Showing papers on "Starting vortex published in 1973"

A family of steady vortex rings

Abstract: Axisymmetric vortex rings which propagate steadily through an unbounded ideal fluid at rest at infinity are considered. The vorticity in the ring is proportional to the distance from the axis of symmetry. Recent theoretical work suggests the existence of a one-parameter family, [npar ]2 ≥ α ≥ 0 (the parameter α is taken as the non-dimensional mean core radius), of these vortex rings extending from Hill's spherical vortex, which has the parameter value α = [npar ]2, to vortex rings of small cross-section, where α → 0. This paper gives a numerical description of vortex rings in this family. As well as the core boundary, propagation velocity and flux, various other properties of the vortex ring are given, including the circulation, fluid impulse and kinetic energy. This numerical description is then compared with asymptotic descriptions which can be found near both ends of the family, that is, when α → [npar ]2 and α → 0.

On the stability of vortex rings

Abstract: The stability of vortex rings is investigated both theoretically and experimentally. The theoretical analysis considers the stability of the vortex-filament ring of small but finite core size in an inviscid fluid to small sinusoidal displacements of its centreline. The effect of the vorticity distribution within the finite vortex core on the self-induced motion of each element of the vortex filament is calculated on the basis of the results presented previously by Widnall, Bliss & Zalay (1970). The results of the analysis show that a vortex ring in an ideal fluid is almost always unstable. The number of waves around the perimeter in the unstable mode depends upon the size of the vortex core. For a given vortex core, only one mode is unstable and the smaller the vortex core, the larger the number of waves in the mode. The instability was investigated experimentally with vortex rings generated in air. A laser Doppler velocimeter was used to measure the velocity along the centreline of the ring and thus the circulation. The properties of the vortex core were inferred from the measurements of circulation, ring radius and velocity. The comparisons between theoretical predictions and experimental results show qualitative agreement in the prediction of the number of waves in the unstable mode and quantitative agreement in the prediction of the amplification rate in the early stages of growth.

An inviscid model of two-dimensional vortex shedding

Abstract: An inviscid model of two-dimensional vortex shedding behind a square-based section is developed. The model uses a discrete-vortex approximation for the free shear layers. The motion of the shear layers is computed from the velocities of the discrete vortices, which in turn are derived through a Schwartz-Christoffel transformation of the section. The flow round the body is impulsively started from rest and initially develops symmetrically. The introduction of a small asymmetric disturbance results in asymmetric interaction of the shear layers amplifying into steady vortex-shedding motion.The model is shown to predict the form of vortex shedding, the Strouhal number and some other flow quantities to a good degree of agreement with experimental results.

The interaction of a vortex ring with a sharp density interface: a model for turbulent entrainment

Abstract: The interaction of a vortex ring with a sharp density interface is investigated in the laboratory. Attention is restricted to the case where the Froude number based on the density difference across the interface, the velocity of propagation of the ring normal to the interface and the diameter of the ring is less than unity. It is found that the depth of maximum penetration of the ring, and the diameter of the region of contact between the ring and the interface, are functions of the Froude number. A simple model of the ring-interface interaction which accounts for the observed motion is proposed. This model is then used to calculate the volume rate of entrainment produced by the vortex rings. It is found that this rate of entrainment is proportional to the cube of the Froude number, a result which agrees with measurements of entrainment across density interfaces caused by grid-generated turbulence (Turner 1968) and by a plume incident on the interface (Baines 1973). Thus the vortex ring would appear to be a good approximation to a turbulent eddy in these situations. The main feature of the model is that it identifies the way in which the kinetic energy of the turbulence is converted into potential energy by entraining fluid across the interface. In particular, it indicates that the essential force balance is inertial, and that it is possible to discuss entrainment across a sharp density interface without explicitly invoking either viscosity or molecular diffusion.

Vortex shedding from bluff bodies in a shear flow

Abstract: Experiments are described in which the vortex shedding from a bluff body and the base pressure coefficient have been measured in a shear flow. It is shown that the shedding breaks down into a number of spanwise cells in each of which the frequency is constant. The division between the cells is thought to be marked by a longitudinal vortex in the stream direction and this is supported by evidence from experiments where a longitudinal vortex was generated in an otherwise uniform flow.

Numerical Studies of Two-Dimensional Vortex Motion by a System of Point Vortices

Abstract: The motions of a vortex tube with an elliptic cross section and of a vortex sheet of finite length in an inviscid, incompressible fluid are simulated by a number of discrete vortex filaments, each vortex moving under the action of the velocity field of all the other vortices. By the use of this simulation, rotation of the vortex tube and rolling-up of the vortex sheet are investigated numerically as initial value problems. Comparison with exact solutions shows the validity of this method of approximation. In order to improve the results, an artificial viscosity is introduced to the equations of motion. This diminishes randomization of vortices inherent to the treatment without viscosity and thus leads to regular rolling-up of a vortex sheet.

A global theory of steady vortex rings in an ideal fluid

Abstract: 5. T H E 5.1. 5.2. 5.3. 5.4. T h e g o v e r n i n g e q u a t i o n s . . . . . . . . . . . . . . . . . . . . . . . . . 16 K n o w n s o l u t i o n s : H i l l ' s v o r t e x a n d r i n g s o f s m a l l c r o s s s e c t i o n . . . . . . . . . 18 R e f o r m u l a t i o n of t h e p r o b l e m . . . . . . . . . . . . . . . . . . . . . . . 19 T h e H i l b e r t s p a c e H(D) . . . . . . . . . . . . . . . . . . . . . . . . . 21 F u r t h e r n o t a t i o n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

Behavior of vortex rings in the vicinity of a wall

Abstract: An experiment is described which shows that a vortex ring traveling toward a wall situated normal to its axis may undergo momentary inversions of its forward velocity. A qualitative analysis of the physics involved is given.

Structure of turbulent line vortices

Abstract: A theory is given to explain the observed dependence on Reynolds number of the decay of turbulent line vortices. It is argued that the turbulent vortex has a triple structure. There is an outer region for r > r1 (r1 is the radius of maximum tangential velocity) with a logarithmic distribution of circulation, and for r < r1 an inner region and viscous core in both of which the motion is close to solid body rotation. It is predicted that r1 ~ (vT1 t2)1/4, where 1 is the circulation at r1. Further, T1/T0 is predicted to be a slowly decreasing function of T0/v, where T0 is the strength of the vortex. The development of an overshoot of circulation in the outer region is discussed, and the axial velocities produced by growth of a trailing vortex are calculated.

The effect of a bevelled trailing edge on vortex shedding and vibration

Abstract: Experiments using a wind tunnel and a flow visualization technique in a towing tank were conducted to investigate the mechanism of vortex shedding from bevelled trailing edges. These reveal an important difference between the wake structures generated by heaving and steady motion. The suppression of vortex-excited vibration by means of bevelled trailing edges is attributed to the intermittency and rapid decay of the vortex trail resulting from an asymmetric circulation distribution in the vortex formation region.

Method and apparatus for elimination of airfoil trailing vortices

Abstract: Herein are disclosed a method and apparatus for eliminating or substantially attenuating the dangerous vortices which typically trail the airfoils of heavier-than-air aircraft in flight. The disclosed method consists of injecting a fluid stream into the core of the vortex (a) in a direction such that the longitudinal axis of the injected fluid stream is substantially colinear and coaxial with the longitudinal axis of the vortex where the injected stream enters the vortex core, and (b) at a momentum flux of such magnitude relative to that of the free air stream that the vortex will be rendered hydrodynamically unstable. The criteria as to the direction and the magnitude of the momentum flux of the injected fluid stream are disclosed as critical to the successful practice of the invention. It is preferable that the departure from colinearity be not more than 4*. The apparatus of the invention comprises, in combination with an airfoil, a pair of nozzles adapted for injecting a fluid stream of the required orientation and of a momentum flux of such magnitude relative to the free air stream into the trailing vortex that the trailing vortex will be rendered hydrodynamically unstable and apparatus for supplying a suitable fluid to the nozzles.

Vortex arrestor and visualization system

Abstract: A nozzle mounted adjacent the tip of an aircraft wing projects rearwardly from its trailing edge into a region most susceptible to abatement of a vortex wake that otherwise develops during flight. Air under a static pressure higher than ambient is supplied to the nozzle and controllably heated to attain a velocity of supersonic value before discharge at high jet velocities from the nozzle causing abatement of early decay of the vortex.

Study of the far wake vortex field generated by a rectangular airfoil in a water tank.

Abstract: Underwater towing experiments were carried out with a rectangular airfoil of aspect ratio 5.3 at 4 and 8 deg angles of attack and at chord-based Reynolds numbers between 2 x 100,000 and 7.5 x 100,000. Quantitative measurements by means of the hydrogen bubble technique indicated lower peak swirl velocities in the range of 100 to 1000 lenghts downstream than have been measured in wind tunnel of flight tests. The maximum circumferential velocity decayed whereas the turbulent eddy viscosity increased. This behavior and other known rates of vortex decay are explained in terms of an analytical solution for the vortex problem with time varying eddy viscosity. It is shown that this case corresponds to nonequilibrium turbulent vortex flow.

The application of laser Doppler velocimetry to trailing vortex definition and alleviation

Abstract: A laser Doppler velocimeter whose focal volume can be rapidly traversed through a flowfield has been used to overcome the problem introduced by excursions of the central vortex filament within a wind tunnel test section. The basic concepts of operation of the instrument are reviewed and data are presented which accurately define the trailing vortex from a square-tipped rectangular wing. Measured axial and tangential velocity distributions are given, both with and without a vortex dissipator panel installed at the wing tip. From the experimental data, circulation and vorticity distributions are obtained and the effect of turbulence injection into the vortex structure is discussed.

Vortex Modification by Mass Injection and by Tip Geometry Variation

Abstract: : The report describes an experimental research program in which the outer section of a UH-1D helicopter blade was modified to incorporate a system for injecting the trailing tip vortex produced by the blade with a mass of linearly-directed air, and also an Ogee-tip section to study its effect as a passive system on vortex dissipation. The effects of mass injection were investigated at low mass flow rates, at near-sonic injection velocities, and with a two-section nozzle. The results are presented in terms of quantitative measurements of circulation strength as a function of mass flow rate and thrust, and are correlated with the results from previous research done at RASA. Also presented are flow-visualization studies which were conducted using illuminated helium bubbles, smoke, and tuft grids. The results of this research program present additional confirming evidence that mass injection of the concentrated tip vortex is a practical approach to the elimination of the strong induced effects on a lifting surface of the circulatory flow associated with a concentrated vortex generated at the tip of a helicopter rotor blade.

Discrete vortex method of two-dimensional jet flaps.

Abstract: A jet flap theory is developed with the aid of a classical cooformal mapping of airfoils onto unit circles and the method is free of any restrictions on the amount of airfoil thickness, camber or angle of attack The jet sheet is supposed to be infinitesimally thin and is approximated by a finite number of discrete vortices placed on a stagnation streamline The strengths of vortices are determined by an iterative procedure which is set up between the transformed and the physical plane Any one of the classical incompressible airfoil theories, such as Theodorsen and Garrick's direct method or LighthilPs inverse one, can be applied to determine the mapping function of airfoils onto unit circles The present approximation will converge to the exact incompressible potential flow theory of two-dimensional airfoil sections with infinitesimally thin jet flaps, if the number of vortices is increased and the distances between the adjacent vortices decreased indefinitely Furthermore, the classical Blasius formulae are modified for jet flaps with discrete vortex approximations; and lift, drag and moment of airfoils are obtained An example of an elliptical section of 125% thickness chord ratio with jet flaps shows a fair agreement with Dimmock's experimental data With the aid of Theodorsen and Garrick's direct and author's inverse method several more examples are worked out

The Calculation of the Lift Distribution and the Near Vortex Wake Behind High and Low Aspect Ratio Wings in Subsonic Flow

Abstract: : A method is presented for the combined calculation of the lift and lift distribution on a wing and also of the trailing vortex flow behind the wing. It is assumed that the lift of a wing is generated by a system of vortices distributed over the complete wing planform and shed away from each elemental area on the planform. Using the concepts of the vortex lattice method, it is assumed in the linear lift variation case, that the vortices are aligned on the wing planform and are shed away from the trailing edges. Vortex line interaction calculations for the trajectories of the vortex lines are programmed. As a result, the leading edge lift vortices which are obtained on slender wings can now be handled. This report contains a description of the numerical method. (Author Modified Abstract)

Longitudinal Response of an Aircraft due to a Trailing Vortex Pair

Abstract: ofoils and Wings," Transonic Aerodynamics, AGARD Conference Proceedings 35, 1968, pp. 11-1 to 11-23. Mager, A., "On the Model of the Free, Shock-Separated, Turbulent Boundary Layer," Journal of the Aeronautical Sciences, Vol. 23, Feb. 1956, pp. 181-184. Smith, D. K., "Wind Tunnel Investigation of the Pressure Distribution on a Two-Dimensional Airfoil with Pylon Mounted Stores at Mach Numbers from 0.70 to 0.90," AEDC-TR-73-71, March 1973, Arnold Engineering Development Center, Arnold Air Force Station, Tenn. Krupp, J. A., "The Numerical Calculation of Plane Steady Transonic Flows Past Thin Lifting Airfoils," PhD. thesis, June 1971, University of Washington, Seattle, Wash. Studwell, V. E., "Investigation of Transonic Aerodynamic Phenomena for Wing Mounted External Stores," PhD. thesis, June 1973, University of Tennessee Space Institute, Tullahoma, Tenn. Fig. 2 Variation of incremental lift coefficient per unit vortex strength with position of left vortex.

Theoretical and Experimental Investigations of Vortex Lift Control by Spanwise Blowing. Volume 2. Three-Dimensional Theory for Vortex-Lift Augmentation

Abstract: : A theoretical description is presented on the experimentally observed phenomenon of wing leading-edge vortex lift control by spanwise mass injection. The vortex and jet initial source/sink strengths and locations are established by a conformal mapping solution, and used as starting conditions for an iterative vortex-lattice simulation. The spanwise jet is shown to augment the stability of a vortex which forms at high angles-of-attack in the leading-edge region where wings of moderate-to-high aspect ratio otherwise exhibit fully turbulent separation. Definitive results are obtained on wing lift and corresponding pressure distributions for comparison with the test data presented in Volume I.

Study of the Electrostatic Field and Charge Distribution in a Vortex Seeded with Dust.

Abstract: : A program was undertaken to investigate the vortex geometry, particle distribution and electric field distribution in a trailing vortex shed from an airfoil tip placed in a dust laden flow. A differential airfoil, positioned in a subsonic wind tunnel, generated the trailing vortex. Dust conditions, typical of a helicopter landing zone, were simulated by seeding the wind tunnel flow with P.V.C. plastic pellets, No. 3 sand, and No. 120 sand. A vaned probe was used to measure the vortex geometry. A particle impact probe and a miniature field meter were used to map the particle distribution and electric field distribution across the trailing vortex. Vortex geometry particle distribution and electric field intensity were measured throughout the plane normal to the wind tunnel axis at several locations downstream from the airfoil. (Modified author abstract)

Vortex flow adjacent to a stationary surface

Abstract: The radius of transition from an inner core of solid body rotation to an outer free vortex motion was determined via the momentum integral method.