Showing papers on "Vortex published in 1974"

Vortex pairing : the mechanism of turbulent mixing-layer growth at moderate Reynolds number

Abstract: A mixing layer is formed by bringing two streams of water, moving at different velocities, together in a lucite-walled channel. The Reynolds number, based on the velocity difference and the thickness of the shear layer, varies from about 45, where the shear layer originates, to about 850 at a distance of 50 cm. Dye is injected between the two streams just before they are brought together, marking the vorticity-carrying fluid. Unstable waves grow, and fluid is observed to roll up into discrete two-dimensional vortical structures. These turbulent vortices interact by rolling around each other, and a single vortical structure, with approximately twice the spacing of the former vortices, is formed. This pairing process is observed to occur repeatedly, controlling the growth of the mixing layer. A simple model of the mixing layer contains, as the important elements controlling growth, the degree of non-uniformity in the vortex train and the ‘lumpiness’ of the vorticity field.

Vortex shedding from spheres

Abstract: Vortex shedding from spheres has been studied in the Reynolds number range 400 < Re < 5 × 106. At low Reynolds numbers, i.e. up to Re = 3 × 103, the values of the Strouhal number as a function of Reynolds number measured by Moller (1938) have been confirmed using water flow. The lower critical Reynolds number, first reported by Cometta (1957), was found to be Re = 6 × 103. Here a discontinuity in the relationship between the Strouhal and Reynolds numbers is obvious. From Re = 6 × 103 to Re = 3 × 105 strong periodic fluctuations in the wake flow were observed. Beyond the upper critical Reynolds number (Re = 3.7 × 105) periodic vortex shedding could not be detected by the present measurement techniques.The hot-wire measurements indicate that the signals recorded simultaneously at different positions on the 75° circle (normal to the flow) show a phase shift. Thus it appears that the vortex separation point rotates around the sphere. An attempt is made to interpret this experimental evidence.

The instability of short waves on a vortex ring

Abstract: A simple model for the experimentally observed instability of the vortex ring to azimuthal bending waves of wavelength comparable with the core size is presented. Short-wave instabilities are discussed for both the vortex ring and the vortex pair. Instability for both the ring and the pair is predicted to occur whenever the self-induced rotation of waves on the filament passes through zero. Although this does not occur for the first radial bending mode of a vortex filament, it is shown to be possible for bending modes with a more complex radial structure with at least one node at some radius within the core. The previous work of Widnall & Sullivan (1973) is discussed and their experimental results are compared with the predictions of the analysis presented here.

The stability of a trailing line vortex. Part 1. Inviscid theory

Abstract: The inviscid stability of swirling flows with mean velocity profiles similar to that obtained by Batchelor (1964) for a trailing vortex from an aircraft is studied with respect to infinitesimal non-axisymmetric disturbances. The flow is characterized by a swirl parameter q involving the ratio of the magnitude of the maximum swirl velocity to that of the maximum axial velocity. It is found that, as the swirl is continuously increased from zero, the disturbances die out quickly for a small value of q if n = 1 (n is the azimuthal wavenumber of the Fourier disturbance of type exp{i(αx + nϕ − αct)}); but for negative values of n, the amplification rate increases and then decreases, falling to negative values at q slightly greater than 1·5 for n = −1. The maximum amplification rate increases for increasingly negative n up to n = −6 (the highest mode investigated), and corresponds to q ≃ 0·85. The applicability of these results to attempts at destabilizing vortices is briefly discussed.

The vortex-street wakes of vibrating cylinders

Abstract: The strength (initial circulation) and spacing of vortices in the wake of a circular cylinder have been obtained for conditions under which the body undergoes lateral vibrations. The vibrations of the cylinder were at all times synchronized with those in the wake, thereby suppressing the natural Strouhal frequency in favour of a common synchronized or ‘locked-in’ frequency for the body-wake system. All experiments were performed at a Reynolds number of 144 or 190. An inverse relation between the initial circulation K and the length lF of the vortex formation region was obtained for cylinder oscillations of up to 50% of a diameter, at vibration frequencies both above and below the Strouhal shedding frequency. The initial circulation K of the vortices was increased by as much as 65%, at lF = 1·6 diameters, from the stationary-cylinder value of K corresponding to lF = 3·2d. An increase in the rate A of vorticity generation of 80% from the stationary-cylinder wake value was obtained with the cylinder vibrating at 30% of a diameter and 110% of the Strouhal frequency. Both flow-visualization and hot-wire results show that the lateral spacing of the vortex street decreases as the vibration amplitude of the cylinder is increased, but that the longitudinal vortex spacing is independent of changes in amplitude. The longitudinal spacing, however, varies inversely with the vibration frequency. The street approaches a single line of vortices of alternating sign as the amplitude of vibration approaches values near a full cylinder diameter, and secondary vortex formation at these large amplitudes is associated with the vanishing lateral spacing of the street. Observation of the wake has elucidated the mechanism of vortex formation; the entrainment processes in the formation region have been observed at small intervals over a cycle of the cylinder's motion.

Vorticity Associated with a Jet in a Cross Flow

Abstract: An extensive wind-tunnel test of a round turbulent jet directed normally through a flat plate into a subsonic cross flow has been conducted. The results of the velocity field measurements are presented in a concise and usable form through the use of simple models to relate the velocity field to empirical values for the strength and location of the pair of contrarotating vortices associated with the jet.

Turbulent vortex rings

Abstract: We consider the motion of the mass of fluid ejected through a sharp-edged orifice by the motion of a piston. The vorticity formed by viscous forces within the separated flow at the sharp edge rolls up to form a concentrated vortex which, after a development period, consists of a core of very fine scale turbulence surrounded by a co-moving bubble of much larger scale turbulence. This bubble entrains outer fluid, mixes with it, and deposits the majority into a wake together with some small fraction of the total vorticity of the ring. Enough fluid is retained to account for the slow growth of the whole fluid mass. A theory which takes account of both the growth process and the loss of vorticity is proposed. By comparison with experimental measurements we have determined that the entrainment coefficient for turbulent vortex rings has a value equal to 0.011 ± 0.001, while their effective drag coefficient is 0.09 ± 0.01. These results seem to be independent of Reynolds number to within experimental accuracy.

A Quasi-Vortex-Lattice Method in Thin Wing Theory

Abstract: A quasi-continuous method is developed for solving thin-wing problems. For the purpose of satisfying the wing boundary conditions, the spanwise vortex distribution is assumed to be stepwise-constant, while the chordwise vortex integral is reduced to a finite sum through a modified trapezoidal rule and the theory of Chebyshev polynomials. Wing-edge and Cauchy singularities are acounted for. The total aerodynamic characteristics are obtained by an appropriate quadrature integration. The two-dimensional results for airfoils without flap deflection reproduce the exact solutions in lift and pitching moment coefficients, the leading edge suction, and the pressure difference at a finite number of points. For a flapped airfoil, the present results are more accurate than those given by the vortex-lattice method. The three-dimensional results also show an improvement over the results of the vortex-lattice method. Extension to nonplanar applications is discussed.

Laser anemometer measurements of trailing vortices in water

Abstract: A series of measurements of trailing vortices behind lifting hydrofoils is described. These measurements were made in the Caltech Free-Surface Water Tunnel, using a laser-Doppler velocimeter to measure two components of velocity in the vortex wake. Two different model planforms were tested, and measurements were made at several free-stream velocities and angles of attack for each. Velocity profiles were measured at distances downstream of the model of from five to sixty chord lengths. These measurements are the first results of a continuing experimental programme. In § 3 of this paper, the theory of trailing vortices is discussed. The effects of ‘vortex wandering’ upon the measurements are computed, and the corrected results are seen to be in reasonable agreement with the theory.

Core structure and low-energy spectrum of isolated vortex lines in clean superconductors at T ≪ T c

Abstract: We present analytic solutions of the Eilenberger equations for the low-frequency Green's functions corresponding to those quasiparticles whose trajectories pass near the center of an isolated vortex. Using these results we find that for type II superconductors in the temperature rangeT c ≫T≫T c 2/eF the order parameter and the supercurrent near the vortex center increase over a lengthξ 1∼ξ BCS T/T c (ξ BCS=BCS coherence length) and that the density of states at the Fermi surface isN 0 2π 3 ξ BCS 2 /3 In (ξ BCS/ξ 1). The results can be reproduced with the Bogoliubov equations for the elementary excitations. It is shown that this peculiar behavior is connected with the low-lying bound states in the vortex core. ForTť c 2/e F one hasξ 1∼k F −1.

A numerical study of the roll-up of a finite vortex sheet

Abstract: A point-vortex representation is used to study numerically the evolution of an initially plane vortex sheet. By introducing a tip vortex to represent the tightly rolled portion of the vortex sheet, the chaotic motion which was a feature of some earlier studies is eliminated and the details of the outer portion of the spiral are calculated. The rate of rolling up is calculated and is shown to be governed by the analytically predicted similarity law of Kaden during the initial stages of the rolling up. The calculations are continued until 99% of the vorticity has been rolled up, at which stage the spiral displays a marked ellipticity.

Structure of a Tropical Cyclone Developed in a Three-Dimensional Numerical Simulation Model

Abstract: A three-dimensional, 11-level, primitive equation model has been constructed for a simulation study of tropical cyclones. The model has four levels in the boundary layer and its 70×70 variable grid mesh encloses a 4000-km square domain with a 20-km resolution near the center. Details of the model, including the parameterization scheme for the subgrid-scale diffusion and convection processes, are described. A weak vortex in the conditionally unstable tropical atmosphere is given as the initial state for a numerical integration from which a tropical cyclone develops in the model. During the integration period of one week, the sea surface temperature is fixed at 302K. The central surface pressure drops to about 940 mb, while a warm moist core is established. The azimuthal component of mean horizontal wind is maximum at about 60 km from the center at all levels. A strong in-flow is observed in the boundary layer. At upper levels, a secondary radial-vertical circulation develops in and around the regi...

Investigation of Acoustic Effects of Leading-Edge Serrations on Airfoils

Abstract: This paper presents and interprets a series of extensive studies of the application of leading-edge serrations as a device for reducing the vortex noise radiated from stationary and rotating airfoils in low Reynolds number flow. In these studies, a variety of serrations were attached at selected locations near the leading edge of stationary and rotating airfoils. The noise levels of the airfoils were reduced considerably with the serrations attached. An explanation of the aeroacoustic flow mechanisms involved is given.

Vortex-Line Pinning by Thickness Modulation of Superconducting Films

Abstract: We present experimental evidence for the interaction of vortex lines with a controlled pinning configuration induced by periodic thickness modulation of superconducting films. The critical current density as a function of a transverse magnetic field shows characteristic peaks at well-defined field values. These features give evidence for matching of the two-dimensional vortex-line lattice with the one-dimensional periodic pinning structure. A model is proposed which accounts for the observed temperature dependence of the matching effects.

Laminar flow past an abruptly accelerated elliptic cylinder at 45° incidence

Abstract: Numerical solutions for laminar incompressible fluid flows past an abruptly started elliptic cylinder at 45° incidence are presented. Various finite-difference schemes for the stream-function/vorticity formulation are used and their merits briefly discussed. Almost steady-state solutions are obtained for Re = 15 and 30, whereas for Re = 200 a Karman vortex street develops. The transient period from the start to the steady or quasi-steady state is investigated in terms of patterns of streamlines and lines of constant vorticity and drag, lift and moment coefficients.

Similitude in Free-Surface Vortex Formations

Abstract: Different fluids were used to investigate the effects of fluid viscosity and surface tension on the incipient conditions for vortex formation and on vortex size and shape. Experiments were conducted in two different sizes of cylindrical tanks with adjustable vanes at the perimetry to allow varying degrees of initial circulation to be generated at the entrance to the test section. The results of the experiments demonstrated that: (1) free surface vortex flow is affected by initial circulation and viscosity, but, for the ranges tested, is not affected by surface tension; (2) the coefficient of the discharge is a function of the Reynolds and circulation numbers; and (3) regions in which an air core will or will not form can be defined by the depth of flow, orifice size, and circulation and Reynolds numbers.

Numerical analysis of vortex motion on Josephson structures

Abstract: The one‐dimensional and two‐dimensional sine‐Gordon equations with dimensionless loss factors and unitless normalized bias are numerically calculated by computer. The results are presented for accelerations, velocities, collisions, coupled states, and two‐dimensional propagation of solitons.

Theoretical Analysis of the Aerodynamic Stability of Multiple, Interdigitated Helical Vortices

Abstract: A small perturbation stability analysis of a doubly infinite array of interdigitated, right circular helical vortices has been formulated. This array corresponds to the vortices trailed from the tips of the blades of a helicopter rotor or propeller in static thrust or axial flight condition and at great distance from the plane of rotation of the blades. A continuum of instability modes has been found associated with all values of wave numbers; only modes with wave numbers 0 and 1 are so much as neutrally stable, and for the case of a single helix. The most unstable modes involve the most axial motion of adjacent vortex segments relative to each other. Maximum divergence rates increase as the helix pitch decreases, increase as the number of helices increase and decrease as the number of cycles of deformations in one turn of the helix (i.e., wave number) increases. The helix filament core diameter can have substantial effect on the stability of a single helix, but not for multiple arrays. The larger the core diameter, the more sensitive the analysis is to the means by which the singularities in the self-induction integrals are eliminated. Increasing core diameters reduces the maximum divergence rates in all cases.

Instability of a Vortex Array in He II

Abstract: We propose an instability of a vortex array in the presence of axial normal-fluid flow in He II. This instability may be responsible for the influence of thermal counterflow on ion-trapping cross sections reported by Cheng, Cromar, and Donnelly.

Photographs of quantized vortex lines in rotating He II

Abstract: The spatial positions of discrete quantized vortex lines in rotating superfluid helium have been directly visualized by a photographic technique. The positions of the lines in the apparatus do not form a regular array.

Turbulent vortex streets and the entrainment mechanism of the turbulent wake

Abstract: The results of an experimental investigation of a turbulent vortex street in the range from 1000 to 20,000 are presented. The vortex street was created by the motion of a circular cylinder in a motionless fluid (mercury). Photographs obtained showed that the turbulent street, created by the vortex shedding behind the cylinder, persisted at longer downstream distances and higher Reynolds numbers than previously reported in the literature. A theory was developed to account for the experimental measurements pertaining to the change of the geometrical characteristics, (the distance between the two rows of vortices and the longitudinal distance between two consecutive vortices on the same row), of the street in the downstream direction. The implications of the structure of the vortex street on the entrainment mechanism of the turbulent wake are discussed.

Local structure and thermodynamic properties of clean type II superconductors near H c1 at arbitrary temperature

Abstract: An iterative procedure has been developed to solve Eilenberger's version of the Gor'kov equations numerically The method has been used to compute the structure of flux lines and the lower critical field for clean superconductors as a function of temperature Some information on the vortex lattice has also been obtained by means of a circular cell approximation We find a pronounced reduction in the size of the coreregion (measured, eg, in units of the temperature-dependent coherence length) with decreasing temperature; this results in considerably steeper slopes of the order parameter and the current density at the vortex center There are indications that, among other peculiar effects, these slopes diverge forT → 0 The field at the center of the isolated vortex apparently increases with decreasing temperature down toT=0 The results are compared with experiments and with similar calculations for the dirty limit

Negative temperature states of two-dimensional plasmas and vortex fluids

Abstract: The two-dimensional guiding centre plasma and a system of interacting line vortices in an ideal fluid are examples of Hamiltonian systems with bounded phase space. The statistical mechanics of such systems is investigated. An interesting feature is that they can exist in negative temperature states which show observable intrinsic characteristics, such as the formation of clusters of particles.

Passage of a Swept Airfoil through an Oblique Gust

Abstract: An analysis is presented which yields an approximate solution for the unsteady aerodynamic response of an infinite swept wing encountering a vertical oblique gust in a compressible stream. The approximate expressions are of closed form and do not require excessive computer storage or computation time, and further, they are in good agreement with the results of exact theory. This analysis is used to predict the unsteady aerodynamic response of a helicopter rotor blade encountering the trailing vortex from a previous blade. Significant effects of three dimensionality and compressibility are evident in the results obtained.

A Conceptual Study of Leading-Edge-Vortex Enhancement by Blowing

Abstract: A conceptual wind-tunnel-test program has been conducted to verify that blowing a stream of highpressure air over a swept-wing surface in a direction roughly parallel to the leading edge enhances the vortex system. The blowing is shown to intensify the leading-edge vortex and thus delay the deleterious effects of vortex breakdown to higher angle of attack. As a result, the vortex-lift is significantly increased and, as the blowing rate is increased, appears to approach the value predicted by the Polhamus suction-analogy for thin wings.

Calculation of Aircraft Wake Velocity Profiles and Comparisonwith Experimental Measurements

Abstract: A method is developed for the calculation of the initial inviscid form of rolled-up wake vortices behind a wing having arbitrary lift distribution. The method makes use of the Betz assumptions of conservation of wake vorticity and moments of vorticity. It is found that a simple relationship exists between the radial distribution of vorticity in the rolled-up wake and the spanwise lift distribution. Computed tangential velocity profiles for DC-7, DC-9, and C-141 aircraft are shown to compare favorably with profiles measured by the FAA during tower flyby tests of these aircraft in both flapped and unflapped configurations.