Vortex rings in radially confined domains

The dynamics of vortex rings generated within confined domains are relevant to important hydrodynamic processes such as flow past heart valves or severe arterial constrictions. However, despite their importance, these flows have not received much attention to date. This study examines the development and evolution of radially confined vortex rings. Time-resolved digital particle image velocimetry was used to investigate two levels of radial confinement and a range of vortex ring strengths. We found that for severely confined vortex rings, the formation time and peak circulation values were unaffected for L/D ₀?<?4 cases and slightly affected for larger L/D ₀ cases. After pinch-off, circulation decay was observed with an approximately constant normalized circulation decay rate. We found that with increasing circulation strength, the nondimensional time delay between the pinch-off and the onset of circulation decay reduced due to an increased vortex ring diameter within the confinement domain and a reduction in the necessary time for the surface induced and core vorticity regions to interact. This study uncovers the dynamics of radially confined vortex rings and show that the nondimensional rate of circulation decay is dependent on the vortex ring confinement ratio (ratio of the vortex ring orifice diameter to the diameter of the outer cylinder), and the time delay between the vortex pinch-off and the onset of circulation is dependent on the vortex ring circulation strength.     

On the flow field generated by a gradually varying flow through an orifice

The motion of a vortex ring generated by gradually varied flows through a thin-edged orifice has been investigated experimentally using particle image velocimetry. This flow reproduces the primary characteristics of many biological flows, such as cardiac flows through valves or jellyfish and squid propulsion. Even though vortex ring formation has been extensively studied, there is still interest in gradually varying inflows, i.e. the ones that are mostly found in previous conditions. The main purpose of this paper is to extend the time scaling already proposed in the literature to the entire cycle of vortex ring formation, pinch-off and free motion. To this end, eight inflow time laws have been tested, with different acceleration and deceleration phases. They have been selected in relation to practical applications by their resemblance to the main characteristics of cardiovascular and pulsed locomotion flows. Analysis of measured velocity and vorticity fields suggested a general criterion to establish the instant of vortex pinch-off directly from the imposed velocity program. This allows the proper scaling of the entire time evolution of the vortex ring for all tested inflows. Since it is quite easy to identify this instant experimentally, these results give a simple, practical rule for the computation of scales in vortex ring formation and development in the case of gradual inflows. The “slug model” has been used to test the proposed scaling and to obtain predictions for the vortex position, circulation and vorticity which are in agreement with experimental data.     

The formation of vortex rings in a strongly forced round jet

The periodic formation of vortex rings in the developing region of a round jet subjected to high-amplitude acoustic forcing is investigated with High-Speed Particle Image Velocimetry. Harmonic velocity oscillations ranging from 20 to 120% of the mean exit velocity of the jet was achieved at several forcing frequencies determined by the acoustic response of the system. The time-resolved history of the formation process and circulation of the vortex rings are evaluated as a function of the forcing conditions. Overall, high-amplitude forcing causes the shear layers of the jet to breakup into a train of large-scale vortex rings, which share many of the features of starting jets. Features of the jet breakup such as the roll-up location and vortex size were found to be both amplitude and frequency dependent. A limiting time-scale of t/T ≈ 0.33 based on the normalized forcing period was found to restrict the growth of a vortex ring in terms of its circulation for any given arrangement of jet forcing conditions. In sinusoidally forced jets, this time-scale corresponds to a kinematic constraint where the translational velocity of the vortex ring exceeds the shear layer velocity that imposes pinch-off. This kinematic constraint results from the change in sign in the jet acceleration between t = 0 and t = 0.33T. However, some vortex rings were observed to pinch-off before t = 0.33T suggesting that they had acquired their maximum circulation. By invoking the slug model approximations and defining the slug parameters based on the experimentally obtained time- and length-scales, an analytical model based on the slug and ring energies revealed that the formation number for a sinusoidally forced jet is L/D ≈ 4 in agreement with the results of Gharib et al. (J Fluid Mech 360:121–140, 1998).     

Effect of an Exit-Wedge Angle on Pinch-off and Mass Entrainment of Vortex Rings in Air

The effects of exit-wedge angle on evolution, formation, pinch-off, propagation and diffusive mass entrainment of vortex rings in air were studied using digital particle image velocimetry. Vortex rings were generated by passing a solenoid-valve-controlled air jet through a cylindrical nozzle. Experiments were performed over a wide range of exit-wedge angles (10° ≤ α ≤ 90°) of the cylindrical nozzle, initial Reynolds numbers (450 ≤ Re ≤ 4,580) and length-to-diameter ratios (0.9 ≤ L/D ≤ 11) of the air jet. For sharp edges (α ≤ 10°), a secondary ring may emerge at high Reynolds numbers, which tended to distort the vortex ring if ingested into it. For blunt edges (α ≥ 45°), by contrast, stable vortex rings were produced. The formation phase of a vortex ring was found to be closely related to its evolution pattern. An exit-wedge angle of 45° was found to be optimal for rapid pinch-off and faster propagation and better stability of a vortex ring. Diffusive mass entrainment was found to be between 35% and 40% in the early stages of a vortex ring propagation and it gradually increased throughout the course of vortex ring propagation. Entrainment fraction was found to be sensitive to the L/D ratio of the initial jet and decreases when the L/D ratio is increased.     

The influence of airfoil kinematics on the formation of leading-edge vortices in bio-inspired flight

The formation process of leading-edge vortices has been investigated experimentally using Particle Image Velocimetry. Various airfoil kinematics have been tested, including asymmetric and peak-shifted plunging motions, and are evaluated for Re = 30,000 and a reduced frequency range of 0.2 ≤ k ≤ 0.33. By measuring the growth in the leading-edge vortex during the dynamic-stall process, the vortex pinch-off process is examined based on the concept of an optimal vortex formation time. The various kinematics are then evaluated with respect to their associated vortex strength, timing and convection into the wake.     

Mechanism of formation of vortex rings

It is demonstrated experimentally that a vortex ring is created by the slowing down of the central part of a stream and that during formation of this ring the amount of the mass of liquid participating in its formation can change. The possibility is also established of obtaining liquid vortex blobs in the form of hemispheres or spheroids.Deceased.Translated from Izvestiya Akademii Nauk SSSR. Mekhanika Zhidkosti i Gaza, No. 2, pp. 19–26, March–April, 1973.In conclusion, the author thanks G. A. Lyubimov and A. T. Onufriev for useful discussions of the data from the investigations, and O. M. Belotserkovskii for interest in the work.     

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.     

Radiation and scattering of sound from a vortex ring

The mechanisms of generation and scattering of sound by a vortex ring are investigated on the basis of fluid dynamics. The vortex ring can serve as a simple dynamic model of the large-scale structures observed in shear flows. Moreover, it is probably the most easily studied vortex element that can be created experimentally. The sound scattering investigation also served to determine the extent to which the vortex is affected by sound, its selectivity with respect to such parameters as the acoustic frequency, the angle of incidence of the wave, etc. The perturbed motion is considered against the background of the steady-state motion of the ring. The perturbed motion in the vortex core is determined on the basis of linear incompressible fluid dynamics. Two terms of the expansion in the M number of the far acoustic field generated by the perturbations in the core are found in accordance with Lighthill's theory. The acoustic power and directivity of the radiation and the acoustic instability growth rate are calculated. It is shown that the scattering of sound by the vortex ring is a resonance effect, and the scattering amplitude near resonance is determined. The acoustic action on the hydrodynamic structure of the flow in the core of the ring is especially intense near the resonances and extends over a period short as compared with the characteristic time of the acoustic instability.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 83–95, May–June, 1987.     

Long-wave instability of a vortex ring

The instability of barrel-shaped vibrations of a vortex ring in an ideal fluid is investigated. These vibrations, stable for a vortex ring with a piecewise-uniform vorticity profile, appear to be unstable for a vortex ring with a smooth vorticity profile. The instability growth rate is found on the basis of the energy balance equation determining the energy transport from perturbations with negative energy in the critical layer to perturbations with positive energy in the rest of the flow. The curvature of the vortex ring, by virtue of which the perturbations with energies of different signs appear to be connected, plays a prominent role in the mechanism under consideration.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 6, pp. 72–78, November–December, 1995.     

Visual study of the three-dimensional flow diagram around a delta wing in a subsonic stream

Experimental methods, particularly visualization methods, permit a sufficiently detailed representation of the flow around bodies of complex shape, whose analysis meets with a considerable number of difficulties. The flow around a delta wing in the 1–90-m/sec free-stream velocity range is studied in this paper by using three-dimensional visual methods. Since stream separation and vortex-system formation play the main role in the flow formation over a wing surface, the main purpose of the experiment was to trace the physical process of dynamic development of the flow resulting in separation and vortex formation.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 190–194, March–April, 1976.     

Vortex formation process in gravity-driven starting jets

Experiments were conducted to investigate the vortex formation process in gravity-driven starting jets at three Reynolds numbers ( 3,528 and 4,716, where D is the nozzle diameter, the average discharging velocity and ν the kinematic viscosity). Planar laser induced fluorescence (PLIF) was used to visualize the flow while particle image velocimetry (PIV) was used to quantify the 2D velocity and vorticity fields. Vortex leapfrogging was found to appear at Re = 2,358, while pinch-off for the leading vortex was observed in the other two cases. Conditions for the vortex pinch-off appeared to be different from those found in the piston-driven starting jets. Although the leading vortex attained the maximum circulation and energy level very quickly after the jet was initiated, its detachment from the main stem may not be achieved necessarily. Attempt had been made to elaborate the different flow characteristics for respective cases from the related distribution of circulation and energy level via the measured velocity field by PIV.     

Computational study of buoyancy effects in a laminar starting jet

Vortical structures formed in evolving jets are important in applications such as fuel injection in diesel engines and fuel leaks. When the jet fluid is different from the ambient fluid, the buoyancy can play an important role in determining the jet flow structure, and hence, the entrainment and fluid mixing processes. In the present study, a jet of helium injected in air is investigated, with emphasis placed on delineating the buoyancy effects on vector–scalar fields during the starting phase. We utilize a computational model, previously validated to predict the flow field of low-density gas jets. The model incorporates finite volume approach to solve the transport equation of helium mass fraction coupled with conservation equations of mixture mass and momentum. Computations were performed for a laminar jet to characterize the advancing jet front, and to capture the formation and propagation of vortex rings and the related pinch-off process. Results show significant effects of buoyancy on jet advancement, as well as on vorticity and helium concentration in the core of the vortex rings.     

Wave formation in explosive welding

A hypothetical analogy between wave formation in explosive welding and the Karman vortex street is analyzed, and the physical laws of the wave formation process are investigated.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 63–72, May–June, 1971.     

The nonlinear evolution of swirling jets

We investigate the mechanisms of vorticity concentration, reorientation and stretching in a swirling jet, whose dynamics is dominated by the competition of a Kelvin-Helmholtz-type vortex sheet instability and a centrifugal Rayleigh instability. To this end, we employ an inviscid Lagrangian vortex filament technique. It is found that the axial jet velocity profile breaks the symmetry of the pure swirling flow. Conversely, the swirl is seen to modify the case dominated by a Kelvin-Helmholtz instability in that it results in the formation of counterrotating vortex rings. A pinch-off mechanism is observed which leads to a dramatic decrease in the local jet diameter. Furthermore, the vortex ring circulation is seen to be time dependent.

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Sommario In questo lavoro si analizza la dinamica della vorticità in un setto rotante in cui siano presenti, ed in competizione reciproca, fenomeni di instabilità di Kelvin-Helmholtz e di Rayleigh. A tale scopo si adotta una metodologia di soluzione non viscosa, Lagrangiana a filamenti vorticosi. Viene mostrato come il profilo di velocità assiale del getto altera la simmetria del moto di pura rotazione. Viceversa, la presenza della rotazione modifica il flusso dominato dall'instabilità di Kelvin-Helmholtz attraverso la formazione di anelli vorticosi controrotanti. L'interazione di questi due campi di velocità porta sia ad una considerevole riduzione del diametro locale del getto, sia ad una variazione temporale della circolazione degli anelli vorticosi.

     

Model of vortex ring formation

A semi-empirical model of vortex ring formation during exhaustion of a pulsed submerged jet from a circular orifice is presented. Formulas for determining the parameters of the vortex ring, depending on the conditions of formation of the latter, are derived. The calculated characteristics of the vortex ring as functions of criteria determining the vortex formation process are demonstrated to be in good agreement with experimental data. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 6, pp. 25–36, November–December, 2008.     

Numerical simulation and PIV study of compressible vortex ring evolution

Formation and evolution of a compressible vortex ring generated at the open end of a short driver section shock tube has been simulated numerically for pressure ratios (PR) of 3 and 7 in the present study. Numerical study of compressible vortex rings is essential to understand the complicated flow structure and acoustic characteristics of many high Mach number impulsive jets where simultaneously velocity, density and pressure fields are needed. The flow development, incident shock formation, shock diffraction, vortex ring formation and its evolution are simulated using the AUSM+ scheme. The main focus of the present study is to evaluate the time resolved vorticity field of the vortex ring and the shock/expansion waves in the starting jet for short driver section shock tubes—a scenario where little data are available in existing literature. An embedded shock and a vortex induced shock are observed for PR =  7. However the vortex ring remains shock free, compact and unaffected by the trailing jet for PR =  3. Numerical shadowgraph shows the evolution of embedded shock and shock/expansion waves along with their interactions. The velocity and vorticity fields obtained from simulation are validated with the particle image velocimetry results and these data match closely. The translational velocity of the vortex ring, velocity across the vortex and the centre line velocity of the jet obtained from simulation also agree well with the experimental results.     

Rising vortex ring in a viscous fluid

Most theoretical results for thermals, whose motion is determined by the complex interaction between dynamics and buoyancy, have been obtained numerically [1–4]. The analytic solutions for a convection element have been limited to consideration of the self-similar regime [5]. At the same time, the preself-similar stage of development of a vortex ring of dynamic origin has been described analytically [6]. This approach is now extended to a rising vortex ring. In this case a modification of the traditional formulation of the problem makes it possible to obtain an analytic solution of the problem of a weak thermal in the form of unsteady temperature, vorticity and stream function fields that tend in the limit to the self-similar regime. The rate of ascent of the convective vortex ring is found. A solution is obtained for the two-dimensional analog of the problem.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 42–48, May–June, 1989.     

Characteristics of counter-rotating vortex rings formed ahead of a compressible vortex ring

Characteristics of high Mach number compressible vortex ring generated at the open end of a short driver section shock tube is studied experimentally using high-speed laser sheet-based flow visualization. The formation mechanism and the evolution of counter rotating vortex ring (CRVR) formed ahead of the primary vortex ring are studied in details for shock Mach number (M) 1.7, with different driver section lengths. It has been observed that the strength of the embedded shock, which appears at high M, increases with time due to the flow expansion in the generating jet. Strength of the embedded shock also varies with radius; it is strong at smaller radii and weak at larger radii; hence, it creates a velocity gradient ahead of the embedded shock. At critical Mach number (M _c ≥ 1.6), this shear layer rolls up and forms a counter rotating vortex ring due to Biot-Savart induction of the vortex sheet. For larger driver section lengths, the embedded shock and the resultant shear layer persists for a longer time, resulting in the formation of multiple CRVRs due to Kelvin–Helmholtz type instability of the vortex sheet. CRVRs roll over the periphery of the primary vortex ring; they move upstream due to their self-induced velocity and induced velocity imparted by primary ring, and interact with the trailing jet. Formation of these vortices depends strongly upon the embedded shock strength and the length of the generating jet. Primary ring diameter increases rapidly during the formation and the evolution of CRVR due to induced velocity imparted on the primary ring by CRVR. Induced velocity of CRVR also affects the translational velocity of the primary ring considerably.     

A note on the cause of rebound in the head-on collision of a vortex ring with a wall

It is well documented that a trailing vortex pair approaching the ground, and a vortex ring colliding head-on with a rigid plane, experience a reversal in axial velocity which is commonly referred to as rebound. One explanation of this phenomenon suggests that it is essentially an inviscid process due to the effect of the finite core-size, whereas another and more widely accepted explanation attributes it to the influence of a secondary vortex which is generated at the surface by viscous effects. The aim of this paper is to assess experimentally the validity of these competing explanations. To achieve this, flow visualization studies of the collision of a vortex ring with a wall are compared with those of the head-on collision of two identical rings. The head-on collision is designed to mimic the inviscid, free-slip case of a ring/wall interaction. This paper describes the experimental findings.A version of this paper was presented at the 10th Australasian Fluid Mechanics Conference, University of Melbourne, Australia, 11–15 December 1989     

Dynamics of thin vortex rings in a low-viscosity fluid

In order to describe the unsteady flow of a viscous fluid induced by a toroidal vorticity distribution we use the two-scale expansion method [6], By this means we obtain a vorticity distribution in the core of the thin vortex ring that is consistent with the external potential flow. The time dependence of the flow characteristics obtained confirms the experimental results for the inertial regime. The interaction of coaxial vortex rings is investigated as an example.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.5, pp. 52–59, September–October, 1992.