Pair Of Vortex Rings Research Articles

On the stability of a pair of vortex rings

The growth of perturbations subject to the Crow instability along two vortex rings of equal and opposite circulation undergoing a head-on collision is examined. Unlike the planar case for semi-infinite line vortices, the zero-order geometry of the flow (i.e. the ring radius, core thickness and separation distance) and by extension the growth rates of perturbations vary in time. The governing equations are therefore temporally integrated to characterize the perturbation spectrum. The analysis, which considers the effects of ring curvature and the distribution of vorticity within the vortex cores, explains several key flow features observed in experiments. First, the zero-order motion of the rings is accurately reproduced. Next, the predicted emergent wavenumber, which sets the number of secondary vortex structures emerging after the cores come into contact, agrees with experiments, including the observed increase in the number of secondary structures with increasing Reynolds number. Finally, the analysis predicts an abrupt transition at a critical Reynolds number to a regime dominated by a higher-frequency, faster-growing instability mode that may be consistent with the experimentally observed rapid generation of a turbulent puff following the collision of rings at high Reynolds numbers.

Λ Polarization and Vortex Rings in Heavy-Ion Collisions at NICA Energies

We review recent studies of vortical motion and the resulting polarization of Λ hyperons in heavy-ion collisions at NICA energies, in particular, within the model of three-fluid dynamics (3FD). This includes predictions of the global Λ polarization and ring structures that appear in Au+Au collisions. The global Λ polarization in Au+Au collisions is calculated, including its rapidity and centrality dependence. The contributions of the thermal vorticity and meson-field term (proposed by Csernai, Kapusta, and Welle) to the global polarization are considered. The results are compared with data from recent STAR and HADES experiments. It is predicted that the polarization maximum is reached at sNN≈ 3 GeV if the measurements are performed with the same acceptance. It is demonstrated that a pair of vortex rings are formed, one at forward rapidities and another at backward rapidities, in ultra-central Au+Au collisions at sNN> 4 GeV. The vortex rings carry information about the early stage of the collision, in particular, the stopping of baryons. It is shown that these rings can be detected by measuring the ring observable RΛ, even in the midrapidity region at sNN= 5–20 GeV. At forward/backward rapidities, the RΛ signal is expected to be stronger. The possibility of observing the vortex-ring signal against the background of non-collective transverse polarization is discussed.

Vortex Ring Formed by a Butterfly Wing and Dynamic Forces

Butterfly generates unsteady dynamic fluid force with a pair of vortex rings. In order to elucidate the flight mechanism of butterflies, it is necessary not only to clarify the vortex rings formed around the wings but also elucidate the characteristics of the unsteady fluid force generated by the flapping motion. By applying the momentum theory to the vortex rings formed during flapping motion, it is possible to estimate the force generated by flapping motion. In this study, we reconstruct a pair of vortex rings formed by flapping motion based on a small number of visualization results and elucidate dynamic fluid force characteristics. A part of estimation result of Lift estimated by the rough shape vortex rings generated by downstroke and upstroke do not match with the direct measurement result. But not only the peak value of estimation result of Lift is near with the direct measurement result quantitatively but also the value of estimation result between upstroke is a small negative as well as the direct measurement result. Although there is a phase difference between the estimation result and direct measurement result, there is a qualitative and quantitative agreement between estimation results and direct measurement result. From those results, butterfly generate the unsteady dynamic Lift between downstroke, especially at butterfly spread wing maximum (t/T = 0.40). After that, the unsteady dynamic Lift decrease and become 0 at upstroke.

Shock generated vorticity in spark discharges

Spark discharges induce a complex flow field consisting of a shock wave at early times (∼1 µs), a pair of vortex rings, and a hot gas kernel. The vortex rings entrain ambient gas into the hot gas kernel and control its cooling and expansion. In this work, we investigate the shock wave’s contribution in producing the vortex ring vorticity. We analyze high-speed (700 kHz) schlieren images of the shock wave for a range of electrical energies to measure the shock properties and estimate shock velocity and curvature. These measurements are combined with a model to calculate the vorticity generated. The measurements show that the highest vorticity is generated near the peak shock curvature location, and the shock curvature and strength increase with electrical energy deposited. A comparison of the vorticity estimated from the model to vorticity measurements from stereoscopic particle image velocimetry shows the results to be statistically equivalent. This suggests that the shock curvature and velocity contribute to the vortex rings induced by spark discharges.

Vortex generation in a finitely extensible nonlinear elastic Peterlin fluid initially at rest

AbstractIt is well known that the mixing of two or more species in flows at low Reynolds numbers cannot be easily achieved since inertial effects are essentially absent and molecular diffusion is slow. To achieve mixing in Newtonian fluids under these circumstances requires innovative new ideas such as the use of external body forces (eg, electromagnetic mixers) or the stretching and folding of fluid elements (eg, chaotic advection). For non‐Newtonian fluids with elasticity, mixing can be achieved by enabling the emergence of elastic instabilities that results in chaotic flows in which mixing is significantly enhanced. In this work, our goal is to demonstrate that clearly identifiable vortical structures (eg, vortex rings) can be generated in a viscoelastic fluid initially at rest by the release of elastic stresses. In turn, these vortex motions promote bulk mixing by transporting fluid elements from one location to another more efficiently than diffusion alone. We demonstrate this first theoretically by using the finitely extensible nonlinear elastic Peterlin (FENE‐P) model to show that elastic forces can generate torque. Using this model, we derive an expression for the time rate of change of vorticity in an elastic fluid initially at rest caused by a sudden release of stored elastic stress. This process can be thought of as the release of elastic energy from a stretched rubber band that is suddenly cut at its center. We confirm this ansatz by performing a series of direct numerical simulations based on an in‐house pseudo‐spectral code that couples the FENE‐P model to the equations of motion for an incompressible fluid. The simulations reveal that a pair of vortex rings traveling in opposite directions, with Reynolds numbers on the order of one, is generated from the sudden release of elastic stresses. Secondary vortical structures are also generated. In the concluding section of this work, we address the potential for vortex motions generated by elastic stresses to promote mixing in microflows, and we describe a possible experiment that may demonstrate this effect.

Hydrodynamics of Vortex Generation during Bell Contraction by the Hydromedusa Eutonina indicans (Romanes, 1876).

Swimming bell kinematics and hydrodynamic wake structures were documented during multiple pulsation cycles of a Eutonina indicans (Romanes, 1876) medusa swimming in a predominantly linear path. Bell contractions produced pairs of vortex rings with opposite rotational sense. Analyses of the momentum flux in these wake structures demonstrated that vortex dynamics related directly to variations in the medusa swimming speed. Furthermore, a bulk of the momentum flux in the wake was concentrated spatially at the interfaces between oppositely rotating vortices rings. Similar thrust-producing wake structures have been described in models of fish swimming, which posit vortex rings as vehicles for energy transport from locations of body bending to regions where interacting pairs of opposite-sign vortex rings accelerate the flow into linear propulsive jets. These findings support efforts toward soft robotic biomimetic propulsion.

Numerical study of supersonic turbulent free shear layer mixing and combustion

 Abstract. Numerical study of two-dimensional supersonic hydrogen-air mixing and combustion in free shear layer is performed. The system of Favre-Averaged Naveir-Stokes equations for multispecies reacting flow is solved using ENO scheme of third-order in accuracy. The k-ε two-equation turbulence models with compressibility correction are applied to calculate the eddy viscosity coefficient. In order to produce the roll-up and pairing of vortex rings, an unsteady boundary condition is applied at the inlet plane. At the outflow, the non-reflecting boundary condition is taken. The influence of different Mach numbers on the formation of vorticity structures and shear layer growth rate are studied. The obtained results are compared with available experimental data and the numerical results of other authors. For the description of reaction pathways of hydrogen, a seven species chemical reaction model by Jachimowski is adopted. The influence of Mach numbers on turbulent mixture and combustion is reported.       G M T   Английский Испанский Итальянский Казахский Китайский Трад Китайский Упр Корейский Русский Турецкий Французский   Английский Испанский Итальянский Казахский Китайский Трад Китайский Упр Корейский Русский Турецкий Французский                 Звуковая функция ограничена 200 символами     Настройки : История : Обратная связь : Donate Закрыть

Vortex break-down during the impact of a starting subsonic compressible gas jet on a multi-plume spray

The impact process and the consequent two-phase interaction for a compressible subsonic starting gas jet colliding on a multi-plume spray are investigated using large eddy simulation with Eulerian/Lagrangian multiphase approach, and the λ 2 criterion is used to visualize the temporal and spatial evolution of the vortical structures in the gas field. It is shown that before the impact a leading tip vortex ring is followed by smaller vortex rings in the quasi-steady region of the starting jet while the vortical structures inside the spray plumes known as spray-induced air jets are formed. After the impact the leading tip vortex ring and the following rings as well as spray-induced air jet vortices start to deform and eventually break down into smaller elongated vortex filaments. Unlike the injection of multi-plume sprays into the core of a steady cross flow gas jet, spray droplets are dispersed in a larger volume in all directions when impacted by the starting gas jet, beneficial for two-phase mixing enhancement. A pair of vortex rings is also observed merging into a new ring before reaching the impact zone.

Transient force augmentation due to counter-rotating vortex ring pairs

Of particular significance to biological locomotion is vortex ring interaction. In the wakes of animals, this unsteady process determines the changes in the impulse of counter-rotating vortex ring pairs (VRPs), which consist of two vortex rings with opposite sense of rotation. In this paper, these VRPs are proposed to be of particular importance to unsteady force generation. We carry out numerical computations, simulating the piston–cylinder apparatus, to study the transient changes in the impulse of counter-rotating VRPs composed of a positive and a negative vortex ring. We model the negative vortex ring (NeVR) of a VRP by making reasonable assumptions about their vorticity distributions and spatial locations, which are initially prescribed. The result of modelling is superimposed on the flow, which has a pre-existing positive vortex ring (PoVR), leading to a VRP. The simulation quantitatively demonstrates that the unsteady force resulting from a VRP is significantly larger compared with an isolated PoVR (without an NeVR). The force enhancement is also correlated to vortex configurations. A normalised force coefficient characterising force augmentation over the entire stroke is given. The force augmentation coefficient grows significantly and then reaches a plateau as the momentum input increases. The results are consistent with those in fully unsteady vortex interaction, which involves the generation of an NeVR. It is suggested that counter-rotating VRPs could offer a new perspective to explain unconventional force generation for biological swimming and flying.

Scattering and leapfrogging of vortex rings in a superfluid

The dynamics of vortex ring pairs in the homogeneous nonlinear Schrödinger equation is studied. The generation of numerically exact solutions of traveling vortex rings is described and their translational velocity compared to revised analytic approximations. The scattering behavior of co-axial vortex rings with opposite charge undergoing collision is numerically investigated for different scattering angles yielding a surprisingly simple result for its dependence as a function of the initial vortex ring parameters. We also study the leapfrogging behavior of co-axial rings with equal charge and compare it with the dynamics stemming from a modified version of the reduced equations of motion from a classical fluid model derived using the Biot-Savart law.

Leapfrogging vortex rings in the Landau–Lifshitz equation

Vortex rings are ubiquitous in fluids, with smoke rings being a familiar example. The interaction of multiple vortex rings produces complex dynamical behaviour, such as the leapfrogging motion first analysed by Helmholtz more than a century and a half ago. Here we report on numerical investigations of vortex ring dynamics in a different setting from fluids, namely, as solutions of the Landau–Lifshitz equation that models the evolution of the local magnetization in a ferromagnetic medium. We present the results of the first study on the dynamics of interacting magnetic vortex rings and provide a novel link between fluids and magnetism, by showing that a range of phenomena familiar in fluids are reproduced in ferromagnets. This includes the leapfrogging motion of a pair of vortex rings and evidence for the chaotic dynamics of a trio of rings.

2D-DNS and 2D-RANS Simulations of Supersonic QUASI-2D Turbulent Reacting Shear Flow

<p>Numerical studies of quasi-2D supersonic turbulent hydrogen-air mixing and combustion in free shear layer configuration are performed using 2D-DNS [1] and RANS equations. In order to produce the roll-up and pairing of vortex rings, an unsteady boundary condition is applied at the inlet plane. Frequencies of<br /> initial velocity perturbations have been taken in accordance with linear stability theory. The influences of different inflow perturbations on mixing layer structure are presented. At the outflow, the non-reflecting boundary condition is adopted. In the case of RANS simulation two-parameter k-e turbulence model is used. Thermal conduction is described by Fourier’s law, while diffusion of species by Fick’s law. Equation of state for thermally perfect multispecies gas is used. Thermodynamic parameters, such as specific heat, enthalpy, entropy and internal energy are determined by fourth order degree polynomial formula, which has dependence on temperature. Temperature is determined using Newton-Raphson iteration procedure. The Wilke’s formula is used to determine the mixture viscosity coefficient. Approximation of convection terms are performed by the ENO-scheme of third-order accuracy and approximation of diffusion terms – by second-order central-difference operators. For the description of reaction pathways of hydrogen, a seven species chemical reaction model by Jachimowski is adopted. Chemical reaction source term implicitly includes in mass fraction transport equations, where linearization is applied using Taylor decomposition. The hydrogen flow parameters are M<sub>0</sub> = 2.0, T<sub>0</sub> = 2000 K, P<sub>0</sub> = 101325 Pa, and air flow parameters are M<sub>¥</sub> = 2.1, T<sub>¥</sub> = 2000 K, p<sub>¥</sub> = 101325 Pa. Convective Mach number is M<sub>c</sub> = 0.38, where effect of compressibility is significant.</p>

Numerical study of supersonic turbulent free shear layer

Numerical study of two-dimensional supersonic turbulent free shear layer is performed. The system of Fa-vre-Averaged Naveir-Stokes equations for multispecies flow is solved using ENO scheme of third-order in accuracy. The k-ε two-equation turbulence models with compressibility correction are applied to calculate the eddy viscosity coefficient. In order to produce the roll-up and pairing of vortex rings, an unsteady boundary condition is applied at the inlet plane. At the outflow, the non-reflecting boundary condition is taken. The obtained results are compared with available experimental data.

Calculation of three-dimensional flows of an incompressible fluid based on a dipole representation of vorticity

A new approach to the solution of timedependent threedimensional Navier-Stokes equations of a vis� cous incompressible fluid in the Lagrangian coordi� nates is suggested. The method is based on the intro� duction of a new vector function D called the density of dipoles, through which the velocity and vorticity in the flow field are expressed. The equations for the evo� lution of the density of dipoles corresponding to vary� ing hydrodynamic fields are derived, and the boundary conditions for it in the form of integrated equation are formulated. A corresponding numerical method or the method of dipole domains (MDD), is constructed. A fundamental distinction from the known three� dimensional vortex methods that use the unclosed vor� tex elements (vortons, etc.) is in the fact that the MDD provides the conservation of solenoidality of the resulting vortex field and fulfillment of hydrodynamic invariants. An example of the direct numerical model� ing of the evolution of a threedimensional interaction of a pair of vortex rings is given. Currently, vortex gridless methods are widely used to calculate the nonstationary flows of a fluid. They are attractive because of the absence of necessity to construct the grids (which is especially topical when calculating the flows with movable boundaries) and

Experimental studies on coaxial vortex loops

An experimental study has been conducted on the formation and propagation of coaxial vortex loops using a shock tube facility. The study aimed at evaluating the flow characteristics of pairs of corotating vortex rings that generate the leapfrogging phenomenon. The driver and driven gas of the shock tube were air. Three driver pressures were used (4, 8, and 12 bars) with the driven gas being at ambient conditions. The Mach numbers of the shock wave generated inside the shock tube were 1.34, 1.54, and 1.66, respectively. The sudden expansion present at the diaphragm location effectively decreased the Mach number value of the traveling shock wave. Results showed that a pair of vortex rings staggered with respect to time and with the same direction rotation lead to leapfrogging. Results also indicated that the number of leapfrogging occurrences is related to the Reynolds number of the vortex ring pairs with a decrease in leapfrogs at higher Reynolds numbers.

Application of mosaic-skeleton approximations in the simulation of three-dimensional vortex flows by vortex segments

The computations in a vortex method for three-dimensional fluid dynamics simulation are accelerated by applying mosaic-skeleton approximations of matrices in the velocity computations. A modified vortex segment method is proposed in which mosaic-skeleton matrix approximations are effectively used to solve the problem of a vorticity field developing in an unbounded three-dimensional domain and in separated flow problems. Examples of the numerical solution of model fluid dynamic problems, such as the motion of a pair of vortex rings, the flow past a hemisphere, and the flow past an octahedral cylinder, are given that illustrate the capability of accelerating the computations while preserving the qualitative and quantitative description of the flow.

Blast-Wave Dynamics in a Circular Duct with a Sudden Expansion

In this study, the problem of a planar blast wave in a duct with a sudden expansion is considered. An incident blast wave that contains two shock waves is arranged so that one pair of vortex rings induced by the first shock wave interacts with the second shock wave of the blast wave and with the reflected shock associated with the first shock wave. A high-resolution Euler/Navier-Stokes solver using a fifth-order weighted essentially nonoscillation scheme is employed to investigate the problem. After the Euler/Navier-Stokes solver is validated to be reasonably accurate, the flow fields induced by the shock/vortex interactions are investigated by computational shadowgraph and computational schlieren techniques. It is found that the trajectories formed by major ring-vortex centers may be different case by case, depending on the arrival time sequence of the second shock wave and the reflected shock wave. In particular, a third vortex ring may be developed, causing the trajectory's turn at some critical time in viscous-flow models. Because of viscous dissipation, consequently stronger vortex-ring strength predicted by the inviscid-flow model than that for the viscous-flow model can result in 14-32% lower pressures at the major ring-vortex centers in the inviscid flow compared with the turbulent flow during the time interval investigated for case A, and 20-32% for case B, and 21-38% for case C. Because of the boundary layer development along the duct wall after the sudden expansion, the reflection type of the first shock wave is changed from a regular reflection in the inviscid-flow case to a single Mach reflection that directly affects the arrival time of the reflected shock wave at the sharp corner. Moreover, the mechanism of the vortex ring formation based on the inviscid-flow model is analyzed. It is found that the term due to the dilation effect also plays a more important role in vorticity generation than the baroclinic term.

Fast vortex method calculation using a special-purpose computer

A mathematical formulation for the 3D vortex method has been developed for calculation using a special-purpose computer MDGRAPE-2 that was originally designed for molecular dynamics simulations. We made an assessment of this hardware for a few representative problems and compared the results with and without it. It is found that the generation of appropriate function tables, which are used to call libraries, embedded in MDGRAPE-2 is of primary importance in order to retain accuracy. The error arising from the approximation is evaluated by calculating a pair of vortex rings impinging to themselves. Consequently, acceleration about 50 times greater is achieved by MDGRAPE-2 while the error in the statistical quantities such as kinetic energy and enstrophy remain negligible.

PIV studies of large scale structures in the near field of small aspect ratio elliptic Jets

The near flow field of small aspect ratio elliptic turbulent free jets (issuing from nozzle and orifice) was experimentally studied using a 2D PIV. Two point velocity correlations in these jets revealed the extent and orientation of the large scale structures in the major and minor planes. The spatial filtering of the instantaneous velocity field using Gaussian convolution kernel shows that while a single large vortex ring circumscribing the jet seems to be present at the exit of nozzle, the orifice jet exhibited a number of smaller vortex ring pairs close to jet exit. The smaller length scale observed in the case of the orifice jet is representative of the smaller azimuthal vortex rings that generate exial vortex field as they are convected. This results in the axis switching in the case of orifice jet and may have a mechanism different from the self induction process as observed in the case of contoured nozzle jet flow.

Measurement of vortex ring characteristics during pairing in a forced subsonic air jet

The pairing of vortex rings in an acoustically excited jet is experimentally investigated. The acoustical forcing of the jet allows a series of particle image velocimetry (PIV) measurements to be performed at a frequency slightly lower than the frequency at which the vortex rings are shed in the shear layer. This technique, here called stroboscopic PIV, provides a time-resolved evolution of the velocity and vorticity fields during the threading and merging of the vortex rings, with a view to the prediction of the sound produced by this interaction. The evolution of the characteristics of the cores of the vortex rings during pairing is determined using an automated vortex detection algorithm. Three stages are distinguished in the evolution of the rings, based on the relative acceleration and deformation of their cores. The conservation of the circulation during the merging is addressed. The accuracy of the measurements is estimated, being a crucial issue for the future prediction of the sound generation based on the experimental description of the flow field.