Spherical Vortex Structures with a Core and a Shell

In this paper we construct and investigate the vortex structure consisting of a spherical vortex (vortex core) inside a spherical vortex layer (shell). A partial case of this structure is a spherical vortex with uniformly helical motion of the fluid within the core and the shell. The strengths of the helical flows in the core and the shell are generally different. The case of identical strengths is analyzed in detail. The streamline pattern is presented. The vortex velocity limit at which the vortex does not collapse is found. This proves to be less by a factor 1.7 than the analogous quantity for a vortex without a shell and 4 times lower than the maximum velocity of the Hill vortex.     

Evolution of a vortex street in the far wake of a cylinder

The evolution of a primary vortex street shed from a circular cylinder in the far wake is experimentally examined for 70 R 154 (R is the Reynolds number). According to the vorticity fields obtained using digital image processing for visualized flow fields, the primary vortex street breaks down into a nearly parallel shear flow of Gaussian profile at a certain downstream distance, before a secondary vortex street of larger scale appears further downstream. The process leading to the nearly parallel flow can be explained as the evolution of the vortex regions of an inviscid fluid if we invoke the observation that the distance between the two rows in the primary vortex street increases with the downstream distance, although the viscous effect probably contributes to this increase. Numerical computations with the discrete vortex method also support this explanation. The wavelengths and speeds of the primary and secondary vortex street are also measured.     

The variation in the maximum loading of a circular cylinder impacted by a 2D vortex with time of impact

Direct numerical simulation is used to study the loading of a rigid, circular cylinder impacted by a 2D vortex. The vortex travels within a stream of fluid characterized by Reynolds number of 150. Vortex impact occurs at twenty-five different times within one vortex shedding cycle. Substantial variation is observed in the maximum values of the drag and lift force coefficients. This variation is due to interaction between the impinging vortex and those attached to the cylinder. As the radius of the impinging vortex is increased from one to three times the cylinder’s diameter, the variation in maximum force coefficients with time of impact decreases. The variation decreases because the larger vortex alters the flow field and vortex shedding cycle prior to impacting the cylinder. For structures impacted by a vortex similar in size, significant under-prediction of the maximum loading may occur if variation in loading with vortex impact time is not considered.     

Acoustic emission from interaction of a vortex ring with a sphere

Acoustic waves emitted by a vortex ring interacting with a fixed solid sphere are studied experimentally and theoretically. The experiments are carried out for two kindsof vortex-sphere arrangement: (A) a vortex ring passes over the sphere, and (B) a vortex ring passes by the sphere. The vortex motion is examined optically by means of a photosensor system, and the pressure signals of the emitted wave are detected by 1/2-inch microphones in the far field. In case A, the measured diameter of the vortex ring after passing the sphere increases from its initial diameter. The observed acoustic wave is dominated mainly by a dipole emission, and some contribution from a quadrupole radiation is present. In case B, the emitted wave is characterized by a rotating dipole emission in which the dipole axis rotates as the vortex position changes relative to the sphere.     

Meander of a fin trailing vortex and the origin of its turbulence

The low-frequency meander of a trailing vortex shed from a tapered fin installed on a wind tunnel wall has been studied using stereoscopic particle image velocimetry in the near-wake at Mach 0.8. Distributions of the instantaneous vortex position reveal that the meander amplitude increases with downstream distance and decreases with vortex strength, indicating meander is induced external to the vortex. Trends with downstream distance suggest meander begins on the fin surface, prior to vortex shedding. Mean vortex properties are unaltered when considered in the meandering reference frame, apparently because turbulent fluctuations in the vortex shape and strength dominate positional variations. Conversely, a large peak of artificial turbulent kinetic energy is found centered in the vortex core, which almost entirely disappears when corrected for meander, though some turbulence remains near the core radius. Turbulence originating at the wind tunnel wall was shown to contribute to vortex meander by energizing the incoming boundary layer using low-profile vortex generators and observing a substantial increase in the meander amplitude, while greater turbulent kinetic energy penetrates the vortex core. An explanatory mechanism has been hypothesized, in which the vortex initially forms at the apex of the swept leading edge of the fin where it is exposed to turbulent fluctuations within the wind tunnel wall boundary layer, introducing an instability into the incipient vortex core.     

Optimal Control of a Vortex Trapped by an Airfoil with a Cavity

An airfoil with a cavity traps a vortex; the lift increases but the vortex shows great receptivity to upstream disturbances. A simple potential flow model confirms that the vortex stability basin is of a reduced extent. In this paper we present a control technique stabilizing the vortex position based on a potential flow model. The actuators are sources/sinks at the wall and the suction/blowing law is obtained by the adjoint optimization method. This revised version was published online in July 2006 with corrections to the Cover Date.     

An experimental study of the effect of free-stream turbulence on a trailing vortex

A study of turbulence evolution and spectra within and just outside the core of a trailing vortex is performed. The vortex is generated by a vortex generator consisting of four blades positioned orthogonally to each other with the same angle of attack and placed in a low-speed wind tunnel. A grid is placed upstream of the vortex generator to produce free-stream turbulence, which wraps around and interacts with the columnar vortex. Instantaneous measurements of the three velocity components are obtained using a miniature four-sensor hot-wire probe. The study focuses on the distribution of turbulence energy and Reynolds stress among the different spectral components of the flow at different positions across the vortex core and different axial positions along the tunnel. The effect of background grid turbulence on the spectral energy distribution of the vortex is examined in comparison to the vortex alone.     

Dynamics of the vortex structure of a jet impinging on a convex surface

Smoke–wire flow visualization is used to investigate the behavior of a round jet issuing from a straight tube and impinging on a convex surface. Video analysis of the impinging jet shows the initiation and growth of ring vortices in the jet shear layer and their interaction with the cylindrical surfaces. Effects of relative curvature, nozzle-to-surface distance, and Reynolds number on vortex initiation, vortex separation from the surface and vortex breakup are described. Examples of vortex merging are discussed.     

Interaction of a line vortex with a round parachute canopy

The interaction of a rectilinear vortex with an inflated round parachute canopy model was studied experimentally in a water tunnel where the vortex core was aligned with the axis of the canopy. Three different canopy diameters were used, and the canopy model was attached to a streamlined forebody. Dye flow visualization indicated that vortex breakdown was present when the core trajectory was within the canopy opening. Vortex breakdown occurred about one to two canopy diameters upstream of the canopy opening. The vortex core completely disintegrated when it interacted with the forebody near the canopy centerline. The vortex breakdown and disintegration caused unsteady, asymmetric deformations on the canopy surface. A reduction in the time-averaged drag and an increase in the fluctuating drag was observed when the vortex core was within the canopy opening. The disintegration of the vortex core near the canopy centerline lessened the drag reduction brought on by the presence of the core.     

Start-up of flow of a FENE-fluid through a 4:1:4 constriction in a tube

The flow of a FENE-fluid through a 4:1:4 constriction in a tube is computed by a split Lagrangian–Eulerian finite element method. In steady flow it is found that the upstream vortex grows with increasing Deborah number, while the down-stream vortex diminishes and disappears. The steady pressure drop decreases with Deborah number unless the finite extensibility L is quite small. Starting from rest at high Deborah number, the upstream vortex grows in two stages, each with their own time scales. A simple model of this growth is proposed.     

Sound emission by a vortex ring passing through a circular hole in a large flat plate

Acoustic emission has been studied experimentally when a vortex ring passes through a circular hole in a large flat plate, along its normal axis. The speed of the vortex ring is made high enough for the sound emission to be detectable, but can be regarded as sufficiently low in comparison to the sound speed. Substantial monopole and quadrupole components are observed in the detected wave profiles. Translational motion of the vortex ring in the presence of the flat plate with a hole has been observed optically, and its relation with the sound emission is determined. In this case, the power law of the acoustic pressure amplitude of monopolar vortex sound versus the translation speed U of the vortex ring is first measured in detail and is found to be U^2.1–U^2.4. This means that experimentally determined powers for the monopole components in the two half-spaces also agree approximately with the corresponding values predicted by the theory of vortex sound.     

Coaxial interactions of two vortex rings or of a ring with a body

Inviscid coaxial interactions of two vortex rings, including head-on collisions and leapfrogging motions, are considered using a contour dynamics technique. Interactions of vortex rings with solid bodies are also investigated by combining the contour dynamics technique with a boundary integral equation method. Numerical results show that a clean, successful passage motion is possible for two vortex rings with not too thick cores. In both cases of head-on collisions and leapfrogging motions, very large core deformations are observed when two vortex rings get close to each other. A head-tail structure is formed in the later stage of a head-on collision of two fat vortices. Numerical results also show that a vortex ring will stretch and slow down when it moves toward a solid boundary, will shrink and speed up when it moves away from a solid boundary, and will either translate steadily or approach an oscillating asymptotic state when it is far away from any boundaries. The project supported by The National Education Commission of China and NASA under cooperative grant agreement #NCC5-34.     

Diffusion of a ring vortex

The diffusion of a ring vortex is investigated in the present paper with allowance for the influence of the initial radius of the toroidal vorticity distribution on the flow structure. The statement of the problem in such a formulation makes it possible to classify and reinterpret results obtained previously. A vortex pair is studied together with a vortex ring. The toroidal vorticity and stream function distributions are obtained analytically. The self-induced lift velocity of the ring vortex is found. The influence of inertial terms is investigated numerically.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 10–15, November–December, 1987.     

Acoustic waves emitted by a vortex ring passing near a wedge-like plate

Acoustic waves emitted by a vortex ring moving near a thin wedge-like plate of finite width have been studied. The experiments are performed for three configurations: the plate (A) is held edgeways to the direction of the vortex motion, (B) is held sideways to the direction, and (C) is held edgeways at an angle of 45° against the vortex motion. The observed sound wave is of dipole radiation type, and the magnitude of the pressure is large in the direction of the normal to the plate plane and small in parallel. The observed pressure is proportional to the third power of the vortex speed. The instantaneous force exerted on the plate by the vortex motion has also been examined. The force vector is mainly normal to the plate plane. The observed profiles agree within a reasonable degree of accuracy with the theoretical ones calculated for the vortex ring interacting with the flat plate of thickness zero.     

Large eddy simulation of a vortex ring impinging on a three-dimensional circular cylinder

A vortex ring impacting a three-dimensional circular cylinder is studied using large eddy simulation (LES) for a Reynolds number Re = 4 × 10⁴ based on the initial translation speed and diameter of the vortex ring. We have investigated the evolution of vortical structures and identified three typical evolution phases. When the primary vortex closely approaches to the cylinder, a secondary vortex is generated and its segment parts move inward to the primary vortex ring. then two large-scale loop-like vortices are formed to evolve in opposite directions. Thirdly, the two loop-like vortices collide with each other to form complicated small-scale vortical structures. Moreover, a series of hair-pin vortices are generated due to the stretching and deformation of the tertiary vortex. The trajectories of vortical structures and the relevant evolution speeds are analyzed. The total kinetic energy and enstrophy are investigated to reveal their properties relevant to the three evolution phases.     

A Numerical Study of the Flow Around a Model Winged Seed in Auto-Rotation

In this study the flow around a winged-seed in auto-rotation is characterized using direct numerical simulations (DNS) at Reynolds number in the range 80–240, based on the descent speed and a characteristic chord length. In this range, the flow is approximately steady when observed from a reference frame fixed to the seed. For all cases, the flow structure consists of a wing tip vortex which describes a helical path, a vortex shed behind the nut of the seed and a stable leading edge vortex above the wing surface which merges with the tip vortex. With increasing Reynolds number, the leading edge vortex becomes more intense and gets closer to the wing surface. The simulation results also show the formation of a spanwise flow on the upper surface of the wing, moving fluid towards the wing tip in a region downstream and beneath the leading edge vortex. This spanwise flow is rather weak inside the core of the leading edge vortex, and the analysis of the streamlines show a very weak transport of vorticity along the vortex for the cases under consideration. The analysis of the flow suggests that the stabilization of the leading edge vortex is mainly due to non-inertial accelerations, although viscous effects may contribute, specially at lower Re. Furthermore, the leading edge vortex has been characterized by analysing the flow variables averaged along cross-sections of the vortex. While some quantities, like the spanwise velocity or the pressure inside the vortex, are rather insensitive to the threshold used to define the leading edge vortex, the same is not true for the circulation of the vortex or its averaged spanwise vorticity, due to the viscous nature of the vortex. Finally, it is observed that the spanwise vorticity scales with the angular rotation of the seed for the different Re.     

Near wake vortex dynamics of a hovering hawkmoth

Numerical investigation of vortex dynamics in near wake of a hovering hawkmoth and hovering aerodynamics is conducted to support the development of a biology-inspired dynamic flight simulator for flapping wingbased micro air vehicles. Realistic wing-body morphologies and kinematics are adopted in the numerical simulations. The computed results show 3D mechanisms of vortical flow structures in hawkmoth-like hovering. A horseshoe-shaped primary vortex is observed to wrap around each wing during the early down- and upstroke; the horseshoe-shaped vortex subsequently grows into a doughnut-shaped vortex ring with an intense jet-flow present in its core, forming a downwash. The doughnut-shaped vortex rings of the wing pair eventu- ally break up into two circular vortex rings as they propagate downstream in the wake. The aerodynamic yawing and rolling torques are canceled out due to the symmetric wing kinematics even though the aerodynamic pitching torque shows significant variation with time. On the other hand, the time- varying the aerodynamics pitching torque could make the body a longitudinal oscillation over one flapping cycle.     

The nonlinear interaction of vortex rings with a free surface

Nonlinear interactions of vortex rings with a free surface are considered in an incompressible, ideal fluid using the vortex contour dynamics technique and the boundary integral equation method. The flow is axisymmetric and the vorticity is linearly distributed in the vortex. Effects of the gravity and the surface tension as well as the initial geometric parameter of the vortex on the interaction process are investigated in considerable detail. The interaction process may be divided into three major stages: the vortex free-traveling stage, the collision stage, and the vortex stretching and rebounding stage. Time evolutions of both the vortex and free surface under various conditions are provided and analyzed. Two kinds of waves exist on the free surface during interaction. In a special case where the gravity and surface tension are very weak or the vortex is very strong, an electric-bulb-like ‘cavity’ is formed on the free surface and the vortex is trapped in the ‘cavity’ for quite a long time, resulting in a large amount of fluid above the mean fluid surface. The project supported by the National Education Commission of China and NASA under cooperative grant agreement # NCC5-34     

Instability of a vertical columnar vortex in a stratified fluid

In this article, we study experimentally the evolution of a vertical columnar vortex in a stratified fluid. Three different measurement techniques are used. Particle image velocimetry allows us to monitor the time evolution of the characteristics of the vortex (Froude and Reynolds numbers). Dye visualizations reveal the existence of an instability for Froude numbers smaller than one, which creates an undulation of the vortex centerline. Synthetic schlieren visualization shows that the density structure of the unstable mode is very similar to the structure found recently numerically for the radiative instability of a Lamb–Oseen vortex (Riedinger et al. in J Fluid Mech, 2010). The experimental stability diagram and unstable wavelengths are compared with these numerical results. A secondary instability associated with the presence of critical layers is also observed for Froude numbers larger than one.