Scaling of the translational velocity of vortex rings behind conical objects

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.

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Flow Visualization for Pulsatile Vortex Ring Actuators

Volume 5: Design, Analysis, Control and Diagnosis of Fluid Power Systems ◽

10.1115/imece2008-68030 ◽

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.

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

Journal of Fluid Mechanics ◽

10.1017/jfm.2016.733 ◽

2016 ◽

Vol 811 ◽

pp. 138-167 ◽

Cited By ~ 3

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.

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Modelling of confined vortex rings

Journal of Fluid Mechanics ◽

10.1017/jfm.2015.261 ◽

2015 ◽

Vol 774 ◽

pp. 267-297 ◽

Cited By ~ 4

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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Vortex rings drive entrainment and cooling in flow induced by a spark discharge

Physical Review Fluids ◽

10.1103/physrevfluids.5.114501 ◽

2020 ◽

Vol 5 (11) ◽

Author(s):

Bhavini Singh ◽

Lalit K. Rajendran ◽

Jiacheng Zhang ◽

Pavlos P. Vlachos ◽

Sally P. M. Bane

Keyword(s):

Spark Discharge ◽

Vortex Rings

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Viscous Flow Around a Rigid Body Performing a Time-periodic Motion

Journal of Mathematical Fluid Mechanics ◽

10.1007/s00021-021-00556-4 ◽

2021 ◽

Vol 23 (1) ◽

Author(s):

Thomas Eiter ◽

Mads Kyed

Keyword(s):

Rigid Body ◽

Sobolev Spaces ◽

Periodic Motion ◽

Viscous Incompressible Fluid ◽

Body Motion ◽

Translational Velocity ◽

Ill Posed ◽

Homogeneous Sobolev Spaces ◽

The Mean ◽

Time Periodic

AbstractThe equations governing the flow of a viscous incompressible fluid around a rigid body that performs a prescribed time-periodic motion with constant axes of translation and rotation are investigated. Under the assumption that the period and the angular velocity of the prescribed rigid-body motion are compatible, and that the mean translational velocity is non-zero, existence of a time-periodic solution is established. The proof is based on an appropriate linearization, which is examined within a setting of absolutely convergent Fourier series. Since the corresponding resolvent problem is ill-posed in classical Sobolev spaces, a linear theory is developed in a framework of homogeneous Sobolev spaces.

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Formation number of confined vortex rings

Physical Review Fluids ◽

10.1103/physrevfluids.3.094701 ◽

2018 ◽

Vol 3 (9) ◽

Cited By ~ 1

Author(s):

I. Danaila ◽

F. Luddens ◽

F. Kaplanski ◽

A. Papoutsakis ◽

S. S. Sazhin

Keyword(s):

Vortex Rings ◽

Formation Number

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Hydrodynamic Forces Exerting on an Oscillating Cylinder under Translational Motion in Water Covered by Compressed Ice

Water ◽

10.3390/w13060822 ◽

2021 ◽

Vol 13 (6) ◽

pp. 822

Author(s):

Yury Stepanyants ◽

Izolda Sturova

Keyword(s):

Lift Force ◽

Wave Motion ◽

Translational Motion ◽

Added Mass ◽

Hydrodynamic Forces ◽

Wave Resistance ◽

Translational Velocity ◽

Damping Coefficients ◽

Incompressible Ideal Fluid ◽

Theoretical Results

This paper presents the calculation of the hydrodynamic forces exerted on an oscillating circular cylinder when it moves perpendicular to its axis in infinitely deep water covered by compressed ice. The cylinder can oscillate both horizontally and vertically in the course of its translational motion. In the linear approximation, a solution is found for the steady wave motion generated by the cylinder within the hydrodynamic set of equations for the incompressible ideal fluid. It is shown that, depending on the rate of ice compression, both normal and anomalous dispersion can occur in the system. In the latter case, the group velocity can be opposite to the phase velocity in a certain range of wavenumbers. The dependences of the hydrodynamic loads exerted on the cylinder (the added mass, damping coefficients, wave resistance and lift force) on the translational velocity and frequency of oscillation were studied. It was shown that there is a possibility of the appearance of negative values for the damping coefficients at the relatively big cylinder velocity; then, the wave resistance decreases with the increase in cylinder velocity. The theoretical results were underpinned by the numerical calculations for the real parameters of ice and cylinder motion.

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