Showing papers on "Vortex published in 1971"

Orderly Structure in Jet Turbulence

Abstract: Past evidence suggests that a large-scale orderly pattern may exist in the noiseproducing region of a jet. Using several methods to visualize the flow of round subsonic jets, we watched the evolution of orderly flow with advancing Reynolds number. As the Reynolds number increases from order 102 to 103, the instability of the jet evolves from a sinusoid to a helix, and finally to a train of axisymmetric waves. At a Reynolds number around 104, the boundary layer of the jet is thin, and two kinds of axisymmetric structure can be discerned: surface ripples on the jet column, thoroughly studied by previous workers, and a more tenuous train of large-scale vortex puffs. The surface ripples scale on the boundary-layer thickness and shorten as the Reynolds number increases toward 105. The structure of the puffs, by contrast, remains much the same: they form at an average Strouhal number of about 0·3 based on frequency, exit speed, and diameter.To isolate the large-scale pattern at Reynolds numbers around 105, we destroyed the surface ripples by tripping the boundary layer inside the nozzle. We imposed a periodic surging of controllable frequency and amplitude at the jet exit, and studied the response downstream by hot-wire anemometry and schlieren photography. The forcing generates a fundamental wave, whose phase velocity accords with the linear theory of temporally growing instabilities. The fundamental grows in amplitude downstream until non-linearity generates a harmonic. The harmonic retards the growth of the fundamental, and the two attain saturation intensities roughly independent of forcing amplitude. The saturation amplitude depends on the Strouhal number of the imposed surging and reaches a maximum at a Strouhal number of 0·30. A root-mean-square sinusoidal surging only 2% of the mean exit speed brings the preferred mode to saturation four diameters downstream from the nozzle, at which point the entrained volume flow has increased 32% over the unforced case. When forced at a Strouhal number of 0·60, the jet seems to act as a compound amplifier, forming a violent 0·30 subharmonic and suffering a large increase of spreading angle. We conclude with the conjecture that the preferred mode having a Strouhal number of 0·30 is in some sense the most dispersive wave on a jet column, the wave least capable of generating a harmonic, and therefore the wave most capable of reaching a large amplitude before saturating.

On stationary and travelling vortex breakdowns

Abstract: This paper describes some experiments in swirling flows in a diverging cylindrical tube in which various types of vortex breakdowns were observed.In one set of experiments, the position of the breakdown, axial component of the velocity of the vortex core, swirl angle distribution ahead of the breakdown, and the pressure distribution along the tube were determined for various flow rates and for various values of circulation imparted to the fluid (water). Basically, three types of vortex breakdown were observed, viz. mild (double helix) breakdown, spiral breakdown (followed by turbulent mixing), and axisymmetric breakdown (followed by a thicker vortex core, then a spiral breakdown, and finally by turbulent mixing). The type and the location of the stationary breakdowns were found to be dependent, for the particular vortex tube used, upon the Reynolds and circulation numbers of the flow. In a spiral breakdown, the vortex core filament maintained the same sense of rotation as the upstream fluid elements. In an axisymmetric breakdown, the bubble included an inclined vortex-ring whose axis gyrated about the axis of the tube.In a second set of experiments, the response of the abrupt structural change along the axis of flow to gradual and abrupt changes in the upstream and downstream flow conditions was examined. The axisymmetric breakdown responded in a manner analogous to the hydraulic jump in open-channel flow before if reached a new stationary position along the axis of the tube.The observations reported and the evidence presented herein revealed that the axisymmetric breakdown is a finite transition between two sequent states of flow as proposed by Benjamin (1962, 1965, 1967) on theoretical grounds.

Predictions of vortex-lift characteristics based on a leading-edge suction analogy.

Abstract: Leading edge suction analogy for predicting low speed lift and drag-due-to-lift characteristics of sharp edge delta and related wing planforms

Structure of a Line Vortex in an Imposed Strain

Abstract: The velocity of a vortex line depends on its structure, i.e. the shape of the cross-section and the detailed vorticity distri­bution. As a first step towards an understanding of how the struc­ture depends on the motion and the construction of a valid approxi­mation for the motion of vortex lines in general flow fields, we consider the structure of straight line vortices in a uniform two-dimensional straining field. Two cases are considered in detail, irrotational strain and simple shear. In the first case, it is shown that steady exact solutions of the inviscid equations exist, in which the boundary of the vortex is an ellipse with principal axes at 45° to the principal axes of strain. There are two possible axis ratios provided e/ωo 0.15, and it is believed from some numerical work that in this case the strain field will cause the vortex to break up. For simple shear, there is one steady shape of elliptical form if the shear rotation and vorticity are in the same sense and e′<ωo, where e′ is the rate of shear. The major axis is parallel to the streamlines and the shape is stable to two-dimensional deformations. For shear rotation and vorticity in opposite senses, there are two steady elliptical shapes if e′/ωo<0.21, with major axes perpendicular to the streamlines. The more elongated form is unstable, and the less elongated one is stable. Disturbances of three-dimensional form are also considered in the limit of extremely large axial wavelength.

Mechanism of bond zone wave formation in explosion-clad metals

Abstract: Results of experiments in which the collision variables were carefully controlled showed that bond zone wave formation during explosion cladding is analogous to the formation of vortex streets in fluid flow around an obstacle or in the collision of liquid streams. The fluid flow analogy explains the observed transition from a smooth metal-to-metal bond zone to a wavy bond zone above a critical collision velocity. This model is capable of predicting the minimum collision velocity necessary for bond zone wave formation in different metal systems and it also predicts correctly the strong dependence of wave size on collision angle. The magnitude of the wave size agrees with that predicted from fluid flow past a flat plate. Two other mechanisms of bond zone wave formation were explored experimentally and found to be invalid.

The spacing, position and strength of vortices in the wake of slender cylindrical bodies at large incidence

Abstract: Extensive schlieren studies and yawmeter traverses of the wake behind slender cone-cylinders at large angles of incidence have shown that the flow pattern is generally steady. Under certain flow conditions, however, the wake exhibits an instability which is not understood. For cross-flow Reynolds numbers in the subcritical region the wake can be described in terms of a cross-flow Strouhal number which has a constant value of 0·2 for cross-flow Mach number components (Mc) up to 0·7 and then increases steadily to a value of 0·6 at Mc = 1·6. The strength of the wake vortices varies substantially with Mc, increasing to a maximum at Mc ≈ 0·7 and then decreasing rapidly for higher values of Mc. Schlieren photographs of the wake have been analysed by means of the impulse flow analogy and also by considering the vortices to be part of a yawed infinite vortex street. The impulse flow analogy is shown to be of use in determining the cross-flow Strouhal number but estimates of vortex strength are too high. The Karman vortex street theory combined with the sweepback principle leads to reliable estimates of vortex strength up to Mc = 1·0.Information is given on the spacing, path and strength of the vortices shed from the body for flow conditions varying from incompressible speeds up to Mc = 1·0. Finally this information is used to determine the vortex drag of a two-dimensional circular cylinder below Mc = 1·0.

Vortex Breakdown in Swirling Conical Flows

Abstract: This paper describes some experiments in swirling flows in a mildly diverging cylindrical tube in which three types of vortex breakdown were observed: double-helix and spiral forms (followed by turbulent mixing), and axisymmetric form (often followed by a spiral breakdown, then by turbulent mixing). The type and location of the breakdowns were found to be dependent upon the Reynolds and circulation numbers of the flow. The observations reported and the evidence presented herein revealed that the axisymmetric breakdown is basically a finite transition between two sequent states of flow, from a uniform state of swirling flow (supercritical) to one (subcritical) featuring a series of standing waves of finite amplitude. The double-helix and spiral forms, which occur in a region well defined by Reynolds and circulation numbers, appear to be a consequence of the instability of the vortical viscous flow to spiral disturbances.

On the Spectrum and Decay of Random Two-Dimensional Vorticity Distributions at Large Reynolds Number

Abstract: The hypothesis is made that the vorticity distribution in a field of random two-dimensional vorticity (two-dimensional turbulence) develops discontinuities. The energy spectrum is then calculated and shown to behave like k^(−4) for large values of the wave-number k. The rates of decay of mean square vorticity and velocity are estimated. An expression for the growth of length scale is obtained and it is noted that the size of turbulent trailing vortices is apparently well fitted by the formula.

Experimental Study on Structure of Gas Flow in Tube Banks with Tube Axes Normal to Flow : Part 1, Karman Vortex Flow from Two Tubes at Various Spacings

Abstract: A gas flow in and behind tube banks with tuber axes normal to the gas flow is highly turbulent containing numerous vortices of different sizes and intensities. Each vortex in this complicated wake is the result of a periodic generation, and the periodicity sometimes induces serious vibration problems in steam generators and heat exchangers. The structure of the flow may be treated ass a complex synthesized result of Karman vortex flow. This paper is the first report of a series of studies carried out form the above mentioned viewpoint, and presents the experimental results about a Karman vortex flow from two tubes at various spacings. The vortex formation region was visualized by means of the Schlieren method and was recorded by a 16mm movie camera. The vortex shedding frequency was systematically studied. The frequency for two tubes is entirely different from that for a single tube. It was found that the size of the vortex formation domain has a dominant effect on the frequency.

Theoretical and Experimental Study of the Stability of a Vortex Pair

Abstract: The linear stability of the trailing vortex pair from an aircraft is discussed. The method of matched asymptotic expansions is used to obtain a general solution for the flow field within and near a curved vortex filament with an arbitrary distribution of swirl and axial velocities. The velocity field induced in the neighborhood of the vortex core by distant portions of the vortex line is calculated for a sinusoidally perturbed vortex filament and for a vortex ring. General expressions for the self-induced motion are given for these two cases. It is shown that the details of the vorticity and axial velocity distributions affect the self-induced motion only through the kinetic energy of the swirl and the axial momentum flux. The presence of axial velocity in the core reduces both the angular velocity of the sinusoidal vortex filament and the speed of the ring. The vortex pair instability is then considered in terms of the more general model for self-induced motion of the sinusoidal vortex. The presence of axial velocity within the core slightly decreases the amplification rate of the instability. Experimental results for the distortion and breakup of a perturbed vortex pair are presented.

Vortex shedding from circular cylinders at low Reynolds numbers

Abstract: Experiments on slightly tapered models of circular cross-section have shown that the vortex wake structure exists in a number of discrete cells having different shedding frequencies. Within each cell shedding is regular and periodic, the frequency being somewhat lower than that from a parallel cylinder of the same diameter. A similar type of wake behaviour has also been observed on a parallel model in a non-uniform mean flow. These results suggest that the discontinuities in the shedding law observed by Tritton could arise through non-uniformities in the flow.

Hydromechanics of swimming propulsion. Part 3. Swimming and optimum movements of slender fish with side fins

Abstract: This paper seeks to evaluate the swimming flow around a typical slender fish whose transverse cross-section to the rear of its maximum span section is of a lenticular shape with pointed edges, such as those of spiny fins, so that these side edges are sharp trailing edges, from which an oscillating vortex sheet is shed to trail the body in swimming. The additional feature of shedding of vortex sheet makes this problem a moderate generalization of the paper on the swimming of slender fish treated by Lighthill (1960a). It is found here that the thrust depends not only on the virtual mass of the tail-end section, but also on an integral effect of variations of the virtual mass along the entire body segment containing the trailing side edges, and that this latter effect can greatly enhance the thrust-making. The optimum shape problem considered here is to determine the transverse oscillatory movements a slender fish can make which will produce a prescribed thrust, so as to overcome the frictional drag, at the expense of the minimum work done in maintaining the motion. The solution is for the fish to send a wave down its body at a phase velocity c somewhat greater than the desired swimming speed U, with an amplitude nearly uniform from the maximum span section to the tail. Both the ratio U/c and the optimum efficiency are found to depend upon two parameters: the reduced wave frequency and a 'proportional-loading parameter', the latter being proportional to the thrust coefficient and to the inverse square of the wave amplitude. The basic mechanism of swimming is examined in the light of the principle of action and reaction by studying the vortex wake generated by the optimum movement.

Quantum Interference Effects of a Moving Vortex Lattice in Al Films

Abstract: An experimental study is reported of steps induced in the flux-flow $I\ensuremath{-}V$ characteristics of superconducting aluminum films by a superimposed rf current, whose frequency is a harmonic or subharmonic of the ratio of the vortex velocity and the lattice parameter.

Flow in a Turbulent Trailing Vortex

Abstract: The structure of turbulent line vortices is examined. A general argument is constructed to show that the vortex must develop an overshoot of circulation if it entrains fluid at a rate greater than that due to molecular diffusion. A weak hypothesis on the distribution of Reynolds stress leads to the logarithmic profile of Hoffman and Joubert and an estimate of the maximum Reynolds stress. The results of a turbulence model due to Saffman are presented and shown to be poor.

The near field within the potential cone of subsonic cold jets

Abstract: This investigation describes a detailed study of the near pressure field within the potential cone of a subsonic circular turbulent jet.The components of the near pressure field in the potential cone in which the potential flow condition exists within the fist four and a half diameter downstream appear to be moving with a phase velocity equal to the local speed of sound. The direction of propagation is roughly normal to the shear layer surrounding the cone. Some components of the hot-wire signal can be associated with the jet structure as a simple complex source, while others are related to the local characteristics of turbulence. Differences in the characteristics of the pressure field within the potential cone exist between the vortex generated noise at very low jet velocity and the eddy generated noise at higher velocity.The power spectra obtained in the potential cone show the peak which is due to the pressure fluctuations and the flat portion due to the turbulence. The frequencies of the dominant components, in terms of the Strouhal number, are functions of both the axial and radial positions.Microphone measurements were made in the near field outside for detailed comparison with the potential cone results.

Boundary Layer Induced by a Potential Vortex

Abstract: A numerical computation of the laminar boundary layer on a fixed circular disk of radius a whose axis is concentric with that of a vortex having circulation Γ is described. The computations were started at the edge of the disk and continued inward toward the axis until the properties of the terminal flow became evident. A two‐layer asymptotic expansion was formulated for the solution of the boundary‐layer equations near the axis, and the terminal‐flow properties revealed by the analysis are shown to be in excellent agreement with the numerical results. The structure of the terminal boundary layer consists of an inner layer next to the surface with thickness O[(ν/Γ)1/2r] in which the flow is primarily radial, and an outer layer with thickness O[(ν/Γ)1/2a] of predominantly inviscid nature in which the flow recovers to the external potential vortex. The mass flux in the outer layer does not vanish as r→0, indicating that the boundary layer must erupt from the surface at r=0in the manner envisioned by Moore.

Vortex shedding from a turbulent jet in a cross-wind

Abstract: Measurements in the wake behind turbulent jets exhausting from a solid surface into a cross-wind indicate that vortex shedding occurs as in the case of flow past solid bluff bodies. The Strouhal numbers for flow past a circular and a blunt jet are in qualitative agreement with those for corresponding solid bodies, provided that the width of the spreading jet some distance from the surface is used rather than the jet exit plane dimension.

Vortex de-aerator

Abstract: In a vortex type de-aerator for separating air and other gases from a flowing liquid, having a central perforate tube located within a vessel having a tangential inlet and a tangential outlet, a vortex stabilising baffle device is located adjacent to the inlet for stabilising the vortex flow and for shielding separated gas from any disturbances at the inlet.

Axisymmetric Flows in the Boundary Layer of a Maintained Vortex

Abstract: The three-dimensional flow in the boundary layer of a tornado-like vortex, with a core region of large vorticity and an outer region of nearly zero vorticity, is obtained by alternatingly solving the two nonlinear boundary-layer equations for the radial and the vertical distributions of the velocities. It is found that in the inner region the flow is of the Ekman-layer type, with an oscillatory distribution of the velocities in the vertical, while in the outer region the flow is of the ordinary boundary-layer type, with the velocity components approaching their respective values asymptotically without oscillation at a large distance from the boundary. This distribution of the radial velocity results in a weak descending motion in the outer region and a relatively strong ascending motion in the inner region with a sharp maximum upward motion occurring inside the radius of the maximum tangential wind where the boundary-layer thickness increases most rapidly outward.

Tip vortices: Velocity distributions

Abstract: Hot-wire anemometer measurements of streamwise magnitudes and normal velocity components of wing tip vortex

Wind-Induced Instability of Structures

Abstract: Forms of wind-induced instability of structures are described, and two of these, typical of long bodies with bluff cross-sections, are selected for more detailed consideration. The first is vortex-induced bending oscillation, a type of resonant response to the periodic surface pressure loading caused by the discrete wake vortex street formed from the shear layers separating from the bluff cross-section. Oscillation phenomena are described, including capture of the vortex frequency by the structural response frequency over a discrete wind speed range and amplification and phase shift of the loading over this range. The second form is transverse galloping, arising from aerodynamic instability of the bluff cross-sectional shape, so that small-amplitude oscillations generate forces which increase the amplitudes to large values. Oscillation phenomena are described, including the occurrence at very nearly natural frequencies, and the relatively large amplitudes (compared to vortex-induced oscillations) increasing with wind speed beyond a critical wind speed dependent on the level o fstructural damping. Effects of body and wind parameters on both forms of oscillation are considered, and methods of analysis and suppression for susceptible structures are described. Some probable future requirements and prospects are considered.

Motions in a Bose condensate. I. The structure of the large circular vortex

Abstract: A procedure is given which in principle permits the exact evaluation of any term in the asymptotic expansion in a/c of the velocity Uo and energy E of a circular vortex line of radius c in a Bose condensate (where a is the healing length). The procedure is used to obtain the two leading terms (previously only inaccurately determined by a variational calculation), namely U0= kappa /4 pi c(In(8c/a)-0.615); E=1/2 rho kappa 2c(1n(8c/a)-1.615); where kappa denotes the quantum of circulation, and rho denotes the fluid density at infinity.

Dynamical evolution of two-dimensional unstable shear flows

Abstract: A direct numerical integration of the time-dependent, incompressible Navier-Stokes equations is used to treat the nonlinear evolution of perturbed, linearly unstable, nearly parallel shear flow profiles in two dimensions. Calculations have been made for infinite (inviscid) and finite Reynolds numbers. The latter results are compared with laboratory measurements of Sato & Kuriki for wakes behind thin flat plates, and many of the detailed features are in excellent agreement, including mean flow profiles with ‘overshoot’ development, first harmonic energy profiles with off-axis nulls, and first harmonic phase profiles. The linear instability saturates by forming a vortex street consisting of elliptical vortex pairs. The solutions are followed for times up to eleven linear exponentiation times of the unstable disturbance. A new low-frequency non-linear oscillation is found, which explains the features of the above experiment, including the nearly periodic phase inversions in the first harmonic component of the longitudinal velocity. It results from a nutation of the elliptical vortices with respect to the mean flow direction. Inertial range spectral energy properties are also examined. Inviscid solutions have large wave-number spectral energies obeying the approximate power law, Ek ∼ k−μ, where μ lies between 3 and 4.

On the Asymmetric Structure of the Tropical Cyclone Outflow Layer

Abstract: ATS-III satellite data and conventional aerological data are used to construct detailed wind analyses of the outflow layer for four hurricanes and one tropical storm Harmonic analysis of these data, and of the data for a mean Atlantic hurricane and a mean Pacific typhoon, shows that wave numbers 1 and 2 around the circumference of the storm account for most of the variance of momentum and kinetic energy Subtraction of the symmetric part of the vortex circulation from the total flow to yield the “asymmetric wind” reveals two eddies located in preferred quadrants of the storm An anticyclonic eddy is found to the right and a cyclonic eddy to the left of the storm motion These eddies transport absolute vorticity inward, opposing the outward transport by the mean circulation They also transport a significant amount of negative relative angular momentum outward The presence of inertial (or dynamic) instability is investigated Although substantial areas of negative absolute vorticity and anomalou

A review of confined vortex flows

Abstract: Modes for using vortices for fluid dynamic containment of gaseous core nuclear reactor, bibliography

The development of concentrated vortices: a numerical study

Abstract: Amongst the more important laboratory experiments which have produced concentrated vortices in rotating tanks are the sink experiments of Long and the bubble convection experiments of Turner & Lilly. This paper describes a numerical experiment which draws from the laboratory experiments those features which are believed to be most relevant to atmospheric vortices such as tornadoes and waterspouts.In the numerical model the mechanism driving the vortices is represented by an externally specified vertical body force field defined in a narrow neighbourhood of the axis of rotation. The body force field is applied to a tank of fluid initially in a state of rigid rotation and the subsequent flow development is obtained by solving the Navier–Stokes equations as an initial-value problem.Earlier investigations have revealed that concentrated vortices will form only for a restricted range of flow parameters, and for the numerical experiment this range was selected using an order-of-magnitude analysis of the steady Navier–Stokes equations for sink vortices performed by Morton. With values of the flow parameters obtained in this way, concentrated vortices with angular velocities up to 30 times that of the tank are generated, whereas only much weaker vortices are formed at other parametric states. The numerical solutions are also used to investigate the comparative effect of a free upper surface and a no-slip lid.The concentrated vortices produced in the numerical experiment grow downwards from near the top of the tank until they reach the bottom plate whereupon they strengthen rapidly before reaching a quasi-steady state. In the quasi-steady state the flow in the tank typically consists of the vortex at the axis of rotation, strong inflow and outflow boundary layers at the bottom and top plates respectively, and a region of slowly-rotating descending flow over the remainder of the tank. The flow is cyclonic (i.e. in the same sense as the tank) in the vortex core and over most of the bottom half of the tank and is anticyclonic over the upper half of the tank away from the axis of rotation.