Showing papers on "Vortex published in 1978"

The structure of vortex breakdown

Abstract: The term 'vortex breakdown', as used in the reported investigation, refers to a disturbance characterized by the formation of an internal stagnation point on the vortex axis, followed by reversed flow in a region of limited axial extent. Two forms of vortex breakdown, which predominate, are shown in photographs. One form is called 'near-axisymmetric' (sometimes 'axisymmetric'), and the other is called 'spiral'. A survey is presented of work published since the 1972 review by Hall. Most experimental data taken since Hall's review have been in tubes, and the survey deals primarily with such cases. It is found that the assumption of axial-symmetry has produced useful results. The classification of flows as supercritical or subcritical, a step that assumes symmetry, has proved universally useful. Experiments show that vortex breakdown is always preceded by an upstream supercritical flow and followed by a subcritical wake. However, a comparison between experiments and attempts at prediction is less than encouraging. For a satisfactory understanding of the structure of vortex breakdown it is apparently necessary to take into account also aspects of asymmetry.

Large-scale structure in the mixing layer of a round jet

Abstract: Late transitional and turbulent flows in the mixing-layer region of a round jet are investigated for a range of Reynolds numbers by using flow-visualization and hotwire techniques. Attention is focused on the vortices in the transition region and the large eddies in the turbulent region. The interaction and coalescence of vortex rings in the transition region are described. The transition region is characterized by a growth of three-dimensional flow due to a wave instability of the cores of the vortex rings. The merging of these distorted vortices produces large eddies which can remain coherent up to the end of the potential-core region of the jet. A conditional sampling technique is used to measure eddies moving near the jet centre-line. These eddies differ significantly from the ring vortices as they are three-dimensional and contain irregular small-scale turbulence. However, when averaged, their structure is similar in cross-section to that of a vortex ring. These sampled eddies contribute greatly to local velocity fluctuations and statistical correlations. The experiments indicate a need for careful consideration of the meanings of terms such as ‘vortex’, ‘eddy’ and ‘turbulent flow’. In particular care must be taken to discriminate between the orderly, easily visualized, vortices in the transition regions of free shear flows and the less clearly visualized, but strong, large eddies in the fully developed turbulent regions.

The Wakes of Cylindrical Bluff Bodies at Low Reynolds Number

Abstract: Experiments on the near wake of a cylinder will be discribed in an attempt to present a coherent picture of the events encountered as the Reynolds number increases from small values up to values of a few thousand. Much work on this subject has already been done, but there are gaps in our description of these flows as well as more fundamental deficiencies in our understanding of them. The subject has been reviewed several times and most recently by Berger & Wille (1972) whose paper covers much of the ground that will be discussed again here. The present work may be regarded as built upon this latest review. I remember with gratitude many helpful discussions with the late Rudolph Wille who contributed so much to this subject. The investigation has concentrated on circular cylinders, but the wakes of bluff cylinders of different cross sectional shapes have also been observed. Bluff cylinders in general are considered in §§4 and 5, together with the effect of splitter plates on circular cylinders in §9. The experiments concern, almost exclusively, flow visualization of the wakes by means of dye washed from the bodies. The patterns of dye observed are, therefore, filament line representations of the flow leaving the separation lines on the body. It must be stressed that the dye does not make visible the vorticity bearing fluid because at low Reynolds number, vorticity diffuses considerably more rapidly than does dye. The ratio of the molecular diffusivity of momentum to that of mass of dye is of the order of 100.

Visual observations of the flow past a sphere at Reynolds numbers between 10 4 and 10 6

Abstract: The wake configuration of a sphere has been determined by means of the surface oil-flow method, the smoke method and the tuft-grid method in a wind tunnel at Reynolds numbers ranging from 104 to 106. It was found that the wake performs a progressive wave motion at Reynolds numbers between 104 and 3·8 × 105, and that it forms a pair of stream wise line vortices at Reynolds numbers between 3·8 × 105 and 106.

On vortex sound at low Mach number

Abstract: A transformation is described which relates the sound generated by low Mach number flow to the flow vorticity. For compact flow fields the apparent sound source is of quadrupole type and linear in the vorticity and therefore also linear in the flow velocity. This scheme is applied to the sound generated by the interaction of two identical thin vortex rings. Then a flow field with a number of compact vortices is discussed. It is found that each vortex can be replaced acoustically by a dipole related to the impulse of the vortex, plus the quadrupole just mentioned plus a spherically symmetric sound source related to the energy of the vortex. An application to low Mach number free-space turbulence shows that the generated sound is related to the vorticity correlation tensor.

Structure and entrainment in the plane of symmetry of a turbulent spot

Abstract: Laser-Doppler velocity measurements in water are reported for the flow in the plane of symmetry of a turbulent spot. The unsteady mean flow, defined as an ensemble average, is fitted to a conical growth law by using data at three streamwise stations to determine the virtual origin in x and t. The two-dimensional unsteady stream function is expressed as ψ=U^2_∞tg(ξ,η) in conical similarity co-ordinates ζ = x/U_∞t and η = y/U_∞t. In these co-ordinates, the equations for the unsteady particle displacements reduce to an autonomous system. This system is integrated graphically to obtain particle trajectories in invariant form. Strong entrainment is found to occur along the outer part of the rear interface and also in front of the spot near the wall. The outer part of the forward interface is passive. In terms of particle trajectories in conical co-ordinates, the main vortex in the spot appears as a stable focus with celerity 0·77U_∞. A second stable focus with celerity 0·64U_∞ also appears near the wall at the rear of the spot. Some results obtained by flow visualization with a dense, nearly opaque suspension of aluminium flakes are also reported. Photographs of the sublayer flow viewed through a glass wall show the expected longitudinal streaks. These are tentatively interpreted as longitudinal vortices caused by an instability of Taylor-Gortler type in the sublayer.

An experimental map of the internal structure of a vortex breakdown

Abstract: The flow field of an 'axisymmetric' vortex breakdown has been mapped using a laser-Doppler anemometer. The interior of the recirculation zone is dominated by energetic, non-axisymmetric, low frequency periodic fluctuations. Spectra for a number of points inside this zone, as well as time-averaged swirl and axial velocity profiles both inside and outside the recirculation zone, have been obtained. The time-averaged streamlines in the interior show an unexpected two-celled structure attributed to the action of the fluctuations. Although the present experiment deals with one particular breakdown, flow-visualization studies indicate that the case examined is typical of the 'axisymmetric' form of breakdown over a range of flow conditions.

The number of waves on unstable vortex rings

Abstract: An explanation is proposed for the dependence on Reynolds number and other parameters of the number of waves which appear on vortex rings formed by pushing fluid out of a tube. It is shown that the number of waves can be sensitive to the vorticity distribution in the core of the ring. The process of ring formation is discussed and it is concluded that peaked vorticity distributions, limited by viscosity, will occur. Quantitative estimates of the number of waves are made. Agreement with observation is satisfactory.

Effect of free-stream turbulence on large structure in turbulent mixing layers

Abstract: Flow-visualization investigations and correlation measurements show that the essentially two-dimensional structures which dominated the turbulent mixing layer of Brown & Roshko (1974) are formed only if the free-stream turbulence is low. If free-stream disturbances are significant, as is likely in most practical cases, including a mixing layer entraining ‘still air’ from the surroundings, three-dimensionality develops at an early stage in transition. Other recent experiments strongly suggest that the Brown-Roshko structure will not form if the initial mixing layer is turbulent or subject to instability modes other than spanwise vortices. Therefore the Brown-Roshko structure will be rare in practice. The alternative large structure in a mixing layer, found by several workers, is intense, but fully three-dimensional and thus less orderly than the Brown-Roshko structure.The balance of evidence suggests that if the Brown-Roshko structure does appear it will eventually relax into the alternative fully three-dimensional form: the Karman vortex street behind a bluff body provides a precedent for slow development of three-dimensionality. However the Brown-Roshko structure, if formed, may well relax so slowly as to be identifiable for the full length of a practical flow.

Dissipation in Two-Dimensional Superfluids

Abstract: Dissipation of energy by a thin film of $^{4}\mathrm{He}$ on an oscillating planar substrate arises both from motion of free vortices and from polarization of bound pairs. Starting from a Langevin equation for vortex diffusion, and taking into account production of free vortices from bound pairs, we estimate this dissipation in various regimes of frequency, amplitude of vibration, and temperature.

The large-scale structure of unsteady self-similar rolled-up vortex sheets

Abstract: Two problems involving the unsteady motion of two-dimensional vortex sheets are considered. The first is the roll-up of an initially plane semi-infinite vortex sheet while the second is the power-law starting flow past an infinite wedge with separation at the wedge apex modelled by a growing vortex sheet. In both cases well-known similarity solutions are used to transform the time-dependent problem for the sheet motion into an integro-differential equation. Finite-difference numerical solutions to these equations are obtained which give details of the large-scale structure of the rolled-up portion of the sheet. For the semi-infinite sheet good agreement with Kaden's asymptotic spiral solution is obtained. However, for the starting-flow problem distortions in the sheet shape and strength not predicted by the leading-order asymptotic solutions were found to be significant.

Laser anemometer study of flow development in curved circular pipes

Abstract: An experimental investigation was carried out of the development of steady, laminar, incompressible flow of a Newtonian fluid in the entry region of a curved pipe for the entry condition of uniform motion. Two semicircular pipes of radius ratios 1/20 and 1/7 were investigated, covering a Dean number range from 138 to 679. The axial velocity and the component of secondary velocity parallel to the plane of curvature of the pipe were measured using laser anemometry. It was observed that, in the upstream region where the boundary layers are thin compared with the pipe radius, the axial velocity within the irrotational core first develops to form a vortex-like flow. In the downstream region, characterized by viscous layers of thickness comparable with the pipe radius, there appears to be three-dimensional separation at the inner wall. There is also an indication of an additional vortex structure embedded within the Dean-type secondary motion. The experimental axial velocity profiles are compared with those constructed from the theoretical analyses of Singh and Yao & Berger. The quantitative agreement between theory and experiment is found to be poor; however, some of the features observed in the experiment are in qualitative agreement with the theoretical solution of Yao & Berger.

Convergence of vortex methods for Euler’s equations

Abstract: A numerical method for approximating the flow of a two dimensional incompressible, inviscid fluid is examined. It is proved that for a short time interval Chorin's vortex method converges superlinearly toward the solution of Euler's equations, which govern the flow. The length of the time interval depends upon the smoothness of the flow and of the particular cutoff. The theory is supported by numerical experiments. These suggest that the vortex method may even be a second order method.

The effect of short regions of high surface curvature on turbulent boundary layers.

Abstract: Measurements, including one-point double, triple or quadruple mean products of velocity fluctuations, have been made in low-speed turbulent, boundary layers on flat surfaces downstream of concave or convex bends with turning angles of 20 or 30 degrees, the length of the curved region being at most 6 times the boundary-layer thickness at entry. These short bends approximate to ‘impulses’ of curvature, and the object of the work was to investigate the impulse response of the boundary layer, essentially the decay of structural changes downstream of the bends. The work can be regarded as a sequel, with much more detailed measurements, to the study by So & Mellor (1972, 1973, 1975) who investigated the response to step increases of curvature: turbulent boundary layers being nonlinear systems, responses to several kinds of curvature history are needed to assemble an adequate description of the flow. The most striking feature of the ‘impulse’ response is that the decay of the high turbulent intensity found at exit from the concave bends is not monotonic; the Reynolds stresses in the outer layer collapse to well below the level at entry, and are still falling slowly at the end of the test rig although in principle they must recover eventually. On the convex (stabilized) side the flow recovers, monotonically in the main, from a low level of turbulent intensity at the exit. The pronounced second-order response on the concave side can be explained qualitatively by interaction between the shear stress and the mean shear and is not peculiar to curved flows, but in the present cases the response is complicated by large changes in the dimensionless structure parameters related to double or triple mean products of velocity fluctuations. Strong spanwise variations, due presumably to longitudinal vortices, further complicate the flow in the concave bends, and decay only very slowly downstream.

A stereoscopic visual study of coherent structures in turbulent shear flow

Abstract: Stereoscopic photography was used to record the three-dimensional motions of fluid elements along a flat-plate turbulent boundary layer flow. The outer region of the boundary layer was dominated by the formation and convection of transverse vortices, formed at the high-speed front between low- and high-speed fluid elements. Vortical motions observed in the wall region consisted of (1) motions of single particles around part of a circle, (2) streamwise vortices, and (3) transverse vortices.

Vortex formation at vertical pipe intakes

Abstract: With the object of determining the similarity criterion, experimental studies on vortex formation at pipe intakes were carried out using two geometrically similar circular vortex tanks, circulation in approach flow was generated by means of adjustable guide vanes Transparent pipe intakes of different sizes and liquids of different viscosities and surface tensions were used in a recirculating system Based on the analysis of data, a method has been proposed according to which a geometrically similar model is operated at the same Froude number as in the prototype and the observed critical submergence is corrected for distortion due to change in the model Reynolds number A criterion to determine the type of vortex for known geometric and kinematic conditions has also been proposed

Motion of a curved vortex filament with decaying vortical core and axial velocity

Abstract: The motion and decay of a vortex filament with large axial and circumferential velocity components in a three-dimensional stream are studied. Solutions are constructed to the Navier–Stokes equations by use of matched asymptotic expansions; the small parameter used is a measure of the ratio of the viscous effects to the vortex strength. The outer flow, which corresponds to the classical Biot–Savart type analysis is matched to the solution in an inner viscous region. The radius of the viscous core is assumed to be much smaller than the radius of curvature. The present viscous analysis yields the classical inviscid theory as a limiting case for the leading term in the outer region and thus can be used to correct various deficiencies in the latter. We show in particular, that the inner solution yields a finite velocity at all points in the filament and we determine how the components of both vorticity and velocity diffuse due to the viscous forces. The matching conditions guarantee the continuity of velocity ...

Similarity Of Free-Vortex At Horizontal Intake

Abstract: An investigation was conducted to study the onset of air-entraining vortices at a horizontal intake, with and without a bellmouthed entry, when the intake was projected into the experimental flume or mounted flush with the side wall. The basic non-dimensional parameters that govern the onset of vortices at a horizontal intake in model and prototype have been derived and determined experimentally. The results of measurements are given as a set of curves, which can be used for the design of a vortex-free intake and also for the selection of appropriate model scales. The results of the measurement showed that flow conditions in an air-entraining vortex is not affected by surface tension and the viscosity of the test fluid when the radial Reynolds number, and the Weber number are larger than 3x104 and 104 respectively. In this case the formation of vortices depends largely on circulation, submergence head and discharge into the intake. It was found that the bellmouth did not improve the performance of the int...

Turbulence memory in self-preserving wakes

Abstract: The persistence of the large vortices formed at the origin of wakes and mixing layers constitutes a kind of memory of initial conditions by the turbulence. In order to study the fading of this turbulence memory, and its effect on the rate of approach to the fully developed state, two wakes with different initial conditions have been examined experimentally. The wake of a sphere was compared with the wake of a porous disk which had the same drag, but did not exhibit vortex shedding. Measurements were made of the mean and fluctuating velocities, the anisotropy of the turbulence, and the intermittency. It was found that the wake of the sphere developed self-preserving behaviour more rapidly than the wake of the disk, and that even after both wakes became self-preserving there were differences between them in the structure of the turbulence and the scale of the mean flow. From this it is concluded that the behaviour of self-preserving wakes does not depend on the drag alone, but also on the structure of the dominant eddies. Generalizing these results, it is suggested that reported differences in the value of the entrainment constant of jets, wakes, and mixing layers are due to differences in the structure of the dominant eddies, rather than differences in the type of flow.

Mechanism of determination of the shedding frequency of vortices behind a cylinder at low Reynolds numbers

Abstract: Two kinds of experiment were made in the wake of a cylinder at Reynolds numbers ranging between 20 and 150. One was a close look at the structure of the vortex street with a stationary cylinder at Reynolds numbers greater than 48. The other experiment was made at lower Reynolds numbers with a cylinder vibrating normal to the flow direction. In this case an artificially induced small-amplitude fluctuation grows exponentially with the rate predicted by the stability theory. Because of the similarity between the two kinds of wake, we postulate that the shedding of the vortex at low Reynolds numbers is initiated by the linear growth, namely, the fluctuation with the frequency of maximum linear growth rate develops into vortex streets. By using the measured width of the wake at the stagnation point in the wake and the result of the stability theory, we could calculate the Strouhal number for Reynolds numbers ranging from 48 to 120. The predicted Strouhal numbers agree well with the values from direct measurements.

The Boundary Layer Due to Rectilinear Vortex

Abstract: The boundary layer created by the motion of a single rectilinear vortex filament above an infinite plane wall is considered. In a frame of reference which moves uniformly with the vortex the inviscid motion is steady; however, the possibility of a corresponding steady boundary-layer solution can be ruled out and it is concluded that the boundary-layer flow is inherently unsteady for all time. To investigate the nature of the unsteady boundary-layer flow, a time-dependent problem, corresponding to the sudden insertion of the plane wall at time $t$ = 0, is considered; separation in the boundary layer is found to take place in a short period of time and the solution shows possibly explosive features as $t$ increases. It is conjectured that an eventual eruption of the boundary-layer flow is to be expected along with a major modification of the inviscid flow. The theory compares favourably with experiments on the flow induced near the ground by trailing aircraft vortices.

The plane turbulent impinging jet

Abstract: This paper presents an experimental study of the turbulent structure on the centre-line of a two-dimensional impinging jet. The mean velocity, turbulent stresses, triple velocity products and temporal derivatives were measured and the energy balances for the three fluctuating components were calculated. The results indicate a selective stretching of vortices in the direction in which the streamlines spread near the wall, causing anisotropy in this region. The distribution of energy among various frequencies was found from spectral measurements. These measurements revealed the existence of a neutral frequency above which the energy was attenuated by viscous dissipation and below which it was augmented by a vortex-stretching mechanism.

Influence of wave dispersion on vortex pairing in a jet

Abstract: The geometry of large-scale structures in the turbulent mixing layer of a moderate Reynolds number jet is deduced from measurements of the fluctuating pressure in the hydrodynamic near field. The structures are rings of concentrated vorticity that distort with downstream distance until statistical axisymmetry disappears. The rings are spaced quasi-periodically and coalesce with each other, producing larger spacings. Statistical and flow-visualization techniques are applied to free and forced jets over a range of Reynolds numbers from 5000 to 50,000 to demonstrate that rings of a given spacing do not coalesce with each other until they are far enough downstream that the local mixing layer has attained some critical thickness which scales with the wavelength of the vortex pair. Wave dispersion is evaluated as a plausible mechanism for localizing the coalescences. The central feature of the model is the observation that a shear layer is dispersive to wavelengths much longer than its thickness and nondispersive to shorter waves.

Lift Enhancement by an Externally Trapped Vortex

Abstract: A theoretical study is made of the performance capabilities of a lift concept that utilizes a spanwise vortex over the upper surface of the wing. The vortex is generated by a vertical flap near the leading edge of the wing and maintained by suction through orifices in endplates at the wingtip. The analysis approximates the three-dimensional flow field with a two-dimensional configuration that is mapped by conformal transformation into the flow about a circle. Theoretical solutions for a range of flap and orifice configurations predict that section lift coefficients up to around 10 can be achieved. It is concluded that such a lift concept is applicable to STOL aircraft if the vortex can be adequately stabilized and if the endplate suction can be generated efficiently.

A comprehensive experimental investigation of tubular entry flow of viscoelastic fluids: Part I. Vortex characteristics in stable flow

Abstract: The characteristics of a vortex found at the entry of a 2:1 and 4:1 contraction for viscoelastic fluids is investigated. Two distinct flow regimes are identified in the contraction flow field: a vortex growth regime and a divergent flow regime. In the vortex flow regime, rheological forces are found to dominate the flow, with the vortex detachment length being a linear function of the Weissenberg number. In the divergent flow regime, the flow is found to diverge at the center line upstream of the vortex detachment plane, and the vortex size decreases with increasing flow rates. Inertial forces are important in the divergent flow regime. The entry flow characteristics for the 2:1 and 4:1 contraction are quantified in terms of the vortex detachment length as a function of Reynolds and Weissenberg number over the range of 0:2 < N′Re < 200 and 0.10 < NWS < 0.7.