Spark-generated bubble collapse near or inside a circular aperture and the ensuing vortex ring and droplet formation

This paper aims to study the oscillation of a sparkgenerated submerged bubble located near or inside a circular aperture made in a flat plate using high-speed visualization technique. In the case of a bubble oscillating near an aperture the initial free surface of the water was set at the bottom surface of the plate. The effects of aperture size and bubblefree surface distance on the bubble behavior as well as on the ensuing droplet dynamics are investigated. It was found that the direction of the bubble reentrant jet was towards the aperture or away from it respectively when the normalized aperture size was smaller or greater than a certain critical value. In addition, a toroidal vortex ring was observed to form, which rotated inwards as it moved away from the aperture. It was also found that if the bubble was incepted at a distance sufficiently away from a supercritical size aperture a single droplet could be produced. In the case of a bub- ble initiated in the middle of a circular aperture submerged just beneath the water free surface, the bubble was found to take the shape of an ellipsoid during its expansion. Then a reentrant jet was initiated and pierced the bubble from its top side.

Lagrangian analysis of the formation and mass transport of compressible vortex rings generated by a shock tube

In order to understand the mass transport and the dynamic genesis associated with a compressible vortex formation,a dynamic analysis of compressible vortex rings (CVRs) generated by shock tubes by using the framework of Lagrangiancoherent structures (LCSs) and finite-time Lyapunov exponents field (FTLE) is performed. Numerical calculation is performed to simulate the evolution of CVRs generated by shock tubes with 70 mm, 100 mm, and 165 mm of the driver sectionat the circumstances of pressure ratio = 3. The formation of CVRs is studied according to FTLE fields. The mass transportduring the formation is obviously seen by the material manifold reveled by FTLE fields. A non-universal formation numberfor the three CVRs is obtained. Then the elliptic LCSs is implemented on three CVRs. Fluid particles separated by ellipticLCSs and ridges of FTLE are traced back to t = 0 to identify the fluid that eventually forms the CVRs. The elliptic LCSsencompass around 60% fluid material of the advected bulk but contain the majority of the circulation of the ring. The otherparts of the ring carrying almost zero circulation advect along with the ring. Combining the ridges of FTLE and the ellipticLCS, the whole CVR can be divided into three distinct dynamic parts: vortex part, entrainment part, and advected part. Inaddition, a criterion based on the vortex part formation is suggested to identify the formation number of CVRs.

Large eddy simulation of a vortex ring impinging on a three-dimensional circular cylinder

Abstract A vortex ring impacting a three-dimensional circular cylinder is studied using large eddy simulation （LES） for a Reynolds number Re = 4 × 10^4 based on the initial translation speed and diameter of the vortex ring. We have investigated the evolution of vortical structures and identified three typical evolution phases. When the primary vortex closely approaches to the cylinder, a secondary vortex is generated and its segment parts move inward to the primary vortex ring. Then two large-scale loop-like vortices are formed to evolve in opposite directions. Thirdly, the two loop-like vortices collide with each other to form complicated small-scale vortical structures. Moreover, a series of hair-pin vortices are generated due to the stretching and deformation of the tertiary vortex. The trajectories of vortical structures and the relevant evolution speeds are analyzed. The total kinetic energy and enstrophy are investigated to reveal their properties relevant to the three evolution phases.

THE NONLINEAR INTERACTION OF VORTEX RINGS WITH A FREE SURFACE

Nonlinear interactions of vortex rings with a free surface are considered in an incompressible, ideal fluid using the vortex contour dynamics technique and the boundary integral equation method. The flow is axisymmetric and the vorticity is linearly distributed in the vortex. Effects of the gravity and the surface tension as well as the initial geometric parameter of the vortex on the interaction process are investigated in considerable detail. The interaction process may be divided into three major stages: the vortex free-traveling stage, the collision stage, and the vortex stretching and rebounding stage. Time evolutions of both the vortex and free surface under various conditions are provided and analyzed. Two kinds of waves exist on the free surface during interaction. In a special case where the gravity and surface tension are very weak or the vortex is very strong, an electric-bulb-like 'cavity' is formed an the free surface and the vortex is trapped in the 'cavity' for quite a. long time, resulting in a large amount, of fluid above the mean fluid surface.

EVOLUTION OF SINGLE ELLIPTIC VORTEX RINGS

The evolution of single elliptic vortex rings for initial aspect ratio (AR) = 2,4,6 has been studied. The incompressible Navier-Stokes equations are solved by a dealiased pseudo-spectral method with 64(3) grid points in a periodic cube. We find that there are three kinds of vortex motion as AR increases and bifurcation occurs at certain AR. The processes of advection, interaction and decay of vortex ring are discussed. Numerical results coincide with experiments and other authors' numerical simulation.

Three-dimensional numerical simulation of a vortex ring impacting a bump

A vortex ring impinging on a three-dimensional bump is studied using large eddy simulation for a Reynolds number Re = 4 × 104 based on the initial translation speed and diameter of the vortex ring. The effects of bump height on the vortical flow phenomena and the underlying physical mechanisms are inves- tigated. Based on the analysis of the evolution of vortical structures, two typical kinds of vortical structures, i.e., the wrapping vortices and the hair-pin vortices, are identified and play an important role in the flow state evolution. The circu- lation of the primary vortex ring reasonably elucidates some typical phases of flow evolution. Furthermore, the mechanism of flow transition from laminar to turbulent state has been revealed based on analysis of turbulent kinetic energy.

Effect of pressure evolution on the formation enhancement in dual interacting vortex rings

In the biological locomotion,the ambit pressure is of particular importance to use as a means of propulsion.The multiple vortex rings have been proved to generate additional thrust by interaction,but the mechanism of this thrust enhancement is still unknown.This study examines the effect of ambit pressure on formation enhancement in interacting dual vortex rings.The vortex rings,which have the same formation time,are successively generated in a piston-cylinder apparatus.The finite-time Lyapunov exponent(FTLE)visualizes the flow fields as an indication of Lagrangian coherent structures(LCSs),and the pressure field is calculated based on the digital particle image velocity(DPIV).We extract the back pressure of the rear vortex in dual vortices and the back pressure circulationΓ_(b),which is defined as a form of overpressure circulationΓ_(p).TheΓ_(b)has a positive linear relationship withΓ_(p).A critical interval distance d*_(cr)in a range of0.32-0.42 is found whereΓbandΓp reach the maximum synchronously,leading to a full-interaction mode.Moreover,an over-interaction mode and an under-interaction mode are proposed when the dimensionless interval distance d*_(is)smaller or larger than d*_(cr).To conclude,the high back pressure caused by vortex interaction can enhance the formation of vortex rings and lead to high thrust.

A modeling method of microburst based on multiple vortex ring

Microburst is a special kind of low-level wind shear, which may do great damage to aircrafts. Modelling of a microburst is significant for flight simulations. In this paper we adopt multiple vortex ring principle to model microburst and propose a new parameter selection method of multiple vortex ring model. We treat the parameters selection as an optimization problem, and introduce the differential evolution algorithm into it. A nested differential evolution algorithm is proposed to complete the two optimization process, objective optimization and intermediate optimization. The simulation results show that this method can flexibly generate microburst with any maximum wind velocity.

ON THE FORMATION OF VORTEX RINGS AND PAIRS

The axisymmetric vortex sheet model developed by Nitsche and Krasny had been extended to study the formation of vortex rings (pairs) at the edge of circular (2D) tube and opening. Computations based on this model were in good agreement with the experiments (Didden (1979) for circular tube and Auerbach (1987) for 2D tube and opening). Using this new model, evidences are provided to show that the main failure of the similarity theory (the false prediction of axial trajectory of vortex ring) is due to its ignorance of the self-induced ring velocity (mutual induction for vortex pair). The Glezer (1988)'s summary on the influence of piston speed upon the shedding circulation was also discussed, and finally the variation of core distribution of vortex ring with turning angle and piston speed was given. (Edited author abstract) 22 Refs.

Interaction of Bubbles with Vortex Ring Launched into Bubble Plume

This study is concerned with an experimental exploration for the interactions of bubbles with a vortex ring launched vertically upward into a bubble plume. A vortex ring launcher, composed of a cylinder and a piston, is mounted at the bottom of a water tank. Small hydrogen bubbles are released into still water from a cathode, which is wound around the cylinder outlet, by the electrolysis of water. The bubbles rise by the buoyant force and induce a bubble plume. The water in the cylinder is discharged into the bubble plume by the piston, resulting in a laminar vortex ring convecting along the central axis of the plume. Just after the launch of the vortex ring, the bubbles are spirally entrained into the vortex ring with the roll up of the shear layer. The void fraction within the vortex ring increases with the convection of the vortex ring until a certain displacement of the vortex ring, where the reduction occurs. The vortex ring convects with a constant velocity higher than that in still water. The entrained bubbles reduce the strength of the vortex ring.

Quality Assuring a Ring Vortex Flow Phantom in Real-Time

Introduction: The ring vortex phantom is a novel, cost-effective prototype which generates complex and well-characterised reference flows in the form of the ring vortex. Although its reproducibility has been demonstrated, with ring speeds routinely behaving within 10% tolerances at speeds of approximately 10 - 70 cm/s, a form of real-time QA of the device at the time of imaging is needed to confirm correct function on demand in any environment. Methods: The technology described here achieves real-time QA, comprising a linear encoder, laser-photodiode array, and Doppler probe, measuring piston motion, ring speed and intra-ring velocity respectively. This instrumentation does not interfere with imaging system QA, but allows QA to be performed on both the ring vortex and the device in real-time. Results: The encoder reports the reliability of the piston velocity profile, whilst ring speed is measured by laser behaviour. Incorporation of a calibrated Doppler probe offers a consistency check that confirms behaviour of the central axial flow. For purposes of gold-standard measurement, all elements can be related to previous Laser PIV acquisitions with the same device settings. Conclusion: Consequently, ring vortex production within tolerances is confirmed by this instrumentation, delivering accurate QA in real-time. This implementation offers a phantom QA procedure that exceeds anything seen in the literature, providing the technology to enhance quantitative assessment of flow imaging modalities.

EXPERIMENT ON THE CHARACTERISTICS OF 3-D VORTEX RING BEHIND A FLEXIBLE OSCILLATING CAUDAL FIN

A test for the wake vortex of a flexible oscillating caudal fin is carried out with Digital Particle Image Velocimetry （DPIV）, and the variation of vortex distance and the vorticity in the range of oscillating frequency from 0.704 Hz to 1.17 Hz are analyzed. It is found that with the increase of the oscillating frequency, the vortex distance decreases and the peak of the vorticity increases, When the Strouhal number is smaller than 0.49, a larger thrust component is obtained. The distribution of the velocity circulation and the vortex distance in the different spanwise section of the caudal fin are given, and then the dimension of the vortex ring is determined. The radius of the vortex ring is 79.3 mm and the average velocity circulation is 28152.9 mm2/s at the oscillating frequency of 0.835 Hz. The model of 3-D vortex ring chain of flexible oscillating caudal fin is constructed based on the information of wake vortex field. Finally, an effective analysis method is provided for establishing the relationship of oscillating parameters for the caudal fin and the wake structure and the intrinsic mechanism of efficient fish swimming is investigated.

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.

Passive scalar mixing induced by the formation of compressible vortex rings

This study aims to determine the relationship between the physical features of a compressible vortex and the mixing process.Such relationship is of significant importance to design combustors that can achieve optimal or most effective mixing.The passive scalar mixing induced by the formation of a canonical compressible vortex ring(CVR)generated at the end of a shock tube is investigated by using numerical simulation.In addition,the method of finite-time Lyapunov exponent(FTLE)field are detected to identify the region of CVR,as well as to analyze the passive scalar mixing during the CVR formation.As the CVR rolls up,the ambient fluid outside the shock tube is entrained into the ring.The entrainment fraction(the mass of entrained fluid to the total mass of CVR)is found to strongly depend on two features of CVRs.One is the compressibility of CVRs,which is characterized by the Mach number of the incident shock denoted by Mach number(Ma).The other is pinch-off of CVRs,which happens at a certain timescale with narrow range of 2–4.As Ma increases,the entrainment fraction of the leading CVR decreases linearly due to smaller vortex core and weaker radial diffusion of vorticity generated by larger compressibility.After CVRs pinch off,trailing vortices appear and show less effective at entrainment than the leading CVRs do.Moreover,the tendency of the rate of entrainment is examined.The results indicate that increasing compressibility and total fluid flux are in favor of the rate of entrainment but restrain the entrainment fraction of total jet.

A NUMERICAL STUDY ON VORTEX RINGS WITH SWIRL

A finite difference scheme in cylindrical coordinates was used to study the three dimensional (3D) motion of a vortex ring with swirl and the passage interaction between two vortex rings. For the 3D evolution of a single thin ring, the azimuthal perturbation modes grow linearly in the early stage. According to their growth rates, two bands of growing waves, which correspond to the first and the second radial mode respectively, can be observed. The result is similar to the prediction of short wave instability theory for swirl free vortex rings. For the passage process between two rings, results show that the azimuthal velocity is in inverse proportion to radius while the azimuthal vorticity is in proportion to radius during the interaction.

Lagrangian analysis of the fluid transport induced by the interaction of two co-axial co-rotating vortex rings

In this paper,the fluid transport in the interaction of two co-axial co-rotating vortex rings are investigated.Vortex rings are generated using the piston-cylinder apparatus,and the resulting velocity fields are measured using digital particle image velocimetry.The interaction process is analysed by means of vorticity contour,as well by investigation of the Lagrangian coherent structures(LCSs)defined by the ridges of the finite-time Lyapunov exponent(FTLE).Experimental results demonstrate that two types of vortex interaction are identified,namely strong and weak interactions,respectively.For the strong interaction,the Lagrangian boundaries of the two vortex rings are merged together and form a flux window for fluid transport.For weak interaction,only the Lagrangian drift induced by the motion of the front vortex ring is observed and affects the Lagrangian boundary of the rear vortex ring.Moreover,the fluids transported in the strong interaction carry considerable momentum but no circulation.By contrast,there are nearly no fluxes occurring in the weak interaction.By tracking the variations of circulation and impulse occupied by the separated regions distinguished by the LCSs,it is found that the circulation nearly has no change,but the impulse occupied by vortex core region has significant change.In the strong interaction,the impulse of rear vortex ring decreases but the impulse of the front vortex ring increases.Based on the impulse law,it is speculated that the fluid force generated by the formation of the rear vortex rings can be enhanced.Therefore,the strong interaction between wake vortices can actually improve the propulsive efficiency of the biological systems by operating the formation of large-scale vortices.

Large Eddy Simulation of a Vortex Ring Impacting a Bump

A vortex ring impacting a three-dimensional bump is studied using large eddy simulation for a Reynolds number Re=4×104 based on the initial diameter and translational speed of the vortex ring.The effects of bump height and vortex core thickness for thin and thick vortex rings on the vortical flow phenomena and the underlying physical mechanisms are investigated.Based on the analysis of the evolution of vortical structures,two typical kinds of vortical structures,i.e.,the wrapping vortices and the hair-pin vortices,are identified and play an important role in the flow state evolution.The boundary vorticity flux is analyzed to reveal the mechanism of the vorticity generation on the bump surface.The circulation of the primary vortex ring reasonably elucidates some typical phases of flow evolution.Further,the analysis of turbulent kinetic energy reveals the transition from laminar to turbulent state.The results obtained in this study provide physical insight into the understanding of the mechanisms relevant to the flow evolution and the flow transition to turbulent state.

Influence of orifice-to-wall distance on synthetic jet vortex ring simpinging on a fixed wall

Two-dimensional particle image velocimetry (PIV) is used to investigate the influence of the orifice-to-wall distance on synthetic jet vortex rings impinging on a fixed wall. Both evolutions of vortical structures and statistical characteristics of flow fields at different orifice-to-wall distances are presented. It is found that different orifice-to-wall distances have different effects in terms of the vortex strength and impinging speed when the vortex rings are approaching the wall. The secondary vortex ring can be observed within the shear layer only when the dimensionless orifice-to-wall distance is close to or less than the dimensionless stroke length. Consequently, an appropriate orifice-to-wall distance plays a vital role in the sense of impingement effect. The statistical analysis of the flow field indicates that a wall jet forms after impingement, while both the decay rate of the maximum radial velocity and the spreading rate of the half-width decrease with the increasing orifice-to-wall distance. The non-dimensional wall jet velocity profiles at different orifice-to-wall distances all exhibit self-similar behaviors, which is consistent with the theoretical solution of the laminar wall jet.

A PREDICTION OF THE VORTEX-RING STATE BOUNDARY BASED ON MODEL TESTS

To understand the vortex-ring state and to develop an approach for predicting its boundary, a series of model rotor tests of vertical descent and oblique descent have been conducted on a newly-built test apparatus - the Whirling Beam. The test results showed some unsteady aerodynamic behavior of the model rotor operating in the vortex-ring state. A very irregular variation of the rotortorque at low rate-of-descent was observed here for the first time. We considered it to be the start of the 'power settling' and determined the critical descent velocity according to this observation. A previous criterion for the vortex-ring state was modified to give a semi-empirical method for predicting the entire vortex-ring state boundary. The computed boundary shows a good correlation with the model test results and the flight experiences.

Compression and stretching of ring-vortex solitons in a bulk nonlinear medium

Compression and stretching of ring-vortex solitons, which is a novel self-similar solution of（2＋1）-dimensional diffraction decreasing waveguide, is investigated analytically and numerically. We obtain the ring-vortex solitons via the similarity transformation method. The distance modulation for the width, the diffraction, and the nonlinear response, strongly affects the form and the behavior of the self-similar vortex, and facilitates the efficient compression of optical waves. This approximate ring-vortex solitons can reflect the real properties of self-similar optical vortex beams during propagation under certain parameter window selection. Specific examples and figures are given to illustrate discussed features. The results obtained in this paper may have potential values for all-optical data-processing schemes and the design of beam compressors and amplifiers.