Showing papers on "Vortex published in 1990"

Elementary Fluid Dynamics

Abstract: Introduction Elementary viscous flow Waves Classical aerofoil theory Vortex motion The Navier-Stokes equations Very viscous flow Boundary layers Instability Appendix hints and answers for exercises Bibliography Index.

Self-dual Chern-Simons vortices.

Abstract: We study vortex solutions in an Abelian Chern-Simons theory with spontaneous symmetry breaking. We show that for a specific choice of the Higgs potential the vortex satisfies a set of Bogomol'nyi-type, or ``self-duality,'' equations.

On the formation and suppression of vortex 'shedding' at low reynolds numbers

Abstract: Vortex 'shedding' behind circular cylinders can be altered and suppressed altogether (or 'controlled') over a limited range of Reynolds numbers, by a proper placement of a second, much smaller, cylinder, in the near wake of the main cylinder. This new and dramatic suppression of vortex 'shedding' is the subject of this paper. Details of the phenomenon are documented through parallel experimental and numerical investigations, including flow visualisation. Temporal growth rate measurements of the velocity fluctuations reveal that the presence of the smaller cylinder reduces the growth rate of the disturbances leading to vortex 'shedding' and that its suppression, accompanied by the disappearance of sharp spectral peaks, coincides with negative temporal growth rates. It is argued that the presence of the secondary cylinder has the effect of altering the local stability of the flow by smearing and diffusing concentrated vorticity in the shear layers behind the body; a related effect is that the secondary cylinder diverts a small amount of fluid into the wake of the main cylinder. A united explanation of the formation and suppression of the vortex street is attempted, and it is suggested that the vortex 'shedding' is associated with temporally unstable eigenmodes which are heavily weighted by the near field. It is also shown that absolute instability is relevant up to a point in explaining vortex 'shedding', whose suppression can similarly be associated with altering the instability in the near wake region from absolute to convective.

An analytical study of transport, mixing and chaos in an unsteady vortical flow

Abstract: We examine the transport properties of a particular two-dimensional, inviscid incompressible flow using dynamical systems techniques. The velocity field is time periodic and consists of the field induced by a vortex pair plus an oscillating strainrate field. In the absence of the strain-rate field the vortex pair moves with a constant velocity and carries with it a constant body of fluid. When the strain-rate field is added the picture changes dramatically; fluid is entrained and detrained from the neighbourhood of the vortices and chaotic particle motion occurs. We investigate the mechanism for this phenomenon and study the transport and mixing of fluid in this flow. Our work consists of both numerical and analytical studies. The analytical studies include the interpretation of the invariant manifolds as the underlying structure which govern the transport. For small values of strain-rate amplitude we use Melnikov's technique to investigate the behaviour of the manifolds as the parameters of the problem change and to prove the existence of a horseshoe map and thus the existence of chaotic particle paths in the flow. Using the Melnikov technique once more we develop an analytical estimate of the flux rate into and out of the vortex neighbourhood. We then develop a technique for determining the residence time distribution for fluid particles near the vortices that is valid for arbitrary strainrate amplitudes. The technique involves an understanding of the geometry of the tangling of the stable and unstable manifolds and results in a dramatic reduction in computational effort required for the determination of the residence time distributions. Additionally, we investigate the total stretch of material elements while they are in the vicinity of the vortex pair, using this quantity as a measure of the effect of the horseshoes on trajectories passing through this region. The numerical work verifies the analytical predictions regarding the structure of the invariant manifolds, the mechanism for entrainment and detrainment and the flux rate.

A study on vortex shedding from spheres in a uniform flow

Abstract: Vortex shedding from spheres at Reynolds numbers from 3 × 102 to 4 × 104 in a uniform flow was investigated experimentally. Standard hot-wire technique were used to measure the vortex shedding frequency from spheres in a low-speed wind tunnel. Flow-visualization experiments were carried out in a water channel. Important results from the investigation were that (i) the variation of the Strouhal number St (=fD/U0 , U0 : freestream velocity, D: diameter of the sphere, f: vortex shedding frequency) with the Reynolds number (= U0 D/v, v: kinematic viscosity) can be classified into four regions, (ii) the Reynolds number at which the hairpinshaped vortices begin to change from laminar to turbulent vortices so that the wake structure behind the sphere is not shown clearly when a Reynolds number of about 800 is reached, and (vi) at Reynolds numbers ranging from 8X102 to 1.5X104 , the higher and lower frequency modes of the Strouhal number coexist.

Intermittent vortex structures in homogeneous isotropic turbulence

Abstract: ALTHOUGH well developed turbulence exhibits complex, chaotic spatial and temporal behaviour, there is much experimental evidence to suggest that a remarkable degree of coherence is also present1. It is known2 that correlations in small-scale turbulent motions show significant deviations from the gaussian statistics usually expected for large, randomly interacting systems. This phenomenon, known as intermittency, has long resisted analytical description because of the lack of a simple, universal characterization of turbulence structures3. Here we report numerical simulations which show that there are remarkably simple spatial structures associated with intermittent regions of vorticity. In particular, in contrast to the classical description of turbulence as an array of 'pancake'- or 'lasagne'-like eddies4, we find that high-amplitude vortex structures are tube-like and that they generate local velocity fields that spiral around them.

Axisymmetric vortex breakdown Part 2. Physical mechanisms

Abstract: : Numerical solutions of the axisymmetric Navier Stokes equations are presented and compared with results from experiments for a confined cylindrical flow. The details of the vortex breakdown phenomenon are calculated with a high degree of accuracy. From solutions over a range of parameters the essential features of the flow are obtained. These solutions also provide flow quantities such as the vorticity and the pressure throughout the volume which would be difficult to obtain from experiments. The solutions are explored and the essential physical mechanisms of vortex breakdown in this particular geometry are identified. These mechanisms, which rely on the production of a negative azimuthal component of vorticity as a result of the stretching and tilting of the predominantly axially directed vorticity vector, are elucidated with the aid of a simple, steady, inviscid, axisymmetric equation of motion. This equation has been a starting point for most studies of vortex breakdown but a departure in the present study is that it is explored directly and not through perturbations of an initial stream function. The findings are then generalised to the case of vortex breakdown in swirling pipe flows. Australia.

Graphical visualization of vortical flows by means of helicity

Abstract: Helicity density and normalized helicity are introduced as important tools for the graphical representation of three-dimensional flowfields that contain concentrated vortices. The use of these two quantities filters out the flowfield regions of low vorticity, as well as regions of high vorticity but low speed where the angle between the velocity and vorticity vectors is large (such as in the boundary layer). Their use permits the researcher to identify and accentuate the concentrated vortices, differentiate between primary and secondary vortices, and mark their separation and reattachment lines. The method also allows locating singular points in the flowfield and tracing the vortex-core streamlines that emanate from them. Nomenclature H = helicity Hd = helicity density Hn — normalized helicity MOO = freestream Mach number ReD = Reynolds number V = velocity a = angle of attack co = vorticity

Time-dependent and time-averaged turbulence structure near the nose of a wing-body junction

Abstract: The behaviour of a turbulent boundary layer on a flat surface as it encounters the nose of a cylindrical wing mounted normal to that surface is being investigated. A three-component laser anemometer has been developed to measure this highly turbulent three-dimensional flow. Measurements of all the non-zero mean-velocity and Reynolds-stress components have been made with this instrument in the plane of symmetry upstream of the wing. These data have been used to estimate some of the component terms of the turbulence kinetic energy equation. Histograms of velocity fluctuations and short-time cross-correlations between the laser anemometer and a hot-wire probe have also been measured in the plane of symmetry. In all, these results reveal much of the time-dependent and time-averaged turbulence structure of the flow here.Separation occurs in the plane of symmetry because of the adverse pressure gradient imposed by the wing. In the time mean the resulting separated flow consists of two fairly distinct regions: a thin upstream region characterized by low mean backflow velocities and a relatively thick downstream region dominated by the intense recirculation of the mean junction vortex. In the upstream region the turbulence stresses develop in a manner qualitatively similar to those of a two-dimensional boundary layer separating in an adverse pressure gradient. In the vicinity of the junction vortex, though, the turbulence stresses are much greater and reach’ values many times larger than those normally observed in turbulent flows. These large stresses are associated with bimodal (double-peaked) histograms of velocity fluctuations produced by a velocity variation that is bistable. These observations are consistent with large-scale low-frequency unsteadiness of the instantaneous flow structure associated with the junction vortex. This unsteadiness seems to be produced by fluctuations in the momentum and vorticity of fluid from the outer part of the boundary layer which is recirculated as it impinges on the leading edge of the wing. Though we would expect these fluctuations to be produced by coherent structures in the boundary layer, frequencies of the large-scale unsteadiness are substantially lower than the passage frequency of such structures. It therefore seems that only a fraction of the turbulent structures are recirculated in this way.

The vortices of two-dimensional turbulence

Abstract: A solution of decaying two-dimensional turbulence at large Reynolds number is analysed by means of an automated vortex census. The census identifies the flow structures which approximately conform to the idealized shape of an isolated, coherent vortex. It also determines vortex characteristics, such as amplitude, size, radial profile, and deformation from the ideal axisymmetric shape. The distributions of these characteristics within the vortex population are examined, as are their time evolutions. Interpretation of these distributions is made with reference to both the random initial conditions for the solution and the dynamical processes of vortex emergence, survival, and interaction.

Vortex-core structure observed with a scanning tunneling microscope.

Abstract: The superconducting-vortex-core spectra show a zero-bias peak which splits within a coherence length of the core. Further away from the core these split peaks merge gradually with the gap edge and give a direct local measure of the superfluid velocity. The vortex-core states are imaged both at the Fermi energy and just below the gap to reveal two different sixfold star-shaped structures. The anisotropy and size of these images may be a consequence of the crystalline band structure with its charge-density-wave gap as well as the interaction of the neighboring vortices of the Abrikosov flux lattice.

Vortex Generator Jets—Means for Flow Separation Control

Abstract: Stalled regions (zones of detached or separated flow sometimes followed by reattachment) in a turbulent boundary layer may be eliminated by a technique called the vortex-generator-jet (VGJ) method. The method employs spanwise arrays of small, skewed, and pitched jets from holes in the surface. Low-speed air-flow experiments are described which 1) demonstrate that the VGJ method creates longitudinal (streamwise) vortices in the boundary layer downstream of the jet holes similar to the vortices behind solid vortex generators and 2) show that the cross-stream mixing associated with these vortices is effective in reduction and elimination of stalled regions.

Axisymmetric vortex breakdown, part 1. confined swirling flow

Abstract: A comparison between the experimental visualization and numerical simulations of the occurrence of vortex breakdown in laminar swirling flows produced by a rotating endwall is presented. The experimental visualizations of Escudier (1984) were the first to detect the presence of multiple recirculation zones and the numerical model presented here, consisting of a numerical solution of the unsteady axisymmetric Navier-Stokes equations, faithfully reproduces these phenomena and all other observed characteristics of the flow. Further, the numerical calculations elucidate the onset of oscillatory flow, an aspect of the flow that was not clearly resolved by the flow visualization experiments. Part 2 of the paper examines the underlying physics of these vortex flows.

Controlling Mechanism of Local Scouring

Abstract: Experimental study of clear water scouring around a circular cylinder shows that the scour mechanism is coupled to the three-dimensional separation of the upstream boundary layer and the periodic vortex shedding in the wake of the cylinder. The first scour appears in the wake of the cylinder. The main scouring agent in the upstream region is a system of horseshoe vortices. The vortices have a periodical character that causes a triple-scour profile to develop in the upstream region. During scouring, the number and periods of horseshoe vortex shedding undergo no appreciable change. Despite the clear water stage, the transport phenomenon is periodical. Transport of sediment takes place through turbulent scales of comparable size to macro-length scales. The size of horseshoe vortices are representative for the macroscale. Wake scouring is caused by the primary wake vortices and the accelerated side flow. The process is characterized by a strong periodical transport and the formation of ripples. The periodicity is controlled by the shedding frequency of the wake vortices. Collars attached to the cylinder cannot prevent the formation of the vortices.

Self-excited oscillations and mixing in a heated round jet

Abstract: An axisymmetric hot-air jet discharging into cold ambient air is investigated experimentally. We consider the transitional regime, that is, Reynolds numbers at which the jet is initially laminar. In the first part of the paper it is demonstrated by several different experiments that, for sufficiently low Reynolds number and a ratio of jet exit to ambient density below approximately 0.7, global oscillations of the ‘jet column’ become self-excited, a behaviour which is related to local absolute instability in the potential core region. The onset of the global oscillations is identified as a Hopf bifurcation and two axisymmetric global modes are observed below the critical density ratio. Finally, it is shown that in the (self-excited) limit-cycle regime the spreading of the hot jet is intermittently quite spectacular, with half-angles in excess of 45°. Using flow visualization, this large spreading of low-density jets is related to the generation of strong ‘side jets’ emanating from the jet column.

Vortex dipole rebound from a wall

Abstract: Accurate numerical simulations of vortex dipoles impinging on flat boundaries have revealed interesting new features. In the case of free‐slip boundaries the dipole does not rebound from the wall. In the case of nonslip walls rebounding occurs and complex interactions of secondary and tertiary vortices appear. The numerical simulation of the first dipole rebound from the wall agrees with experimental visualizations. Numerical experiments extending in time beyond the real experiments show multiple rebounding. Each rebound is associated with the detachment of a secondary vorticity layer from the wall, these layers merge, and at a value of Reynolds number Re=1600, form a new dipole. This dipole has sufficient circulation to induce on itself a motion in the opposite direction to the motion of the initial dipole.

Small-scale transition in a plane mixing layer

Abstract: An experimental study was conducted to investigate the generation process of random small-scale turbulence in an originally laminar mixing layer. The evolutions of the two types of deterministic structures, the spanwise and streamwise vortices, were first clarified in order to determine their roles in the transition process. A scaling rule for the streamwise distance from the trailing edge of the splitter plate to the vortex merging position was found for various velocity ratios. After this stremwise lengthscale was determined, it became clear that the spanwise wavelength of the streamwise vortices doubled after the merging of the spanwise structures which nominally doubled streamwise wavelengths. The most interesting finding was that the random small-scale eddies were produced by the interactions between the merging spanwise structures and the streamwise vortices.

Thermal fluctuations of vortex lines, pinning, and creep in high-Tc superconductors.

Abstract: Thermal fluctuations of vortex lines are shown to be capable of strongly reducing the value of the critical current in the mixed state of high-${\mathit{T}}_{\mathit{c}}$ superconductors. The theory of pinning in the presence of thermal fluctuations is developed. The current relaxation law in the regime of single-vortex pinning is obtained.

Experiments on vortex dynamics in pure electron plasmas

Abstract: Magnetically confined columns of electrons are excellent experimental manifestations of two‐dimensional (2‐D) vortices in an inviscid fluid. Surface charge perturbations on the electron column (diocotron modes) are equivalent to surface ripples on extended vortices; and unstable diocotron modes on hollow electron columns are examples of the Kelvin–Helmholtz instability. Experiments demonstrate that the stable and unstable modes are distinct and may coexist, having different frequencies and radial eigenfunctions. For azimuthal mode number l=1, an exponentially unstable mode is observed on hollow columns, in apparent contradiction to 2‐D fluid theory. For l=2, a similar unstable mode is observed, consistent with fluid theory. These diocotron instabilities on hollow columns saturate with the formation of smaller vortex structures, and radial transport is determined by the nonlinear interaction of these secondary vortices. The vortex pairing instability has been observed for isolated, well‐controlled vortices, and the instability is found to depend critically on the vortex separation distance.

On a class of steady confined Stokes flows with chaotic streamlines

Abstract: The general incompressible flow uQ(x), quadratic in the space coordinates, and satisfying the condition uQ-n = 0 on a sphere r = 1, is considered. It is shown that this flow may be decomposed into the sum of three ingredients - a poloidal flow of Hill’s vortex structure, a quasi-rigid rotation, and a twist ingredient involving two parameters, the complete flow uQ(x) then involving essentially seven independent parameters. The flow, being quadratic, is a Stokes flow in the sphere. The streamline structure of the general flow is investigated, and the results illustrated with reference to a particular sub-family of ‘ stretch-twist-fold ’ (STF) flows that arise naturally in dynamo theory. When the flow is a small perturbation of a flow ul(x) with closed streamlines, the particle paths are constrained near surfaces defined by an ‘adiabatic invariant ’ associated with the perturbation field. When the flow u1 is dominated by its twist ingredient, the particles can migrate from one such surface to another, a phenomenon that is clearly evident in the computation of Poincar6 sections for the STF flow, and that we describe as ‘ trans-adiabatic drift ’. The migration occurs when the particles pass a neighbourhood of saddle points of the flow on r = 1, and leads to chaos in the streamline pattern in much the same way as the chaos that occurs near heteroclinic orbits of low-order dynamical systems. The flow is believed to be the first example of a steady Stokes flow in a bounded region exhibiting chaotic streamlines.

An experimental study of a turbulent vortex ring

Abstract: A turbulent vortex ring having a relatively thin core is formed in water by a momentary jet discharge from an orifice in a submerged plate. The necessary impulse is provided by a pressurized reservoir and is controlled by a fast programmable solenoid valve. The main aim of the research is to verify the similarity properties of the mean flow, as defined by ensemble averaging, and to find the distribution of mean vorticity, turbulent energy, and other quantities in the appropriate non-steady similarity coordinates. The velocity field of the vortex is measured for numerous realizations with the aid of a two-channel tracking laser-Doppler velocimeter. The problem of dispersion in the trajectories of the individual rings is overcome by development of a signature-recognition technique in two variables. It is found that the turbulence intensity is largest near the vortex core and that at least the radial component is not negligible in the near wake. The slow growth of the ring structure is controlled by a slight excess of entrainment over de-entrainment. An important inference is that the growth process and the process of turbulence production probably involve secondary vortices wrapped around the core in azimuthal planes.

Low drag vortex generators

Abstract: A generally V-shaped device (40) that is installed on a surface (48) over which there is a flowing medium (50) whose viscosity causes a boundary layer to form between free-stream medium and the surface. The point (46) of the V-shape generator (40) is oriented facing the down stream direction. Usually a plurality of generators (40) are positioned in a line crosswise to the flow spaced so that the vortices created thereby do not interfere. Flow between the arms (42 and 44) of each generator (40) generates a pair of counterrotating vortices (64 and 68) with diameters (66) much larger than the height of the generator to provide stronger flow control with less parasitic drag than prior art vortex generators. The height of the generator (40) is usually less than the height of the local boundary layer (73), but may extend above the boundary layer (73) especially when the generator (40) is use to control spanwise flow or to reduce tip vortices.

Resistivity of high-Tc superconductors in a vortex-liquid state.

Abstract: The theory of pinning of a vortex liquid by weak disorder is developed. Two different vortex-liquid dissipative regimes are shown to exist: the flux flow above some crossover temperature ${\mathit{T}}_{\mathit{k}}$, where the vortex liquid is unpinned, and the thermally assisted flux flow below ${\mathit{T}}_{\mathit{k}}$. The activation barriers in the latter regime are those associated with the plastic motion of the vortices in the liquid.

Unsteady flow past a rotating circular cylinder at reynolds numbers 103 and 104

Abstract: The unsteady flow past a circular cylinder which starts translating and rotating impulsively from rest in a viscous fluid is investigated both theoretically and experimentally in the Reynolds number range 103 [les ] R [les ] 104 and for rotational to translational surface speed ratios between 0.5 and 3. The theoretical study is based on numerical solutions of the two-dimensional unsteady Navier–Stokes equations while the experimental investigation is based on visualization of the flow using very fine suspended particles. The object of the study is to examine the effect of increase of rotation on the flow structure. There is excellent agreement between the numerical and experimental results for all speed ratios considered, except in the case of the highest rotation rate. Here three-dimensional effects become more pronounced in the experiments and the laminar flow breaks down, while the calculated flow starts to approach a steady state. For lower rotation rates a periodic structure of vortex evolution and shedding develops in the calculations which is repeated exactly as time advances. Another feature of the calculations is the discrepancy in the lift and drag forces at high Reynolds numbers resulting from solving the boundary-layer limit of the equations of motion rather than the full Navier–Stokes equations. Typical results are given for selected values of the Reynolds number and rotation rate.

Convergence of the point vortex method for the 2-D euler equations

Abstract: We prove consistency, stability and convergence of the point vortex approximation to the 2-D incompressible Euler equations with smooth solutions. We first show that the discretization error is second-order accurate. Then we show that the method is stable in l p norm. Consequently the method converge in l p norm for all time. The convergence is also illustrated by a numerical experiment

Thrust generation by an airfoil in hover modes

Abstract: A small airfoil is operated in combined harmonic plunging and pitching motions to generate thrust in a still air environment. By full utilization of dynamic stall vortices large thrust coefficients were attained. The vortical signature of thrust is a simple vortex street with the character of a jet stream.

An investigation of supersonic oscillatory cavity flows driven by thick shear layers

Abstract: Flows around two-dimensional rectangular cavities driven by thick shear layers are investigated experimentally at two supersonic Mach numbers (Me = 1.5 and 2.5) to show the effects of variations in Mach number and length to depth ratio of the cavity. Flow oscillation is observed in the cavity. The characteristics of the oscillatory behaviour are determined by Mach number and the length of depth ratio of the cavity, as well as the shear layer spanning the cavity. Two oscillatory mechanisms can be identified: one in which a strong trailing-edge vortex and vortices which are shed from the leading-edge interact, the other in which a transverse oscillation of a single vortex occurs within the cavity. Changes in the time-dependent and the time-mean flow characteristics at different flow conditions are discussed. The time-dependent experimental results are compared with existing theoretical analyses of the frequencies. For one of these characteristic types of oscillation, the longitudinal oscillation, an existing theoretical description is improved with a modified phase relation.