Showing papers on "Vortex shedding published in 1988"

The Existence of Two Stages in the Transition to Three-Dimensionality of a Cylinder Wake

Abstract: The transition to three‐dimensionality in the near wake of a circular cylinder involves two successive transitions, each of which corresponds with a discontinuity in the Strouhal–Reynolds number relationship. The first discontinuity [between Reynolds numbers (Re) of 170 to 180] is associated with the inception of vortex loops, and it is hysteretic. The second discontinuity (between Re=230 to 260) corresponds with a change to a finer‐scale streamwise vortex structure. At this discontinuity there is no hysteresis, and it is suggested that two modes of vortex shedding alternate in time.

Defining a universal and continuous Strouhal–Reynolds number relationship for the laminar vortex shedding of a circular cylinder

Abstract: The existence of a discontinuity in the Strouhal–Reynolds number relationship for the laminar vortex shedding of a cylinder is found to be caused by a change in the mode of oblique shedding. By ‘‘inducing’’ parallel shedding (from manipulating end conditions) the resulting Strouhal curve becomes completely continuous and agrees very well with the oblique‐shedding data, if it is transformed by S0=Sθ/cos θ (where Sθ is the Strouhal number corresponding with the oblique‐shedding angle θ). The curve also agrees with data from a completely different facility. This provides evidence that this Strouhal curve (S0) is universal (for a circular cylinder).

Flow structure from an oscillating cylinder Part 1. Mechanisms of phase shift and recovery in the near wake

Abstract: Cylinders of various cross-section were subjected to controlled oscillations in a direction transverse to the incident flow. Excitation was at frequency fe, relative to the formation frequency f*0 of large-scale vortices from the corresponding stationary cylinder, and at Reynolds numbers in the range 584 [les ] Re [les ] 1300. Modifications of the near wake were characterized by visualization of the instantaneous flow structure in conjunction with body displacement-flow velocity correlations.At fe/f*0 = ½, corresponding to subharmonic excitation, as well as at fe/f*0 = 1, the near wake structure is phase-locked (synchronized) to the cylinder motion. However, the synchronization mechanism is distinctly different in these two regimes. Near or at fe/f*0 = 1, the phase of the shed vortex with respect to the cylinder displacement switches by approximately π. Characteristics of this phase switch are related to cylinder geometry. It does not occur if the cylinder has significant afterbody.Over a wide range of fe/f*0, the perturbed near wake rapidly recovers to a largescale antisymmetrical mode similar in form to the well-known Karman vortex street. The mechanisms of small-scale (fe) vortex interaction leading to recovery of the large-scale (f0) vortices are highly ordered and repeatable, though distinctly different, for superharmonic excitation (fe/f*0 = n = 2, 3, 4) and non-harmonic excitation (non-integer values of fe/f*0).The frequency f0 of the recovered vortex street downstream of the body shows substantial departure from the shedding frequency f*0 from the corresponding stationary body. It locks-on to resonant modes corresponding to f0/fe = 1/n. This wake response involves strictly hydrodynamic phenomena. It shows, however, a resonant behaviour analogous to that of coupled flow-acoustic systems where the shear layer is convectively unstable

The absolute and convective nature of instability in two-dimensional wakes at low Reynolds numbers

Abstract: The linear parallel and incompressible stability of a family of bluff‐body wake profiles is studied at Reynolds numbers close to the onset of Karman vortex shedding The family of mean flow profiles allows for the variation of the wake depth as well as for a variable ratio of wake width to mixing layer thickness The absolute or convective nature of the sinuous instability is determined as a function of the profile parameters and Reynolds number A comparison of this survey with experimental data shows that in bluff‐body near wakes a region of local absolute instability begins to form at a Reynolds number of approximately one‐half the critical value for Karman vortex shedding Hence, at the onset of the global response (Karman vortex shedding), a substantial region of local absolute instability already exists in the wake This confirms the qualitative model prediction of Chomaz, Huerre, and Redekopp [submitted to Phys Rev Lett] and also shows that the prediction of vortex shedding frequencies, when based on local stability properties alone, is somewhat arbitrary even at the critical Reynolds number

Large structure in the far wakes of two-dimensional bluff bodies

Abstract: Smoke-wire flow visualization and hot-wire anemometry have been used to study near and far wakes of two-dimensional bluff bodies. For the case of a circular cylinder at 70 < Re < 2000, a very rapid (exponential) decay of velocity fluctuations at the Karman-vortex-street frequency is observed. Beyond this region of decay, larger-scale (lower wavenumber) structure can be seen. In the far wake (beyond one hundred diameters) a broad band of frequencies is selectively amplified and then damped, the centre of the band shifting to lower frequencies as downstream distance is increased. The far-wake structure does not depend directly on the scale or frequency of Karman vortices shed from the cylinder; i.e. it does not result from amalgamation of shed vortices. The growth of this structure is due to hydrodynamic instability of the developing mean wake profile. Under certain conditions amalgamation can take place, but is purely incidental, and is not the driving mechanism responsible for the growth of larger-scale structure. Similar large structure is observed downstream of porous flat plates (Re [approximate] 6000), which do not initially shed Karman-type vortices into the wake. Measured prominent frequencies in the far cylinder wake are in good agreement with those estimated by two-dimensional locally parallel inviscid linear stability theory, when streamwise growth of wake width is taken into account. Finally, three-dimensionality in the far wake of a circular cylinder is briefly discussed and a mechanism for its development is suggested based on a secondary parametric instability of the subharmonic type.

On vortex formation from a cylinder. part 1: the initial instability

Abstract: Vortex shedding from a circular cylinder is examined over a tenfold range of Reynolds number, 440 ≤ Re ≤ 5040. The shear layer separating from the cylinder shows, to varying degrees, an exponential variation of fluctuating kinetic energy with distance downstream of the cylinder. The characteristics of this unsteady shear layer are interpreted within the context of an absolute instability of the near wake. At the trailing-end of the cylinder, the fluctuation amplitude of the instability correlates well with previously measured values of mean base pressure. Moreover, this amplitude follows the visualized vortex formation length as Reynolds number varies. There is a drastic decrease in this near-wake fluctuation amplitude in the lower range of Reynolds number and a rapid increase at higher Reynolds number. These trends are addressed relative to the present, as well as previous, observations.

Investigation of the flow between a pair of circular cylinders in the flopping regime

Abstract: The wakes of a pair of circular cylinders are grossly unsteady when the cylinders are separated in a direction normal to the approaching flow by less than one cylinder diameter. The wakes flop randomly between two asymmetric states. The time-scale for the flopping is several orders of magnitude longer than the timescale of vortex shedding, and also several orders of magnitude longer than the timescale for instability of the separating shear layers. When a splitter plate is positioned suitably on the centerline of the cylinders, the flopping can be stopped and the flow made to assume either of the asymmetric states, or a symmetric steady state. For a range of plate positions a new, periodic oscillation occurs. Acoustic excitation can also destroy the flopping mean flow, replacing it by a symmetric flow.

Flow structure from an oscillating cylinder. part 2: mode competition in the near wake

Abstract: A circular cylinder subjected to forced oscillations at angle α with respect to the free stream shows a number of admissible modes of vortex formation synchronized with the body motion. These modes can be categorized into two basic groups: symmetrical vortex formation; and antisymmetrical vortex formation. Whereas there is a single symmetrical mode, there are four basic antisymmetrical modes. Three of these antisymmetrical modes show period doubling relative to the classical Karman mode. This doubling arises from the symmetrical perturbation component induced by the cylinder motion at α ± 90°. Synchronization, i.e. phase-locking of the vortex shedding with the cylinder motion, is possible for all of these modes. It occurs even when streamwise (α = 0°) motion induces an antisymmetrical mode.When synchronization does not occur, there is competition between the symmetrical and antisymmetrical modes; the near-wake structure successively locks-on to each mode over a defined number of cycles, abruptly switching between modes. The number of occurrences of each mode is a well-defined function of excitation frequency and angle α.If, in contrast to steady-state motion of the cylinder, there is an initial transient motion, the transition between symmetrical and antisymmetrical modes has a markedly different character, emphasizing the importance of initial conditions. Abrupt onset of sinusoidal motion produces an initially synchronized symmetrical mode, which gradually decays to an antisymmetrical mode. The number of excitation cycles to onset of decay to antisymmetrical mode is highly repeatable. Moreover, the mechanism of decay of the near wake from the symmetrical to antisymmetrical mode can occur deterministically over a defined number of cycles.

Observations of the frequencies in a sphere wake and of drag increase by acoustic excitation

Abstract: Vortex shedding and instability wave frequencies have been measured in the wakes of spheres in the Reynolds number range 500

On vortex formation from a cylinder. Part 2. Control by splitter-plate interference

Abstract: Control of vortex formation from a circular cylinder by a long plate in its wake is examined over the Reynolds number range 140 < Re < 3600. There are two basic flow regimes: a pre-vortex formation regime, in which the plate precludes formation of a large-scale vortex upstream of the tip of the plate; and a post-vortex formation regime in which one or more large-scale vortices are formed upstream of the edge. The unsteady pressure loading at the tip of the plate increases by over an order of magnitude during transition from the pre- to post-vortex formation regime. If the plate is located near the cylinder, it is possible to more than double the vortex formation length, relative to the case of the free wake. Moreover, these observations suggest that: there is a minimum streamwise lengthscale for development of the absolute instability of the near wake and thereby the large-scale vortex; and the vortex formation length may also be influenced by the downstream vorticity dynamics. When the plate is located downstream of the initially formed vortex, effective control is possible when the near-wake fluctuation level and mean base pressure of the corresponding free (non-impinging) wake are sufficiently small. This occurs in the low and moderate subcritical regimes; the substantial control by the wake-plate interaction in this range of Reynolds number implies low strength of the absolute instability of the near wake. However, in the pure von Karman regime, selfcontrol of the near wake dominates that imposed by the wake-edge interaction, suggesting a strong absolute instability of the near wake.

Three-dimensional shear layers via vortex dynamics

Abstract: The evolution of the two- and three-dimensional structures in a temporally growing plane shear layer is numerically simulated with the discrete vortex dynamics method. We include two signs of vorticity and thus account for the effect of the weaker boundary layer leaving the splitter plate which is used to create a spatially developing mixing layer. The interaction between the two layers changes the symmetry properties seen in a single vorticity-layer calculation and results in closer agreement with experimental observations of the interface between the two streams. Our calculations show the formation of concentrated streamwise vortices in the braid region between the spanwise rollers, whereas the spanwise core instability is observed to grow only initially. Comparison with flow visualization experiments is given, and we find that the processes dominating the early stages of the mixing-layer development can be understood in terms of essentially inviscid vortex dynamics.

A study of forces, circulation and vortex patterns around a circular cylinder in oscillating flow

Abstract: Measurements of sectional and total forces and the spanwise correlation of vortex shedding are presented for a circular cylinder in planar oscillatory flow at Keulegan-Carpenter numbers, KC, in the range from about 4 to 55. The viscous parameter β is in the range from around 100 to 1665. Circulation measurements around a circuit close to and enclosing the cylinder, are also presented. A mode-averaging technique was used for both sectional forces and circulation measurements and this gave, for typical modes of vortex shedding, time histories over an average cycle. The transverse force and the circulation tend to fluctuate in sympathy with each other, except around the instant of flow reversal when the force changes sign but the circulation remains high. Values of the strength of shed vortices, estimated from the measured circulation, are found to be comparable with steady-flow results. For KC [lsim ] 30, modes of vortex shedding occur over distinct ranges of KC with spanwise correlation high at the centre of a KC-range for a particular mode of shedding but low at the boundaries. Above KC ≈ 30 the correlation is no longer very sensitive to KC and the correlation length is estimated to be equal to 4.65 cylinder diameters. In the transverse vortex-street regime (8 [lsim ] KC [lsim ] 15) the cylinder was found to experience a steady transverse force, the coefficient of which is estimated to be about 0.5 at KC = 14.

An upwind differencing scheme for the time-accurate incompressible Navier-Stokes equations

Abstract: The two-dimensional incompressible Navier-Stokes equations are solved in a time-accurate manner in using the method of pseudocompressibility. Using this method, subiterations in pseudotime are required to satisfy the continuity equation at each time step. An upwind differencing scheme based on flux-difference splitting is used to compute the convective terms. The upwind differencing is biased based on the sign of the local eigenvalue of the Jacobian matrix. Third-order or fifth-order spatial accuracy is maintained throughout the interior grid points. The equations are solved using an implicit line-relaxation scheme. This solution scheme is stable and is capable of running at large time steps in pseudotime, leading to fast convergence for each physical time step. A variety of computed results are presented to validate the present scheme. Results for the flow over an oscillating plate are compared with the exact analytic solution, good agreement is seen. Excellent comparison is obtained between the computed solution and the analytical results for inviscid channel flow with an oscillating back pressure. Flow solutions over a circular cylinder with vortex shedding are also presented. Finally, the flow past an airfoil at -90 deg angle-of-attack is also computed.

A note on vortex shedding from axisymmetric bluff bodies

Abstract: The linear parallel and incompressible stability of a family of axisymmetric wake profiles is studied in the range of Reynolds numbers where helical vortex shedding from bluff bodies of revolution is observed The family of mean flow profiles allows for the variation of the wake depth as well as for a variable ratio of wake width to mixing-layer thickness It is found that, even without reverse flow, the first helical mode is absolutely unstable in the near wake for Reynolds numbers, based on wake diameter and free-stream velocity, in excess of 33 × 103 A survey of the region of local absolute instability as a function of profile parameters and Reynolds number suggests that the large-scale helical vortex shedding, which is observed between Reynolds numbers of 6000 and 3 × 105 for spheres, may be ‘driven’ by a self-excited oscillation in the near wake

Moving wall effects in unsteady flow

Abstract: L'effet de paroi mobile est present aussi bien dans les ecoulements bidimensionnels que tridimensionnels. Influence sur le decollement des couches limites laminaires et turbulentes et sur la transition des couches limites

Nonlinear dynamics of the wake of an oscillating cylinder.

Abstract: The wake of an oscillating cylinder at low Reynolds numbers is a nonlinear system in which a limit cycle due to natural vortex shedding is modulated, generating in phase space a flow on a torus. We experimentally show that the system displays Arnol'd tongues for rational frequency ratios, and approximates the devil's staircase along the critical line. The ``singularity spectrum'' as well as spectral peaks at various Fibonacci sequences accompanying quasiperiodic transition to chaos shows that the system belongs to the same universality class as the sine circle map.

Phenomena of vortex shedding and flow interference of three cylinders in different equilateral arrangements

Abstract: This paper describes how the flows around three equal circular cylinders arranged in an equilateral-triangular manner interact at different angles of incidence and spacing ratios. Some vortex-shedding-frequency data evaluated from flow visualisation experiments conducted at Reynolds numbers of 2.1 x 10E3 and 3.5 x 10E3, based on the diameter of a single cylinder, using a dye-injection technique, are presented. In order to provide additional insight to the understanding of the flow structure around this particular cylinder array, some photographs indicating the typical flow patterns for various arrangements are also presented. The investigation indicates that the flows interact in a complex fashion for spacing ratios smaller than 2.29 and it also reveals that, at this range of spacing ratios, bistable flow characteristic exists. Moreover, for spacing ratios approximately smaller than 4.65 there always exists an angle at which the vortex shedding behind an upstream cylinder is suppressed by a nearest downstream cylinder. This angle is found not to remain constant but increases as the spacing ratio increases. For illustration and comparisons, some numerical results obtained from the application of the surface-vorticity method have also been presented.

Resonant sound caused by flow past two plates in tandem in a duct

Abstract: Two plates placed in tandem in a duct flow shed vortices, which can excite and sustain an acoustic resonance associated with the duct. The sound can in turn ‘feed back’ and ‘lock’ the vortex shedding rate to the sound frequency. The experimental conditions under which loud resonant sound is sustained are described in this paper. The acoustic sources are predicted by combining a vortex model of the flow field with a finite-element solution of the sound field, and then using Howe’s theory of aerodynamic sound to calculate the energy exchange between the flow and the sound field. Only in certain regions near the plates is substantial net energy exchange possible; the direction of energy transfer depends on the spacing of the plates. The region around the trailing edge of the upstream plate is found to be always a net acoustic source during resonance, while the region around the downstream plate is a net source or sink depending on the phase of the acoustic cycle at which vortices arrive there, which in turn depends on plate spacing and flow velocity. The net source region around the downstream plate is suppressed over a wide range of plate spacings by splitting this plate at midspan and rejoining it so that one half is offset in the flow direction by the distance a vortex travels in half a sound cycle.

The structure of a shear layer bounding a separation region. part 2: effects of free-stream turbulence

Abstract: Detailed measurements throughout the separated region behind a flat plate placed normal to a turbulent stream are reported. A long, central, downstream splitter plate prevented vortex shedding and led to a relatively extensive reversed flow region. Mean flow and turbulence data are compared with results obtained in the (nominal) absence of free-stream turbulence, and attention is concentrated on the changes in the shear-layer structure resulting from the different nature of the upstream flow. Many aspects of the results confirm those obtained recently by other workers. Free-stream turbulence enhances shear-layer entrainment rates, reduces the distance to reattachment and modifies the relatively low-frequency ‘flapping’ motion of the shear layer. In addition, however, extensive use of pulsed wire anemometry has allowed detailed measurements of the turbulence structure throughout the flow and it is shown that this is also modified significantly by the stream turbulence.

Effect of vortex shedding on the coupled roll response of bodies in waves

Abstract: Hydrodynamic damping of floating bodies is due mainly to wave radiation and viscous damping. The latter is particularly important in controlling those responses of the body for which the wave damping is small. The roll response of ship hulls near resonance in beam seas is an example of this. The present paper applies a discrete vortex method as a local solution to model vortex shedding from the bilges of a barge hull of rectangular cross-section and hence provides an analytic method for predicting its coupled motions in three degrees of freedom, including the effects of the main component of viscous damping. The method provides a frequency-domain solution satisfying the full linearized boundary conditions on the free surface.

Vortex flowmeter transducer

Abstract: A vortex flowmeter including a differential pressure transducer with high common mode rejection. No diaphragms are required. A relatively thick machined recess at one end of the vortex shedding body concentrates and transmits the vortex shedding differential pressure to strain transducers located outside the fluid flow conduit. Embodiments are disclosed in which piezoelectric elements and reflective optical fibers are used as strain transducers. The described arrangements allow the mechanical clamping of the transducers and their easy removal without a flow shut down. The shedder shape is optimized in relation to the differential transducer to strengthen the shed vortices and improve the linearity and repeatability of the meter.

A Hydrodynamic Study of the Oscillation Motion in Swimming

Abstract: The purpose of this study was to determine the validity of the quasi-static assumption—that fluid forces exerted under unsteady flow conditions are equal to those exerted under similar steady flow conditions—in the case of a cylindrical model oscillating in a vertical plane about a transverse axis normal to the flow. The findings indicated that the quasi-static approach is applicable only to cyclic motions with low frequencies and small accelerations. For swimming motions that involve high frequencies and high accelerations, like those that occur in competitive swimming, the vortex shedding effect and the added mass effect must be taken into account if accurate values are to be obtained for hydrodynamic forces.