Elliptic Vortex Ring Research Articles

Interaction between an elliptic vortex ring and a bubble: effect of capture angle

Interaction between an elliptic vortex ring and a bubble: effect of capture angle

Probing dynamics of elliptical vortex rings via direct vorticity measurements with digital inline holography

Probing dynamics of elliptical vortex rings via direct vorticity measurements with digital inline holography

Influence of nozzle aspect ratio and orientation on flow characteristics of multiple elliptic jets

An experimental study is conducted to investigate the flow characteristics of multiple elliptic jets issuing from a 6×6 nozzle array at a relatively low-Reynolds number (Re (= Ub·de/ν) = 4.3×103). Two aspect ratios of the multiple elliptic nozzles (equivalent diameter, de, of a nozzle was 6 mm), namely a/b = 2.25 and 6.25, where a and b are the radii of the major and minor axes of an elliptic nozzle, respectively, and two nozzle azimuthal orientations, namely the same and alternate azimuthal orientation arrangements, were used. The mean and fluctuating velocities were measured using a constant-temperature hot-wire anemometer. The multiple jets located at the side of the ambient fluid were stretched due to interactions between the self-induced flow of an elliptic vortex ring and the secondary flow caused by the entrainment of the ambient fluid. For a/b = 2.25, axis switching occurred only once in the range of 1 < x/de ≤ 3 for both nozzle azimuthal orientations. For a/b = 6.25 and the same azimuthal orientation arrangement, axis switching occurred only once at 3 < x/de ≤ 5; axis switching did not occur for the alternate azimuthal orientation arrangement. Thus, the flow characteristics of multiple elliptic jets are influenced by the azimuthal orientation of adjoining nozzles.

Collision and reconnection of viscous elliptic vortex rings

It is well known that head-on collision of two identical circular vortex rings at moderate Reynolds numbers generates secondary vortex ringlets that propagate radially away from the center of the primary rings. In this paper, we show through numerical simulations that deforming vortex ring shape from a circle to an ellipse can lead to drastic changes in flow topology during the collision. The computations are performed for a range of flow parameters, including the aspect ratio of elliptic rings, the core size ratio (η), and the azimuthal angle between their major axes (θ). Results show that if two elliptic rings are identical and in the absence of azimuthal perturbation, the collision leads to the generation of two subelliptic vortex rings that propagate away from each other along a line approximately perpendicular to the original direction of approach of the primary rings. If, however, azimuthal perturbation is present, besides the two subelliptic rings, secondary vortex ringlets are generated on the remaining perimeter of the primary rings. On the other hand, if two primary elliptic rings are of unequal core sizes or if their major axes are not aligned to each other, the orientation and direction of travel of the two subelliptic rings generated deviate significantly from those involving two identical primary rings. If azimuthal perturbation is also present in these scenarios, more fine scale structures are generated and superimposed on the two subelliptic rings as well as the formation of secondary vortex ringlets. These findings may help us to explain some of the experimental observations reported in the literature and provide useful insights into the mixing processes of two directly opposed impinging elliptic jets.

Evolution of elliptic synthetic jets at low Reynolds number

The influence of the nozzle aspect ratio ($AR=1$, 2 and 4), stroke length ($L_{0}=1.85$, 3.7 and 5.55) and Reynolds number ($Re=79$, 158, 316 and 632) on the behaviour of elliptic synthetic jets is studied experimentally. Laser-induced fluorescence and two-dimensional and stereoscopic particle image velocimetry are used to analyse the vortex dynamics and evolution mechanism. It is found that the fluid elements around the major axis of an elliptic vortex ring move downstream faster and tend to approach the centreline, while the fluid elements around the minor axis move downstream at a slower speed and away from the centreline, thereby resulting in the occurrence of the well-known axis-switching phenomenon for elliptic synthetic jets. During this process, a pair of arc-like vortices forms ahead of the primary vortex ring, and they are constituted by streamwise vortices in the leg part and spanwise vortices in the head part; two pairs of streamwise vortices form from the inside of the primary vortex ring and develop in the tails. The streamwise vortices are pushed away progressively from the centreline by the synthetic jet vortex rings that are formed during the subsequent periods. These additional vortical structures for non-circular synthetic jets show regular and periodic characteristics, which are quite different from the previous findings for non-circular jets. Their mutual interaction with the vortex ring causes significant changes in the topology of elliptic synthetic jets, which further results in the variation of the statistical characteristics. Increasing the aspect ratio, stroke length and Reynolds number will make the evolution of the synthetic jet become more unstable and complex. In addition, the entrainment rate of an elliptical synthetic jet is larger than that of a circular synthetic jet and it increases with the nozzle aspect ratio ($AR\leqslant 4$) and Reynolds number. It is indicated that the formation of streamwise vortices could enhance the entrainment rate. This finding provides substantial evidence for the potential application of elliptic synthetic jets for effective flow control.

Reynolds-number scaling of vortex pinch-off on low-aspect-ratio propulsors

Impulsively started, low-aspect-ratio elliptical flat plates have been investigated experimentally to understand the vortex pinch-off dynamics at transitional and fully turbulent Reynolds numbers. The range of Reynolds numbers investigated is representative of those observed in animals that employ rowing and paddling modes of drag-based propulsion and manoeuvring. Elliptical flat plates with five aspect ratios ranging from one to two have been considered, as abstractions of propulsor planforms found in nature. It has been shown that Reynolds-number scaling is primarily determined by plate aspect ratio in terms of both drag forces and vortex pinch-off. Due to vortex-ring growth time scales that are longer than those associated with the development of flow instabilities, the scaling of drag is Reynolds-number-dependent for the aspect-ratio-one flat plate. With increasing aspect ratio, the Reynolds-number dependency decreases as a result of the shorter growth time scales associated with high-aspect-ratio elliptical vortex rings. Large drag peaks are observed during early-stage vortex growth for the higher-aspect-ratio flat plates. The collapse of these peaks with Reynolds number provides insight into the evolutionary convergence process of propulsor planforms used in drag-based swimming modes over diverse scales towards aspect ratios greater than one.

Evolution of an elliptic vortex ring in a viscous fluid

The evolution of a viscous elliptic vortex ring in an initially quiescent fluid or a linear shear flow is numerically simulated using a lattice Boltzmann method. A wide range of parameters are considered, namely, aspect ratios (AR) (1 ≤ AR ≤ 8), core radius to ring radius ratios (σ0) (0.1 ≤ σ0 ≤ 0.3), Reynolds number (Re) (500 ≤ Re ≤ 3000), and shear rate (K) (0 ≤ K ≤ 0.12). The study aims to fill the gap in the current knowledge of the dynamics of an elliptic vortex ring in a viscous fluid and also to address the issue of whether an elliptic ring undergoes vortex stretching and compression during axis-switching. In a quiescent fluid, results show that for fixed Re and σ0, there exists a critical aspect ratio (ARc), below which an elliptic ring undergoes oscillatory deformation with the period that increases with increasing AR. Above ARc, the vortex ring breaks up into two or three sub-rings after the first half-cycle of oscillation. While higher Reynolds number enhances vortex ring breakup, larger core size has the opposite effect. Contrary to an inviscid theory, an elliptic ring does undergo vortex stretching and compression during oscillatory deformation. In the presence of a linear shear flow, the vortex ring undergoes not only oscillatory deformation and stretching but also tilting as it propagates downstream. The tilting angle increases with the shear rate K and is responsible for inducing a “tail” that consists of a counter-rotating vortex pair (CVP) near the upstream end of the initial major axis after the first half-cycle of oscillation. For a high shear rate, the CVP wraps around the ring and transforms its topological structure from a simple elliptic geometry to a complicated structure that eventually leads to the generation of turbulence.

On vortex evolution in the wake of axisymmetric and non-axisymmetric low-aspect-ratio accelerating plates

Impulsively started, low-aspect-ratio elliptical and rectangular flat plates were investigated to determine the role of geometric asymmetries on vortex evolution. Dye visualizations, force measurements, and particle image velocimetry were used throughout to characterize the variation between shapes. For all the shapes studied, aspect ratio was observed to have the largest influence on force production and vortex evolution. Non-uniform curvature and edge discontinuities characteristic of ellipses (with aspect ratios other than one) and rectangles, respectively, play a secondary role. Furthermore, it was shown that stably attached vortex rings form behind the circular and square flat plates, which reduce the instantaneous drag force of each plate until the vortex rings break down. In contrast, all flat plates with aspect ratios other than one are subjected to fast-modulating elliptical vortex rings in the wake. These vortex rings increase the drag force of each plate until pinch-off occurs. Finally, pinch-off was identified with the streamwise pressure-gradient field and compared with formation numbers calculated using the circulation-based methodology, yielding good agreement for all plates with aspect ratios greater than one.

Experimental Investigation of the Evolution and Head-On Collision of Elliptic Vortex Rings

The head-on collision process of elliptic vortex rings was experimentally investigated using flow-visualization technique as well as particle image velocimetry (PIV). Elliptic vortex rings were generated by the movement of a free moving elliptic piston–cylinder arrangement. It was found that the Q value is positive in the vortex core region while negative in the regions around the vortex core, which indicates the rotational effect is dominated in the vortex core and strain effect is dominated around the vortex core. When two elliptic vortex rings move toward each other, both rings slow down and expand in diameter direction until they merge and expand in diameter direction rapidly. The collision process of two elliptic vortex rings and the newly generated vortex structure after collision are dominated by the elliptic vortex ring with larger aspect ratio and the trajectories of vortex core almost coincide in different Reynolds numbers.

Ontogenetic propulsive transitions by medusaeSarsia tubulosa

While swimming in their natural environment, marine organisms must successfully forage, escape from predation, and search for mates to reproduce. In the process, planktonic organisms interact with their fluid environment, generating fluid signatures around their body and in their downstream wake through ontogeny. In the early stages of their life cycle, marine organisms operate in environments where viscous effects dominate and govern physical processes. Ontogenetic propulsive transitions in swimming organisms often involve dramatic changes in morphology and swimming behavior. However, for organisms that do not undergo significant changes in morphology, swimming behavior or propulsive mode, how is their swimming performance affected? We investigated the ontogenetic propulsive transitions of the hydromedusa Sarsia tubulosa, which utilizes jet propulsion and possesses a similar bell morphology throughout its life cycle. We used digital particle image velocimetry and high-speed imaging to measure the body kinematics, velocity fields and wake structures induced by swimming S. tubulosa with bell exit diameters from 1 to 10 mm. Our experimental observations revealed three distinct classes of hydrodynamic wakes: elongated vortex rings for 10<Re<30 (1-2 mm bell exit diameter), classical elliptical vortex rings for Re>30 (larger than 2 mm bell exit diameter) and elliptical vortex rings (or leading vortex rings) followed by trailing jets for most instances where Re>100 (larger than 4 or 5 mm bell exit diameter). The relative travel distance and propulsive efficiency remained unchanged throughout ontogeny, and the swimming proficiency and hydrodynamic cost of transport decreased non-linearly.

Vortex tube reconnection at Re = 104

We present simulations of the long-time dynamics of two anti-parallel vortex tubes with and without initial axial flow, at Reynolds number Re = Γ/ν = 104. Simulations were performed in a periodic domain with a remeshed vortex method using 785 × 106 particles. We quantify the vortex dynamics of the primary vortex reconnection that leads to the formation of elliptical rings with axial flow and report for the first time a subsequent collision of these rings. In the absence of initial axial flow, a −5/3 slope of the energy spectrum is observed during the first reconnection of the tubes. The resulting elliptical vortex rings experience a coiling of their vortex lines imparting an axial flow inside their cores. These rings eventually collide, exhibiting a −7/3 slope of the energy spectrum. Studies of vortex reconnection with an initial axial flow exhibit also the −7/3 slope during the initial collision as well as in the subsequent collision of the ensuing elliptical vortex rings. We quantify the detailed vortex dynamics of these collisions and examine the role of axial flow in the breakup of vortex structures.

Numerical investigation of the evolution of elliptic vortex ring

In this paper, a three-dimensional vortex filament method is implemented to study the axis-switching period of an elliptic vortex ring. The change of the semi-axis length and the projection of a single elliptic ring are first compared with the literature. Then, the evolution of elliptic vortex rings with different circulations, aspect ratios and core radius-to-ring radius ratios are numerically reproduced, and the evolution of the velocity and aspect ratios are also studied to determine their influence on the motion of vortex rings. Furthermore, the axis-switching periods of elliptic rings for different cases are investigated, and an expression to fit all the cases is obtained.

Coherent structures in plasma-actuator controlled supersonic jets: Axisymmetric and mixed azimuthal modes

High-fidelity simulations are employed to study the effect of eight localized arc filament plasma actuators placed around the periphery of a Mach 1.3 converging-diverging nozzle exit. Emphasis is placed on understanding the coherent structures generated by axisymmetric (m = 0), flapping or first mixed (m = ±1) and second mixed (m = ±2) modes, which are excited at the jet column-mode frequency corresponding to a Strouhal number based on jet diameter of 0.3. Baseline (no control) and constant excitation (actuators on continuously) cases are also simulated. Comparisons with experimental results indicate that the computational model reproduces the main features induced by the actuators. Furthermore, the mean flow exhibits many similarities with the theoretical predictions of Cohen and Wygnanski [J. Fluid Mech. 176, 221 (1987)]. Overall, the results indicate a complex coherent structure generation, evolution, and disintegration process. For m = ±1, the phase-averaged flow reveals successive distorted elliptic vortex rings with axes in the flapping plane but alternating on either side of the jet axis. This generates a chain of structures each of which interacts with its predecessor on one side of the major plane and its successor on the other. Through self and mutual induction, the leading segment of each loop is pinched and passes through the previous ring before rapidly breaking up. The m = ±2 mode yields elliptic structures with major axes of successive rings being aligned with the two symmetry planes, which are orthogonal to each other. The minor axis side is pulled downstream faster than the rest of the structure because of the higher velocity near the jet centerline and self-induced effects, yielding a horse-shoe shape when viewed in profile. The m = 0 mode exhibits axisymmetric roll-up events, with vortex ribs in the braid regions connecting successive large coherent structures. The constant excitation (with largest energy input) and baseline cases are similar to each other, indicating that the direct effect of heating is negligible.

Experiments on long-wavelength instability and reconnection of a vortex pair

We present results from an experimental study of the long-wavelength “Crow” instability of a counter-rotating vortex pair. Employing a vortex generator in a water tank, comprising rotating horizontal computer-controlled flaps, we follow the vortices, marked by laser-induced fluorescence, using dual simultaneous light-sheets to determine the growth rate of the Crow instability as a function of the perturbation wavelength. In order to make a meaningful comparison to theory [S. C. Crow, AIAA J. 8, 2172 (1970); S. E. Widnall, Annu. Rev. Fluid Mech. 4, 141 (1975)], one requires, as input to the theory, the distribution of circumferential velocity and thereby the “equivalent” core size of the vortices. These distributions are measured using particle image velocimetry. The resulting agreement of the growth rates, between theory and experiment, appears to be very good. Of relevance to this study, we compute a stability diagram using the exact expression for the self-induced rotation speed of perturbation waves on the vortices. Measurement of the nondimensional reconnection time, when the vortex pair evolves into a series of rings at later times, is compared to existing numerical simulations, and we find evidence to suggest it varies with the inverse curvature of the vortices where they approach each other. The major axes of the resulting elliptical vortex rings switch with their minor axes, as the rings descend in the fluid, leading to a surprising phenomenon where the rings reconnect for the second time. By considering the conservation of impulse, and a linear relationship between the major axis length and the vortex spacing, we find that the relative descent speed of the rings increases with Reynolds number. It is coincidentally only at our chosen value that the descent speed of the subsequent rings appears to be close to the initial speed of the vortex pairs. Finally, the paper presents clear visualizations of the Crow instability phenomenon.

Fluid–structure interaction simulation of an avian flight model

A three-dimensional numerical avian model was developed to investigate the unsteady and turbulent aerodynamic performance of flapping wings for varying wingbeat frequencies and flow velocities (up to 12 Hz and 9 m s(-1)), corresponding to a reduced frequency range of k=0.22 to k=1.0 and a Reynolds number range of Re=16,000 to Re=50,000. The wings of the bird-inspired model consist of an elastic membrane. Simplifying the complicated locomotion kinematics to a sinusoidal wing rotation about two axes, the main features of dynamic avian flight were approximated. Numerical simulation techniques of fluid-structure interaction (FSI) providing a fully resolved flow field were applied to calculate the aerodynamic performance of the flapping elastic wings with the Reynolds averaged Navier-Stokes (RANS) approach. The results were used to characterize and describe the macroscopic flow configurations in terms of starting, stopping, trailing and bound vortices. For high reduced frequencies up to k=0.67 it was shown that the wake does not consist of individual vortex rings known as the discrete vortex ring gait. Rather, the wake is dominated by a chain of elliptical vortex rings on each wing. The structures are interlocked at the starting and stopping vortices, which are shed in pairs at the reversal points of the wingbeat cycle. For decreasing reduced frequency, the results indicate a transition to a continuous vortex gait. The upstroke becomes more aerodynamically active, leading to a consistent circulation of the bound vortex on the wing and a continuous spanwise shedding of small scale vortices. The formation of the vortices shed spanwise in pairs at the reversal points is reduced and the wake is dominated by the tip and root vortices, which form long drawn-out vortex structures.

Hydrodynamics of caudal fin locomotion by chub mackerel, Scomber japonicus (Scombridae).

As members of the derived teleost fish clade Scombridae, mackerel exhibit high-performance aquatic locomotion via oscillation of the homocercal forked caudal fin. We present the first quantitative flow visualization of the wake of a scombrid fish, chub mackerel Scomber japonicus (20-26 cm fork length, FL), swimming steadily in a recirculating flow tank at cruising speeds of 1.2 and 2.2FL s(-1). Thrust was calculated from wake measurements made separately in the horizontal (frontal) plane and vertical (parasagittal) planes using digital particle image velocimetry (DPIV) and compared with drag measurements obtained by towing the same specimens of S. japonicus post mortem. Patterns of flow indicated that the wake consisted of a series of linked elliptical vortex rings, each with central jet flow. The length of the minor axis (height) of the vortex rings was approximately equal to caudal fin span; the length of the major ring axis was dependent on swimming speed and was up to twice the magnitude of ring height. Profiles of wake velocity components were similar to theoretical profiles of vortex rings. Lift, thrust and lateral forces were calculated from DPIV measurements. At 1.2FL s(-1), lift forces measured relative to the X axis were low in magnitude (-1+/-1 mN, mean +/- S.D., N=20) but oriented at a mean angle of 6 degrees to the body axis. Reaction forces tend to rotate the fish about its center of mass, tipping the head down. Thus, the homocercal caudal fin of S. japonicus functions asymmetrically in the vertical plane. Pitching moments may be balanced anteriorly via lift generation by the pectoral fins. Thrust estimates for the two smallest fish based on DPIV analysis were not significantly different from drag measurements made by towing those same animals. At a speed of 1.2FL s(-1), thrust magnitude was 11+/-6 mN (mean +/- S.D, N=40). Lateral force magnitudes were approximately double thrust magnitudes (22+/-6 mN, mean +/- S.D., N=20), resulting in a mean mechanical performance ratio (thrust/total force) of 0.32 at 1.2FL s(-1). An increase in speed by a factor of 1.8 resulted in a mean increase in thrust by a factor of 4.4, a mean increase in lateral forces by a factor of 3, no change in the magnitude of lift produced and an increase in mean mechanical performance to 0.42. The relatively high lateral forces generated during swimming may be a necessary consequence of force production via propagated waves of bending.

Stationary configurations of a vortex filament in background flows

We investigate the three-dimensional configurations of a thin vortex filament embedded in background flows of an inviscid incompressible fluid, based on the localized induction approximation. An analogy is found between stationary configurations of a vortex filament in a steady flow and trajectories of a charged particle in a steady magnetic field. An analogy with trajectories of a sound ray in a steady low-Mach number flow is drawn as well. These analogies allow us to use the Lagrangian and Hamiltonian formalism of classical mechanics for calculating fully nonlinear forms of a vortex filament. The equations for the filament curve are integrable when the background flow has two spatial symmetries. Only integrable cases are explored in some detail. To illustrate the advantages of use of the analogy, we re-examine the invariant shapes of a vortex filament moving through a still fluid obtained by Kida (1981). Analogies of the Kida class with the motions of a heavy symmetrical top and a charged spherical pendulum in the field of a magnetic monopole are discussed. As next examples, we consider a point source (sink) and a line source (sink) flows. A filament takes the form of a non-uniform helix wound around a cone. The last example is a circular jet of a parabolic velocity profile. We construct a closed filament with azimuthal waves, lying on a plane orthogonal to the flow direction. Among them, an elliptic vortex ring is found to be distinct from higher waves.

SOUND RADIATION FROM ELLIPTIC VORTEX RINGS: EVOLUTION AND INTERACTION

Sound generation from the evolution and interaction of elliptic vortex rings is calculated numerically. An elliptic vortex ring emits a strong sound signal due to significant distortion and stretching of the vortex filament. At the far field, the acoustic pressure is linearly dependent on the third time derivatives of the vortex positions. Therefore, a numerical scheme on high resolution is employed to describe in detail the elliptic vortex ring motions, which are highly non-linear. Discretized vortex filaments are interpolated by using a parametric blending function to remove a possible numerical instability. The distorted vortex filament, owing to the self-induced velocity and the induced velocity from the other vortex segments, is redistributed at each time step. The accuracy and efficiency of the scheme are validated by comparisons with the analytic solution of circular vortex ring interaction. Acoustic signals from the evolution of a single elliptic vortex ring are obtained with various aspect ratios of the axes. Vortex motions and acoustic signals from two identical elliptic vortex rings, placed initially with selected separation distances, are calculated. Distinct periods are obtained from the evolution of each single elliptic vortex ring and the pairing process of two elliptic vortex rings. The calculated periods in the acoustic signals depend to a significant degree on the initial aspect ratio of the ring and the separation distance.

Evolution of single elliptic vortex rings

The evolution of single elliptic vortex rings for initial aspect ratio (AR)=2,4,6 has been studied. The incompressible Navier-Stokes equations are solved by a dealiased pseudo-spectral method with 643 grid points in a periodic cube. We find that there are three kinds of vortex motion asAR increases and bifurcation occurs at certainAR. The processes of advection, interaction and decay of vortex ring are discussed. Numerical results coincide with experiments and other authors' numerical simulation.

Three-dimensional vortex/wall interaction: Entrainment in numerical simulation and experiment

Three-dimensional interactions between an elliptic vortex ring and two no-slip parallel walls are visualized in a numerical simulation and an experiment. The vortex ring induces a surface vorticity layer on the wall which reconnects with the vortex ring. During the interaction core-area-varying axial waves are generated and carry the surface layer away from the wall. The vortex ring then becomes two tornado-like structures with strong upward helical flows near the wall surface, which provides entrainment of the surface fluid into the vortex structure. Similarities between the entrainment mechanisms of vorticity in the simulation and dye in the experiment from the surface layer are identified.