Showing papers on "Vortex published in 1975"

Contributions to the theory of aerodynamic sound, with application to excess jet noise and the theory of the flute

Abstract: This paper describes a reformulation of the Lighthill (1952) theory of aerodynamic sound. A revised approach to the subject is necessary in order to unify the various ad hoc procedures which have been developed for dealing with aerodynamic noise problems since the original appearance of Lighthill's work. First, Powell's (1961 a) concept of vortex sound is difficult to justify convincingly on the basis of Lighthill's acoustic analogy, although it is consistent with model problems which have been treated by the method of matched asymptotic expansions. Second, Candel (1972), Marble (1973) and Morfey (1973) have demonstrated the importance of entropy inhomogeneities, which generate sound when accelerated in a mean flow pressure gradient. This is arguably a more significant source of acoustic radiation in hot subsonic jets than pure jet noise. Third, the analysis of Ffowcs Williams & Howe (1975) of model problems involving the convection of an entropy ‘slug’ in an engine nozzle indicates that the whole question of excess jet noise may be intimately related to the convection of flow inhomogeneities through mean flow pressure gradients. Such problems are difficult to formulate precisely in terms of Lighthill's theory because of the presence of an extensive, non-acoustic, non-uniform mean flow. The convected-entropy source mechanism is actually absent from the alternative Phillips (1960) formulation of the aerodynamic sound problem.In this paper the form of the acoustic propagation operator is established for a non-uniform mean flow in the absence of vortical or entropy-gradient source terms. The natural thermodynamic variable for dealing with such problems is the stagnation enthalpy. This provides a basis for a new acoustic analogy, and it is deduced that the corresponding acoustic source terms are associated solely with regions of the flow where the vorticity vector and entropy-gradient vector are non-vanishing. The theory is illustrated by detailed applications to problems which, in the appropriate limit, justify Powell's theory of vortex sound, and to the important question of noise generation during the unsteady convection of flow inhomogeneities in ducts and past rigid bodies in free space. At low Mach numbers wave propagation is described by a convected wave equation, for which powerful analytical techniques, discussed in the appendix, are available and are exploited.Fluctuating heat sources are examined: a model problem is considered and provides a positive comparison with an alternative analysis undertaken elsewhere. The difficult question of the scattering of a plane sound wave by a cylindrical vortex filament is also discussed, the effect of dissipation at the vortex core being taken into account.Finally an approximate aerodynamic theory of the operation of musical instruments characterized by the flute is described. This involves an investigation of the properties of a vortex shedding mechanism which is coupled in a nonlinear manner to the acoustic oscillations within the instrument. The theory furnishes results which are consistent with the playing technique of the flautist and with simple acoustic measurements undertaken by the author.

High-Lift Aerodynamics

Abstract: c. f = chord fraction, see Eq. (5.1) H = shape factor of the boundary layer, d*/0 £ = plate length L = lift m = exponent in Cp=x flows, also lift magnification factor (5.1) M = Mach number p = pressure q = dynamic pressure Q = flow rate R = Reynolds number (= u Ox/v in Stratford flows) R6 = Reynolds number based on momentum thickness uee/v S = Stratford's separation constant (4.10); also peripheral distance around a body or wing area / = blowing slot gap, also thickness ratio of a body u = velocity in x-direction u0 = initial velocity at start of deceleration in canonical and Stratford flows v = velocity normal to the wall V = a general velocity x = length in flow direction, or around surface of a body measured from stagnation point if used in connection with boundary-layer flow

Statistical dynamics of two-dimensional flow

Abstract: The equilibrium statistical mechanics of inviscid two-dimensional flow are re-examined both for a continuum truncated at a top wavenumber and for a system of discrete vortices. In both cases, there are negative-temperature equilibria for finite flows. But for spatially infinite flows, there are only positive-temperature equilibria, and both the continuum and discrete system exhibit proper, extensive, thermodynamic limits a t all realizable values of the energy and enstrophy density. The negative-temperature behaviours of the continuum and discrete system are semi-quantitatively the same, except for a supercondensation phenomenon in the discrete case a t the smallest realizable values of negative temperature. The supercondensed states have very large energy and in them all vortex cores of the same sign are clumped within an area small eompared with the mean area per vortex. The approach of the continuum system to absolute equilibrium by enstrophy cascade to high wavenumbers and energy cascade to low wavenumbers is examined. It is argued that the enstrophy cascade is closely analogous to distortion of a passive scalar field by straining of large spatial scale. This implies that high intermittency of spatial derivatives of the vorticity field can develop but that there is no associated change in the previously proposed log-corrected k−1 enstrophy spectrum law. On the other hand, intermittency build-up in the downward energy cascade can result in a change of the exponent in the energy spectrum law to a negative value of smaller magnitude than 5/3. Intermittency effects in the non-equilibrium energy cascade seem a more plausible explanation for vortex clumping observed in recent computer experiments than do the spatially smooth condensation phenomena associated with the negative-temperature absolute equilibria.

The instability of a straight vortex filament in a strain field

Abstract: A straight infinite vortex of finite cross section is deformed by the action of weak irrotational plane strain. The deformed vortex is shown, in the absence of axial flow, to be unstable to disturbances whose axial wavelengths lie in a narrow band, whose width is proportional to the imposed strain. The band is centred on the wavelength of the helical wave which does not propagate on the unstrained circular vortex. Thus support is given to the instability mechanism proposed recently by Widnall, Bliss & Tsai (1974). The argument depends, however, on the mirror image of the helical wave also being a possible non-propagating disturbance on the unstrained vortex.

A proposed model of the bursting process in turbulent boundary layers

Abstract: A model is proposed which attempts to explain the complete ‘burst cycle’. This model views the wall streak as a sub-boundary layer, within the conventionally defined boundary layer, and the lift-up stage of bursting either as an upwelling motion of this sub-boundary layer which is similar to a local, convected separation or, equivalently, as the consequence of a vortex roll-up. ‘Sweeps’ are thought to represent the passage of a previous burst from further upstream. They appear either to impress on the wall streak the temporary adverse pressure gradient required to bring about its lifting or, alternatively, to provide the outer vortex which rolls up with the vortex associated with the wall streak. The model is also used to explain how the interactions between a burst and a sweep bring about (i) breakup, as well as (ii) new wall streaks further downstream.Arguments are presented to demonstrate that the three kinds of oscillatory growth reported by Kim, Kline & Reynolds (1971) may be associated with just one type of flow structure: the stretched and lifted vortex described by Kline et al. (1967).

On turbulence and noise of an axisymmetric shear flow

Abstract: The noise produced by mean flow-turbulence interaction of a circular subsonic jet is investigated theoretically, and expanded in azimuthal constituents of the turbulent pressure fluctuations. It is found that the low-order azimuthal constituents are the most efficient sound sources. On the basis of pressure correlation measurements, the azimuthal constituents are determined in a low Mach number jet. It is found that, in a range of Strouhal numbers between 0·2 and 1, the first three to four azimuthal constituents clearly dominate over the rest of the turbulent source quantity. A strictly axisymmetric ring vortex model for the coherent structure of the turbulence is, however, shown to be inappropriate.

The Structure and Dynamics of Vortex Filaments

Abstract: Recent concern over the hazard presented by the trailing vortices produced by large aircraft has stimulated research into one of the oldest subjects in fluid mechanics: the study of flows with concentrated vorticity in free motion. Since these vortices can be strong and persistent enough to pose a safety hazard to other aircraft, it is clearly desirable to be able to predict the structure, position, and persistence of such vortices as well as to understand the mechanisms by which vortex wakes are dissipated. Under most conditions, trailing vortices undergo a natural sinusoidal instability that eventually causes them to touch and break into a series of crude vortex rings. This process destroys the initial wake structure more rapidly than viscous or turbulent decay of the individual filaments. The character and potential hazard of the residual wake structure after the completion of the sinusoidal instability are still not well understood. It is apparent, however, that the motion, structure, and stability of flows with concentrated vorticity is of great practical interest and leads to an examination of many fundamental problems in fluid mechanics. The first organized attempt to compile what was known about the behavior of aircraft vortices, the process of generation and resulting structure, the hazard created by wake turbulence, and the possibilities for detection, avoidance, or destruction of wake vortices can be found in the proceedings of the conference on "Aircraft Wake Turbulence and Its Detection," edited by Olsen, GGldburg & Rogers (1971). Wc do not attempt a review of all of the technical activities in the field of aircraft wake turbulence; we arc here specifically interested in the fluid mechanics of trailing vortices and vortex rings as well as in the more general problem of the structure, motion, and stability of free vortices: compact regions of concentrated vorticity in free motion in a surrounding fluid that is either homogeneous and at rest or with weak background vorticity or stratification. In a very basic sense, the study of the motion of an incompressible homogeneous

Simple model for the vortex core in a type II superconductor

Abstract: In order to model the core of an isolated vortex in a type II superconductor, a variational trial function for the magnitude of the normalized order parameter of the form f = ϱ/R is assumed, where ϱ is the radial coordinate, R = (p 2 + ξv 2)1/2, and ξ v is a variational core radius parameter. Remarkably simple analytic expressions for the magnetic flux density and supercurrent density that solve Ampere's law and the second Ginzburg-Landau equation are obtained. An analytic result for the free energy of the isolated vortex is then derived by integrating the Ginzburg-Landau free energy functional. The value of ξ v that minimizes the free energy is calculated as a function of the Ginzburg-Landau parameter κ = λ/ξ and is found to range from ξ v = 0.935ξ for κ = 0.707 to ξ v ≈ 1.414ξ for κ > 1. A simple expression for the form factor or the Fourier transform of the flux density is obtained, which may be useful in the analysis of neutron diffraction experiments.

An inviscid model of two-dimensional vortex shedding for transient and asymptotically steady separated flow over an inclined plate

Abstract: A potential flow model of two-dimensional vortex shedding behind an inclined plate is developed. The free shear layers which emanate from the sides of the plate are represented by discrete vortices through the use of the appropriate complex-velocity potential, the Kutta condition and the Joukowsky transformation between a circle and the plate cross-section. The analysis is then applied to predict the kinematic and dynamic characteristics of the flow for various angles of attack. The results compare favourably with the available experimental data as far as the form of vortex shedding and the Strouhal number are concerned. The calculated normal-force coefficients are 20−25% yo larger than those measured by Fage & Johansen (1927).

The density of organized vortices in a turbulent mixing layer

Abstract: It is argued on the basis of exact solutions for uniform vortices in straining fields that vortices of finite cross-section in a row will disintegrate if the spacing is too small. The results are applied to the organized vortex structures observed in turbulent mixing layers. An explanation is provided for the disappearance of these structures as they move downstream and it is deduced that the ratio of average spacing to width should be about 3·5, the width being defined by the maximum slope of the mean velocity. It is shown in an appendix that walls have negligible effect.

Vortex Wakes of Conventional Aircraft

Abstract: : A review is made of the present state of our knowledge of the vortex wakes of conventional aircraft. Included are discussions of wake rollup, geometry, instability, and turbulent aging. In the light of these discussions, a brief review is made of the persistence of vortices in the atmosphere, and design techniques which might be used to minimize wake hazard are considered.

The vortex-street structure of ‘turbulent’ jets. Part 1

Abstract: It was suggested by Lau, Fisher & Puchs (1972) that the basic structure of a ‘turbulent’ round jet might consist, essentially, of an axial array of fairly evenly spaced vortices moving downstream in the mixing region of the jet. The present experimental study is an attempt to establish this hypothesis on a sound footing. The problem which was posed was first to find proof of the existence of a fairly regular pattern in the mixing region, and second to extract detailed information on the component parts of this pattern to identify the nature of the structure.Hot-wire signals in the mixing layer are known to possess a predominance of spikes. In the region closer to the high velocity side of the layer, these spikes tend to be downward ones whilst in the opposite region, they are upward. These spikes have been attributed to the entrainment mechanism in the mixing layer and had been thought to be random. A closer study of time-history curves of these hotwire signals suggests that they might not be as random as would appear at first glance. A probability analysis was conducted of the time intervals between the successive downward spikes in the u′ signals, and it was found that indeed the highest probability occurred when the time interval corresponded to a frequency equal to the vortex passing frequency.A time-domain averaging (or eduction) technique was used to try to identify the nature of the flow structure using the spikes to trigger the eduction process. On the basis of these results it would seem that the suggestion of a vortex street is well founded. Furthermore, it appears that, as the individual vortices in the street move downstream, they are continuously transporting fluid masses across the mixing layer, and it is this effect which is producing the Reynolds stresses in the mixing layer, and causing the spikes in the u’ signals in this region.

Starting vortex, separation bubbles and stall: a numerical study of laminar unsteady flow around an airfoil

Abstract: The stalling characteristics of an airfoil in a laminar viscous incompressible fluid are investigated. The governing equations in terms of the vorticity and stream function are solved using an implicit finite-difference scheme and point successive relaxation procedure. The development of the impulsively started flow, the initial generation of circulation, and the behavior of the forces at large times are studied. Following the impulsive start, the lift is at first very large and then it rapidly drops. The subsequent growth of circulation and lift is associated with the starting vortex. After incipient separation, the lift increases owing to enlargement of the separation bubble and intensification of the flow rotation in it. The extension of this bubble beyond the trailing edge causes it to rupture and brings about the stalling characteristics of the airfoil. Subsequently, new bubbles are formed near the upper surface of the airfoil and are swept away. The behavior of the lift acting on the airfoil is explained in terms of the strength and sense of these bubbles.

Ideal plug-flow properties of taylor vortex flow

Abstract: Mixing properties of Taylor vortex flow with small constant axial flow rates were investigated in an annulus between two concentric rotating cylinders by injecting a salt-solution tracer or by suspending small soluble particles. Longitudinal intermixing of fluid elements between the neighboring vortices was examined by a method of two-point measurement. Circumferential mixing in each cellular vortex was also evaluated by comparing two successive time variations of concentration at a certain point in the case of no axial flow. The modes of flow were mapped in terms of Taylor number and Reynolds number. This vortex flow has been found to be an ideal plug-flow for the range of 51.4

Two-dimensional turbulence in inviscid fluids or guiding center plasmas

Abstract: Analytic theory for two-dimensional turbulent equilibria for the inviscid Navier-Stokes equations is examined mathematically. Application of the technique to electrostatic guiding center plasma is discussed. A good fit is demonstrated for the approach to a predicted energy per Fourier mode obtained from a two-temperature canonical ensemble. Negative as well as positive temperature regimes are explored. Fluctuations about the mean energy per mode also compare well with theory. In the regime of alpha less than zero, beta greater than zero, with the minimum value of alpha plus beta times k squared near zero, contour plots of the stream function reveal macroscopic vortex structures similar to those seen previously in discrete vortex simulations. Eulerian direct interaction equations, which can be used to follow the approach to inviscid equilibrium, are derived.

Unsteady Lifts and Wakes of Oscillating Rectangular Prisms

Abstract: Measurements are made of the unsteady lifts and wakes of rectangular prisms oscillating transversely in a uniform flow with the short sides normal to the flow direction. Rectangular prisms tested have three different side ratios of l, 2, and 4, respectively, and the tests are carried out in a wind tunnel. The phase angles of the frequency response components of both the unsteady lift and the near-wake velocity show abrupt change when the critical reduced wind velocity for vortex shedding is approached. This is suggested to be one of the key phenomena to solving the problem of vortex excitation of bluff structures. For all of the three rectangular prisms tested, the linear quasi-steady aerodynamic theory of galloping is found to be applicable until reduced wind velocity is lowered fairly closely to the aforementioned critical reduced wind velocity. However, the reason why the applicability of the theory to such low reduced wind velocities may be fortuitous is also mentioned. Further analyses are made of the instability occurring in a restricted range of reduced wind velocity well below the critical.

Tornado-type wind turbine

Abstract: Atmospheric wind is admitted tangentially into a vertically extending structure and directed against the interior curved surface of the structure to produce vortex flow. The structure is open ended and spaced from ground or connected to a ram-air subterranean tunnel. The vortex flow and corresponding low pressure core draws ambient and/or ram air into the bottom of the structure to drive a horizontal turbine.

Far-Field Wake-Vortex Characteristics of Wings

Abstract: Velocity measurements have been made in the wake of wings that were being towed underwater. As the wake aged, measurements of the tangential and axial velocity profiles were made with a two-dimensional scanning laser velocimeter at downstream distances of 5 to 200 span lengths behind wings with different span loadings. The results identify two characteristic flow regions for the dependence of vortex maximum tangential velocity on downstream distance. The first, a region with little, if any, change in maximum tangential velocity, extends from wake rollup to downstream distances as great as 100 span lengths, depending on span loading and angle of attack. This is followed by a decay region in which the maximum tangential velocity decreases with downstream distance at rates nominally proportional to the inverse one-half power.

Colliding vortex rings

Abstract: Laboratory observations of the interaction between pairs of vortex rings during certain collisions are described. A theory is advanced, based on the resonance of the forced motion with the elliptical mode of oscillation of a single vortex, and is found to be in agreement with the observed behavior.

Stability of a pair of co‐rotating vortices

Abstract: The linear stability of a pair of co‐rotating vortex filaments is studied with a view toward clarifying the behavior of these pairs in the shear layer. The configuration is found to be stable within the long wave approximation.

Transport of Heat Across a Plane Turbulent Mixing Layer

Abstract: Publisher Summary A well-known characteristic of turbulent shear flows is that the spread of scalar quantities—that is, heat or matter, is faster than the spread of momentum This chapter describes a model for the transport mechanism of a scalar quantity in typical turbulent shear flows In the present state of the investigation, measurements of the temperature field alone have been obtained and the temperature field is mathematically represented by four equations; the equation of motion, the continuity equation for the mean velocities, the heat-transfer equation, and the equation of the balance of temperature fluctuations The chapter provides some important observations, such as based on the shape of the temperature fluctuations as well as the mean quantity distributions it can be assumed that the transport mechanism is largely due to a large scale vortical motion, the mean temperature distribution in the turbulent domain is largely homogeneous, the temperature across a single vortex is linear in the mean, and the temperature fluctuation variance in the turbulent domain is approximately constant

On vortex structure in the wake of a sphere

Abstract: Results showing the three‐dimensional vortex shedding structure when a sphere is towed at a constant velocity through a stratified fluid are presented. It is found that for small Richardson numbers (weak stratification) and Reynolds numbers in the range from 4×103 to 2×104 the vortex is shed three‐dimensionally. However, stratification quickly and effectively inhibits the vertical motion and the initially turbulent wake collapses and reveals the vertically oriented portion of the vortex structure, reminiscent of a two‐dimensional vortex street behind a circular cylinder when viewed from above. The structure is, however, distinctly three‐dimensional. It is also found that the estimated vortex shedding frequency is in reasonable agreement with previously published results for a sphere in a homogeneous fluid. It is suggested that a weak stratification is an excellent means for revealing the vortex structure of a three‐dimensional body in a homogeneous fluid, and that the vortex tube in the wake of a sphere in a homogeneous fluid has a closed‐end double helical structure. Two branches of the double helix are continuously unwinding in an opposite sense from the formation region. Moreover, the present double helical model satisfies Thompson’s circulation theorem in contrast to previously proposed helical models.

Augmentation of Vortex Lift by Spanwise Blowing

Abstract: An investigation has been conducted to evaluate the aerodynamic effects associated with blowing a jet spanwise over a wing's upper surface in a direction parallel to the leading edge. Experimental pressure and force data were obtained on wings with sweep angles of 30 and 45 degrees and showed that spanwise blowing aids in the formation and control of the leading-edge vortex and, hence, significantly improves the aerodynamic characteristics at high angles of attack. Full vortex section lift is achieved at the inboard span station with a small blowing rate, but successively higher blowing rates are necessary to attain the full vortex-lift level at increased span distances. Spanwise blowing generates large increases in lift at high angles of attack, improves the drag polars, and extends the linear pitching moment to high lifts.