Deformation and breakup of bubbles interacting with single vortex rings

2021 ◽  
pp. 103734
Author(s):  
F.J. Foronda-Trillo ◽  
J. Rodríguez-Rodríguez ◽  
C. Gutiérrez-Montes ◽  
C. Martínez-Bazán
Keyword(s):  
Vortex Rings ◽  
Single Vortex

scholarly journals About bubbles and vortex rings

2015 ◽  
Vol 780 ◽  
pp. 1-4 ◽  
Author(s):  
C. Martínez-Bazán
Keyword(s):  
Vortex Rings ◽  
Complex Mechanism ◽  
Complex Interplay ◽  
Single Vortex ◽  
Vortical Structures ◽  
Turbulent Eddies ◽  
Deformation Dynamics ◽  
Bubble Interaction ◽  
Elongation Process ◽  
Shed Light

Bubble interaction with turbulence has a number of applications in engineering processes and nature. The complex interplay between the vortical structures present in a turbulent flow and the bubbles drives their deformation dynamics, which may lead to bubble rupture under the appropriate conditions. Such a process includes nonlinear interaction among the turbulent eddies and between the eddies and the bubbles. Thus, the coupled evolution of a single vortex ring with a bubble represents an idealized scenario that can provide a framework to shed light on understanding such a common and complex mechanism. Jha & Govardhan (J. Fluid Mech., vol. 773, 2015, pp. 460–497) have performed elegant experiments generating controlled vortex rings and injecting bubbles of known volume. They have reported interesting results on the elongation process of the bubble and its impact on vortex dynamics.

scholarly journals Structure of the vortex wake in hovering Anna's hummingbirds ( Calypte anna )

2013 ◽  
Vol 280 (1773) ◽  
pp. 20132391 ◽  
Author(s):  
M. Wolf ◽  
V. M. Ortega-Jimenez ◽  
R. Dudley
Keyword(s):  
Flow Visualization ◽  
Vortex Structure ◽  
Force Production ◽  
Vortex Rings ◽  
Vortex Wake ◽  
Secondary Vortex ◽  
Single Vortex ◽  
Discrete Vortex ◽  
Weight Support ◽  
Calypte Anna

Hummingbirds are specialized hoverers for which the vortex wake has been described as a series of single vortex rings shed primarily during the downstroke. Recent findings in bats and birds, as well as in a recent study on Anna's hummingbirds, suggest that each wing may shed a discrete vortex ring, yielding a bilaterally paired wake. Here, we describe the presence of two discrete rings in the wake of hovering Anna's hummingbirds, and also infer force production through a wingbeat with contributions to weight support. Using flow visualization, we found separate vortices at the tip and root of each wing, with 15% stronger circulation at the wingtip than at the root during the downstroke. The upstroke wake is more complex, with near-continuous shedding of vorticity, and circulation of approximately equal magnitude at tip and root. Force estimates suggest that the downstroke contributes 66% of required weight support, whereas the upstroke generates 35%. We also identified a secondary vortex structure yielding 8–26% of weight support. Lift production in Anna's hummingbirds is more evenly distributed between the stroke phases than previously estimated for Rufous hummingbirds, in accordance with the generally symmetric down- and upstrokes that characterize hovering in these birds.

scholarly journals XX. The potential of an anchor ring.-Part II

1893 ◽  
Vol 184 ◽  
pp. 1041-1106 ◽  
Keyword(s):  
Vortex Ring ◽  
Cross Section ◽  
Steady Motion ◽  
Vortex Rings ◽  
Laplace’S Equation ◽  
Single Vortex ◽  
Laplace's Equation ◽  
The Stability ◽  
Work Done

This paper is a continuation of that at pp. 43-95 suprd , on “The Potential of an Anchor Bing.” In that paper the potential of an anchor ring was found at all external points; in this/its value is determined at internal points. The annular form of rotating gravitating fluid was also discussed in that paper; here the stability of such a ring is considered. In addition, the potential of a ring whose cross-section is elliptic, being of interest in connection with Saturn, is obtained. The similarity of the methods employed, as well as of the analysis, has led me to give in this paper also a determination of the steady motion of a single vortex-ring in an infinite fluid, and of several fine vortex rings on the same axis. In Section I. solutions of Laplace’s equation applicable to space inside an anchor ring are obtained. These results are applied to obtain the potential of a solid ring at internal points, and also of a distribution of matter on the surface of the ring. The work done in collecting the ring from infinity is obtained.

scholarly journals The vibrations of an infinite system of vortex rings

1927 ◽  
Vol 116 (774) ◽  
pp. 352-379 ◽  
Keyword(s):  
Infinite System ◽  
Vortex Rings ◽  
Critical Ratio ◽  
Single Vortex ◽  
Natural Modes ◽  
Finite Section ◽  
Modes Of Vibration ◽  
Central Filament ◽  
Set Up ◽  
The Stability

The vibrations that may be set up and maintained in the central filament of a single vortex ring of small but finite section have been investi­gated by Thomson and others, but no corresponding investigation appears to have been undertaken for a system of parallel rings, although the matter is of some importance in connection with the state of motion behind a moving body. In a previous paper the authors have examined the stability of an infinite system of equal vortex rings situated in parallel planes with their centres evenly spaced along an infinite line and with their planes at right angles to that line. Instability was there found to occur for disturbances confined to displacements of the centre of each ring along the central axis, the filament of each ring still remaining circular. In the present paper the investigation is extended to deformation of the vortex filaments, and some interesting conclusions are drawn regarding natural modes of vibration of the infinite system of vortex rings, such as may occur without the longitudinal instability referred to in the previous paper becoming apparent. It is found, for example, that for any given ratio of radius of ring section to radius of ring there exists a critical ratio of ring spacing to radius, separating the region of stable oscillation from that of instability, a result in some respects closely analogous to that found by Kármán for the stability of two infinite parallel rows of rectilinear vortices.

Internal structure of vortex rings and helical vortices

2015 ◽  
Vol 785 ◽  
pp. 219-247 ◽  
Author(s):  
Francisco J. Blanco-Rodríguez ◽  
Stéphane Le Dizès ◽  
Can Selçuk ◽  
Ivan Delbende ◽  
Maurice Rossi
Keyword(s):  
Internal Structure ◽  
Strain Field ◽  
Stokes Equations ◽  
External Solution ◽  
Quantitative Agreement ◽  
Vortex Rings ◽  
Radius Of Curvature ◽  
Asymptotic Results ◽  
Single Vortex ◽  
Helical Vortices

The internal structure of vortex rings and helical vortices is studied using asymptotic analysis and numerical simulations in cases where the core size of the vortex is small compared to its radius of curvature, or to the distance to other vortices. Several configurations are considered: a single vortex ring, an array of equally-spaced rings, a single helix and a regular array of helices. For such cases, the internal structure is assumed to be at leading order an axisymmetric concentrated vortex with an internal jet. A dipolar correction arises at first order and is shown to be the same for all cases, depending only on the local vortex curvature. A quadrupolar correction arises at second order. It is composed of two contributions, one associated with local curvature and another one arising from a non-local external 2-D strain field. This strain field itself is obtained by performing an asymptotic matching of the local internal solution with the external solution obtained from the Biot–Savart law. Only the amplitude of this strain field varies from one case to another. These asymptotic results are thereafter confronted with flow solutions obtained by direct numerical simulation (DNS) of the Navier–Stokes equations. Two different codes are used: for vortex rings, the simulations are performed in the axisymmetric framework; for helices, simulations are run using a dedicated code with built-in helical symmetry. Quantitative agreement is obtained. How these results can be used to theoretically predict the occurrence of both the elliptic instability and the curvature instability is finally addressed.

On the formation and propagation of vortex rings and pairs of vortex rings

1997 ◽  
Vol 332 ◽  
pp. 121-139 ◽  
Author(s):  
S. L. Wakelin ◽  
N. Riley
Keyword(s):  
Similarity Theory ◽  
Laminar Flows ◽  
Plane Boundary ◽  
Vortex Rings ◽  
Single Vortex ◽  
Circular Annulus ◽  
Circular Orifice ◽  
High Reynolds ◽  
Two Parameters ◽  
Gap Width

Axisymmetric high-Reynolds-number laminar flows are simulated numerically. In particular, we consider the formation and propagation of single vortex rings from a circular orifice in a plane boundary, and pairs of vortex rings from a circular annulus in a plane boundary. During formation, single rings grow within an essentially potential flow, as in the similarity theory of Pullin (1979). When released they are shown to propagate in an almost inviscid manner, as described by Saffman (1970). Pairs of vortex rings, formed at a circular annulus, have been studied by Weidman & Riley (1993), both experimentally and computationally. They conclude from their observations that the behaviour of the rings depends primarily upon two parameters, namely the impulse applied to the fluid, during ring formation, and the gap width of the annulus. The results we present in this paper confirm the dependence of the flow on these parameters.

A universal time scale for vortex ring formation

1998 ◽  
Vol 360 ◽  
pp. 121-140 ◽  
Author(s):  
MORTEZA GHARIB ◽  
EDMOND RAMBOD ◽  
KARIM SHARIFF
Keyword(s):  
Vortex Ring ◽  
Vortex Rings ◽  
Water Tank ◽  
Single Vortex ◽  
Piston Cylinder ◽  
Vortex Ring Formation ◽  
Image Velocimetry ◽  
Wide Range ◽  
Formation Number ◽  
Piston Stroke

The formation of vortex rings generated through impulsively started jets is studied experimentally. Utilizing a piston/cylinder arrangement in a water tank, the velocity and vorticity fields of vortex rings are obtained using digital particle image velocimetry (DPIV) for a wide range of piston stroke to diameter (L/D) ratios. The results indicate that the flow field generated by large L/D consists of a leading vortex ring followed by a trailing jet. The vorticity field of the leading vortex ring formed is disconnected from that of the trailing jet. On the other hand, flow fields generated by small stroke ratios show only a single vortex ring. The transition between these two distinct states is observed to occur at a stroke ratio of approximately 4, which, in this paper, is referred to as the ‘formation number’. In all cases, the maximum circulation that a vortex ring can attain during its formation is reached at this non-dimensional time or formation number. The universality of this number was tested by generating vortex rings with different jet exit diameters and boundaries, as well as with various non-impulsive piston velocities. It is shown that the ‘formation number’ lies in the range of 3.6–4.5 for a broad range of flow conditions. An explanation is provided for the existence of the formation number based on the Kelvin–Benjamin variational principle for steady axis-touching vortex rings. It is shown that based on the measured impulse, circulation and energy of the observed vortex rings, the Kelvin–Benjamin principle correctly predicts the range of observed formation numbers.

Evolution and breakup of vortex rings in straining and shearing flows

1994 ◽  
Vol 273 ◽  
pp. 285-312 ◽  
Author(s):  
J. S. Marshall ◽  
J. R. Grant
Keyword(s):  
Linear Theory ◽  
Vortex Pair ◽  
Small Strain ◽  
Oscillation Period ◽  
Numerical Calculations ◽  
Vortex Rings ◽  
Single Vortex ◽  
Discrete Vortex ◽  
Initial Plane ◽  
Shear Rates

A study of the effect of external straining and shearing flows on the evolution and form of breakup of vortex rings has been performed. Two orientations each of straining and shearing flows are considered. A theoretical analysis of the ring motion for small strain and shear rates is performed, and it is found that for shearing and straining flows in the plane of the ring, the ring may oscillate periodically. For a straining flow with compression normal to the initial plane of the ring, the linear theory predicts that the ring radius will expand with time. For shearing flow normal to the initial plane of the ring, the linear theory predicts tilting of the ring in the direction of the shear flow rotation.Numerical calculations are performed with both single vortex filaments and with a three-dimensional discrete vortex element method. The numerical calculations confirm the predictions of the linear theory for values of strain and shear rates below a certain critical value (which depends on the ratio R/σ0 of initial ring to core radii), whereas for strain and shear rates above this value the ring becomes very elongated with time and eventually pinches off. Three distinct regimes of long-time behaviour of the ring have been identified. Regime selection depends on initial ring geometry and orientation and on values of strain and shear rates. These regimes include (i) periodic oscillations with no pinching off, (ii) pinching off at the ring centre, and (iii) development of an elongated vortex pair at the ring centre and wider ‘heads’ near the ends (with pinching off just behind the heads). The boundaries of these regimes and theoretical reasons for the vortex behaviour in each case are described. It is also shown that the breakup of stretched vortex rings exhibits a self-similar behaviour, in which the number and size of ‘offspring’ vortices, at the point of pinching-off the ring, may be scaled by the product of the strain rate e (or shear rate s) and the oscillation period τ of a slightly elliptical ring with mean radius R.

Numerical Investigation of Vortex Ring Ground Plane Interactions

2017 ◽  
Vol 139 (7) ◽  
Author(s):  
K. Bourne ◽  
S. Wahono ◽  
A. Ooi
Keyword(s):  
Vortex Ring ◽  
Ground Plane ◽  
Vortex Structures ◽  
Vortex Rings ◽  
Angle Of Incidence ◽  
Flow Conditions ◽  
Single Vortex ◽  
Wall Flow ◽  
The Impact ◽  
Near Wall

The interaction between multiple laminar thin vortex rings and solid surfaces was studied numerically so as to investigate flow patterns associated with near-wall flow structures. In this study, the vortex–wall interaction was used to investigate the tendency of the flow toward recirculatory behavior and to assess the near-wall flow conditions. The numerical model shows very good agreement with previous studies of single vortex rings for the case of orthogonal impact (angle of incidence, θ = 0 deg) and oblique impact (θ = 20 deg). The study was conducted at Reynolds numbers 585 and 1170, based on the vortex ring radius and convection velocity. The case of two vortex rings was also investigated, with particular focus on the interaction of vortex structures postimpact. Compared to the impact of a single ring with the wall, the interaction between two vortex rings and a solid surface resulted in a more highly energized boundary layer at the wall and merging of vortex structures. The azimuthal variation in the vortical structures yielded flow conditions at the wall likely to promote agitation of ground based particles.

Elliptic instability of a curved Batchelor vortex

2016 ◽  
Vol 804 ◽  
pp. 224-247 ◽  
Author(s):  
Francisco J. Blanco-Rodríguez ◽  
Stéphane Le Dizès
Keyword(s):  
Growth Rate ◽  
Vortex Ring ◽  
Flow Parameter ◽  
Axial Flow ◽  
Vortex Rings ◽  
Single Vortex ◽  
General Stability ◽  
Helical Vortices ◽  
Helical Vortex ◽  
Instability Growth

The occurrence of the elliptic instability in rings and helical vortices is analysed theoretically. The framework developed by Moore & Saffman (Proc. R. Soc. Lond. A, vol. 346, 1975, pp. 413–425), where the elliptic instability is interpreted as a resonance of two Kelvin modes with a strained induced correction, is used to obtain the general stability properties of a curved and strained Batchelor vortex. Explicit expressions for the characteristics of the three main unstable modes are obtained as a function of the axial flow parameter of the Batchelor vortex. We show that vortex curvature adds a contribution to the elliptic instability growth rate. The results are applied to a single vortex ring, an array of alternate vortex rings and a double helical vortex.

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