On Approximating the Translational Velocity of Vortex Rings

2013 ◽  
Vol 135 (12) ◽  
Author(s):  
Michael Krieg ◽  
Kamran Mohseni
Keyword(s):  
Radial Velocity ◽  
Vortex Ring ◽  
Vortex Rings ◽  
Jet Flows ◽  
Volume Flux ◽  
Translational Velocity ◽  
Vortex System ◽  
Ring Configuration ◽  
Wide Range ◽  
Total Circulation

A method is presented whereby the translational velocity of a vortex ring can be approximated from the total circulation, impulse, and kinetic energy of the vortex system. Assuming a uniform vorticity density, these bulk quantities define a unique stable vortex ring configuration, and the translational velocity can be inferred from this configuration and the system scaling. Here, the accuracy of this approximation is presented for vortex rings formed from starting jets, and the translational velocity is also characterized as it relates to the driving parameters. The translational velocity is well approximated for a wide range of experimentally generated vortex rings. It is observed that starting jets with a converging radial velocity create vortex rings with a significantly higher translational velocity. The converging radial velocity was observed to increase translational velocity by as much as 30% over parallel jet flows with identical volume flux and nozzle diameter, but the exact increase is specific to the nozzle arrangement and driving conditions.

scholarly journals Collisions of solid particles with vortex rings in superfluid helium

2008 ◽  
Vol 605 ◽  
pp. 367-387 ◽  
Author(s):  
DEMOSTHENES KIVOTIDES ◽  
S. LOUISE WILKIN
Keyword(s):  
Vortex Ring ◽  
Superfluid Helium ◽  
Kelvin Waves ◽  
Solid Particles ◽  
Vortex Rings ◽  
Dynamical Process ◽  
Particle Vibrations ◽  
Wide Range ◽  
Self Consistent ◽  
Increasing Temperature

We have performed self-consistent computations of the interactions between a superfluid vortex-ring and a solid particle for two different vortex-ring sizes and over a wide range of temperatures. In all cases, the particle and the vortex eventually separate. For temperature T = 0 K, larger rings tend to trap the particle more effectively than smaller rings. Trying to escape the vortex, the particle follows a spiralling trajectory that could be experimentally detected. The dominant dynamical process is the excitation and propagation of Kelvin waves along the vortices. For T > 0 K, particle–vortex collision induces particle vibrations that are normal to the particle's direction of motion and might be experimentally detectable. In contrast to the T = 0 K case, smaller rings induce larger particle oscillation velocities. With increasing temperature, enhanced mutual friction damping of Kelvin waves leads to the damping of both the intensity and frequency of post-collision particle vibrations. Moreover, higher temperatures increase the relative impact of the Stokes drag force on particle motion.

Formation of vortex rings from falling drops

1967 ◽  
Vol 29 (1) ◽  
pp. 177-185 ◽  
Author(s):  
David S. Chapman ◽  
P. R. Critchlow
Keyword(s):  
Reynolds Number ◽  
Vortex Ring ◽  
Liquid Drop ◽  
Prolate Spheroid ◽  
Ring Formation ◽  
Vortex Rings ◽  
Surface Tensions ◽  
Wide Range ◽  
The Moment

A study of the formation of vortex rings when a liquid drop falls into a stationary bath of the same liquid has been made. The investigation covered liquids with a wide range in surface tensions, densities and viscosities. The results confirm the reported existence of optimum dropping height from which the drop develops into a superior vortex ring. The optimum heights are analysed, by a photographic study, in terms of the liquid drop oscillation. It is found that vortex rings are formed best if the drop is spherical and changing from an oblate to a prolate spheroid at the moment of contact with the bath. A Reynolds number has been determined for vortex rings produced at optimum dropping heights; these numbers are approximately 1000. A possible mechanism for the ring formation is suggested.

Optimal Vortex Ring Formation: A Study of Vortex Ring Formation in Starting and Pulsed Jets (Keynote)

2003 ◽  
Author(s):  
Morteza Gharib
Keyword(s):  
Vortex Ring ◽  
Basic Element ◽  
Ring Formation ◽  
Nozzle Diameter ◽  
Vortex Rings ◽  
Jet Flows ◽  
Ambient Fluid ◽  
Pulsed Jets ◽  
Vortex Ring Formation ◽  
Maximization Principle

Pulsatile jet flows are found in many industrially relevant fluid mechanical problems. A common feature of these flows is that they are fundamentally a series of fluid pulses. This aspect of pulsatile jets implies vortex rings are a basic element of the resulting flow. The significance of this observation is based in part on the tendency of vortex rings to entrain ambient fluid during their formation, but more so on the recent discovery of the phenomenon of vortex ring pinch off. This phenomenon was characterized for starting jets (individual pulses) showing that for pulses sufficiently long with respect to the nozzle diameter (i.e., sufficiently large L/D), the vortex ring stops forming and pinches off from the generating jet. This represents a maximization principle for vortex ring formation and suggests that any effects associated with vortex ring formation in pulsatile jets (e.g., enhanced entrainment), might be able to be optimized by properly selecting the L/D for each pulse.

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.

scholarly journals The role of optimal vortex formation in biological fluid transport

2005 ◽  
Vol 272 (1572) ◽  
pp. 1557-1560 ◽  
Author(s):  
John O Dabiri ◽  
Morteza Gharib
Keyword(s):  
Vortex Ring ◽  
Fluid Transport ◽  
Biological Fluid ◽  
Ring Formation ◽  
Vortex Rings ◽  
Jet Flows ◽  
Vortex Ring Formation ◽  
Biological Studies ◽  
Macro Scale ◽  
Animal Phyla

Animal phyla that require macro-scale fluid transport for functioning have repeatedly and often independently converged on the use of jet flows. During flow initiation these jets form fluid vortex rings, which facilitate mass transfer by stationary pumps (e.g. cardiac chambers) and momentum transfer by mobile systems (e.g. jet-propelled swimmers). Previous research has shown that vortex rings generated in the laboratory can be optimized for efficiency or thrust, based on the jet length-to-diameter ratio ( L / D ), with peak performance occurring at 3.5< L / D <4.5. Attempts to determine if biological jets achieve this optimization have been inconclusive, due to the inability to properly account for the diversity of jet kinematics found across animal phyla. We combine laboratory experiments, in situ observations and a framework that reduces the kinematics to a single parameter in order to quantitatively show that individual animal kinematics can be tuned in correlation with optimal vortex ring formation. This new approach identifies simple rules for effective fluid transport, facilitates comparative biological studies of jet flows across animal phyla irrespective of their specific functions and can be extended to unify theories of optimal jet-based and flapping-based vortex ring formation.

Flow Visualization for Pulsatile Vortex Ring Actuators

2008 ◽  
Author(s):  
Torin K. Clark ◽  
Michael Krieg ◽  
Kamran Mohseni
Keyword(s):  
Flow Visualization ◽  
Vortex Ring ◽  
Semimajor Axis ◽  
Time History ◽  
Vortex Rings ◽  
Translational Velocity ◽  
Vortex Ring Formation ◽  
History Of ◽  
Formation And Evolution ◽  
Visualization Techniques

Formation and evolution of vortex rings produced from pulsatile vortex ring thrusters are studied using flow visualization techniques. A vortex ring thruster consists of a cavity with an orifice at one end and an oscillating plunger at the opposite end which periodically creates a volume change in the cavity forcing a jet emission of fluid through the orifice into the surrounding reservoir. The ratio of the cylindrical jet length to its diameter, known as the stroke ratio, is a primary factor in the vortex ring formation characteristics. Flow visualization is employed in order to measure the translational velocity of the leading vortex ring for the range of stroke ratios of 2.96–5.92. The velocity time history of the vortex rings is studied with the results comparing well with theoretical approximations. Additionally vortex ring dimensions, including semimajor axis, semiminor axis, the ratio of these dimensions, and core to core radius, are considered. Also the volume of the vortex ring atmosphere is studied. The variations of these parameters with respect to stroke ratio, time, and distance from the orifice are investigated.

Stroke-averaged lift forces due to vortex rings and their mutual interactions for a flapping flight model

2010 ◽  
Vol 654 ◽  
pp. 453-472 ◽  
Author(s):  
X. X. WANG ◽  
Z. N. WU
Keyword(s):  
Vortex Ring ◽  
Lift Force ◽  
Flapping Flight ◽  
Vortex Rings ◽  
Moment Theory ◽  
Vortex System ◽  
Vortex Model ◽  
Negative Peak ◽  
Lift Forces ◽  
Flight Model

The stroke-averaged lift forces due to various vortex rings and their mutual interactions are studied using a flapping flight vortex model (Rayner, J. Fluid Mech., vol. 91, 1979, p. 697; Ellington, Phil. Trans. R. Soc. Lond. B, vol. 305, 1984b, p. 115). The vortex system is decomposed into the wing plane (wing-linked) vortex ring, a loop closed by the bound vortex and (arc-shaped) trailing vortex and the wake (the vortex rings shed previously). Using the vorticity moment theory (Wu, AIAA J., vol. 19, 1981, p. 432) we are able to identify the roles of vortex rings in lift production or reduction and express the lift as function of areal contraction or expansion of vortex rings. The wake vortex rings induce areal contraction of the trailing vortex, which should decrease the lift, but this decrease is exactly compensated by the inducing effect of the trailing arc on the wake. The wake reduces the lift through inducing a downwash velocity on the wing plane. The lift force is shown to drop to a minimum at the second half stroke, and then increases to an asymptotic value slightly below the lift at the first half stroke, in such a way following the experimental observation of Birch & Dickinson (Nature, vol. 412, 2001, p. 729). The existence of the negative peak of lift is due to the first shed vortex ring which, just at the second half stroke, lies in the close vicinity to the wing plane, leading to a peak of the wing plane downwash velocity.

Generation and characteristics of vortex rings free of piston vortex and stopping vortex effects

2016 ◽  
Vol 811 ◽  
pp. 138-167 ◽  
Author(s):  
Debopam Das ◽  
M. Bansal ◽  
A. Manghnani
Keyword(s):  
Vortex Ring ◽  
Early Stage ◽  
Bubble Diameter ◽  
Velocity Variation ◽  
Vortex Rings ◽  
Translational Velocity ◽  
Core Diameter ◽  
Stage Of Development ◽  
Theoretical Predictions ◽  
Ring Diameter

This paper presents a novel method for generating vortex rings that circumvents some of the drawbacks associated with existing methods in producing them. The predominant effects that occur in previously used methods are due to the presence of some of the other vortices such as the stopping vortex, piston vortex, image vortex and orifice lip generated vortices in the early stage of development. These disturbances influence the geometric, kinematic and dynamic characteristics of a vortex ring and lead to mismatches with classical theoretical predictions. It is shown in the present study that the disturbance free vortex rings produced follow the classical theory. Flow visualization and particle image velocimetry experiments are carried out in the Reynolds number (defined as the ratio of circulation ($\unicode[STIX]{x1D6E4}$) and kinematic viscosity ($\unicode[STIX]{x1D708}$)) range, $2270<Re_{\unicode[STIX]{x1D6E4}}<6790$, to find the translational velocity, total and core circulation, core diameter, ring diameter and bubble diameter. In reference to the earlier studies, significant differences are noted in the variations of the vortex ring diameter and core diameter. A model for the core diameter during the formation stage is proposed. The translational velocity variation with time shows that the second-order accurate formula derived using Hamilton’s equation by Fraenkel (J. Fluid Mech., vol. 51, 1972, pp. 119–135) predicts it best.

scholarly journals Modelling of confined vortex rings

2015 ◽  
Vol 774 ◽  
pp. 267-297 ◽  
Author(s):  
Ionut Danaila ◽  
Felix Kaplanski ◽  
Sergei Sazhin
Keyword(s):  
Vortex Ring ◽  
Vortex Rings ◽  
Translational Velocity ◽  
Ring Model ◽  
Axisymmetric Vortex ◽  
Integral Characteristics ◽  
Practical Engineering ◽  
Time Variations ◽  
Physical Features ◽  
Phd Thesis

This paper is focused on the investigation of vortex rings evolving in a tube. A new theoretical model for a confined axisymmetric vortex ring is developed. The predictions of this model are shown to be in agreement with available experimental data and numerical simulations. The model combines the viscous vortex ring model, developed by Kaplanski & Rudi (Phys. Fluids, vol. 17, 2005, 087101), with Brasseur’s (PhD thesis, Stanford University) approach to deriving a wall-induced streamfunction correction. Using the power-law assumption for the time variation of the viscous length of the vortex ring, the time variations of the main integral characteristics, circulation, kinetic energy and translational velocity are obtained. Direct numerical simulation (DNS) is used to test the range of applicability of the model and to investigate new physical features of confined vortex rings recently reported in the experimental study by Stewart et al. (Exp. Fluids, vol. 53, 2012, pp. 163–171). The model is shown to lead to a very good approximation of the spatial distribution of the Stokes streamfunction, obtained by DNS. The vortex signature and the time evolution of the energy of the vortex are also accurately predicted by the model. A procedure for fitting the model with realistic vortex rings, obtained by DNS, is suggested. This opens the way to using the model for practical engineering applications.

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