Vortex Velocity Field Research Articles

Validated numerical analysis of vortical structures in 3D AC electro-osmotic flows

This paper presented an experimental validation of a numerical study on the vortical structures in AC electro-osmotic (ACEO) flows. First, the 3D velocity field of ACEO vortices above the symmetric electrodes was experimentally investigated using astigmatism microparticle tracking velocimetry. The experimentally obtained velocities were used to validate an extended nonlinear Gouy–Chapman–Stern model accounting for the surface conduction effect. A qualitative agreement between the simulations and experiments was found for the velocity field when changing AC voltage (from 0.5 to 2 V) and the frequency (from 50 to 3,000 Hz). However, the predicted magnitude of the velocity profiles was much higher than the experimentally obtained ones, except in some cases at low frequency. For frequencies higher than 200 Hz, a correction factor was introduced to make the numerical results quantitatively comparable to the experimental ones. In addition, the primary circulation, given in terms of the spanwise component of vorticity, was numerically and experimentally analyzed as function of frequency and amplitude of the AC voltage. The outline of the vortex boundary was determined via the eigenvalues of the strain-rate tensor estimated from the velocity field. It revealed that the experimental circulation was frequency dependent, tending to zero at both low and high frequency and the maximum changing from around 600 Hz for 1 V to 300 Hz for 2 V. The variation in the predicted vortex circulation as function of frequency and voltage, after using the above correction factor, was in good correspondence with the experiments. These results yield first insights into the characteristics of 3D ACEO flows and the ability of current numerical models to adequately describe them.

Increasing the stability of high contraction ratio flow of Boger fluids by pre-deformation

In this paper we investigate the stabilizing effect of pre-deforming the flow of a PEO/PEG Boger fluid before entering a microfabricated 83:1:83 planar contraction–expansion. Applying pre-deformation has a dramatic effect on the size and stability of the recirculation zones upstream of the contraction. This pre-deformation is generated by a cylinder placed in front of the contraction. Transverse flow past an unbounded cylinder is a combination of both shear and elongational flow, at the cylinder walls and the downstream wake respectively. The deformation of the polymer by the shear and elongational flow temporarily changes the rheological properties of the solution before it relaxes back to the original state. Deformation rates up to γ˙ of 12000s−1 are attained in the microfluidic device, resulting in the following ranges of dimensionless numbers for experiments performed: 0.003<Re<0.019, 8<Wi<60 and El=2758. Streak images and μ-PIV measurements are used to quantify vortex length and velocity field. The distance between cylinder and contraction is chosen such, that at the lowest flow rate the deformation caused by the cylinder is remembered by the fluid before entering the contraction. Applying pre-deformation gives rise to a new type of vortex evolution which is different from the standard contraction case. Moreover a change in the divergence of streamlines is observed. At low deformation rates (Wi<16) a distinct type of vortices occur which undergo a transition to lip vortices at higher deformation rates (Wi>16). Pre-deforming the flow is found to reduce vortex length up to 20% and to reduce the divergence of streamlines and vortex growth with increasing Weissenberg number significantly.

Vortical Structures in Wall-Bounded Turbulent Flow with Recirculation

Hairpin or horse-shoe vortices are a widely-accepted feature of the wall-bounded flows. These vortical structures have mostly been studied in canonical flows. Relatively few studies have been conducted on the characteristics of the vortical structures in wall-bounded flows with adverse pressure gradient and still fewer on the detached flows with recirculation. In the present contribution, vortices have been educed using a DNS database of incompressible flow over a 2-dimensional surface bump in a converging-diverging channel at a Reynolds number Reτ of 617, based on the friction velocity at inlet. Vortices have been educed from the instantaneous velocity field in streamwise/wall-normal and spanwise/wall-normal planes using the signed swirling strength criterion. Vortex validation is done through a fit of the vortex velocity field to the Oseen vortex model. The effects of a strong adverse pressure gradient and flow reciruclation on the population density and sizes of the streamwise and spanwise-oriented vortices have been studied. It has been found that a strong adverse pressure gradient and flow recirculation leads to the generation of a new near-wall peak of small spanwise prograde vortex population. Furthermore, this peak of vortex density has been found to coincide and hence relate to the outward movement of the peak of streamwise rms velocity fluctuations typical of adverse pressure gradient wall-bounded turbulent flows.

Acoustic trapping of particle by a periodically structured stiff plate

We present a study on the acoustic radiation forces exerted on a cylindrical particle near the surface of a periodically structured brass plate. When resonance of the structured plate occurs, this configuration shows an interesting trapping effect, which essentially arises from the gradient force induced by gradient vortex velocity field near the surface. This artificial structure for providing a geometrically modulated trapping force may be of interest for acoustic manipulation and sorting in various complex mechanical systems.

On electric fields created by quantized vortices

It is shown that in a magnetic field the quantized vortices in a superfluid acquire a real quantized electric charge concentrated in the vortex core. This charge is compensated by an opposite surface charge, located at macroscopic distance from the vortex axis. It is found that polarization caused by the vortex velocity field does not give rise to electric fields outside an infinite cylinder. The vortex-created electric fields can be observed only near the cylinder end surfaces, which must be covered by dielectric covers in order to prevent leakage of the superfluid. The influence of cover properties on the vortex-created potential is studied here. The potentials created by vortices on point and ring electrodes are calculated.

Experimental Investigation of Intake Ground Vortices During Takeoff

A quantitative experimental investigation has been conducted to simulate intake ground vortex formation during aircraft takeoff under headwind conditions. The experiments were performed using a small-scale intake model in conjunction with a rolling ground plane in a low-speed wind tunnel. The Reynolds number was fixed at 1.26 x 10 6 based on the inner diameter and average intake velocity. Stereoscopic particle image velocimetry was used to measure the ground vortex velocity field, and in-duct total pressure measurements have been performed to assess the internal flow. Measurements were taken for an extensive range of configurations, including a static and simulated moving intake under a variety of headwind conditions. A moving intake was simulated in the wind tunnel by synchronizing the ground and tunnel wind velocities and using extensive suction to remove the approaching boundary layer. The results show that at high velocity ratios there are no substantial differences due to the moving ground plane. At low velocity ratios, the simulated moving intake results in a significantly different flowfield in which the ground vortex is weaker, steadier in space, and more symmetric relative to the static ground case. These results indicate the relative importance of the ground vortex vorticity sources and highlight the importance of including the effects of a moving ground when simulating an aircraft takeoff.

Vortex velocity field in inhomogeneous media: A numerical study in Bose-Einstein condensates

We present a numerical calculation of the velocity field of an off-axis vortex within a harmonic trapping potential. We consider a condensate with a large number of particles which, in spite of being in the ThomasFermi regime, possesses a non-totally-negligible vortex core size. Via a simple, yet realistic, modeling of the vortex-state density, we derive, by treating the equation of continuity outside and inside the vortex core, respective equations for the velocity field and the vortex precession velocity. We find that the vortex precession velocity is given by two contributions: the background velocity field evaluated around the border of the core and another term which depends on the core shape. Our findings concerning the velocity field outside the vortex core are in good agreement with previous theoretical predictions in a narrow region around it, while far away from the vortex we observe a field with a large asymmetry with respect to the vortex position. We show that a better approximation may be obtained by adding the velocity field produced by an antivortex located outside the condensate.

Nonpremixed ignition of H 2/air in a mixing layer with a vortex

The ignition of a laminar non-premixed H 2/air mixing layer with an embedded vortex was computationally studied with detailed chemistry and transport. The initial vortex velocity and pressure fields were specified based on the stream function of an incompressible nonviscous vortex. The fuel side is pure hydrogen at 300 K, and the oxidizer side is air at 2000 K. The vortex evolution process was found to consist of two ignition events. The first ignition occurs in a diffusion mode with chain branching reactions dominating. The second ignition takes place in the premixed mode, with more chemical reactions involved, and is significantly affected by the heat and species generated in the first ignition event. The coupling between the most reactive mixture fraction and scalar dissipation rate was verified to be crucial to the ignition delay. The effects of the vortex strength, characteristic size, and its center location were individually investigated. For all vortex cases, the ignition delay was shorter than that of the 1D case. Furthermore, the ignition delay has a nonmonotonic dependence on all the vortex parameters.

Topological Vortices in the Modified Two-Dimensional Gross—Pitaevskii Theory

It is shown that there exists an elementary vortex topological current in the modified two-dimensional Gross—Pitaevskii theory. An explicit expression for the vortex velocity field as a function of the order parameter is derived. The evolution of vortices is studied from the topological properties of the order parameter field. It is found that vortices generate or annihilate at the limit points and encounter, split, or merge at the bifurcation points of the order parameter field ψ.

803 周期的撹乱を付加した縦渦による壁面噴流の操縦 : 縦渦の発達と平均速度場

803 周期的撹乱を付加した縦渦による壁面噴流の操縦 : 縦渦の発達と平均速度場

Axial motion and scalar transport in stretched spiral vortices

We consider the dynamics of axial velocity and of scalar transport in the stretched-spiral vortex model of turbulent fine scales. A large-time asymptotic solution to the scalar advection-diffusion equation, with an azimuthal swirling velocity field provided by the stretched spiral vortex, is used together with appropriate stretching transformations to determine the evolution of both the axial velocity and a passive scalar. This allows calculation of the shell-integrated three-dimensional spectra of these quantities for the spiral-vortex flow. The dominant term in the velocity (energy) spectrum contributed by the axial velocity is found to be produced by the stirring of the initial distribution of axial velocity by the axisymmetric component of the azimuthal velocity. This gives a k−7/3 spectrum at large wave numbers, compared to the k−5/3 component for the azimuthal velocity itself. The spectrum of a passive scalar being mixed by the vortex velocity field is the sum of two power laws. The first is a k−1 Batchelor spectrum for wave numbers up to the inverse Batchelor scale. This is produced by the axisymmetric component of the axial vorticity but is independent of the detailed radial velocity profile. The second is a k−5/3 Obukov–Corrsin spectrum for wave numbers less than the inverse Kolmogorov scale. This is generated by the nonaxisymmetric axial vorticity and depends on initial correlations between this vorticity and the initial scalar field. The one-dimensional scalar spectrum for the composite model is in satisfactory agreement with experimental measurement.

ON THE SCATTERING OF SOUND BY A RECTILINEAR VORTEX

A re-examination is made of the two-dimensional interaction of a plane, time-harmonic sound wave with a rectilinear vortex of small core diameter at low Mach number. Sakov [1] and Ford and Smith [2] have independently resolved the “infinite forward scatter” paradox encountered in earlier applications of the Born approximation to this problem. The first order scattered field (Born approximation) has nulls in the forward and back scattering directions, but the interaction of the wave with non-acoustically compact components of the vortex velocity field causes wavefront distortion, and the phase of the incident wave to undergo a significant variation across a parabolic domain whose axis extends along the direction of forward scatter from the vortex core. The transmitted wave crests of the incident wave become concave and convex, respectively, on opposite sides of the axis of the parabola, and focusing and defocusing of wave energy produces corresponding increases and decreases in wave amplitude. Wave front curvature decreases with increasing distance from the vortex core, with the result that the wave amplitude and phase are asymptotically equal to the respective values they would have attained in the absence of the vortex. The transverse acoustic dipole generated by translational motion of the vortex at the incident wave acoustic particle velocity, and the interaction of the incident wave with acoustically compact components of the vortex velocity field, are responsible for a system of cylindrically spreading, scattered waves outside the parabolic domain.

High temperature superconductivity in the mixed state and the dynamics of charge carriers

A model to calculate the temperature and magnetic field dependence of the scattering time τ ν( H, T) of quasiparticles by bound electron states in a vortex in high-temperature superconductors is proposed. In this model, the hydrodynamic interaction of a moving gas of quasiparticles with the discrete states of the vortex velocity field is regarded as quasielastic scattering and the resulting scattering time of quasiparticles is different from scattering of individual vortices. The normalized scattering time was found to decrease exponentially with increasing temperature. This behavior is due to the suppression of the amplitude of the superconducting order parameter as the temperature increases. This model accounts for the observed temperature and field dependence of the scattering time particularly at low-field regime.

Simulating vortex pairs interacting with mixing-layer vortices

Numerical simulations of interactions between rolled-up vortices in a plane mixing layer and a vortex pair by a vortex blob method, with the aim of enhancing the growth of the mixing layer and its turbulence level are made. Evolution of vortex patterns and velocity fields during the interaction are presented. Parameter studies are made for the ratio of circulation of the vortex pair to that of the mixing layer vortices γ, the initial position of introduction of the vortex pair, and the attitude of the vortex pair. The momentum thickness of the mixing layer increases with increasing circulation of the vortex pair, while the increase tends to saturate at γ≈2.5, where the vortex pair passes through the mixing layer. Moreover, the momentum thickness attains a maximum at a particular longitudinal position of the introduction because this position determines how the vortex pair encounters the vortices in the mixing layer.

Vortex Velocities in theO(n)Symmetric Time-Dependent Ginzburg-Landau Model

An explicit expression for the vortex velocity field as a function of the order parameter field is derived for the case of point defects in the $O(n)$ symmetric time-dependent Ginzburg-Landau model. This expression is used to find the vortex velocity probability distribution in the Gaussian closure approximation in the case of phase ordering kinetics for a nonconserved order parameter. The velocity scales as ${L}^{\ensuremath{-}1}$ in scaling regime where $L\ensuremath{\approx}{t}^{1/2}$ and $t$ is the time after the quench.

NUMERICAL SIMULATION OF A SELF-SUSTAINED WAKE-EDGE INTERACTION

The characteristics of the two-dimensional flow structures resulting from the interaction between a bluff trailing edge wake and a downstream leading edge are described by using a Discrete Vortex Method simulation. The typical characteristics of the self-sustained oscillations of impinging wake flow are presented through the use of instantaneous vortex distribution, streamlines and velocity fields. An attempt is made to simulate the formation of a secondary vortex due to vortex-edge interaction from the tip of a sharp leading edge as a self-generating phenomenon. It is shown that satisfactory computer simulation results can be obtained for the complex flow-edge interaction mechanisms.

Azimuthally propagating ring vortices in a model for nonaxisymmetric Taylor vortex flow.

We report on some surprising structures of particle paths in the velocity field of wavy Taylor vortices using velocity fields from a model of Davey, DiPrima, and Stuart [J. Fluid Mech. 31, 17-52 (1968)]. We observe that there are regions of chaotic mixing in the boundaries between the vortices and, more surprisingly, find evidence of ring vortices propagating azimuthally around the cylinder at the speed of the wave propagation.

Stabilization of trapped vortices by alternating blowing suction

Motion of a free point vortex near a circular cylinder in a uniform oncoming flow is considered. There is a point at which the point vortex velocity is zero. This stationary position is unstable. Introducing two periodic point sources of zero mean flow rate modifies the point vortex velocity field so that instead of the stationary position there is a periodic trajectory. The corresponding periodic motion of the vortex is found to be stable over a certain range of characteristics of periodic blowing/suction modeled with periodic sources. In particular, for stabilization the amplitude of the source flow rate oscillations must not exceed a certain limit. The results are believed to bear on the problem of enhancing lift at high angle of attack with the use of trapped vortices.

The fully nonlinear development of Görtler vortices in growing boundary layers

The fully nonlinear development of small-wavelength Görtler vortices in a growing boundary layer is investigated by a combination of asymptotic and numerical methods. The starting point for the analysis is the weakly nonlinear theory of Hall ( J. Inst. Math. Applies 29, 173 (1982)) who discussed the initial development of large-wavenumber small-amplitude vortices in a neighbourhood of the location where they first become linearly unstable. That development is unusual in the context of nonlinear stability theory in that it is not described by the Stuart-Watson approach. In fact, the development is governed by a pair of coupled nonlinear partial differential evolution equations for the vortex flow and the mean flow correction. Here the further development of this interaction is considered for vortices so large that the mean flow correction driven by them is as large as the basic state. Surprisingly it is found that such a nonlinear interaction can still be described by asymptotic means. It is shown that the vortices spread out across the boundary layer and effectively drive the boundary layer. In fact, the system obtained by the equations for the fundamental component of the vortex generates a differential equation for the basic state. Thus the mean flow adjusts so as to make these large amplitude vortices locally neutral. Moreover in the region where the vortices exist the mean flow has a ‘square-root’ profile and the vortex velocity field can be written down in closed form. The upper and lower boundaries of the region of vortex activity are determined by a free-boundary problem involving the boundary-layer equations. In general it is found that this region ultimately includes almost all of the original boundary layer and much of the free stream. In this situation the mean flow has essentially no relation to the flow that exists in the absence of the vortices.

An experimental investigation of blade-vortex interaction at normal incidence

An experimental investigation has been conducted for the blade-vortex interaction (BVI) of a rotor at normal incidence, where the vortex is generally parallel to the rotor axis. Tip Mach number, radial BVI station, and free stream velocity were varied during measurements of fluctuating blade pressures, far field sound pressure levels and directivity, incident vortex velocity field, and blade-vortex interaction angles. The experimental setup is representative of the chopping of helicopter main rotor tip vortices by the tail rotor. This interaction is found to generate impulsive noise which radiates primarily ahead of the blade.