Showing papers on "Vortex published in 1976"

The stability of short waves on a straight vortex filament in a weak externally imposed strain field

Abstract: The stability of short-wave displacement perturbations on a vortex filament of constant vorticity in a weak externally imposed strain field is considered. The circular cross-section of the vortex filament in this straining flow field becomes elliptical. It is found that instability of short waves on this strained vortex can occur only for wavelengths and frequencies at the intersection points of the dispersion curves for an isolated vortex. Numerical results show that the vortex is stable at some of these points and unstable at others. The vortex is unstable at wavelengths for which ω = 0, thus giving some support to the instability mechanism for the vortex ring proposed recently by Widnall, Bliss & Tsai (1974). The growth rate is calculated by linear stability theory. The previous work of Crow (1970) and Moore & Saffman (1971) dealing with long-wave instabilities is discussed as is the very recent work of Moore & Saffman (1975).

Vortex shedding from a cylinder vibrating in line with an incident uniform flow

Abstract: A study has been made of the wake of a cylinder vibrating in line with an incident steady flow. The Reynolds number for the experiments was 190, and the vortex shedding was at all times synchronized with the vibrations of the cylinder, which were in a range of frequencies near twice the Strouhal shedding frequency for the stationary cylinder. Two distinct vortex wake patterns were encountered. The first is a complex regime in which two vortices are shed during each cycle of the vibration and form an alternating pattern of vortex pairs downstream. The second pattern is an alternating street which results from the shedding of a single vortex during each cycle of the cylinder's motion. The street geometry in the latter case shares many basic characteristics with the wake of a cylinder vibrating in cross-flow. These include the effects of vibration amplitude and frequency on the longitudinal and transverse spacing of the vortices. The results obtained from these experiments in air are in agreement with previous findings from free- and forced-vibration experiments in water at both higher and lower Reynolds numbers.

Classical vortex solution of the Abelian Higgs model

Abstract: An exact vortex solution for the Abelian Higgs model is found when a particular relation between the coupling constants is satisfied. For this case (in which the masses of the scalar and vector bosons are the same), we decouple the classical field equations and solve them. We obtain power-series expansions and asymptotic expressions for the solution. The values of the fields are explicitly calculated for a one-quantum-of-flux solution, and bounds are established for the $n$-quanta case. Finally, we discuss the field form factors.

Lifespan of trailing vortices in a turbulent atmosphere

Abstract: The lifespan of aircraft trailing vortices is controlled by a mutual induction instability excited by atmospheric turbulence. The instability itself is well understood. The purpose here is to incorporate the effects of turbulence and thereby predict wake lifespan as a function of meteorologica l conditions. Eddies of the relevant size are assumed to lie in the Kolmogorov inertial subrange, characterized by an energy dissipation rate e. The appropriate dimensionless measure of turbulence intensity proves to be T/ = (€^) 1/3/(T/27r&), where T is the circulation around the vortices, and b is their separation. Similarity considerations imply a mean wake lifespan of the form (2-Kb2/r)r(ij), where T is a universal function of rj. A statistical definition of lifespan is proposed, and T is computed in the limit of large 17, when the vortices are too weak to influence their own deformation. Vortex induction then is included, and T is computed in the opposite limit of small i? by the method of stationary phase. In that limit, vertical currents are the chief excitors of instability. The two asymptotic forms for 7(17) join in a smooth curve in reasonable agreement with the few published data. The paper concludes with a review of a practical method for actively exciting the mutual induction instability. The method would shorten the typical lifespan of a 747 wake by a factor of 3.

The initial region of subsonic coaxial jets

Abstract: This paper describes part of a detailed study of the initial region of coaxial jets of three different mean-velocity ratios. Similarity of the mean-velocity and turbulent-intensity profiles within the two mixing regions inside the initial merging zone, and within the mixing region inside the fully-merged zone, has been observed. Similarity with single-jet results has been obtained. Overall pressure measurements and hot-wire and microphone spectra inside coaxial jets yield two pronounced peaks, suggesting the existence of two types of vortices at different frequencies. The higher-frequency or primary vortices are found to be generated in the primary or inner mixing region, and the lower-frequency or secondary ones in the secondary or outer mixing region. It seems that the former are generated further upstream than the latter. Both types of vortices are found in the initial merging zone. However, their growth or decay and their dominance depend on the mean-velocity ratio. Low mean-velocity ratios indicate the dominance of the high-frequency vortices. At high mean-velocity ratios, the low-frequency vortices are dominant. The Strouhal number of the vortices plays an important part in their growth and decay. The complicated flow structure of coaxial jets can be very simply related to, and described by, the much simpler structure of single jets.

Statistical mechanics of two‐dimensional vortices in a bounded container

Abstract: The equilibrium statistics of a large number of two‐dimensional point vortices of arbitrary sign, evolving in an arbitrary domain closed by a bounded curve, are investigated in the microcanonical formulation. The resulting differential equations for the spatial distribution function of the vortices are numerically integrated in various cases and the associated thermodynamic functions are computed. The case of a globally neutral, spatially uniform distribution is particularly studied for its connections with two‐dimensional turbulence and the use of the random phase approximation. Some numerical simulations of vortex motion in a circular domain support the theoretical development.

The locking-on of vortex shedding due to the cross-stream vibration of circular cylinders in uniform and shear flows

Abstract: The frequencies of vortex shedding from circular cylinders forced to oscillate transversely in low-turbulence uniform and shear flows were investigated. The stream velocity in the shear flow varied linearly with spanwise distance.In both flows the vortex shedding frequency locked on to the cylinder frequency and to submultiples of the cylinder frequency. In uniform flow the range of cylinder frequencies for locking-on was dependent on the amplitude of oscillation and Reynolds number. At the boundaries of locking-on at the cylinder frequency locked-on shedding was intermittent with unforced shedding and locking-on was accompanied by a change in wake width. At a particular cylinder frequency near mid-range it is conjectured that the wake width jumped from being greater to being less than that for the stationary cylinder. In shear flow the spanwise extent of locking-on at the cylinder frequency was explained by considering the uniform flow results and the inclination of shed vortices in shear flow. At the spanwise boundaries of this locking-on, locked-on cells were shed intermittently with unforced cells which were more stable in frequency than the corresponding cells for the stationary cylinder.

Taylor-vortex instability and annulus-length effects

Abstract: Critical speeds for the onset of Taylor vortices and for the later development of wavy vortices have been determined from torque measurements and visual observations on concentric cylinders of radius ratios R1/R2 = 0·894–0·954 for a range of values of the clearance c and length L: c/R1 = 0·0478–0·119 and L/c = 1–107. Effectively zero variation of the Taylor critical speed with annulus length was observed. The speed at the onset of wavy vortices was found to increase considerably as the annulus length was reduced and theoretical predictions are realistic only for L/c values exceeding say 40. The results were similar for all four clearance ratios examined. Preliminary measurements on eccentrically positioned cylinders with c/R1 = 0·119 showed corresponding effects.

Experiments on a viscous fluid flow between concentric rotating spheres

Abstract: Some experimental results on incompressible viscous fluid flow in the gap between two concentric rotating spheres are discussed. The flow field in the spherical gap has been studied qualitatively by flow visualization (photographs) and quantitatively by measurements by the hot-wire technique. For a wide range of Reynolds numbers, the friction torque was measured for several gap widths and a relatively simple method of determining the torque theoretically is given. At higher Reynolds numbers instabilities appear. Their different behaviour for relatively small and large gap widths is demonstrated. For the larger gap widths, the different appearance of the Taylor–Gortler vortices, the reason for their generation, their regimes of existence as well as their influence on the friction torque are thoroughly treated. Detailed information is given on the new effect of the dependence of the wavelength of the vortices on the Reynolds number.

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.

Vortex shedding and resistance in harmonic flow about smooth and rough circular cylinders at high reynolds numbers

Abstract: : This report presents the results on an extensive experimental investigation of the in-line and transverse forces acting on smooth and rough circular cylinders placed in oscillatory water flow at Reynolds numbers up to 700,000, Keulegan-Carpenter numbers up to 150, and relative roughnesses from 0. 002 to 0.02. The drag and inertia coefficients have been determined through the use of the Fourier analysis and the least-squares method. The transverse force (lift) has been analyzed in terms of its maximum, semi-peak-to-peak, and root- mean-square values. In addition, the frequency of vortex shedding and the Strouhal number have been determined.

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.

On the Development of Spiral Bands in a Tropical Cyclone

Abstract: Development of the band structure in a tropical cyclone is investigated by solving an eigenvalue problem for perturbations of spiral shape. The perturbations are superposed on a baroclinic circular vortex accompanied with a radial and vertical basic flow. It is shown that the spiral bands in three different modes may be intensified in an inner area of a tropical cyclone. The baroclinicity of a basic field is not required for the development of bands in any mode. A spiral band which propagates outward can grow in the presence of the horizontal shear of the basic azimuthal flow. Without the basic circular vortex, this band is reduced to a neutral gravity-inertia wave with a particular vertical structure. The unstable spiral in this mode takes a pattern which extends clockwise from the center of a storm in the Northern Hemisphere. An azimuthal wavenumber 2 and a radial scale (twice the band width) of 200 km are preferred by this band. Another band with the characteristics of an inward propagating gr...

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.

Vortex generators for internal mixing in a turbofan engine

Abstract: Method and apparatus for reducing jet noise in a turbofan engine by causing internal mixing of fan and primary air to reduce the maximum velocity of gases at the nozzle exit plane by creating a particular type of vortex flow at a distance of at least one nozzle diameter forward of the nozzle exit plane. In one preferred embodiment for a JT8D engine an array of eight roll-top vortex generators are provided on each side of the splitter wall between fan and primary flows, and a portion of the fan air may be introduced into the central portion or core of the hot primary air.

Centrifugal Instability of a Stokes Layer: Linear Theory

Abstract: The instability of the flow induced by a circular cylinder oscillating in an infinite viscous fluid is investigated. The flow is shown to be unstable to a Taylor vortex mode of instability. A series solution of the partial differential system governing the stability of the flow is obtained. The method used has several advantages over the numerical methods used by different authors for related problems. The instability predicted by the theory leads to a flow with no mean velocity component tangential to the cylinders. The disturbance velocity field decays exponentially at the edge of the Stokes layer. The theoretical results are qualitatively confirmed by an experimental investigation of the problem.

Helium II thermal counterflow: Temperature- and pressure-difference data and analysis in terms of the Vinen theory

Abstract: An extensive investigation of the temperature and pressure difference associated with the thermal counterflow of He II in long capillary tubes is reported. For heat currents that are not too large, our temperature data are in excellent agreement with the Vinen theory in which mutual friction is regarded as arising from a homogeneous mass of quantized vortex line. Our pressure data, which are obtained simultaneously with the temperature data, are used to determine the eddy viscosity of the vortex lines. The Vinen theory is reviewed and somewhat modified in the light of these and other recent results. It is suggested that the vortex-line model of thermal counterflow is one of the few successful quantitative models of nonlinear hydrodynamics effects in He II. (AIP)

Angular momentum diffusion and the initiation of cyclones

Abstract: IT is possible to explain1,2 the intensification of a cyclone vortex once the stream lines in a weak depression close around a core of higher vorticity, but it is less clear how the process starts. Scorer3 proposed that convection might diffuse angular momentum within a field of initially uniform rotation to localised regions, thereby concentrating cyclonic vorticity. Experiments failed to demonstrate the effect4–7, and although strong vortices could be produced through the breaking of inertial waves8, the effects were open to misinterpretation. We present here new experimental results showing that first, angular momentum or relative vorticity can be diffused at a rate comparable with the diffusion of relative velocity (turbulent ‘viscosity’). This distinctive property seems to be intrinsic to weak turbulence in rotation, and can be parameterised very simply. Second, such diffusion occurs only when the turbulence is sufficiently weak to be constrained by rotation to an essentially two-dimensional structure. This might explain the failure of earlier experiments. Our results could have many applications to geophysics, including tropical cyclogenesis.

Jet-type axial pulverizer

Abstract: A jet-type grinding mill having a circular chamber wherein a rotating vortex is formed by gaseous fluid injected into the chamber, the material to be ground being fed into the mill through a feed means at the center of the vortex, there being a central recess at the bottom of the chamber below the feed inlet which has upwardly inclined walls to direct the fed particles upwardly and outwardly into the vortex.

Quantum mechanical streamlines. IV. Collision of two spheres with square potential wells or barriers

Abstract: Quantum mechanical streamlines and probability density contours help in the understanding of collision dynamics by showing what happens during the collision. This is illustrated by considering the elastic scattering of two particles which interact with a spherically symmetric square potential, V (r) =0 when r≳a and V (r) =C when r

Experimental Study of the Effect of Span Loading on Aircraft Wakes

Abstract: Measurements were made in the NASA-Ames 40- by 80-Foot Wind Tunnel of the rolling moment induced on a following model in the wake 13.6 spans behind a subsonic transport model for a variety of trailing edge flap settings of the generator. It was found that the rolling moment on the following model was reduced substantially, compared to the conventional landing configuration, by reshaping the span loading on the generating model to approximate a span loading, found in earlier studies, which resulted in reduced wake velocities. This was accomplished by retracting the outboard trailing edge flaps. It was concluded, based on flow visualization conducted in the wind tunnel as well as in a water tow facility, that this flap arrangement redistributes the vorticity shed by the wing along the span to form three vortex pairs that interact to disperse the wake.

A vortex-lattice method for the mean camber shapes of trimmed noncoplanar planforms with minimum vortex drag

Abstract: A new subsonic method has been developed by which the mean camber surface can be determined for trimmed noncoplanar planforms with minimum vortex drag. This method uses a vortex lattice and overcomes previous difficulties with chord loading specification. A Trefftz plane analysis is utilized to determine the optimum span loading for minimum drag, then solved for the mean camber surface of the wing, which provides the required loading. Sensitivity studies, comparisons with other theories, and applications to configurations which include a tandem wing and a wing winglet combination have been made and are presented.

Unsteady motion of airfoils with boundary-layer separation

Abstract: It is shown that the condition that determines circulation about an airfoil with boundary layers is identical with the usual inviscid-flow condition based on conservation of total circulation and the Kutta-Joukowski condition, in both steady and unsteady flow. This implies interesting relationships between the viscous and inviscid models, namely, between boundary-layer vorticity and bound-vortex strength, viscous-wake vorticity and freevortex strength, and vortex/vorticity fluxes, in both steady and unsteady flow. The unsteady aerodynamics of airfoils with rounded trailing edges is discussed in this light, and it is concluded that a dual model is needed, involving a boundary-layer calculation over a smooth body to determine circulation, and a vortex-sheet model to determine the perturbed potential flowfield needed in this calculation, as well as forces and moments on the airfoil.