Showing papers on "Starting vortex published in 1976"

Solutions of the Navier-Stokes equations for vortex breakdown

Abstract: Steady solutions of the Navier-Stokes equations, in terms of velocity and pressure, for breakdown in an unconfined viscous vortex are obtained numerically using the artificial compressibility technique of Chorin combined with an ADI finite-difference scheme. Axisymmetry is assumed and boundary conditions are carefully applied at the boundaries of a large finite region in an axial plane while resolution near the axis is maintained by a coordinate transformation. The solutions, which are obtained for Reynolds numbers up to 200 based on the free-stream axial velocity and a characteristic core radius, show that breakdown results from the diffusion and convection of vorticity away from the vortex core which, because of the strong coupling between the circumferential and axial velocity fields in strongly swirling flows, can lead to stagnation and reversal of the axial flow near the axis.

Correlation of turbulent trailing vortex decay data

Abstract: A correlation function, derived on the basis of self similar variable eddy viscosity decay, is introduced and utilized to correlate aircraft trailing vortex velocity data from ground and flight experiments. The correlation function collapses maximum tangential velocity data from scale model and flight tests to a single curve. The resulting curve clearly shows both the inviscid plateau and the downstream decay regions. A comparison between experimental data and numerical solution shows closer agreement with the variable eddy viscosity solution than the constant viscosity analytical solution.

A comparison of the wake structure of a stationary and oscillating bluff body, using a conditional averaging technique

Abstract: A conditional averaging technique to extract the underlying vortex pattern from a turbulent bluff body wake is described. Ensemble averages of wake velocities are developed on the basis of a reference phase position, determined from the outer flow irrotational fluctuations. The method is applied to the wakes of a stationary and oscillating D-shape cylinder, where, in the latter case, the vortex shedding is locked to the frequency of body movement. Direct comparisons of average circulation and vortex street spacings are obtained and these demonstrate the significant change in wake structure that accompanies and sustains vortex-induced vibrations. It is observed in both conditions that only 25% of the estimated shed vorticity is found in the fully developed wake. In addition the analysis produces profiles of vorticity and velocity in an ‘average vortex cycle’. A model, developed to help interpret these results, suggests that a good representation of an average wake situation is obtained by the addition of considerable mean shear to a street of finite area axisymmetric vortices.

The influence of vortex shedding on the generation of sound by convected turbulence

Abstract: This paper discusses the theory of the generation of sound which occurs when a frozen turbulent eddy is convected in a mean flow past an airfoil or a semi-infinite plate, with and without the application of a Kutta condition and with and without the presence of a mean vortex sheet in the wake. A sequence of two-dimensional mathematical problems involving a prototype eddy in the form of a line vortex is examined, it being argued that this constitutes the simplest realistic model. Important effects of convection are deduced which hitherto have not been revealed by analyses which assume quadrupole sources to be at rest relative to the plate or airfoil. It is concluded that, to the order of approximation to which the sound from convected turbulence near a scattering body is usually estimated, the imposition of a Kutta condition at the trailing edge leads to a complete cancellation of the sound generated when frozen turbulence convects past a semi-infinite plate, and to the cancellation of the diffraction field produced by the trailing edge in the case of an airfoil of compact chord.

Experiments on vortex stability

Abstract: The tip vortex of a laminar flow wing was studied at a sectional lift‐to‐drag ratio of 60. The vortex Reynolds number was Γ0/ν=7.8×104, where Γ0 is the total circulation and ν is the kinematic viscosity. At and near the wing the vortex core was turbulent with an axial jet. Downstream of the wing the jet rapidly dissipated and a wake developed in the core and intensity of turbulent velocities decreased. From 13 to 40 chord length periodic oscillations dominated the velocity fluctuations with little background turbulence. These instabilities had a symmetric and a helical mode with wavelength of the same order as the core diameter. In this range of distances along the vortex core the maximum axial, swirl, and fluctuating velocities vary slowly. At 40 chord lengths behind the wing there is a rapid change in these velocities. This change of state of the vortex core is accompanied by change of velocity fluctuations from periodic to turbulent. The core showed spatial excursions. Measurements up to 80 chord lengths downstream showed no self‐similar decay.

Formation and Interaction of Two Parallel Vortex Streets

Abstract: The instability of two pairs of infinitely long parallel vortex sheets for initial disturbances is investigated by a linear analysis in an inviscid incompressible fluid, and it is shown paradoxically that two pairs of parallel vortex sheets can not exist at a gap distance between two pairs less than the distance between vortex sheets of each pair. By calculating the non-linear growth in time of periodic disturbances in the vortex sheets, the essential features of the formation and interaction of two parallel vortex streets are analysed, and it is explained that the initially antisymmetric disturbance is more apt to cause the interaction between two vortex streets in their developing stage than the symmetric one. These theoretical results are compared with the experimental ones which were observed in a flow past two circular cylinders spaced in the direction perpendicular to a uniform flow.

Vortex shedding from a blunt trailing edge with equal and unequal external mean velocities

Abstract: A flow visualization study showed that strong Karman vortices are developed behind the blunt trailing edge of a plate when the free stream velocities over both surfaces are equal. These vortices tend to disappear when the surface velocities are unequal. This observation provided an explanation for the occurrence and disappearance of the lip noise often present in coaxial jets. Vortex formation and lip noise occurred at a Strouhal number of about 0.2 based on the lip thickness and the average of the external steady-state velocities. Results from theoretical calculations of the vortex formation, based on an inviscid, incompressible analysis of the motion of point vortices, were in good agreement with the experimental observations.

Calculation of vortex sheets in unsteady flow and applications in ship hydrodynamics

Abstract: This paper presents a new method for the numerical calculation of the movement of free shear layers in two-dimensional and quasi-three-dimensional flow. This method greatly reduces the numerical error which is associated with principal value integrals. New sets of equivalent vortices are created at each time step in the computation, giving rather better simulation of the behavior of vortex sheets. The authors review the most important earlier papers and recalculate some of their results. Solutions for vortex sheet development for several other problems of interest are also presented.

Numerical studies of three-dimensional breakdown in trailing vortex wakes

Abstract: Finite element, three dimensional relaxation methods are used to calculate the development of vortex wakes behind aircraft for a considerable downstream distance. The inclusion of a self-induction term in the solution, dependent upon local curvature and vortex core radius, permits calculation of finite lifetimes for systems for which infinite life would be predicted two dimensionally. The associated computer program is described together with single-pair, twin-pair, and multiple-pair studies carried out using it. It is found, in single-pair studies, that there is a lower limit to the wavelengths at which the Crow-type of instability can occur. Below this limit, self-induction effects cause the plane of the disturbance waves to rotate counter to the vortex direction. Self induction in two dimensionally generated twin spiral waves causes an increase in axial length which becomes more marked with decreasing initial wavelength. The time taken for vortex convergence toward the center plane is correspondingly increased. The limited parametric twin-pair study performed suggests that time-to-converge increases with increasing flap span. Limited studies of Boeing 747 configurations show correct qualitative response to removal of the outer flap and to gear deployment, as compared with wind tunnel and flight test experience.

The effects of vortex coherence, spacing, and circulation on the flow-induced forces on vibrating cables and bluff structures

Abstract: : The vortex wake of a vibrating flexible cable was studied by means of velocity measurements and correlation, frequency spectra, and flow visualization. Three distinct spanwise regimes were identified according to wake structure. Near the cable nodes the flow resembles that of a stationary cable. Adjacent to the node is a transition regime which extends up to the locked-in or synchronized wake flow about the cable antinode. Each regime was characterized by spectral content, degree of spanwise correlation, and local vortex street geometry. Measured downstream velocity profiles and vortex spacing were matched with a mathematical model to obtain the vortex strength and its relation to cable vibration conditions. The von Karman drag formula was used to compute the steady drag coefficients directly, and the distributions of fluctuating lift and drag were inferred from the data. The vortex strength and fluid forces on the vibrating cable were found to be as much as 65 percent larger for locked-in conditions than in the stationary case. Where comparisons were possible, there was good agreement between present results and previous results for vortex-excited rigid cylinders, including some direct measurements of the increased drag. (Author)

Vortex generators in axial flow compressor

Abstract: An axial flow compressor having a vortex generator system positioned upstream of a rotor with the height of the blades of the vortex generator system being greater then the running clearance of the rotor. The vortex generator system has at least three blades for each of the rotor blades and is spaced from the rotor blades such that the leading edge of the rotor is a distance from the vortex generator system greater then ten times the height of the vortex generator blades and the trailing edge of the rotor blades is a distance from the leading edge of the vortex generator system less then eighty times the height of the vortex generator blades. The spacing between the vortex generator blades is at least four times the height of the vortex generator blades.

Vortex Rings in a Stratified Fluid

Abstract: Unsteady motions of vortex rings in a stably stratified fluid, of which the density profile has a gradual step change, have been observed using an electrolytic flow visualization technique. Some new types of distorted vortex rings wave observed to from in the nonhomogeneous fluid.

An improved method for the prediction of completely three-dimensional aerodynamic load distributions of configurations with leading edge vortex separation

Abstract: The application of a higher-order subsonic potential flow panel method to the solution of three-dimensional flow about wing and wing-body combinations with leading-edge vortex separation is presented. The governing equations are the linear flow differential equation and nonlinear boundary conditions which require that the flow be parallel to the wing and body surfaces and that the free vortex sheet, springing from the leading and trailing edges, be aligned with the local flow and support no pressure jump. The vortex core is modeled as a simple line vortex which receives vorticity from the free sheet through a connecting sheet. The Kutta condition is imposed on all appropriate edges of the wing. This set of nonlinear equations is solved by an iterative procedure. The Goethert rule accounts for compressibility. The method has been programmed for the CDC 6600. Delta wings, gothic wings, arrow wings, cambered wings, and wing with body have been analyzed. Initial studies involving variations of panel density, vortex sheet sizing, Jacobian update, and initial geometry demonstrate that the present method generally exhibits good convergence characteristics.

Wake Vortex Structure and Aerodynamic Origin in Severe Thunderstorms

Abstract: The radar and surface structure of a severe thunderstorm's wake vortex on 25 June 1969 are examined. Two probable aerodynamic causes for wake vortex formation are Karma vortices and starting vortices to the updraft lee. Karman vortices would form, as do those observed, within the echo core at the updraft lee “edges” and move downstream with the ambient flow. However, in contrast to Karman theory, radar reflectivity distributions consistently suggest anticyclonic flow. Starting vortices should develop as observed, during transition of a thunderstorm updraft from non-rotational to rotational state, as a vortex of comparable strength but opposite circulation. Four other thunderstorms examined also produced severe weather, increased intensity rapidly, and turned right or formed hook echoes contemporaneously with vortex shedding.

An Experimental Investigation of Wing Trailing Vortex Formation

Abstract: : The incompressible flowfield in the vicinity of a lifting rectangular finite wing is investigated experimentally to ascertain the nature and detailed characteristics of the formation and early development of a trailing vortex. The apparatus was designed and fabricated to facilitate a direct comparison of real flow data with existing theories and flow models. The inboard potential flow region was observed to exhibit the simplifying characteristic of a spanwise cross-flow velocity component which is independent of the surface normal coordinate. As a result, a possible ambiguity in the determination of the stream-wise vorticity component was removed. Graphs of the near-surface (bound) vorticity distribution are presented along with a map of Prandtl bound vortex filaments. The associated bound circulation function could be expressed approximately as the product of two separable functions of the planform spatial coordinates. Measurements at the wing trailing edge are employed to show that the properly non-dimensionalized characteristic vorticity distribution in this region is independent of angle of attack.

Extended applications of the vortex lattice method

Abstract: The application of the vortex lattice method to problems not usually dealt with by this technique is considered It is shown that if the discrete vortex lattice is considered as an approximation to surface-distributed vorticity, then the concept of the generalized principal part of an integral yields a residual term to the vortex-induced velocity that renders the vortex lattice method valid for supersonic flow Special schemes for simulating non-zero thickness lifting surfaces and fusiform bodies with vortex lattice elements are presented Thickness effects of wing-like components are simulated by a double vortex lattice layer, and fusiform bodies are represented by a vortex grid arranged on a series of concentric cylindrical surfaces Numerical considerations peculiar to the application of these techniques are briefly discussed

Energy cross term for a quantum vortex ring

Abstract: The energy cross term Ec between an initial fluid flow v0 and the flow from a vortex ring is normally written as v0⋅P, where P is the momentum of the vortex ring. There is some uncertainty about how to calculate P. Ec is computed exactly for flow around a closed circuit (a ring) in an incompressible fluid where circulation is quantized. v0 is allowed to be a function of position. The vortex rings are assumed not to be created impulsively. The result is that Ec is equal to the circulation times the mass of fluid that v0 causes to flow through the vortex ring per second. This reduces to the usual result P=ρκπr2 when v0 is constant in the neighborhood of the vortex ring.

Vortex interactions in multiple vortex wakes behind aircraft

Abstract: A flow visualization technique has been developed which allows the nature of lift-generated wakes behind aircraft models to be investigated. Several different configurations of a 0.61-m span model of a Boeing 747-type transport aircraft were tested to allow observation of typical vortex interactions and merging in multiple vortex wakes. The vortices were identified by emitting tracer dyes from selected locations on the model. Wing span loading and model attitude were found to effect both vortex motions within the wake and resulting far-field wake velocity. Landing gear deployment caused a far-field reformation of vorticity behind a model configuration which dissipated concentrated vorticity in the near-field wake. A modified landing configuration was developed which appeared to significantly alleviate the concentrated wake vorticity.

Vortex/Jet/Wing Viscous Interaction Theory and Analysis.

Abstract: : A computational fluid mechanical model has been developed for analyzing the loads and flow mechanism due to vortex/wing/jet interaction. Examples are leading edge vortices formed on highly swept delta wings or moderately swept wings with vortex control by jets or passive control such as strakes. The computational model is applicable to a wide class of viscous flows but is particularly suitable for calculating vortex-type flows near no-slip or solid boundaries. The model is based on reducing the full Navier-Stokes equations to parabolic form with respect to one of the three space coordinates. The method is particularly attractive because of the economy of computing time. Minutes rather than hours bring the solution of the Navier-Stokes equations into the engineering realm. Further development of the model is required, but its present state is quite useful for evaluating certain flow mechanisms. Examples of computations for various vortex/wing/jet interactions are presented in the report. Experimental pressure, laser velocimeter, and flow visualization data are presented for an unswept wing with leading edge vortex control by spanwise blowing. These data are used to analyze the formation and strength of the leading edge vortex and as examples of typical input/output data for the computational model. (Author)

Application of the vortex-lattice technique to the analysis of thin wings with vortex separation and thick multi-element wings

Abstract: Two techniques for extending the range of applicability of the basic vortex-lattice method are discussed. The first improves the computation of aerodynamic forces on thin, low-aspect-ratio wings of arbitrary planforms at subsonic Mach numbers by including the effects of leading-edge and tip vortex separation, characteristic of this type wing, through use of the well-known suction-analogy method of E. C. Polhamus. Comparisons with experimental data for a variety of planforms are presented. The second consists of the use of the vortex-lattice method to predict pressure distributions over thick multi-element wings (wings with leading- and trailing-edge devices). A method of laying out the lattice is described which gives accurate pressures on the top and part of the bottom surface of the wing. Limited comparisons between the result predicted by this method, the conventional lattice arrangement method, experimental data, and 2-D potential flow analysis techniques are presented.

Axisymmetric vortex source (sink)

Abstract: A vortex analog is found for a potential three-dimensional source. The possibility of extending the known method of superposition to the case of axisymmetric vortex flows is indicated. Considered as an illustration is the axisymmetric homogeneous helical flow around a half-body. It is shown that the pressure is constant in an axisymmetric vortex stream without a circumferential velocity.

Influence of density variation on the stability of a vortex with a top‐hat jet core

Abstract: The stability of a potential vortex with an injected rotating and nonrotating jet core is considered for different density ratios of the vortex to the jet. Growth rates are given for different ratios of the vortex strength to the axial jet velocity. It is shown that the vortex is less unstable as the density ratio increases.