The experiments were conducted in a water tunnel facility and were aimed at investigating the merging process of co-rotating wake vortices in ground effect. A corresponding two-dimensional analytical model was also introduced based on experimental results. The two like-sign vortices were generated with equal size and strength above the ground plane. The evolution of vortex pair was attained by using particle image velocimetry at a series of downstream locations. The main finding is that the ground effect promotes the merging process and accelerates the vortices' rotation around one another. Vertical movements, known as vortex rebound, and lateral movements are observed. The ground effect also leads to the emergence of a secondary vortex (SV), which adds to the complexity of the vortex system. Prediction of the modified potential model, which takes vortex decay, viscous drag and the evolution of the SV into account, is compared with the experimental data. The results show that the vortex merging and rebound of a co-rotating vortex pair is successfully predicted and the prediction of vortex orientation and lateral motion are also improved by this model.

Experimental study of interaction between a vortex ring and a solid surface for a wide range of ring velocities

Experiments were carried out for interaction of water-travelling vortex ring with a solid surface with the normal impingement to the surface; the vortex velocity was varied by factor of 30 and the Reynolds number had 60-times span. Laminar and turbulent vortex rings have been studied. The ratio of the vortex diameter at the moment of rebound from the surface to the vortex diameter before impingement is almost independent of the vortex velocity and Reynolds number. Within the experimental accuracy, the diameter of the vortex ring after rebound equals the footprint of the vortex on the solid surface. This brings assumption that the previously observed restrictions on the trace were related to the vortex rebound from the solid surface.

The effect of slip length on vortex rebound from a rigid boundary

The problem of a dipole incident normally on a rigid boundary, for moderate to large Reynolds numbers, has recently been treated numerically using a volume penalisation method by Nguyen van yen, Farge, and Schneider [Phys. Rev. Lett. 106, 184502 (2011)]. Their results indicate that energy dissipating structures persist in the inviscid limit. They found that the use of penalisation methods intrinsically introduces some slip at the boundary wall, where the slip approaches zero as the Reynolds number goes to infinity, so reducing to the no-slip case in this limit. We study the same problem, for both no-slip and partial slip cases, using compact differences on a Chebyshev grid in the direction normal to the wall and Fourier methods in the direction along the wall. We find that for the no-slip case there is no indication of the persistence of energy dissipating structures in the limit as viscosity approaches zero and that this also holds for any fixed slip length. However, when the slip length is taken to vary inversely with Reynolds number then the results of Nguyen van yen et al. are regained. It therefore appears that the prediction that energy dissipating structures persist in the inviscid limit follows from the two limits of wall slip length going to zero, and viscosity going to zero, not being treated independently in their use of the volume penalisation method.

The impact of a vortex ring on a porous screen

In this paper, we re-examine the issue raised by Morton (2000) regarding the impact of a vortex ring on a porous screen. We show, through a systematic experiment, that Morton's observation can only occur at very low Reynolds number or above a certain critical Reynolds number, which is dependent on the porosity of the screen. In particular, we found that a primary vortex ring of moderate Reynolds number impacting a porous screen can also undergo vortex rebound similar to that observed in vortex ring–solid wall interaction. At a higher Reynolds number, the self-induced flow of the primary vortex ring around the axis of symmetry passes through the screen as a jet-like flow, which later regenerates into a new vortex ring of the same sign but weaker circulation. At an even higher Reynolds number, the primary vortex ring has sufficient energy to pass through the screen via a possible mechanism of vortex stretching and reconnection, and continues as a modified ring in its lee.

Inviscid dipole-vortex rebound from a wall or coast

A vortex approaching a no-slip wall ‘rebounds’ due to the creation of vorticity at the wall in a viscous boundary layer. Here it is demonstrated that a purely inviscid mechanism can also produce vortex rebound from a slip wall. In inviscid vortex rebound, vortex tube stretching generates the necessary vorticity to allow rebound, eliminating the need for viscous vorticity generation. This vortex stretching mechanism is demonstrated through numerical simulations and laboratory experiments on dipole-vortex rebound from a boundary. In an application to oceanography, numerical simulations of both quasi-geostrophic and shallow water dynamics are used to show that the β-effect at an eastern boundary can produce this inviscid rebound. Through a series of numerical experiments in which the strength of the β-effect is varied, a formula for predicting the point of separation of the vortices from the boundary in a dipole–coast collision is deduced. Through simulations, the flux of vorticity and fluid away from the boundary is measured as a function of β and initial angle of incidence. It is found that, in contrast to viscous vortex rebound, which typically does not produce a flux of material away from the boundary farther than a distance comparable to the initial vortex radius, the β-induced rebound does carry fluid far from the coast. Laboratory experiments in a rotating tank are used to show that a sloping bottom can also provide an inviscid mechanism for dipole-vortex rebound from the wall of the tank under certain conditions. A relation determining the conditions under which inviscid or viscous processes will dominate in the rebound of the dipole from a boundary is obtained.

Numerical simulation of a viscous vortex ring interaction with a density interface

The incompressible, variable-density Navier–Stokes equations in axisymmetric coordinates are solved for the interaction of a vortex ring with a density interface. The effect of progressively weakening stratification and variation in Reynolds number are examined. Secondary and tertiary ring formation, vortex rebound, and backflow jets are some of the features observed in the interactions.