Showing papers on "Vortex published in 1985"

Higher-order derivative correlations and the alignment of small-scale structures in isotropic numerical turbulence

Abstract: In a three dimensional simulation higher order derivative correlations, including skewness and flatness factors, are calculated for velocity and passive scalar fields and are compared with structures in the flow. The equations are forced to maintain steady state turbulence and collect statistics. It is found that the scalar derivative flatness increases much faster with Reynolds number than the velocity derivative flatness, and the velocity and mixed derivative skewness do not increase with Reynolds number. Separate exponents are found for the various fourth order velocity derivative correlations, with the vorticity flatness exponent the largest. Three dimensional graphics show strong alignment between the vorticity, rate of strain, and scalar-gradient fields. The vorticity is concentrated in tubes with the scalar gradient and the largest principal rate of strain aligned perpendicular to the tubes. Velocity spectra, in Kolmogorov variables, collapse to a single curve and a short minus 5/3 spectral regime is observed.

The derivation and numerical solution of the equations for zero mach number combustion

Abstract: We present a limiting system of equations to describe combustion processes at low Mach number in either confined or unbounded regions and numerically solve these equations for the case of a flame propagating in a closed vessel. This system allows for large heat release, substantial temperature and density variations, and substantial interaction with the hydrodynamic flow field, including the effects of turbulence. This limiting system is much simpler than the complete system of equations of compressible reacting gas flow since the detailed effects of acoustic waves have been removed. Using a combination of random vortex techniques and flame propagation algorithms specially designed for turbulent combustion, we describe a numerical method to solve these zero Mach number equations. We use this method to analyze the competing effects of viscosity, exothermicity, boundary conditions and pressure on the rate of combustion for a flame propagating in a swirling flow inside a square.

Three-dimensional vortex dynamics in superfluid 4He: Line-line and line-boundary interactions.

Abstract: The dynamical behavior of arbitrarily configured, interacting quantized vortex filaments is investigated by means of numerical experiments and analytical estimates. Several prototype situations of interest in the theory of superfluid turbulence and critical velocities are considered. It is shown that if a vortex loop approaches a surface to within a critical distance, a localized cusplike deformation is generated which drives the vortex into the surface at a well-defined point. If the vortex is reconnected to the surface in this limit, the two ends which now terminate on the surface quickly move apart. The entire process can be well approximated by making a simple reconnection at the critical distance. A similar process is found to occur when two vortex filaments try to cross, with two cusps developing which bring the lines together at a point in such a way that a line-line reconnection naturally ensues. More complicated versions of the reconnection process occur when a vortex terminates on a flat surface which contains a pinning site in the form of a local protrusion. Such a vortex is captured by the pinning site when it approaches to within a critical distance. Once a vortex is pinned, it requires a finite flow velocitymore » to free it from the pinning site. At the depinning velocity, the vortex reconnects to the flat surface and moves off. An analytical depinning criterion involving both normal and superfluid velocities is derived, and found to be in good agreement with the numerical experiments.« less

Computing Three-Dimensional Incompressible Flows with Vortex Elements

Abstract: The techniques, capabilities and applicability of numerical models of three-dimensional, unsteady vortical flows with high Re are assessed. Vorticity is calculated only in appropriate regions and the velocity field is derived from the boundary conditions. Vorticity is assumed to take the shape of tubes with uniform core structures in the case of turbulence. The efforts being made to simplify equations for dense collections of vortex filaments in order to make them tractable to computer simulations are described. The effectiveness of vorticity arrow representations for accurately describing vorticity fields near surfaces is discussed, along with Lagrangian vortex elements, which may be of use in modelling the rotational part of flows around bluff bodies, nonuniform density flows and chemically reacting flows.

Evolution of a single wake behind a pair of bluff bodies

Abstract: In this paper the flow behind a pair of bluff bodies placed side by side in a stream is studied using a variety of flow-visualization methods. Above a critical gap size between the bodies, vortex-shedding synchronization occurs, either in phase or in antiphase. It has previously been assumed that such synchronization forms a wake comprising two parallel vortex streets in phase and in antiphase respectively. In the present paper we find that two antiphase streets are indeed formed, although in-phase shedding leads to the development of a single large-scale wake. The vortices which are formed simultaneously at the cylinders rotate around one another downstream, each pair forming a ‘binary vortex’. The combined wake comprises a street of such vortices, which we term a binary vortex street. Below a critical gap size between the bluff bodies the flow becomes asymmetric. We observe in this regime certain harmonic modes of vortex shedding whereby the shedding frequency on one side of the wake is a multiple of that on the other. Again, a large-scale wake is formed downstream. The present observations lead to a new interpretation of hot-wire-frequency data from other studies in terms of the harmonic modes.

On Vortex Methods

Abstract: We give error estimates for fully discretized two- and three-dimensional vortex methods and introduce a new wy of evaluating the stretching of vorticity in three-dimensional vortex methods. The convergence theory of Beale and Majda is discussed and a simple proof of Cottet’s consistency result is presented. We also describe how to obtain accurate two-dimensional vortex methods in which the initial computational points are distributed on the nodes of nonrectangular grids, and compare several three-dimensional vortex methods.

Self-organization processes in continuous media

Abstract: This review considers the dynamical behaviour of dissipative continuous media which can be described by nonlinear partial differential equations having more than two non-trivial conserved quantities in the absence of dissipation. Such a medium often exhibits a spectral condensation of a certain physical quantity to a specific wavenumber region resulting in the formation of an ordered structure, even when starting from an initially turbulent state or one driven by a stochastic field. Examples discussed here include two-dimensional incompressible fluids, two-and three-dimensional magnetohydrodynamic fluids, the atmospheres of rotating planets, the electrostatic potential in inhomogeneous magnetized plasmas, and the solition gas as described by the Korteweg-de Vries equation. The relationship between the onset of chaos and self-organization in a soliton system, as well as in some localized vortex solutions, is also discussed.

Magnetostatic equilibria and analogous Euler flows of arbitrarily complex topology. Part 1. Fundamentals

Abstract: The well-known analogy between the Euler equations for steady flow of an inviscid incompressible fluid and the equations of magnetostatic equilibrium in a perfectly conducting fluid is exploited in a discussion of the existence and structure of solutions to both problems that have arbitrarily prescribed topology. A method of magnetic relaxation which conserves the magnetic-field topology is used to demonstrate the existence of magnetostatic equilibria in a domain [Dscr ] that are topologically accessible from a given field B0(x) and hence the existence of analogous steady Euler flows. The magnetostatic equilibria generally contain tangential discontinuities (i.e. current sheets) distributed in some way in the domain, even although the initial field B0(x) may be infinitely differentiable, and particular attention is paid to the manner in which these current sheets can arise. The corresponding Euler flow contains vortex sheets which must be located on streamsurfaces in regions where such surfaces exist. The magnetostatic equilibria are in general stable, and the analogous Euler flows are (probably) in general unstable.The structure of these unstable Euler flows (regarded as fixed points in the function space in which solutions of the unsteady Euler equations evolve) may have some bearing on the problem of the spatial structure of turbulent flow. It is shown that the Euler flow contains blobs of maximal helicity (positive or negative) which may be interpreted as ‘coherent structures’, separated by regular surfaces on which vortex sheets, the site of strong viscous dissipation, may be located.

Sinusoidal flow relative to circular cylinders

Abstract: The motions of vortices around single cylinders and around pairs of cylinders in relative sinusoidal flow are investigated in this paper. Using simultaneous flow visualization and force measurements, the vortex motions are related to the fluid-induced lift and in-line forces. For the single cylinder, several repeatable patterns of vortex shedding are identified within particular ranges of flow amplitude. The process of pairing of vortices from a previous half cycle with those in a present half cycle is fundamental to all the patterns. Visualization is shown to be more effective in a reference frame which is fixed with respect to the undisturbed fluid rather than with respect to the cylinders. For this reason, the examples of vortex motions are taken from a rig in which vertical cylinders are oscillated in a tank of fluid. By oscillating a pair of cylinders over a range of gaps, orientations and amplitudes, it is found that the vortex-shedding patterns identified for a single cylinder can synchronize either in phase or in antiphase between the two cylinders. Such observations help to explain how lift and in-line forces are influenced by cylinder proximity and in some cases these forces are significantly magnified. Force coefficients are evaluated for both the single cylinder and the pair of cylinders.

Structure of large-scale vortices and unsteady reverse flow in the reattaching zone of a turbulent separation bubble

Abstract: This paper describes experiments concerning the structure of large-scale vortices and the unsteady reverse-flow properties in the reattaching zone of a nominally two-dimensional separation bubble formed at the leading edge of a blunt flat plate with right-angled corners. The experiment was performed in a wind tunnel with a constant Reynolds number 2.6 × 104 (based on the main-flow velocity and the thickness of the plate). Split-film probes, being sensitive to instantaneous reversals of flow direction, were extensively employed. An important feature of this study is a judicious use of surface-pressure fluctuations as a conditioning signal to educe the structure of the large-scale vortices.Distributions of fluctuating-velocity vectors and contour lines of high-frequency turbulent energy in a few space–time domains are presented and discussed. The most economical interpretation of these space-time distributions is that the large-scale vortices in the reattaching zone are hairpin vortices whose configuration is sketched in the text. The unsteady flow in the reattaching zone is mainly governed by two agents; the motion of the large-scale vortices and the low-frequency unsteadiness. The unsteady flow is clarified in terms of the motion (in a space–time domain) of zeros of the longitudinal velocity close to the surface of the plate; the effects of the two agents on this motion are presented separately. On the basis of these results, a mathematical model of the unsteady flow in the reattaching zone is suggested and found to yield good comparison with measured reverse-flow intermittency and frequency of local-flow reversals. It appears that the separation bubble experiences shrinkage and enlargement in connection with the low-frequency unsteadiness and that the speed of shrinkage is much greater than that of enlargement. The strength of the large-scale vortices in the reattaching zone seems to be dependent on the phase of the low-frequency unsteadiness.

The structure of the vorticity field in turbulent channel flow. I - Analysis of instantaneous fields and statistical correlations

Abstract: An investigation into the existence of hairpin vortices in turbulent channel flow is conducted using a database generated by the large-eddy simulation technique. It is shown that away from the wall the distribution of the inclination angle of vorticity vector gains its maximum at about 45° to the wall. Two-point correlations of velocity and vorticity fluctuations strongly support a flow model consisting of vortical structures inclined at 45° to the wall. The instantaneous vorticity vectors plotted in planes inclined at 45° show that the flow contains an appreciable number of hairpins. Vortex lines are used to display the three-dimensional structure of hairpins, which are shown to be generated from deformation (or roll-up) of sheets of transverse vorticity.

Unsteady separation in a boundary layer produced by an impinging jet

Abstract: A vortex-induced unsteady separation was investigated experimentally in the laminar boundary layer produced by an axisymmetric jet impinging normally onto a flat plate. By forcing the air jet, primary ring vortices were periodically generated in the jet shear layer. Phase-locked flow visualization showed that the wall-jet boundary layer separated periodically and evolved into a secondary vortex counter rotating with respect to the primary vortex. The unsteady separation is induced by the primary vortex and moves downstream in the radial mean-flow direction. Phase-averaged hot-wire measurements using a parallel-wire sensor in the vicinity of the unsteady separation provided data for locating the onset of separation in space and time. The data revealed that the unsteady separation originated from a local shear layer which was initiated by the unsteady adverse pressure gradient produced by the primary vortex.

Forces on cylinders in viscous oscillatory flow at low Keulegan-Carpenter numbers

Abstract: This paper presents a comparison between theory and experiment for the in-line forces on cylinders of general cross-section in planar oscillatory flows of small amplitude. The theoretical analysis evaluates corrections to the standard inviscid inertial force at low Keulegan-Carpenter numbers which arise from the presence of viscous laminar boundary layers and from the development of vortex shedding. The boundary-layer contribution due to both skin friction and displacement effects is calculated to first order in the Stokes parameter β−½. The contribution to the in-line force from separation and vortex shedding, for which the results presented only apply to sharp-edged bodies, is taken from previous work on vortex shedding from isolated edges using the discrete vortex modelling technique. The resulting force has components both in phase with the fluid acceleration (inertia) and in phase with the velocity (drag).The theoretical results are compared to measurements taken in a [xcup ]-tube water channel on a number of cylinders of different cross-section including circular cylinders and sharp-edged sections. The comparisons suggest that the theory is valid for Keulegan–Carpenter numbers below about 3 and for moderately high values of the β parameter.

The Heton, an Elementary Interaction Between Discrete Baroclinic Geostrophic Vortices, and Its Implications Concerning Eddy Heat-Flow

Abstract: Among the interactions of two discrete baroclinic geostrophic vortices in a two-layer system there is one class of interaction that is non-trivial; when the two vortices are of opposite sign and in different layers, and close enough together, they transport heat. Because this particular interaction can transport heat, we propose to call it the heton. It is a tilted baroclinic pair. In the Northern Hemisphere it transports heat to the left of the direction toward which its top tilts. Two warm or two cold hetons repel one another when outside the radius of deformation. A warm and a cold heton attract one another. A simple two-heton engine that exhibits vortex splitting, loss of available potential energy, and meridional heat transport is presented.

The stability and energetics of corotating uniform vortices

Abstract: Equilibrium shapes of two-dimensional rotating configurations of uniform vortices are numerically calculated for two to eight corotating vortices. Additionally, a perturbation series is developed which approximately describes the vortex shapes. The equilibrium configurations are subjected to a linear stability analysis. This analysis both confirms existing results regarding point vortices and shows that finite vortices may destabilize via a new form of instability derived from boundary deformations. Finally, we examine the energetics of the equilibrium configurations. We introduce a new energy quantity called ‘excess energy’, which is particularly useful in understanding the constraints on the evolution of unstable near-equilibrium configurations. This theory offers a first glance at nonlinear stability. As an example, the theory explains some features of the merger of two vortices.

Particle dispersion by coherent structures in free shear flows

Abstract: The dispersion of particles in turbulent flows is poorly understood. Previous approaches to this problem have been found to be inadequate for nonisotropic turbulent flows. An approach involving a new physical concept is presented. This approach assumes that coherent vortex structures control the particle dispersion process in free shear flows. A simple computational model employing Stuart's vortices is used to simulate particle motion in a two-dimensional free shear layer. The results of this simulation are in reasonable agreement with previous experiments. For the first time, experimental observations indicating particle dispersion rates greater than fluid dispersion rates in free shear flows can be plausibly explained.

Time-dependent viscous flow past an impulsively started rotating and translating circular cylinder

Abstract: A numerical study is made of the development with time of the two-dimensional flow of a viscous, incompressible fluid around a circular cylinder which suddenly starts rotating about its axis with constant angular velocity and translating at right angles to this axis with constant speed. The governing partial differential equations in two space variables and time are reduced to sets of time-dependent equations in one space variable by means of Fourier analysis. By truncating the Fourier series to a finite number of terms, a finite set of differential equations is solved to give an approximation to the theoretical flow. The solutions are obtained by numerical methods. Results are given for the initial development with time of the asymmetrical wake at the rear of the cylinder at Reynolds numbers R [ges ] 200, based on the diameter of cylinder, and at small rotation rates. The detailed results show the formation of a Karman vortex street. The time development of this separated flow is compared in detail at R = 200 with recent experimental results. The details of the formation and movement of the vortices behind the cylinder and the velocity profiles in several locations are virtually identical in the experimental and theoretical studies. The variations with time of the lift, drag and moment exerted by the fluid on the cylinder are determined both by calculations and by means of approximate analytical expressions. The agreement between these results at small times is excellent.

The onset of turbulence in finite-amplitude Kelvin-Helmholtz billows

Abstract: Two-dimensional finite-amplitude Kelvin–Helmholtz waves are tested for stability against three-dimensional infinitesimal perturbations. Since the nonlinear waves are time-dependent, the stability analysis is based upon the assumption that they evolve on a timescale which is long compared with that of any instability which they might support. The stability problem is thereby reduced to standard eigenvalue form, and solutions that do not satisfy the timescale constraint are rejected. If the Reynolds number of the initial parallel flow is sufficiently high the two-dimensional wave is found to be unstable and the fastest-growing modes are three-dimensional disturbances that possess longitudinal symmetry. These modes are convective in nature and focused in the statically unstable regions that form during the overturning of the stratified fluid in the core of the nonlinear vortex. The nature of the instability in the high-Reynolds-number regime suggests that it is intimately related to the observed onset of turbulence in these waves. The transition Reynolds number above which the secondary instability exists depends strongly on the initial conditions from which the primary wave evolves.

The discrete vortices from a delta wing

Abstract: Introduction: The Classical View T HE flow over delta wings at an angle of attack is dominated by two large bound vortices that result from the flow separation at the leading edge. The classical view of these vortices is sketched in Fig. la and has been discussed by Hoerner and Borst among others. With a sharp leading edge at an angle of attack a, the flow is separated along the entire leading edge forming a strong shear layer. The shear layer is wrapped up in a spiral fashion, resulting in the large bound vortex as sketched. These vortices appear on the suction surface and increase in intensity downstream. The low pressure associated with the vortices produces an additional lift on the wing, often called nonlinear or vortex lift, which is particularly important at large angles of attack. As sketched in Fig. la, small secondary vortices also appear on the wing near the points of reattachment as a result of the strong lateral flow toward the leading edge.

Collapse and amplification of a vortex filament

Abstract: A single filament with a variable core size parameter is used to model how a vortex tube breaks down in the Euler equations. The first singularity is a self‐similar collapse which brings two antiparallel pieces of filament together at a point. This pairing then quickly encompasses a finite fraction of the initial data and the arclength begins to grow faster than exponential. A local model should exist which would allow one to understand the stage of rapid stretching in terms of simpler processes.

Stability experiments in the flow over a rotating disk

Abstract: An experimental study of the transitional flow over a flat disk rotating in quiescent ambient air has been conducted. Using digitized hot-wire data, the axes of the stationary spiral vortices, which are the primary instability mechanisms for the disk flow, have been mapped out in terms of both spatial coordinates and velocity fluctuations. Data are presented for a clean disk and a disk with a single, isolated roughness element. The data show that the spiral vortices are generated at discrete roughness disturbance sites on the disk and that they propagate and grow as wave packets. The familiar vortex pattern of 30 or so vortices results only when these wave packets have merged and filled the entire circumference. The appearance of stationary, secondary instabilities prior to turbulent breakdown has also been observed.

The turbulent mixing layer: geometry of large vortices

Abstract: Several means for visualizing large-scale vortex structure in a turbulent mixing layer are proposed. Most of the observations are recorded along the low-speed side of the mixing layer, external to the rotational portion of the flow. Conventional correlation measurements in both the streamwise and spanwise directions indicate that the vortex structure becomes independent of the downstream coordinate in a non-dimensional distance of order λx/θi = 300–400, where is the speed ratio and θi is the initial integral thickness. Simultaneous hot-wire measurements at 12 spanwise positions allow computer reconstruction of the velocity field as a function of span and time. These visualizations show the vortex structures to be primarily aligned across the span of the flow, but to contain irregularities. Spanwise correlation lengths are of the order of 3–5δω (δω is the local vorticity thickness). However, the large vortices typically have lengths of order 20δω when the irregularities along the span are ignored.

Simulation of blunt-fin-induced shock wave and turbulent boundary-layer interaction

Abstract: The Reynolds-averaged Navier-Stokes equations are solved numerically for supersonic flow over a blunt fin mounted on a flat plate. The fin shock causes the boundary layer to separate. which results in a complicated, three-dimensional shock-wave and boundary-layer interaction. The computed results are in good agreement with the mean static pressure measured on the fin and the flat plate. The main features, such as peak pressure on the fin leading edge and a double peak on the plate. are predicted well. The role of the horseshoe vortex is discussed. This vortex leads to the development of high-speed flow and, hence, low-pressure regions on the fin and the plate. Different thicknesses of the incoming boundary layer have been studied. Varying the thicknesses by an order of magnitude shows that the size of the horseshoe vortex and, therefore, the spatial extent of the interaction are dominated by inviscid flow and only weakly dependent on the Reynolds number. Colored graphics are used to show details of the interaction flow field.

Combustion instability sustained by unsteady vortex combustion

Abstract: The determination of an internal feedback mechanism which leads to combustion instability inside a small scale laboratory combustor is presented in this paper. During combustion instability, the experimental findings show that a large vortical structure is formed at an acoustic resonant mode of the system. The subsequent unsteady burning, within the vortex as it is convected downstream, feeds energy into the acoustic field and sustains the large resonant oscillations. These vortices are formed when the acoustic velocity fluctuation at the flameholder is a large fraction of the mean flow velocity. The propagation of these vortices is not a strong function of the mean flow speed and appears to be dependent upon the frequency of the instability. Continued existence of large vortical structures which characterize unstable operation depends upon the fuel-air ratio, system acoustics, and fuel type.

Observation of waves during oscillatory channel flow

Abstract: We have observed steady and oscillatory flow through a two-dimensional channel expansion. The experimental results are supported by numerical solutions of the unsteady Navier–Stokes equations. This work was prompted by the recent discovery of vortex waves during steady flow past a moving indentation in a channel wall. Our work deals with both asymmetric channels, in which we show that vortex waves are observed during oscillatory flow with rigid walls, and with symmetric channels, in which a vortex street is observed. We believe that the vortex street is not a vortex wave, but the result of a shear-layer instability.