Showing papers on "Starting vortex published in 1974"

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.

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.

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.

Trailing Vortex Wind-Tunnel Diagnostics with a Laser Velocimeter

Abstract: A two-dimensiona l laser 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 operation of the instrument is 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. From the experimental data, circulation and vorticity distributions are obtained and the effect of turbulence injection into the vortex structure is discussed. Nomenclature wing span wing chord lift coefficient radial coordinate from vortex center wind-tunnel mainstream velocity axial velocity component tangential velocity component maximum tangential velocity stream wise ordinate, aft from trailing edge normal ordinate, above upper wing surface from trailing edge normal location of vortex center angle of attack, deg slope of velocity distribution in core region vorticity

Unsteady Aerodynamic Response of a Two-Dimensional Airfoil at High Reduced Frequency

Abstract: An experimental technique is described which corroborates the predictions of several new analyses of the unsteady response of an airfoil to high frequency flow fluctuations. The periodically fluctuating flowfield was produced by the natural shedding of vortices from a transverse cylinder to yield a reduced frequency of 3.9 based on airfoil semichord. Unsteady pressure measurements were made on an instrumented airfoil mounted downstream and above the turbulent wake of the cylinder. These unsteady pressures were found to be in good agreement with current compressible theories and show a chordwise variation of pressure phase angle which is not predicted by the incompressible analysis of Sears. Large reductions of the unsteady lift and phase angle were also observed for large airfoil incidence angles.

Extension of a vortex-lattice method to include the effects of leading-edge separation

Abstract: Vortex-lattice methods have been used successfully to obtain the aerodynamic coefficients of lifting surfaces without leading-edge separation. It is shown how an existing vortex-lattice method can be modified to include the effects of leading-edge separation. The modified version is then used to calculate the aerodynamic loads on a highly swept delta wing. The results are compared with Peckham's (1958) experimental data.

Water Tank Study of the Decay of Trailing Vortices

Abstract: Underwater towing experiments were carried out with a rectangular airfoil of aspect ratio 5.3 at 4° and 8° angles of attack and at chord-based Reynolds numbers between 2.2 x 10 5 and 7.5 x 10 5. Tangential velocity measurements in the downstream region between 100 and 1000 chord lengths indicate rates of vortex decay proportional to r 7/8 at 8°, whereas previous flight tests show that the decay rate approaches £~ 1/2 far downstream. The observed behavior is explained in terms of an analytical solution that includes time dependence of the turbulent eddy viscosity, VT ~ tm. It shows that, for m > 0, an isolated turbulent vortex decays faster than t~1/2. In this case, the decay is accompanied by increasing vr, or levels of turbulence, which corresponds to turbulent nonequilibrium flow. The special case of vortex decay with equilibrium flow (m = 0) leads to the well-known decay rate 2. Since, in towing tank experiments at low Reynolds number, turbulent vortex decay may occur predominantly in nonequilibrium, it is doubtful that such tests correctly predict the late stage of decay of aircraft trailing vortices, when turbulence is the only dissipating mechanism.

Methods for the Design and Analysis of Jet-Flapped Airfoils

Abstract: Methods for solving both the direct and inverse jet flap airfoil potential flow problems are described. The direct airfoil analysis method is a completely nonlinear iterative method which is applicable to either thick or thin airfoils of arbitrary shape. The very general surface singularity formulation has been extended to include multielement airfoils, ground effects, nonuniform freestreams, inlet flows, jet entrainment effects, etc. Comparisons are given with the results of previous linear and nonlinear methods as well as with experimental data. The inverse (design) method is a more approximate method in which camber and thickness distributions are designed separately. Section shapes are shown for several airfoils designed to have only very small regions of adverse pressure gradient. Nomenclature c = length of airfoil chord cp = coefficient of pressure d = coefficient of lift cu = coefficient of jet momentum h = height of airfoil leading edge above ground plane R = radius of curvature of the jet sheet s = coordinate along the jet sheet t = airfoil thickness V = local flow speed V = average flow speed across a vortex sheet Vj - jet flow speed Vn = component of velocity normal to a surface V = freestream flow speed x = coordinate parallel to the freestream = coordinate perpendicular to the freestream = jet deflection angle at the trailing edge relative to the airfoil chord line 7 = strength of a vortex sheet 0 = local angle of inclination of the jet sheet relative to the freestream 0 = velocity potential

Vortex ring generator

Abstract: A vortex generator including a heat source in the base of a cylindrical member with a circular ringwing in the shape of an airfoil which is lifted upward and then impulsively released to move rapidly downward and thus generate a vortex behind it. The vorticity in the core of the vortex is highly concentrated and moves rapidly upward through cloud cover. A strong light in the center of the vortex will shine to great heights making it especially useful as an airport beacon or the like. When the invention is used with a chimney, the effluents therein are caused to proceed rapidly upward through atmospheric obstacles such as thermal inversions which have been cleared by the action of the vortex.

Correlation for estimating vortex rotational velocity downstream dependence

Abstract: Description of a correlation, derived from water tank measurements in the wake of wings towed under water, that makes it possible to predict the downstream distance behind an aircraft in flight where its trailing vortex will begin to decay. Comparisons of measured and predicted data are discussed.

Domain of Stable Periodic Vortex in a Viscous Fluid between Concentric Circular Cylinders

Abstract: A systematic procedure is presented for determining an equilibrium periodic vortex flow of finite amplitude in a viscous fluid between concentric circular cylinders The equations of motion for the vortex flow is solved by expanding the solution in power series of the amplitude The stability of the vortex flow thus determined for a wide gap case is studied to axisymmetric small disturbances The amplification factor of the disturbance is calculated up to the fifth order approximation The domain of the wave number of stable mode of perturbation is predicted fairly narrower than by the existing third order theory This is in more quantitative agreement with experiments on the non-uniqueness of vortex flows

On the Calculation of Non-Linear Aerodynamic Characteristics and the near Vortex Wake,

Abstract: : This investigation presents methods for the calculation of the distribution of vortices on the wing planform and on the trailing vortex wake by iterative procedures based on the application of the vortex lattice method concepts. In the case when the trailing vortices are taken to leave the wing at the trailing edge only the calculation results in determining the linear aerodynamic characteristics and the shape of a rolled up wake. The present investigation considers the cases when the vortices from each cell are allowed to leave the wing planform at a fixed angle, and the case when the vortex shedding can be limited to the planform edges only. In these cases non-linear aerodynamic characteristics are evaluated. The corresponding trailing vortex wakes were first calculated by using discrete ideal vortices. It is now proposed to use a finite core vortex model thereby eliminating some of the numerical problems associated with the use of the ideal vortices.

Lift-induced wing-tip vortex attenuation

Abstract: It has been shown by a new static airflow visualization method that a drogue device properly positioned downstream of the wing tip causes vortex breakdown. This same result has been obtained by mounting a jet engine simulator at the wing tip and directing the high-energy jet blast downstream into the vortex. These configurations, among others, are now under intensive investigation in the new Langley Vortex Research Facility. In this facility a balance mounted vortex generating model is propelled along the 1800-foot track while a second model trailed at 160 feet (scale distance of 1 mile) measures the far-field rolling moment induced by the vortex of the generating model.

The Vortex Lattice Method for the Rotor-Vortex Interaction Problem

Abstract: The rotor blade-vortex interaction problem and the resulting impulsive airloads which generate undesirable noise levels are discussed A numerical lifting surface method to predict unsteady aerodynamic forces induced on a finite aspect ratio rectangular wing by a straight, free vortex placed at an arbitrary angle in a subsonic incompressible free stream is developed first Using a rigid wake assumption, the wake vortices are assumed to move downsteam with the free steam velocity Unsteady load distributions are obtained which compare favorably with the results of planar lifting surface theory The vortex lattice method has been extended to a single bladed rotor operating at high advance ratios and encountering a free vortex from a fixed wing upstream of the rotor The predicted unsteady load distributions on the model rotor blade are generally in agreement with the experimental results This method has also been extended to full scale rotor flight cases in which vortex induced loads near the tip of a rotor blade were indicated In both the model and the full scale rotor blade airload calculations a flat planar wake was assumed which is a good approximation at large advance ratios because the downwash is small in comparison to the free stream at large advance ratios The large fluctuations in the measured airloads near the tip of the rotor blade on the advance side is predicted closely by the vortex lattice method

Double slotted circulation control airfoil

Abstract: A circulation control airfoil includes at least two slot blades supported by a rib structure positioned in the airfoil trailing or leading edge. The rib structure is attached to a main spar, to the airfoil trailing edge (or leading edge) and to the slot blades thereby maintaining the blowing jet slot heights and the geometric integrity of the trailing (or leading) edge of the airfoil.

Vortex Wake Behind a Helicopter

Abstract: : Research into the vortex wake behind a helicopter was recently carried out. It was found that vortex cords and cores created behind a helicopter are complex structures and are quite stable. The phenomenon of secondary vortex generation was studied on a model with various numbers of blades.

Low-speed aerodynamic characteristics of airfoil sections with rounded trailing edges in forward and reverse flow

Abstract: Low-speed wind-tunnel tests were conducted to determine the two-dimensional aerodynamic characteristics of 6-, 12-, and 18-percent-thick airfoil sections with rounded trailing edges in both forward and reverse flow. The shapes incorporated camber with both the leading and trailing edges rounded to provide reasonable aerodynamic performance with either edge directed toward the free-stream flow. The tests were conducted with the airfoils in both normal and reverse orientations relative to the free stream. The Mach number was varied from 0.16 to 0.36 and the angle of attack was varied from minus 10 to 24 million. Reynolds number, based on the airfoil chord, was varied from about 1.0 to 12.0 million.

The Measurement of the McDonnell-Douglas DC9 Trailing Vortex System Using the Tower Fly-By Technique

Abstract: The results are presented of a series of low-altitude (approximately 200 feet above ground level) fight tests in which the trailing vortices of the McDonnell-Douglas DC9 airplane were investigated, using a 140-foot instrumented tower. Data presented consists of plots of vortex tangential velocity distribution, peak velocity as a function of time, airplane configuration and windspeed, vortex descent rates, and lateral transport rates. Principal findings were that: (1) Within the time period 30 - 100 seconds after vortex generation, the peak velocities within the vortices were bounded by the function V sub theta = 396exp(-.0347t), with a half-life of 20 seconds; (2) Vortex cores were uniformly small (1 - 2 feet) in both configurations tested (takeoff and landing), and little or no growth with time was found; (3) Vortex lateral transport velocities correlated well with the crosswind measured at 140 feet; and (4) The presence of a temperature inversion markedly retarded the vortex descent rates. The highest peak recorded tangential velocity was 120 - 130 feet per second, found to occur in both configurations tested.

High Lift Characteristics of an Airfoil Placed in a Narrow Channel

Abstract: Aerodynamic characteristics of an airfoil moving in a narrow channel bounded by two parallel walls, i.e. ground and ceiling, are studied theoretically and experimentally. Lift acting on an airfoil at a positive attack angle increases as the airfoil approaches either ground orceiling. This study deals with the combination of ground and ceiling effects to realize a high lift wing. A theory is presented for the calculation of two-dimensional inviscid flow around an arbitrary airfoil placed in a narrow channel, using singularity method in which proper circulation is distributed directly on the airfoil contours. Sample calculation shows the influences of ground and ceiling on the lift and moment coefficients of the airfoil. Two-dimensional experiment is conducted to measure the pressure distribution of airfoil, from which lift and pressure drag coefficients are evaluated. Theoretical and experimental results are compared and the characteristics of this kind of high lift wings are discussed.

Investigation of Strength and Paths of Vortices Shed from Vortex Generators in a Pipe and Application to Conical Diffusers

Abstract: A simple linearised theory is presented to investigate the strength and the paths of trailing vortices being shed from vortex generators in a pipe, and the prediction is experimentally proved. Then various types of vortex generators are applied to conical diffusers. According to the tests, the one recommended by the theory makes the best pressure recovery.

The Theory of the Vortex Drop

Abstract: A compact method is described of calculating the relation between the head and the discharge of water down a vortex drop of specified dimensions.