D. Rockwell

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

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

On vortex formation from a cylinder. Part 1. The initial instability

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.

Flow structure from an oscillating cylinder Part 2. Mode competition in the near wake

Un cylindre circulaire soumis a des oscillations forcees sous un angle α par rapport au courant libre presente un grand nombre de modes admissibles de formation de tourbillons synchronisee avec le mouvement du corps. Ces modes sont classes en deux groupes: mode symetrique et mode antisymetrique de formation

A combined direct numerical simulation-particle image velocimetry study of the turbulent near wake

We investigate the near wake of a cylinder at values of Reynolds number corresponding to the onset and development of shear-layer instabilities. By combining quantitative experimental imaging (particle image velocimetry, PIV) and direct numerical simulations at Re = 3900/4000 and 10 000, we show that the flow structure is notably altered. At higher Reynolds number, the lengths of both the wake bubble and the separating shear layer decrease substantially. Corresponding patterns of velocity fluctuations and Reynolds stress contract towards the base of the cylinder. The elevated values of Reynolds stress at upstream locations in the separated layer indicate earlier onset of shear-layer transition. These features are intimately associated with the details of the shear-layer instability, which leads to small-scale vortices. The simulated signatures of the shear-layer vortices are characterized by a broadband peak at Re = 3900 and a broadband high spectral-density ‘plateau’ at Re = 10 000 in the power spectra. The shear-layer frequencies from the present direct numerical simulations study agree well with previous experimentally measured values, and follow the power law suggested by other workers.

The organized nature of flow impingement upon a corner

Oscillations of impinging flows, which date back to the jet-edge phenomenon (Sondhaus 1854), have been observed for a wide variety of impingement configurations. HOWever, alteration of the structure of the shear layer due to insertion of an impingement edge (or surface) and the mechanics of impingement of vortical structures upon an edge have remained largely uninvestigated. In this study, the impingement of a shear layer upon a cavity edge (or corner) is examined in detail. Water is used as a working fluid and laser anemometry and hydrogen bubble flow visualization are used to characterize the flow dynamics. Reynolds numbers (based on momentum thickness at separation) of 106 and 324 are employed. Without the edge, the shear layer produces the same sort of non-stationary (variable) velocity autocorrelations observed by Dimotakis & Brown (1976). When the edge is inserted, the organization of the flow is dramatically enhanced as evidenced by a decrease in variability of autocorrelations and appearance of well-defined peaks in the corresponding spectra. This enhanced organization is not locally confined to the region of the edge but extends along the entire length of the shear layer, thereby reinforcing the concept of disturbance feedback. Comparison of spectra with and without insertion of the edge reveals a remarkable similarity to those of a non-impinging shear layer with and without application of sound at a discrete frequency (Browand 1966; Miksad 1972); with enhanced organization at the fundamental frequency, simultaneous enhancement occurs also at the sub - and higher - har monics . Visualization of the vortical structures in the vicinity of the impingement edge shows that an impinging structure may experience one of three possible events: complete clipping, whereby the structure is swept down into the cavity; partial clipping, which results in severing of the vortex; or escape, involving deformation of the vortex while it is swept (intact) downstream past the edge. In general, no one of these events persisted continuously over a long period, but tended to occur alternately, meaning that ‘jitter’ of an impinging structure occurs. Plots of paths of these structures versus time showed that the convective speed of the vortex was locally influenced a distance of about four momentum thicknesses upstream of impingement, which is less than the estimated diameter of an impinging vortical structure. Furthermore, this upstream influence of the edge is also evident in the distributions of transverse velocity. Laser measurements indicate that the presence of the edge substantially increases the local value of transverse velocity fluctuation in the region immediately upstream of the edge.

ON SECONDARY VORTICES IN THE CYLINDER WAKE

The wake of a circular cylinder is investigated for Reynolds numbers between 160 and 500 by means of particle image velocimetry (PIV). For the first time cross‐stream velocity fields are determined for two classes of secondary vortices (A‐mode and B‐mode). The circulation of the A‐mode secondary vortices in this plane is approximately twice the circulation of the B‐mode secondary vortices. The spanwise wavelength of the secondary vortices is four to five cylinder diameters for the A‐mode and one diameter for the B‐mode. The spatio‐temporal development of the wake is analyzed by acquiring a time sequence of PIV images covering several Karman periods. On the basis of the vorticity field, the A‐ and B‐modes can be identified as topologically different vortex structures. Two vortex models are developed to explain the differences between these modes.

High image-density particle image velocimetry using laser scanning techniques

Laser scanning, corresponding to time-dependent deflections of laser beam across a field of interest, can provide relatively high illumination intensity of small particles, thereby allowing implementation of high image-density particle image velocimetry (PIV). Scanning techniques employing a rotating (multi-faceted) mirror, an oscillating mirror, and an acousto-optic deflector are addressed. Issues of illumination intensity and exposure, rate of scan of the laser beam, and retrace time of the scanning beam are assessed. Representative classes of unsteady separated flows investigated with laser-scanning PIV are described.

Timing of vortex formation from an oscillating cylinder

The instantaneous structure of the near‐wake of a cylinder subjected to forced oscillations is examined using particle imaging, which leads to representations of the streamline patterns and distributions of vorticity. As the frequency of excitation of the cylinder is increased relative to the inherent vortex formation frequency, the initially formed concentration of vorticity moves closer to the cylinder until a limiting position is reached; at this position, the vorticity concentration abruptly switches to the opposite side of the cylinder. This process induces abrupt changes of the topology of the corresponding streamline patterns; such topological patterns alone, however, do not properly suggest the existence and rearrangement of the vorticity concentrations. Moreover, this vorticity‐switching concept persists to high values of Reynolds number, where the values of the mean base pressure coefficient and vortex formation length differ substantially from those at low Reynolds number. The switching mechani...

Flow past a cylinder close to a free surface

Flow past a cylinder beneath a free surface gives rise to fundamental classes of nearwake structure that are distinctly different from the wake of a completely submerged cylinder. A central feature is the generation of a vorticity layer from the free surface due to: localized separation, in the form of small-scale breaking of a free-surface wave; or complete separation from the free surface. This vorticity layer appears adjacent to a layer from the surface of the cylinder, thereby forming a jet-like flow. It is shown that the instantaneous vorticity flux on either side of this jet is rapidly balanced immediately after the onset of separation from the free surface.

Evolution of a quasi-steady breaking wave

The stages of evolution of a quasi-steady breaker from the onset of a capillary pattern to a fully evolved breaking wave are characterized using high-image-density particle image velocimetry, which provides instantaneous representations of the free surface and the patterns of vorticity beneath it. The initial stage, which sets in at a low value of Froude number, involves a capillary pattern along each trough-crest surface of a quasi-stationary wave. The successive crests of the capillary pattern exhibit increasing scale and culminate in a single largest-scale crest of the free surface. Immediately upstream of the large-scale crest, the capillary pattern shows counterclockwise concentrations of vorticity at its troughs and regions of clockwise vorticity beneath its crests. The onset of the final, largest-scale crest exhibits two basic forms : one involving no flow separation; and the other exhibiting a small-scale separated mixing layer. At an intermediate value of Froude number, a breaker occurs and the capillary pattern is replaced by large-scale distortions of the free surface. The onset of separation, which involves flow deceleration along a region of the free surface having a large radius of curvature, leads to formation of a long mixing layer, which has substantial levels of vorticity. Downstream of this breaker, the long-wavelength wave pattern is suppressed. At the largest value of Froude number, the onset of flow separation rapidly occurs in conjunction with an abrupt change in slope of the surface, giving rise to vorticity concentrations in the mixing layer.