Instability of secondary vortices generated by a vortex pair in ground effect

2012 ◽  
Vol 700 ◽  
pp. 148-186 ◽  
Author(s):  
D. M. Harris ◽  
C. H. K. Williamson
Keyword(s):  
Ground Plane ◽  
Point Vortex ◽  
Vortex Pair ◽  
Ground Effect ◽  
Secondary Vortex ◽  
Primary Vortex ◽  
Single Vortex ◽  
Displacement Mode ◽  
Instability Modes ◽  
Secondary Vortices

AbstractIn this work, we investigate the approach of a descending vortex pair to a horizontal ground plane. As in previous studies, the primary vortices exhibit a ‘rebound’, due to the separation of secondary opposite-sign vortices underneath each primary vortex. On each side of the flow, the weaker secondary vortex can become three-dimensionally unstable, as it advects around the stronger primary vortex. It has been suggested in several recent numerical simulations that elliptic instability is the origin of such waviness in the secondary vortices. In the present research, we employ a technique whereby the primary vortices are visualized separately from the secondary vortices; in fact, we are able to mark the secondary vortex separation, often leaving the primary vortices invisible. We find that the vortices are bent as a whole in a Crow-type ‘displacement’ mode, and, by keeping the primary vortices invisible, we are able to see both sides of the flow simultaneously, showing that the instability perturbations on the secondary vortices are antisymmetric. Triggered by previous research on four-vortex aircraft wake flows, we analyse one half of the flow as an unequal-strength counter-rotating pair, noting that it is essential to take into account the angular velocity of the weak vortex around the stronger primary vortex in the analysis. In contrast with previous results for the vortex–ground interaction, we find that the measured secondary vortex wavelength corresponds well with the displacement bending mode, similar to the Crow-type instability. We have analysed the elliptic instability modes, by employing the approximate dispersion relation of Le Dizés & Laporte (J. Fluid Mech., vol. 471, 2002, p. 169) in our problem, finding that the experimental wavelength is distinctly longer than predicted for the higher-order elliptic modes. Finally, we observe that the secondary vortices deform into a distinct waviness along their lengths, and this places two rows of highly stretched vertical segments of the vortices in between the horizontal primary vortices. The two rows of alternating-sign vortices translate towards each other and ultimately merge into a single vortex row. A simple point vortex row model is able to predict trajectories of such vortex rows, and the net result of the model’s ‘orbital’ or ‘passing’ modes is to bring like-sign vortices, from each secondary vortex row, close to each other, such that merging may ensue in the experiments.

Interaction of impulsively generated vortex pairs with bodies

1988 ◽  
Vol 197 ◽  
pp. 571-594 ◽  
Author(s):  
J. Homa ◽  
M. Lucas ◽  
D. Rockwell
Keyword(s):  
Phase Shift ◽  
Large Scale ◽  
Vortex Formation ◽  
Vortex Pair ◽  
The Body ◽  
Secondary Vortex ◽  
Primary Vortex ◽  
Vortex Pairs ◽  
Order Of Magnitude ◽  
Secondary Vortices

A vortex pair, impulsively generated from a planar nozzle, is shown to have a degree of vorticity concentration in good agreement with inviscid theory, providing well-posed initial conditions for interaction with basic types of bodies (cylinders and plates). The scale of these bodies ranges from the same order as, to over an order of magnitude smaller than, the scale (distance between centres) of the incident vortex pair.The fundamental case of a (primary) vortex pair symmetrically incident upon a very small cylinder shows rapid growth of a secondary vortex pair. These secondary vortices quickly attain a circulation of the same order as that of the corresponding primary vortices within a distance smaller than the lengthscale of the primary vortex pair. At this location, the temporal variation of integrated vorticity of primary and secondary vortices attains a maximum simultaneously. This zero phase shift between arrival of vorticity maxima provides the basis for formation of counter-rotating, primary–secondary vortex pairs, where both the primary and secondary vortices move at the same phase speed.Visualization shows that the mode of secondary vortex formation is highly sensitive to the degree of symmetry of the initial encounter of the incident vortex pair with the body. The symmetrical mode of (in-phase) secondary vortex formation shows very rapid growth of large-scale secondary vortices; their development is relatively independent of the particulars of body shape and scale. On the other hand, the antisymmetrical mode takes two basic forms: large-scale secondary vortex formation, with the phase shift between their formation determined by the lengthscale of the body; and small-scale, antisymmetrical shedding of secondary vortices from the body occurring for a body lengthscale an order of magnitude smaller than that of the incident vortex pair. Correspondingly, there are several types of distortion of the cores and trajectories of the primary (incident) vortices.

scholarly journals On annihilation of the relativistic electron vortex pair in collisionless plasmas

2018 ◽  
Vol 84 (6) ◽  
Author(s):  
K. V. Lezhnin ◽  
F. F. Kamenets ◽  
T. Zh. Esirkepov ◽  
S. V. Bulanov
Keyword(s):  
Magnetic Field ◽  
Collisionless Plasma ◽  
Vortex Formation ◽  
Vortex Pair ◽  
Skin Depth ◽  
Secondary Vortex ◽  
Vortex System ◽  
Collisionless Plasmas ◽  
Secondary Vortices ◽  
The Magnetic Field

In contrast to hydrodynamic vortices, vortices in a plasma contain an electric current circulating around the centre of the vortex, which generates a magnetic field localized inside. Using computer simulations, we demonstrate that the magnetic field associated with the vortex gives rise to a mechanism of dissipation of the vortex pair in a collisionless plasma, leading to fast annihilation of the magnetic field with its energy transforming into the energy of fast electrons, secondary vortices and plasma waves. Two major contributors to the energy damping of a double vortex system, namely, magnetic field annihilation and secondary vortex formation, are regulated by the size of the vortex with respect to the electron skin depth, which scales with the electron$\unicode[STIX]{x1D6FE}$factor,$\unicode[STIX]{x1D6FE}_{e}$, as$R/d_{e}\propto \unicode[STIX]{x1D6FE}_{e}^{1/2}$. Magnetic field annihilation appears to be dominant in mildly relativistic vortices, while for the ultrarelativistic case, secondary vortex formation is the main channel for damping of the initial double vortex system.

Influence of a wall on the three-dimensional dynamics of a vortex pair

2017 ◽  
Vol 817 ◽  
pp. 339-373 ◽  
Author(s):  
Daniel J. Asselin ◽  
C. H. K. Williamson
Keyword(s):  
Ground Plane ◽  
Rebound Effect ◽  
Three Dimensional ◽  
Vortex Pair ◽  
Vortex Rings ◽  
Wave Instability ◽  
Long Wave ◽  
Wall Interaction ◽  
Secondary Vortices ◽  
Crow Instability

In this paper, we are interested in perturbed vortices under the influence of a wall or ground plane. Such flows have relevance to aircraft wakes in ground effect, to ship hull junction flows, to fundamental studies of turbulent structures close to a ground plane and to vortex generator flows, among others. In particular, we study the vortex dynamics of a descending vortex pair, which is unstable to a long-wave instability (Crow, AIAA J., vol. 8 (12), 1970, pp. 2172–2179), as it interacts with a horizontal ground plane. Flow separation on the wall generates opposite-sign secondary vortices which in turn induce the ‘rebound’ effect, whereby the primary vortices rise up away from the wall. Even small perturbations in the vortices can cause significant topological changes in the flow, ultimately generating an array of vortex rings which rise up from the wall in a three-dimensional ‘rebound’ effect. The resulting vortex dynamics is almost unrecognizable when compared with the classical Crow instability. If the vortices are generated below a critical height over a horizontal ground plane, the long-wave instability is inhibited by the wall. We then observe two modes of vortex–wall interaction. For small initial heights, the primary vortices are close together, enabling the secondary vortices to interact with each other, forming vertically oriented vortex rings in what we call a ‘vertical rings mode’. In the ‘horizontal rings mode’, for larger initial heights, the Crow instability develops further before wall interaction; the peak locations are farther apart and the troughs closer together upon reaching the wall. The proximity of the troughs to each other and the wall increases vorticity cancellation, leading to a strong axial pressure gradient and axial flow. Ultimately, we find a series of small horizontal vortex rings which ‘rebound’ from the wall. Both modes comprise two small vortex rings in each instability wavelength, distinct from Crow instability vortex rings, only one of which is formed per wavelength. The phenomena observed here are not limited to the above perturbed vortex pairs. For example, remarkably similar phenomena are found where vortex rings impinge obliquely with a wall.

Chaos in body–vortex interactions

2010 ◽  
Vol 466 (2119) ◽  
pp. 1871-1891 ◽  
Author(s):  
Johan Roenby ◽  
Hassan Aref
Keyword(s):  
Body Shape ◽  
Mass Density ◽  
Relative Equilibrium ◽  
Large Body ◽  
Point Vortex ◽  
Cylindrical Body ◽  
The Body ◽  
Body Motion ◽  
Single Vortex ◽  
Vortex Interactions

The model of body–vortex interactions, where the fluid flow is planar, ideal and unbounded, and the vortex is a point vortex, is studied. The body may have a constant circulation around it. The governing equations for the general case of a freely moving body of arbitrary shape and mass density and an arbitrary number of point vortices are presented. The case of a body and a single vortex is then investigated numerically in detail. In this paper, the body is a homogeneous, elliptical cylinder. For large body–vortex separations, the system behaves much like a vortex pair regardless of body shape. The case of a circle is integrable. As the body is made slightly elliptic, a chaotic region grows from an unstable relative equilibrium of the circle-vortex case. The case of a cylindrical body of any shape moving in fluid otherwise at rest is also integrable. A second transition to chaos arises from the limit between rocking and tumbling motion of the body known in this case. In both instances, the chaos may be detected both in the body motion and in the vortex motion. The effect of increasing body mass at a fixed body shape is to damp the chaos.

scholarly journals Vortex Interactions Subjected to Deformation Flows: A Review

Fluids ◽  
2019 ◽  
Vol 4 (1) ◽  
pp. 14 ◽  
Author(s):  
Konstantin Koshel ◽  
Eugene Ryzhov ◽  
Xavier Carton
Keyword(s):  
Review Paper ◽  
Point Vortex ◽  
Passive Scalar ◽  
Dynamical System Theory ◽  
Single Vortex ◽  
Vortex Interactions ◽  
Rotational Components ◽  
Coherent Vortices ◽  
Numerical And Analytical Methods ◽  
Submerged Obstacles

Deformation flows are the flows incorporating shear, strain and rotational components. These flows are ubiquitous in the geophysical flows, such as the ocean and atmosphere. They appear near almost any salience, such as isolated coherent structures (vortices and jets) and various fixed obstacles (submerged obstacles and continental boundaries). Fluid structures subject to such deformation flows may exhibit drastic changes in motion. In this review paper, we focus on the motion of a small number of coherent vortices embedded in deformation flows. Problems involving isolated one and two vortices are addressed. When considering a single-vortex problem, the main focus is on the evolution of the vortex boundary and its influence on the passive scalar motion. Two vortex problems are addressed with the use of point vortex models, and the resulting stirring patterns of neighbouring scalars are studied by a combination of numerical and analytical methods from the dynamical system theory. Many dynamical effects are reviewed with emphasis on the emergence of chaotic motion of the vortex phase trajectories and the scalars in their immediate vicinity.

Detached-Eddy Simulation of Ground Effect on the Wake of a High-Speed Train

2017 ◽  
Vol 139 (5) ◽  
Author(s):  
Chao Xia ◽  
Xizhuang Shan ◽  
Zhigang Yang
Keyword(s):  
Vortex Shedding ◽  
High Speed ◽  
Vortex Pair ◽  
Ground Effect ◽  
Longitudinal Vortex ◽  
High Speed Train ◽  
Detached Eddy Simulation ◽  
Side Force ◽  
Eddy Simulation ◽  
Delayed Detached Eddy Simulation

The influence of ground effect on the wake of a high-speed train (HST) is investigated by an improved delayed detached-eddy simulation. Aerodynamic forces, the time-averaged and instantaneous flow structure of the wake are explored for both the stationary ground and the moving ground. It shows that the lift force of the trailing car is overestimated, and the fluctuation of the lift and side force is much greater under the stationary ground, especially for the side force. The coexistence of multiscale vortex structures can be observed in the wake along with vortex stretching and pairing. Furthermore, the out-of-phase vortex shedding and oscillation of the longitudinal vortex pair in the wake are identified for both ground configurations. However, the dominant Strouhal number of the vortex shedding for the stationary and moving ground is 0.196 and 0.111, respectively, due to the different vorticity accumulation beneath the train. A conceptual model is proposed to interpret the mechanism of the interaction between the longitudinal vortex pair and the ground. Under the stationary ground, the vortex pair embedded in a turbulent boundary layer causes more rapid diffusion of the vorticity, leading to more intensive oscillation of the longitudinal vortex pair.

Passive Wingtip Vortex Control by Using Tip-Mounted Half Delta Wings in Ground Effect

2019 ◽  
Vol 142 (2) ◽  
Author(s):  
Anan Lu ◽  
Tim Lee
Keyword(s):  
Vortex Flow ◽  
Ground Effect ◽  
Tip Vortex ◽  
Secondary Vortex ◽  
Flow Properties ◽  
Delta Wings ◽  
Vortex Control ◽  
Physical Mechanisms ◽  
Induced Drag ◽  
Wingtip Vortex

Abstract The ground effect on the wingtip vortex generated by a rectangular semiwing equipped with tip-mounted regular and reverse half delta wings was investigated experimentally. The passive tip vortex control always led to a reduced lift-induced drag as the ground was approached. In close ground proximity, the presence of the corotating ground vortex (GV) added vorticity to the tip vortex while the counter-rotating secondary vortex (SV) negated its vorticity level. The interaction of the GV and SV with the tip vortex and their impact on the lift-induced drag were discussed. Physical mechanisms responsible for the change in the vortex flow properties in ground effect were also provided.

Theoretical Analyses of the Number of Backflow Vortices on an Axial Pump or Compressor

2019 ◽  
Author(s):  
Yu Ito ◽  
Yuhei Sato ◽  
Takao Nagasaki
Keyword(s):  
Contact Surface ◽  
Tip Clearance ◽  
The Other ◽  
Vortex Center ◽  
Secondary Vortex ◽  
Axial Pump ◽  
Cylindrical Casing ◽  
Axial Pumps ◽  
Secondary Vortices ◽  
Theoretical Analyses

Abstract This paper presents theoretical analyses of flow fields on an axial pump or compressor, where the main flow enters from one side of the cylindrical casing, whereas an axially reverse and tangentially whirling flow enters from the tip clearance between the casing and the impeller, which sucks in the mixed flow. In this flow field, several secondary vortices exist in the mixing zone across the contact surface between the main and the axially reverse tangentially whirling flow. This type of secondary vortex is called a “backflow vortex.” The backflow vortices are tornado-like, parallel to the casing axis, and periodically distributed on the contact surface; they revolve around the casing axis and rotate around themselves. Regarding the backflow vortices, the relationships between their number (N), revolving diameter (d), revolving angular velocity (ω), and the ratio of the forced vortex region to the distance between the secondary-vortex center and the cylindrical wall (f) were all theoretically investigated. The five major findings are as follows: First, between d, ω, N, and f, any parameter can be determined if the other three are specified. Second, ω decreases, N increases, or f increases when d is increased and the other two are fixed. Third, d decreases, N increases, or f increases when ω is increased and the other two are fixed. Fourth, d increases, ω increases, or f decreases when N is increased and the other two are fixed. Fifth, d increases, ω increases, or N decreases when f is increased and the other two are fixed. To validate these theoretical results, “backflow vortex cavitation,” which occurs around the center of the backflow vortices on a rotating inducer as a representative of axial pumps or compressors, was observed. The backflow vortex cavitation is visible; therefore, d, ω, and N become quantitatively measurable. The test inducer was a triple-threaded helical inducer with a diameter of 65.3 mm and a rotational speed range of 3000–6000 rpm. It was experimentally confirmed that the proposed theoretical analysis is true.

A New Quasi-Steady In-Ground Effect Model for Rotorcraft Unmanned Aerial Vehicles

2019 ◽  
Author(s):  
Xiang He ◽  
Kam K. Leang
Keyword(s):  
Unmanned Aerial Vehicles ◽  
Ground Plane ◽  
Ground Effect ◽  
P Value ◽  
Model Parameters ◽  
Blade Element Theory ◽  
Aerial Vehicles ◽  
Effect Model ◽  
3D Printed ◽  
Induced Velocity

Abstract This paper introduces a new quasi-steady in-ground effect model for rotorcraft unmanned aerial vehicles to predict the aerodynamic behavior when the vehicle’s rotors approach ground plane. The model assumes that the compression of the outflow due to the presence of ground plane induces a change in the induced velocity that can drastically affect the thrust and power output. The new empirical model describes the change in thrust as a function of the distance to an obstacle for a rotor in hover condition. Using blade element theory and the method of image, the model parameters are described in terms of the rotor pitch angle and solidity. Experiments with off-the-shelf, fixed-pitch propellers and 3D-printed variable pitch propellers are carried out to validate the model. Experimental results suggest good agreement with 9.5% root-mean-square error (RMSE) and 97% p-value of statistic significance.

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