Development Of Vortex Ring Research Articles

The mechanisms of jetting, vortex sheet, and vortex ring development in asymmetric bubble dynamics

Bubble dynamics near a rigid boundary at Reynolds numbers of O(10–100) exhibit significant viscous effect, associated with ultrasonic cavitation and cavitation damage. We study this phenomenon experimentally using high-speed photography of spark-generated bubble oscillation in silicone oils, whose viscosity is about three orders larger than water. Comparing to bubbles in water, bubble surfaces in silicone oil are more stable and thus more cycles of oscillations may be observed and studied. Additionally, we investigate this phenomenon numerically using the volume of fluid method. We propose a non-reflective boundary condition, reducing the computational domain's dimensions tenfold based on the far-field asymptotic behavior. This paper pays particular attention in the mechanism for the bubble jetting, the vortex sheet, and the vortex ring development. Initially, a stagnation point at the bubble center moves away from the wall owing to asymmetric bubble expansion, leaving the bubble around the moment the bubble reaches its maximum volume. During this process, a vortex sheet forms inside the bubble. As the vortex sheet approaches the bubble interface, it transfers momentum to the gas–liquid interface, influencing the flow near the bubble wall. The high-pressure zone at the stagnation point drives the distal bubble surface to collapse first and fastest subsequently. This asymmetric collapse generates circulation around the bubble's side cross section, leading to the development of a vortex ring within the bubble gas at the outer rim of the decaying vortex sheet. The vortex ring, with its core inside the bubble gas, functions like a bearing system in accelerating the jet.

Noninvasive Determination of Vortex Formation Time Using Transesophageal Echocardiography During Cardiac Surgery.

Trans-mitral blood flow produces a three-dimensional rotational body of fluid, known as a vortex ring, that enhances the efficiency of left ventricular (LV) filling compared with a continuous linear jet. Vortex ring development is most often quantified with vortex formation time (VFT), a dimensionless parameter based on fluid ejection from a rigid tube. Our group is interested in factors that affect LV filling efficiency during cardiac surgery. In this report, we describe how to use standard two-dimensional (2D) and Doppler transesophageal echocardiography (TEE) to noninvasively derive the variables needed to calculate VFT. We calculate atrial filling fraction (β) from velocity-time integrals of trans-mitral early LV filling and atrial systole blood flow velocity waveforms measured in the mid-esophageal four-chamber TEE view. Stroke volume (SV) is calculated as the product of the diameter of the LV outflow track measured in the mid-esophageal long axis TEE view and the velocity-time integral of blood flow through the outflow track determined in the deep transgastric view using pulse-wave Doppler. Finally, mitral valve diameter (D) is determined as the average of major and minor axis lengths measured in orthogonal mid-esophageal bicommissural and long axis imaging planes, respectively. VFT is then calculated as 4 × (1-β) × SV/(πD3). We have used this technique to analyze VFT in several groups of patients with differing cardiac abnormalities. We discuss our application of this technique and its potential limitations and also review our results to date. Noninvasive measurement of VFT using TEE is straightforward in anesthetized patients undergoing cardiac surgery. The technique may allow cardiac anesthesiologists and surgeons to assess the impact of pathological conditions and surgical interventions on LV filling efficiency in real time.

Properties of velocity field in the vicinity of synthetic jet generator

The paper presents the results of experimental investigation of velocity field in the vicinity of synthetic jet actuator as a function of Stokes number and for constant Reynolds number. A constant temperature hot-wire anemometer with tungsten-platinum coated single wire probe used for the velocity measurements. Synthetic jet flow visualization was presented, especially process of vortex ring development. Synthetic jet velocity profiles were compared with a solution to fully-developed pipe flow with an oscillating pressure gradient.

Recent development of vortex ring impinging onto the wall

It has been more than one hundred years for the study on vortex structure, which is a very important flow structure in the fluid mechanics. Recently, the interaction between vortex ring and solid wall has attracted more and more attentions, for not only it is a very common phenomenon in the engineering, but also it could benefit the understanding of the mechanism of interaction between the vortex and the boundary layer. The interaction between the vortex ring and the wall is reviewed in this paper, including the evolution of vortex ring, the mechanics of vortex ring azimuthal instabilities, the achievements of synthetic vortex ring impinging onto the solid wall, its potential application to heat transfer, and the influence of vortex ring compression. Besides, the latest results of vortex ring impinging onto porous wall are presented, and the future possible investigation direction on this issue is suggested.

A single camera volumetric particle image velocimetry and its application

Volumetric particle image velocimetry (VPIV) refers to a PIV-based technique which can obtain full velocity components in a three-dimensional measurement volume. A new VPIV method with a single lens was developed. A three-vision prism was used to make viewing from different angles using one camera. The technique was tested and successfully applied to a three-dimensional three-component (3D3C) measurement of a zero-net-mass-flux jet flow. The accuracy of the measurement was investigated, specifically in steps of calibration, self-calibration and particle triangulation. Time sequence of a vortex ring development was presented. It was shown that the measurement has high accuracy with validation rate of velocity vector reaching about 95%. The flow with vortex ring passing the measurement volume was studied using both swirl strength and vorticity magnitude criteria. Through comparison, the swirl criterion was found to be superior to the criterion of vorticity in differentiating the rotation motion and the free shear.

Dynamics of vortex rings and spray-induced vortex ring-like structures

Analytical formulae, predicted by recently developed vortex ring models, in the limit of small Reynolds numbers ( R e ), are compared with numerical solutions of the underlying equation for vorticity and experimental data. Particular attention is focused on the recently developed generalised vortex ring model in which the time evolution of the thickness of the vortex ring core L is approximated as a t b , where a and b are constants ( 1 / 4 ≤ b ≤ 1 / 2 ). This model incorporates both the laminar model for b = 1 / 2 and the fully turbulent model for b = 1 / 4 . A new solution for the normalised vorticity distribution is found in the form ω 0 + R e ω 1 , where ω 0 is the value of normalised vorticity predicted by the classical Phillips solution. This solution shows the correct trends in the redistribution of vorticity due to the Reynolds number effect, and it predicts the increase in the volume of fluid carried inside the vortex ring. It is emphasised that although the structures of vortex rings predicted by analytical formulae, based on the linear approximation, and numerical calculations for arbitrary R e are visibly different for realistic Reynolds numbers, the values of integral characteristics, such as vortex ring translational velocity and energy, predicted by both approaches, turn out to be remarkably close. The values of velocities in the region of maximal vorticity, predicted by the generalised vortex ring model, are compared with the results of experimental studies of vortex ring-like structures in gasoline engine-like conditions with a high-pressure (100 bar) injector. The data analysis is focused on the direct measurements of droplet axial velocities in the regions of maximal vorticity. Most of the values of these velocities lie between the theoretically predicted values corresponding to the later stage of vortex ring development between b = 1 / 4 (fully developed turbulence) and 1 / 2 (laminar case).

Experimental studies of the influence of parameters on axisymmetric synthetic jets

This paper studies the influences of two dimensionless parameters, the Reynolds number and dimensionless stroke, on an axisymmetric synthetic jet by using flow visualization and particle image velocimetry (PIV) techniques. The flow visualization results and the relevant analyses, such as the formation and state of the vortex ring, the time-averaged streamwise velocity and kinetic energy of the fluctuating motion, etc., are provided. It was found that the Reynolds number does not influence the formation location of vortex rings; however, with increasing Reynolds number, the vortex rings go through the laminar–turbulent transition and tend to lose stability, leading to breakdown. In addition, the similarity of the jet kinetic energy distribution of fluctuating motion can be reached in a short distance downstream from the orifice, and the characteristics of conventional turbulent jets also appear as the Reynolds number is increased to a certain value. The dimensionless stroke strongly influences the formation and development of vortex rings. Furthermore, the experimental investigations on an axisymmetric synthetic jet actuated by a novel actuator signal, proposed by Zhang and Wang [16], are implemented in the present paper, and the ‘actual efficient stroke’ concept is introduced.

Impact of buoyancy on vortex ring development in the near field

The development of a buoyant vortex ring in the near field was examined experimentally, and the findings were compared with those of a non-buoyant ring with a similar Reynolds number. The experiments were performed in a water tank, and the vortices were produced by a cylindrical tube of aspect ratio 2. Laser sheet flow visualization and PIV measurements were carried out. In the near field, the initial column of the buoyant fluid breaks down due to the presence of Rayleigh–Taylor instability at the buoyant fluid interface. Subsequently, a large diameter vortex ring with a large spreading rate, compared with the non-buoyant ring, emerges. The celerity of buoyant vortex continued to decrease throughout the range examined, in contrast to the constant celerity of the non-buoyant ring. The vorticity in the core of buoyant and non-buoyant vortex rings is symmetric and has a Gaussian distribution. However, the buoyant vortex ring evolves into a thin core ring, whereas the non-buoyant ring becomes a thick core ring shortly after the ring formation. This difference is brought on by the rapid entrainment and the significant growth of the buoyant ring following the breakup of the initial formation.

Hydrodynamics of pulsed jetting in juvenile and adult brief squid Lolliguncula brevis: evidence of multiple jet `modes' and their implications for propulsive efficiency

The dynamics of pulsed jetting in squids throughout ontogeny is not well understood, especially with regard to the development of vortex rings, which are common features of mechanically generated jet pulses (also known as starting jets). Studies of mechanically generated starting jets have revealed a limiting principle for vortex ring formation characterized in terms of a ;formation number' (F), which delineates the transition between the formation of isolated vortex rings and vortex rings that have; pinched off' from the generating jet. Near F, there exists an optimum in pulse-averaged thrust with (potentially) low energetic cost, raising the question: do squids produce vortex rings and if so, do they fall near F, where propulsive benefits presumably occur? To better understand vortex ring dynamics and propulsive jet efficiency throughout ontogeny, brief squid Lolliguncula brevis ranging from 3.3 to 9.1 cm dorsal mantle length (DML) and swimming at speeds of 2.43-22.2 cms(-1) (0.54-3.50 DMLs(-1)) were studied using digital particle image velocimetry (DPIV). A range of jet structures were observed but most structures could be classified as variations of two principal jet modes: (1) jet mode I, where the ejected fluid rolled up into an isolated vortex ring; and (2) jet mode II, where the ejected fluid developed into a leading vortex ring that separated or ;pinched off' from a long trailing jet. The ratio of jet length [based on the vorticity extent (L(omega))] to jet diameter [based on peak vorticity locations (D(omega))] was <3.0 for jet mode I and >3.0 for jet mode II, placing the transition between modes in rough agreement with F determined in mechanical jet studies. Jet mode II produced greater time-averaged thrust and lift forces and was the jet mode most heavily used whereas jet mode I had higher propulsive efficiency, lower slip, shorter jet periods and a higher frequency of fin activity associated with it. No relationship between L(omega)/D(omega) and speed was detected and there was no apparent speed preference for the jet modes within the speed range considered in this study; however, propulsive efficiency did increase with speed partly because of a reduction in slip and jet angle with speed. Trends in higher slip, lower propulsive efficiency and higher relative lift production were observed for squid <5.0 cm DML compared with squid >/=5.0 cm DML. While these trends were observed when jet mode I and II were equally represented among the size classes, there was also greater relative dependence on jet mode I than jet mode II for squid <5.0 cm DML when all of the available jet sequences were examined. Collectively, these results indicate that approximately 5.0 cm DML is an important ontogenetic transition for the hydrodynamics of pulsed jetting in squids. The significance of our findings is that from early juvenile through to adult life stages, L. brevis is capable of producing a diversity of vortex ring-based jet structures, ranging from efficient short pulses to high-force longer duration pulses. Given that some of these structures had L(omega)/D(omega)s near F, and F represented the delineation between the two primary jet modes observed, fluid dynamics probably played an integral role in the evolution of squid locomotive systems. When this flexibility in jet dynamics is coupled with the highly versatile fins, which are capable of producing multiple hydrodynamic modes as well, it is clear that squid have a locomotive repertoire far more complex than originally thought.

On vortex rings around vortices: an optimal mechanism

Stable columnar vortices subject to hydrodynamic noise (e.g. turbulence) present recurrent behaviours, such as the systematic development of vortex rings at the periphery of the vortex core. This phenomenon lacks a comprehensive explanation, partly because it is not associated with an instability stricto sensu. The aim of the present paper is to identify the physical mechanism triggering this intrinsic feature of vortices using an optimal perturbation analysis as a tool of investigation. We find that the generation of vortex rings is linked to the intense and rapid amplification of specific disturbances in the form of azimuthal velocity streaks that eventually evolve into azimuthal vorticity rolls generated by the rotational part of the local Coriolis force. This evolution thus appears to follow a scenario opposite to the classical lift-up view, where rolls give rise to streaks.

Vortex rings in pure water under static external electric field

The reproducible development of vortex rings in pure water under the action of a static external electric field is demonstrated. The phenomenon results from the electrochemical decomposition of water. Given the low conductivity of water in the absence of electrolyte, the field-driven buildup of hydroxide ions at the anode becomes essential to the proton release, which in turn is the result of the molecular O2(g) evolution. Water recombination processes, which have protons flowing in a hydroxide background, as a key ingredient produce the phenomenon.

Penetration length and diameter development of vortex rings generated by impacting water drops

The formation of water drops underneath nozzles was studied numerically to provide the basis for repeatable experimental drop formation. The drops detached from the nozzle and impacted on a free water surface forming vortex rings. Experimental results obtained through kinematographic studies of the penetration and growth of these vortex rings are presented. Variations of the penetration depth were measured, depending on the nozzle height above the water surface where the drops were formed. The experiments revealed that it is the state of oscillation at impact that defines the penetration length. Interesting variations of the vortex ring diameter with time were recorded. A good overall understanding of the behavior of the diameter variation was obtained when it was plotted as a function of the penetration depth.

Dynamics of vortex rings in crossflow

The spread and mixing of a fluid jet into an ambient stream occurs at a rate which deserves further study to improve efficient mixing. Mixing enhancement techniques, such as introduction of periodic disturbances into the jet flow, are used to increase mixing between a jet and the surrounding fluid. Pulsations were generated by the periodic closing and opening of a jet flow. The dynamics and trajectories of vortex rings, formed by the pulsation of the jet in a uniform crossflow, are studied. In particular, the effects of pulsation on the development of vortex rings and their penetration in a crossflow were investigated. Detailed measurements were made using flow visualization techniques including laser-induced fluorescence and hot-film anemometry. Vortex rings generated in a crossflow at one specific frequency (1 Hz) were measured using a hot-film probe. Measurements indicated that vortex rings were fully-formed at a distance of three times the jet exit diameter. To simulate the dynamics of vortex rings in crossflows, a numerical experiment was performed based on a Lagrangian, grid-free, three-dimensional vortex element method. At low frequencies, the fluid in the vortex rings penetrated into the crossflow to a height much greater than that for either high frequency pulsation or for a steady jet. At low frequencies, interaction between sequentially generated vortex rings was negligible; therefore, each ring behaved as a single discrete vortex ring. The vortex rings moved into the flow occasionally tilting up to about 30°, depending on the ring’s strength. Numerical simulation indicated that the tilting of the ring was due to the combined effects of viscosity and the crossflow. It is postulated that the increased penetration combined with the discretization of a jet into vortex rings results in a more efficient mixing rate.

Comment on "Influence of Initial and Boundary Conditions on Vortex Ring Development"

Comment on "Influence of Initial and Boundary Conditions on Vortex Ring Development"

Influence of initial and boundary conditions on vortex ring development

THIS paper presents the results of an experimental investigation comparing the mass and energy content of fully formed laminar vortex rings in air with that of the original pulse that generated them for a variety of initial and boundary conditions. In particular, the fractional entrainment of mass and the partition of initial energy between kinetic energy of translation and kinetic energy of rotation are studied. It is found that these characteristics depend strongly on the boundary conditions. A technique is presented which enables calculation of kinetic energy of rotation from motion picture sequences. The ratio of characteristi c translational speed to characteristic rotational speed is shown to be a useful parameter for correlation of data. Data on vortex size and speed are presented using this correlation, and it is seen that all data, regardless of initial and boundary conditions, fall on a single curve. A theoretical curve is derived, and it is seen that the data compare well with it. Contents In many applications utilizing nonsteady flow, it is of importance to understand the mechanisms of mass, momentum, and energy exchange between a primary flow and a secondary flow. The present work attempts to shed light on such mechanisms by ultilizing a simple example: the formation of vortex rings. A sketch of the system under study is shown in Fig. 1. We consider that, at time £ = 0, a uniform pulse is initiated with velocity Uj(t) for a duration Tp through a chimney of height H and diameter D0. Note that, when //=0, we have a simple orifice. After a certain period of time, the pulse becomes a fully formed vortex ring of diameter D which propagates at a speed U. The nature of the vortex ring will depend on the boundary conditions (H, DQ) and on the initial conditions luj(t), T p }. Since all of the vorticity essential to the existence of a vortex is generated in boundary layers prior to formation, different geometries will produce different amounts of vorticity. Furthermore, in the case of the simple orifice, vorticity of opposite sense is generated on the outside of the orifice by the boundary layer formed from the entrained flow, passing over the solid surface, thereby impeding the influx of entrained flow and diminishing the net available vorticity. These effects will result in the generation of vortices with different sizes and different propagation speeds, as well as differences in internal flowfields. In the experimental investigation, vortex rings were generated in still air for various sizes of simple orifices and chimneys by means of a large loudspeaker energized by a step in voltage, producing a controllable jet-pulse intensity. The pulse intensity and duration were monitored by means of a hot-film anemometer. Oscillographic records of the

Generation and Decay of Viscous Vortex Rings

Decay of a vortex ring in a viscous fluid is discussed by using a solution in the form of an asymptotic expansion for large time t . It is found that the velocity of the vortex ring varies as t -1.5 in the final state of low Reynolds number. The asymptotic expansion is not uniformly valid, and an improvement is made by using the method of matched asymptotic expansions. Generation and development of vortex rings are simulated by numerical integration of the Navier-Stokes equation as an initial and boundary value problem. Time variations of physical quantities such as total energy, impulse and velocity of the vortex rings, etc. are obtained, and have been shown to approach asymptotically to those obtained from the asymptotic expansion. Comparison with experimentally produced vortex rings is also given briefly.