Velocity Of Vortex Ring Research Articles

Effect of thermal buoyancy on vortex ring air supply mode

Owing to the air buoyancy effect in the non-isothermal environment, the air supply efficiency will be greatly reduced due to the severe interference of the air distribution and air supply performance. Although the vortex ring air supply mode shows better air supply efficiency than the symmetrical round jet under the isothermal conditions, it is still unclear under non-isothermal conditions. Therefore, the dynamic mesh method is applied to the formation of the air vortex ring. Then the influence of non-isothermal conditions on the transport characteristics of the air vortex ring is studied, and the temperature attenuation trend of the vortex ring air supply mode are evaluated. The results show that the attenuation of the translational velocity of the vortex ring under isothermal conditions can be used to approximate the translational velocity of the thermal air vortex ring, with a deviation of no more than 3%; second, the vortex ring air supply mode has better directionality, and the deviation can be reduced by 85% compared with the symmetrical round jet; third, an improvement method of the vortex ring air supply mode is proposed, the vortex core temperature increased by 4.5 °C; finally, the temperature attenuation of the thermal vortex ring is 25.8% lower than that of the thermal jet in the range of Lpath/D < 20.

Scaling of the translational velocity of vortex rings behind conical objects

Ring vortices are efficient at transporting fluid. They are often produced by ejecting a volume of fluid through a circular orifice. The impulse given to the vortex rings results in a propulsive force on the generator. Propulsive vortex rings have been widely studied and characterised. After four convective times, the vortex moves faster than the shear layer it originates from, and separates. This separation corresponds to a maximum in circulation and a maximal spread of the vorticity, quantified by the non-dimensional energy. The simultaneity of these three events obfuscates the causality between them. To analyse the temporal evolution of the non-dimensional energy of ring vortices independent of their separation, we analyse the development of vortices generated in the wake of cones. Cones with different apertures and diameters were accelerated from rest to produce a wide variety of vortex rings and their energy, circulation, and velocity were extracted based on time-resolved velocity field measurements. The rings that form behind the cones have a self-induced velocity that causes them to follow the cone and they continue to grow as the cone travels well beyond the limiting vortex formation times scales observed for propulsive vortices. The non-dimensional circulation, based on the vortex diameter, and the non-dimensional energy of the drag vortex rings converge after three convective times to values comparable to their propulsive counterparts. This result proves that vortex pinch-off does not cause the non-dimensional energy to reach a minimum value. The limiting values of the non-dimensional circulation and energy are mostly independent of the cone geometry and translational velocity and fall within an interval of 10% around the mean value. With only 6% of variation, the velocity of the vortex is the most unifying quantity that governs the formation of vortex rings behind cones.

Numerical Analysis of Charged Particles Transport in Air Based on Vortex Rings

Charged particles are widely used in the fields of defogging, haze removal and artificial rainfall. A novel transport strategy of charged particles based on the vortex rings is presented in this paper, to expand the effective action region and enhance the effect of charged particles. Transport distance and transport velocity (TV) of charged particles are the crucial two evaluation indexes. For the vortex rings generated by a piston-cylinder device, the transport velocity is closely related to Reynolds number and formation time. Based on the k-ω turbulence model, this paper verifies the relationship between vortex ring circulation, transport velocity and Formation Number in air by finite element methods, and studies the influence on the formation of vortex rings of an insulating bell mouth placed at the outlet of cylinder. The simulation results show that the Formation Number of vortex rings in the air is 4.0 ~ 5.0, and the growth rate of transport velocity of vortex ring slows down when the formation time is larger than Formation Number. The study also indicates that the bell mouth has little effect on the velocity of the vortex ring, when the bell mouth angle is greater than 45° and the length of generatrix is between 0.2 m and 1.0 m. Therefore, the research results can provide a reference for the design and optimization of a vortex ring generator for transporting charged particles to a certain target area.

On the scaling of propagation of periodically generated vortex rings

The propagation of periodically generated vortex rings (period$T$) is numerically investigated by imposing pulsed jets of velocity$U_{jet}$and duration$T_{s}$(no flow between pulses) at the inlet of a cylinder of diameter$D$exiting into a tank. Because of the step-like nature of pulsed jet waveforms, the average jet velocity during a cycle is$U_{ave}=U_{jet}T_{s}/T$. By using$U_{ave}$in the definition of the Reynolds number ($Re=U_{ave}D/\unicode[STIX]{x1D708}$,$\unicode[STIX]{x1D708}$: kinematic viscosity of fluid) and non-dimensional period ($T^{\ast }=TU_{ave}/D=T_{s}U_{jet}/D$, i.e. equivalent to formation time), then based on the results, the vortex ring velocity$U_{v}/U_{jet}$becomes approximately independent of the stroke ratio$T_{s}/T$. The results also show that$U_{v}/U_{jet}$increases by reducing$Re$or increasing$T^{\ast }$(more sensitive to$T^{\ast }$) according to a power law of the form$U_{v}/U_{jet}=0.27T^{\ast 1.31Re^{-0.2}}$. An empirical relation, therefore, for the location of vortex ring core centres ($S$) over time ($t$) is proposed ($S/D=0.27T^{\ast 1+1.31Re^{-0.2}}t/T_{s}$), which collapses (scales) not only our results but also the results of experiments for non-periodic rings. This might be due to the fact that the quasi-steady vortex ring velocity was found to have a maximum of 15 % difference with the initial (isolated) one. Visualizing the rings during the periodic state shows that at low$T^{\ast }\leqslant 2$and high$Re\geqslant 1400$here, the stopping vortices become unstable and form hairpin vortices around the leading ones. However, by increasing$T^{\ast }$or decreasing$Re$the stopping vortices remain circular. Furthermore, rings with short$T^{\ast }=1$show vortex pairing after approximately one period in the downstream, but higher$T^{\ast }\geqslant 2$generates a train of vortices in the quasi-steady state.

Three-dimensional flow separation over a surface-mounted hemisphere in pulsatile flow

Flow separation over a surface-mounted obstacle is prevalent in numerous applications. Previous studies of 3D separation around protuberances have been limited to steady flow. In biological and geophysical flows, pulsatile conditions are frequently encountered, yet this situation has not been extensively studied. Primarily motivated by our previous studies of the flow patterns observed in various human vocal fold pathologies such as polyps, our research aimed to fill this gap in the knowledge concerning unsteady 3D flow separation. This is achieved by characterizing velocity fields surrounding the obstacle, focused primarily on the vortical flow structures and dynamics that occur around a hemispheroid in pulsatile flow. As part of this study, two-dimensional, instantaneous and phase-averaged particle image velocimetry data in both steady and pulsatile flows are presented and compared. Coherent vortical flow structures have been identified by their swirling strength. This analysis revealed flow structures with dynamics dependent on the pulsatile forcing function. A mechanism to explain the formation and observed dynamics of these flow structures based on the self-induced velocity of vortex rings interacting with the unsteady flow is proposed.

Numerical Simulation of Wind Field over Complex Terrain and its Application in Jiuzhaihuanglong Airport

A numerical simulation method for the wind field over complex terrain was developed. The complex terrain was represented by a surface, which was established by the surface spline method based on the contour line of the map. Then it was divided into panels containing vortex ring singularities. The singularity distribution was solved by combining with the potential flow theory and the boundary condition of terrain surface. Finally, the wind filed was simulated by linear superposition of uniform stream and induced velocity of vortex rings. An example was studied, and the result was also compared with Weather Research and Forecasting (WRF) method. It indicates that the method proposed could describe the terrain much more accurately and provide a reasonable result of wind field distribution.

Self-Induced Velocity of a Vortex Ring Using Straight-Line Segmentation

The accuracy of discretized induced velocity calculations that can be obtained using straight-line vortex elements has been reexamined, primarily using the velocity field induced by a vortex ring as a reference. The induced velocity of a potential (inviscid) vortex ring is singular at the vortex ring itself. Analytical results were found by using a small azimuthal cutoff in the Biot–Savart integral over the vortex ring and showed that the singularity is logarithmic in the cutoff. Discrete numerical calculations showed the same behavior, with the self-induced velocity exhibiting a logarithmic singularity with respect to the discretization, which introduces an inherent cutoff in the Biot–Savart integral. Core regularization or desingularization can also eliminate the singularity by using an assumed “viscous” core model. Analytical approximations to the self-induced velocity of a thin-cored vortex ring have shown that the self-induced velocity has a logarithmic singularity in the core radius. It is further shown that the numerical calculations require special treatment of the self-induced velocity caused by curvature, which is lost by the inherent cutoff in the straight-line discretization, to correctly recover this logarithmic singularity in the core radius. Numerical solution using straight-line vortex segmentation, augmented with curved vortex elements only for the self-induced velocity calculation, is shown to be second-order accurate in the discretization.

Application of Vortex Lattice Method and Surface Spline Function in Terrain-Induced Wind Field

A numerical simulation method for the wind field over complex terrain is developed in this paper. The complex terrain is represented by a surface, which is established by the surface spline method basing on the contour line of the map. Then it is divided into panels containing vortex ring singularities. The singularity distribution is solved by combining with the potential flow theory and the boundary condition of terrain surface. Finally, the wind field is simulated by linear superposition of the uniform stream and the induced velocity of vortex rings. A numerical example is studied, and the result indicates that the method proposed in this paper could describe the terrain much more accurately and provide a reasonable result of wind field distribution, but has a simple and efficient procedure, which is suitable for the engineering use in flight dynamics.

Energy cascade with small-scale thermalization, counterflow metastability, and anomalous velocity of vortex rings in Fourier-truncated Gross-Pitaevskii equation

The statistical equilibria of the (conservative) dynamics of the Gross-Pitaevskii equation (GPE) with a finite range of spatial Fourier modes are characterized using a new algorithm, based on a stochastically forced Ginzburg-Landau equation (SGLE), that directly generates grand-canonical distributions. The SGLE-generated distributions are validated against finite-temperature GPE-thermalized states and exact (low-temperature) results obtained by steepest descent on the (grand-canonical) partition function. A standard finite-temperature second-order λ transition is exhibited. A mechanism of GPE thermalization through a direct cascade of energy is found using initial conditions with mass and energy distributed at large scales. A long transient with partial thermalization at small scales is observed before the system reaches equilibrium. Vortices are shown to disappear as a prelude to final thermalization and their annihilation is related to the contraction of vortex rings due to mutual friction. Increasing the amount of dispersion at the truncation wave number is shown to slow thermalization and vortex annihilation. A bottleneck that produces spontaneous effective self-truncation with partial thermalization is characterized in the limit of large dispersive effects. Metastable counterflow states, with nonzero values of momentum, are generated using the SGLE algorithm. Spontaneous nucleation of the vortex ring is observed and the corresponding Arrhenius law is characterized. Dynamical counterflow effects on vortex evolution are investigated using two exact solutions of the GPE: traveling vortex rings and a motionless crystal-like lattice of vortex lines. Longitudinal effects are produced and measured on the crystal lattice. A dilatation of vortex rings is obtained for counterflows larger than their translational velocity. The vortex ring translational velocity has a dependence on temperature that is an order of magnitude above that of the crystal lattice, an effect that is related to the presence of finite-amplitude Kelvin waves. This anomalous vortex ring velocity is quantitatively reproduced by assuming equipartition of energy of the Kelvin waves. Orders of magnitude are given for the predicted effects in weakly interacting Bose-Einstein condensates and superfluid ^{4}He.

Vortex splitting in subcritical nonlinear Schrödinger equations

Vortices and axisymmetric vortex rings are considered in the framework of the subcritical nonlinear Schrödinger equations. The higher order nonlinearity present in such systems models many-body interactions in superfluid systems and allows one to study the effects of negative pressure on vortex dynamics. We find the critical pressure for which the straight-line vortex becomes unstable to radial expansion of the core. The energy of the straight-line vortices and energy, impulse and velocity of vortex rings are calculated. The effect of a varying pressure on the vortex core is studied. It is shown that under the action of the periodically varying pressure field a vortex ring may split into many vortex rings and the conditions for which this happens are elucidated. These processes are also relevant to experiments in Bose–Einstein condensates where the strength and the sign of two-body interactions can be changed via Feshbach resonance.

Vortex ring velocity and minimum separation in an infinite train of vortex rings generated by a fully pulsed jet

A pulsed jet with a period of no flow between pulses (i.e., a fully pulsed jet) produces a multiplicity of vortex rings whose characteristics are determined by the jet pulsing parameters. The present study analyzes the case of impulsively initiated and terminated jet pulses in the limit of equal pulse duration and period to determine the minimum possible vortex ring separation obtainable from a fully pulsed jet. The downstream character of the flow is modeled as an infinite train of thin, coaxial vortex rings. Assuming inviscid flow and matching the circulation, impulse, kinetic energy, and frequency of the jet and vortex ring train allow the properties of the vortex ring train to be determined in terms of the ratio of jet slug length-to-diameter ratio (L/D) used for each pulse. The results show the minimum ring separation may be made arbitrarily small as L/D is decreased and the corresponding total ring velocity remains close to half the jet velocity for L/D 1.5. The results are discussed in the context of models of pulsed-jet propulsion.

Vortex Rings Generated by a Shrouded Hartmann-Sprenger Tube

The pulsed flow emitted from a shrouded Hartmann-Sprenger tube was sampled with high-frequency pressure transducers and with laser particle imaging velocimetry, and found to consist of a train of vortices. Thrust and mass flow were also monitored using a thrust plate and orifice, respectively. The tube and shroud lengths were altered to give four different operating frequencies. From the data, the radius, velocity, and circulation of the vortex rings was obtained. Each frequency corresponded to a different length to diameter ratio of the pulse of air leaving the driver shroud. Two of the frequencies had length to diameter ratios below the formation number, and two above. The formation number is the value of length to diameter ratio below which the pulse converts to a vortex ring only, and above which the pulse becomes a vortex ring plus a trailing jet. A modified version of the slug model of vortex ring formation was used to compare the observations with calculated values. Because the flow exit area is an annulus, vorticity is shed at both the inner and outer edge of the jet. This results in a reduced circulation compared with the value calculated from slug theory accounting only for the outer edge. If the value of circulation obtained from laser particle imaging velocimetry is used in the slug model calculation of vortex ring velocity, the agreement is quite good. The vortex ring radius, which does not depend on the circulation, agrees well with predictions from the slug model.

Scaling in the shock–bubble interaction

The passage of a shock wave through a spherical bubble results in the formation of a vortex ring. In the present study, simple dimensional analysis is used to show that the circulation is linearly dependent on the surrounding material speed of soundcsand the initial bubble radiusR. In addition, it is shown that the velocities characterizing the flow field are linearly dependent on the speed of sound, and are independent of the initial bubble radius. The dependence of the circulation on the shock wave Mach numberMis derived by Samtaney and Zabusky (1994) as (1 + 1/M+ 2/M2) (M− 1). Experiments were performed for slow/fast (air-helium) and fast/slow (air-SF6) interactions. Full numerical simulations were conducted resulting in good agreement. From the results, it is seen that in both cases, according to the proposed scaling, the vortex ring velocity is bubble radius independent. The numerical results for the slow/fast interaction show that the proposed Mach scaling is valid forM&lt; 2. AboveM≅ 2, the topology of the bubble changes due to a competition between the upstream surface of the bubble and the undisturbed shock wave.

Behavior of Vortex Ring Induced by Pulsatile Jet in a Stenosed Tube.

The effect of pulsatile flow conditions on vortex behavior downstream of stenosed was studied experimentally by means of PTV methods. Phase mean velocity vectors in the downstream region of stenosed model with 89% area reduction were measured under the condition of sinusoidal pulsatile flow of mean Reynolds number Re= 100∼300 and Stokes number St =151∼410. It was observed that, in all conditions, vortex ring was produced with a trailing jet downstream of a stenosed during the period of increase in flow rate. In the case of higher St number, the second vortex ring was produced in contiguity with the leading vortex ring. In the case of higher Re number, a row of small vortex rings was produced along the shear layer of the trailing jet. These vortex rings were propagated downstream field with constant velocity, and breakdown was followed. The position of vortex ring breakdown was only influenced by St number, and the ratio of propagation velocity of vortex ring to mean velocity in a period at the stenosed was constant under the all conditions.

Generation of a Vortex Ring with High Reynolds Number by an Exploding Wire in Water

A method is presented for generating a vortex ring in water by an exploding wire installed in a metal pipe. As a vapor bubble accompanied by wire explosion grows, water starts to flow with a high speed resulting in a formation of a vortex ring at the outlet of the pipe. The growth speed of a vapor bubble by the exploding wire in water is measured as 10∼20 m/s, in consistent with measurements of the translational velocity, 4∼5 m/s, of vortex ring and the rotational velocity, about 10 m/s, of fluid at the edge of vortex core. The Reynolds number based on the diameter of orifice, the velocity of vortex ring and the kinematic viscosity reaches the order of 10 5 . The magnitude of vorticity and the circulation are in the order of 10 3 /s and 10 -1 m 2 /s. These values are larger by about 10 times than those reported previously.

The vortex ring velocity resulting from an impacting water drop

Experimental observations are reported on the evolution of a vortex ring for the first 70 ms after it is created by the impact of a dyed water drop upon a pool of clear water. The 2.6 mm diameter drops were released from two heights. The drops impacted the pool with Weber numbers of 23.2 and 16.6 and Froude numbers of 25.2 and 18.0. The Reynolds number of the resulting relaminarized vortex rings based on their diameter was in the range of 320 to 390. Precisely controlled multiple exposure photographs were used to measure the position and shape of the vortex ring versus time, and calculate velocity. It is proposed here that the appropriate time scale is the time it takes for the impact crater to reach its maximum depth. Excellent agreement was found when using this scaling to compare both the present data sets and that previously published for a larger drop.