Vortex Dislocations Research Articles

Three-dimensional study of flow past a square cylinder at low Reynolds numbers

The spatial evolution of vortices and transition to three-dimensionality in the wake of a square cylinder have been numerically studied. A Reynolds number range between 150 and 500 has been considered. Starting from the two-dimensional Kármán vortex street, the transition to three-dimensionality is found to take place at a Reynolds number between 150 and 175. The three-dimensional wake of the square cylinder has been characterized using indicators appropriate for the wake of a bluff body as described by the earlier workers. In these terms, the secondary vortices of Mode-A are seen to persist over the Reynolds number range of 175–240. At about a Reynolds number of 250, Mode-B secondary vortices are present, these having predominantly small-scale structures. The transitional flow around a square cylinder exhibits an intermittent low frequency modulation due to the formation of a large-scale irregularity in the near-wake, called vortex dislocation. The superposition of vortex dislocation and the Mode-A vortices leads to a new pattern, labelled as Mode-A with dislocations. The results for the square cylinder are in good accordance with the three-dimensional modes of transition that are well-known in the circular cylinder wake. In the case of a circular cylinder, the transition from periodic vortex shedding to Mode-A is characterized by a discontinuity in the Strouhal number–Reynolds number relationship at about a Reynolds of 190. The transition from Mode-A to Mode-B is characterized by a second discontinuity in the frequency law at a Reynolds number of ≈250. The numerical computations of the present study with a square cylinder show that the values of the Strouhal number and the time-averaged drag-coefficient are closely associated with each other over the range of Reynolds numbers of interest and reflect the spatial structure of the wake.

The effects of wall proximity on vortex shedding from a square cylinder: Three-dimensional effects

The three-dimensional nature of turbulent vortex shedding from a square cylinder in the vicinity of a solid wall is investigated for a Reynolds number of 18 900 as a function of the gap height, S/D. Spanwise surface pressure measurements on the cylinder faces and on the solid wall are complemented by velocimetry data. It is observed that parallel and oblique shedding modes arise naturally. The number of vortex dislocations is clearly related to the variations in the oblique shedding angle. Dislocations occur with increasing probability as the gap height is decreased to S/D≈0.7. The dislocations are strongly associated with Type A instabilities and vortex splitting, which contribute significantly to phase-jitter. For gap heights close to that for vortex shedding suppression (0.5<S/D<0.7), dislocations occur less frequently. The vortex formation process is increasingly two-dimensional in this range, resulting in strong spanwise correlations and lower phase-jitter. These changes are observed as more sharply peaked frequency spectra, which have been interpreted as shedding frequency “tuning” in earlier studies.

Control of a coupled map lattice model for vortex shedding in the wake of a cylinder

The flow behind a vibrating flexible cable at low Reynolds numbers can exhibit complex wake structures such as lace-like patterns, vortex dislocations and frequency cells. These structures have been observed in experiments and numerical simulations, and are predicted by a previously developed low-order coupled map lattice (CML). The discrete (in time and space) CML models consist of a series of diffusively coupled circle map oscillators along the cable span. Motivated by a desire to modify the complex wake patterns behind flexible vibrating cables we have studied the addition of control terms into the highly efficient CML models and explored the resulting dynamics. Proportional, adaptive proportional and discontinuous non-linear (DNL) control methods were used to derive the control laws. The first method employed occasional proportional feedback. The adaptive method used spatio-temporal feedback control. The DNL method used a discontinuous feedback linearization procedure, and the controller was designed for the resulting linearized system using eigenvalue assignment. These techniques were applied to a modeled vortex dislocation structure in the wake of a vibrating cable in uniform freestream flow. Parallel shedding patterns were achieved for a range of forcing frequency-forcing amplitude combinations studied to validate the control theory. The adaptive proportional and DNL methods were found to be more effective than the proportional control method due to the incorporation of a spatially varying feedback gain across the cylinder span. The DNL method was found to be the most efficient controller of the low-order CML model. The required control level across the cable span was correlated to the 1/1 lock-on behavior of the temporal circle map.

OBLIQUE VORTEX SHEDDING BEHIND TAPERED CYLINDERS

The vortex shedding in the wake behind linearly tapered circular cylinders has been considered for the two taper ratios 75:1 and 100:1. The Reynolds number based on the velocity of the incoming flow and the largest diameter was in the range from 130 to 180. The low Reynolds number assured that laminar flow prevailed in the entire flow field. The full unsteady three-dimensional Navier–Stokes equations were solved numerically with the view of exploring the rather complex vortex shedding phenomena caused by the variation of the natural shedding frequency along the span of the cylinder. The accurate computer simulations showed that this variation gave rise to discrete shedding cells, each with its own characteristic frequency and inclined with respect to the axis of the cylinder. Flow visualizations revealed that vortex dislocation and splitting took place in the numerically simulated flow fields. The computer simulations compared surprisingly well with the extensive laboratory experiments reported by Piccirillo & Van Atta in 1993 for a range of comparable conditions; this has enabled detailed analyses of other flow variables (notably pressure and vorticity) than those readily accessible in a physical experiment. However, distinct differences in the vortex dynamics are observed in some of the cases.

Study of Vortex Dislocations in the Wake of a Flat Plate with Finite Thickness

Wake structures of a flat plate with finite thickness are studied using the rake of X-wires techniques. Parallel and oblique shedding modes in the wake flow are investigated. These modes depend on the flat plate end conditions. In the present paper, we demonstrate that manipulation of the end conditions yields vortex dislocations that appear at the same location. By manipulating the end conditions, vortex chain structures branching inside the dislocations are analyzed by means of pseudo-flow visualization of the X-wire rake data. The appearance of branching vortex chains is due to misfit between two oblique vortex shedding cells. Power spectra of velocity fluctuations show growth of the low-frequency mode due to subtraction of the two fundamental shedding modes of different frequency across the span. The small difference between the two fundamental shedding modes explains the large intermittent velocity irregularities in the large-scale structure downstream that occur in natural transition.

Generation of large-scale vortex dislocations in a three-dimensional wake-type flow

Numerical study of three-dimensional evolution of wake-type flow and vortex dislocations is performed by using a compact finite diffenence-Fourier spectral method to solve 3-D incompressible Navier-Stokes equations. A local spanwise nonuniformity in momentum defect is imposed on the incoming wake-type flow. The present numerical results have shown that the flow instability leads to three-dimensional vortex streets, whose frequency, phase as well as the strength vary with the span caused by the local nonuniformity. The vortex dislocations are generated in the nonuniform region and the large-scale chain-like vortex linkage structures in the dislocations are shown. The generation and the characteristics of the vortex dislocations are described in detail.

Successive stages and the role of natural vortex dislocations in three-dimensional wake transition

The time-history of the development of the three-dimensional transition features in a nominally two-dimensional flow configuration is established for Reynolds number 220 in a cylinder wake. The identification of the successive stages that evolve very fast during experiments is possible by means of direct numerical simulation. The physical processes related to the creation of streamwise and vertical vorticity components and their impact on the spanwise waviness of the main von Kármán vortex filaments are analysed by means of the Craik–Leibovich shearing instability mechanism and a comparative discussion is given with respect to the elliptic stability theory. This study proves the existence of a further stage in the three-dimensional transition, which substantially modifies the regular spanwise undulation. This is a systematic and repetitive development of natural vortex dislocations in the near wake. The definition of this kind of structure is provided, as well as its properties related to a drastic reduction of the fundamental frequency and to the selection of a lower path in the Strouhal–Reynolds number relation. The induced amplitude modulation of the flow properties along the span is also evaluated. Quantification of these properties is carried out by using wavelet analysis and autoregressive modelling of the time series. The reasons for the development of natural vortex dislocations are analysed and related to specific modulations of the spanwise structure of the longitudinal velocity upstream separation. From this part of the study an optimum shape for the spanwise distribution of this component can be specified, able to trigger the vortex dislocations in wake flows and therefore useful to apply in the context of stability theory analyses and in further DNS studies.

VORTEX DISLOCATIONS AND FORCE DISTRIBUTION OF LONG FLEXIBLE CYLINDERS SUBJECTED TO SHEARED FLOWS

We present DNS results of vortex-induced vibrations (VIV) of flexible cylinders with aspect ratio greater than 500, subjected to linear and exponential sheared flows. The maximum Reynolds number is Rem=1000 resulting in a turbulent near-wake. The first case corresponds to lock-in of the third mode (n=3), while the second case is a multi-mode response with excited modes as high as n=12 and 14. We observed vortex dislocations similar to the structures visualized in experiments for stationary cylinders, and obtained corresponding force distributions. Strong vortex dislocations can result in substantial modulation of the forces on the body, and such effects have to be taken into account when constructing low-dimensional predictive models.

Computation of three-dimensional flows past circular cylinder of low aspect ratio

Results are presented for finite element simulation of three-dimensional unsteady flows past cylinders of low aspect ratio. The end-conditions are specified to model the effect of a wall that may correspond to the flow in a wind tunnel, water channel or a tow-tank experiment with a cylinder having large end-plates. Results are computed for Reynolds number 100, 300, and 1000 for a cylinder of aspect ratio 16. The computations confirm that it is the end conditions for the finite cylinder that determine the mode of vortex shedding (parallel or oblique). Preliminary results for Re=106 flow past a cylinder of aspect ratio 8 are also presented. The Re=100 and 1000 flows exhibit oblique mode of vortex shedding. The flow for Re=100 is very organized, devoid of any vortex dislocations and is associated with only one cell along the cylinder span. The flow at Re=1000 is interspersed with vortex dislocations and the vortex shedding angle varies, both, temporally and spatially. The presence of vortex dislocations is responsible for the breakdown of spanwise coherence of vortex structures. Mode B pattern of vortex shedding is observed. Flow at Re=300 results in flow patterns that correspond to the wake transition regime. Mode A and Mode B patterns of vortex shedding in addition to vortex dislocations are observed at different time instants. The present results indicate that the wake transition regime, that is known to occur in the Re range 190–250 for large aspect-ratio cylinders, is either extended and/or delayed for a cylinder of small aspect ratio with “no-slip” walls.

Study of Vortex Dislocations in the Wake of a Flat Plate with Finite Thickness.

Wake structures of a flat plate with finite thickness are studied using the rake of X-wires techniques. Parallel and oblique shedding modes in the wake flow are investigated. These modes depend on the flat plate end conditions. In the present paper, we demonstrate that manipulation of the end conditions yields a vortex dislocation that appears periodically at the same location. Vortex linkup dynamics phenomena in the dislocations are observed with smoke-wire flow visualization. Flow patterns of dislocation are analyzed by mean of the pseudo-flow visualization of the rake data. The linkup structure due to a misfit of two oblique shedding vortices appears periodically in the flow patterns. Evolutions of the power spectra of velocity fluctuations explain the generation of large-scale turbulent structure downstream due to the growth of a low-frequency mode and the cascade process of low/high frequency components.

The 3D Transition to Turbulence in Wake Flows by Means of Direct Numerical Simulation

The three-dimensional transition to turbulence in flows around bodies of non-rectangular configuration has been analysed physically by performing direct numerical simulation to solve the system of Navier-Stokes equations. The successive stages of 3D transition, beyond the first bifurcation, have been detected first in the incompressible regime, for a circular cylinder configuration. The generation of streamwise vorticity, organised according to spanwise periodic cells has been associated with the development of large-scale coherent spanwise undulations of the originally rectilinear (nominally 2D) alternating vortex rows. The wavelengths of these undulations have been determined as a function of Reynolds number. As this parameter increases, a further inherent change of the flow transition is obtained and analysed, the natural vortex dislocations pattern. Beyond this change, the increase of Reynolds number yields an abrupt shortening of the spanwise wavelength and the flow undergoes another transition step, whose critical Reynolds number is evaluated by the present DNS approach in association with the Ginzburg-Landau model. Therefore, the linear and non-linear parts of the flow transition have been quantified by means of the amplitude evolution versus time obtained by the present DNS, in conjunction with the mentioned global oscillator model.

Vortex pinning by Ni point defects inBi2Sr2Ca(Cu1−xNix)2O8+δsingle crystals

We study the vortex pinning of ${\mathrm{Bi}}_{2}{\mathrm{Sr}}_{2}{\mathrm{CaCu}}_{2}{\mathrm{O}}_{8+\ensuremath{\delta}}$ (Bi2212) single crystals doped with up to 2 at. % of Ni atoms on the Cu position using measurements of the dynamic magnetic relaxation. We find that below an optimum Ni-doping level of about 1 at. % the thermal activation energy for vortex creep and the critical current density definitely increase with the Ni concentration. This proves that Ni point defects contribute to the pinning forces, as expected within the theory of weak collective pinning. At higher Ni concentrations we observe a strong decrease of the activation energy, probably caused by an overlap of the vortex potentials from neighboring Ni sites. The dynamic behavior of the vortex system at low temperatures and magnetic fields is dominated by elastic creep of single vortices whereas at higher temperatures and fields plastic creep of vortex dislocations becomes dominant. The phase with plastic creep grows in the $(B,T)$ plane with increasing strength of the collective pinning forces.

Direct observation of the interaction between a vortex lattice and dislocations in a superconducting Nb crystal

Using a cryo-Lorentz electron microscope, we have succeeded in observing directly the interaction between a vortex lattice and dislocations in a Nb film, to which magnetic fields were externally applied up to 200 G at 5 K. At 100 G, vortices were clearly pinned by dislocations and a vortex lattice was locally formed around the pinned sites. Its extension and the density of the vortices increase with the increase of magnetic-field strength to form “the Abrikosov lattice.” At 200 G, it is not perfect yet but consists of “domains” with disordered areas at their boundaries. When the specimen temperature was raised above the critical temperature (9.2 K), with keeping the magnetic field at 200 G, the vortex lattice disappeared. When the temperature was successively decreased back to 5 K, a similar vortex lattice appeared again but with a slightly changed orientation. The reorientation suggests that the interaction between vortices and dislocations pinning them is rather weak.

A low-order model for vortex shedding patterns behind vibrating flexible cables

A recent focus in studies of vortex shedding behind circular cylinders has been on the use of low-order dynamical systems such as circle maps to predict wake dynamics. These purely temporal models have been limited by their inability to describe three-dimensional spatial flow variations along the cylinder span, a hallmark of transitional flows such as the cylinder wake. In the present work this limitation is overcome through development of a spatial-temporal map lattice which utilizes a series of coupled circle map oscillators along the cylinder span. This model allows for the study of vortex shedding patterns and wake dynamics behind vibrating flexible cables. Required input for the model includes the forcing frequency, amplitude, mode shape, aspect ratio and wavelength of the cable, Reynolds number, vortex convection velocity, and various phase angles. Model output parameters studied in this work include vortex shedding patterns and wake response frequency. Standing wave mode shapes and traveling waves along the cable span are modeled. Lacelike vortex patterns are observed for the standing wave case. A physical mechanism for the lacelike patterns is postulated. For traveling waves oblique shedding patterns are confirmed. Nonharmonic forcing outside the classical lock-on region yields vortex dislocation patterns in the wake. Honeycomb patterns are also observed for higher-order mode shapes at large forcing amplitudes. The current work establishes a new class of models based on circle maps for modeling spatially varying cylinder wakes.

Potential and vortex features of optical speckle fields and visualization of wave-front singularities

The feasibility of noninterferometric methods to measure phase distribution in a laser beam cross section for visualization of the vortex dislocations of an optical speckle-field wave front is analyzed. Peculiarities of the phase retrieved from the measured intensity distribution (the phase problem in optics) and from the wave-front slopes measured by a Hartmann sensor are discussed. A concept of the vortex and the potential parts of the phase is introduced. An analytic formula to retrieve the potential phase from the measured intensity has been obtained. We show that the considered means of measurements allow the positions of the dislocation centers to be sensed and the spatial configuration of the intensity zero lines to be reconstructed.

Experimental study of cellular shedding vortices behind a tapered circular cylinder

The dynamic behavior of shedding vortices in turbulent wake behind a tapered circular cylinder is experimentally studied by hot-wire measurements in a low-speed wind tunnel. Four tapered cylinders with the same fineness ratio but different tapered ratio are used in the investigations. The Reynolds number based on the cylinder's mean diameter ranges from 4.0×10 3 to 1.4×10 4. Data show that two to three constant-frequency vortex cells of the shedding vortices along the spanwise direction are observed in the operating Reynolds number range. The corresponding Strouhal number based on the vortex shedding frequency and the cylinder's local diameter varies with respect to the taper ratio of the cylinder. It is also found that most of the spanwise shedding vortices are well aligned across the intersection region of the vortex cells except the vortex dislocation occurs to cause vortex lines discontinuous, in which the phase difference between the adjacent vortex cells jumps from π to − π. By applying the pseudo-visualization technique in conjunction with the peak-valley counting method, a simplified model is proposed to explain the relationship between the velocity modulation and the vortex dislocation.

Developments in the Understanding of Bluff Body Flows.

The understanding of bluff body flows and their prediction are important in many areas of industrial development. The complex nature of these flows provides a challenge to both experimental and computational fluid dynamicists. Some of the more recent advances are reviewed, including the understanding of the near wake region and the instabilities that develop there. The role of vortex dislocations is discussed and it is shown how encouraging their formation can reduce drag. In addition to describing the improved insight that can be provided by computational fluid dynamics, the likely impact of new, non-intrusive measurement techniques is also assessed.

A direct numerical simulation study of flow past a freely vibrating cable

We present simulation results of flow-induced vibrations of an infinitely long flexible cable at Reynolds numbers Re = 100 and Re = 200, corresponding to laminar and early transitional flow states, respectively. The question as to what cable motions and flow patterns prevail is investigated in detail. Both standing wave and travelling wave responses are realized but in general the travelling wave is the preferred response. A standing wave cable response produces an interwoven pattern of vorticity, while a travelling wave cable response produces oblique vortex shedding. A sheared inflow produces a mixed standing wave/travelling wave cable response and chevron-like patterns with vortex dislocations in the wake. The lift force on the cable as well as its motion amplitudes are larger for the standing wave response. At Re = 200, the cable and wake response are no longer periodic, and the maximum amplitude of the cable is about one cylinder diameter, in agreement with experimental results.

Three-dimensional effects in turbulent bluff-body wakes

There has recently been a surge in activity concerning the development of three-dimensionality in the wakes of nominally two-dimensional bluff bodies, yielding the realization that end effects can influence the wake vortex shedding pattern over long spanlengths. Much of this work has been focused on low Reynolds numbers (Re), but virtually no studies have investigated to what extent it is possible to control shedding patterns at higher Reynolds numbers, through the use of end manipulation. In the present paper, we demonstrate that it is possible to induce parallel shedding, oblique shedding and vortex dislocations, by manipulation of the end conditions, over a large range of Reynolds number. Such patterns affect the frequency of primary wake instability and its amplitude of fluctuation, as they do at low Reynolds number, although distinct differences are found at the higher Reynolds numbers.We find that imposition of oblique shedding conditions at high Reynolds number leads to a spatial variation of both the oblique shedding angle and shedding frequency across the span, and to sparse dislocations which are not restricted to the spanwise end regions, as they are at low Reynolds numbers (under similar geometrical conditions). In the wake transition regime (Re=190–250), it is confirmed that the spontaneous appearance of vortex dislocations in mode-A shedding precludes the control of shedding patterns using end manipulation. However, it has proven possible to extend the regime of Reynolds number where dislocations ‘naturally’ exist to Re>250, by introducing them artificially through end control, where they would otherwise not occur. The possibility of introducing dislocations and of inducing oblique vortex shedding at higher Reynolds numbers has practical significance, if one can deliberately decorrelate the vortex shedding, and hence reduce the spanwise-integrated unsteady fluid forces on the body.We confirm the existence of a transition in the mode of shedding at Re≈5000 (originally found by Norberg 1987) under conditions where parallel shedding is attempted. This mode transition displays similarities to an inverse of the mode A→mode B transition that is found in the wake transition regime. It is clear that vortex dislocations occur beyond Re=5000, although it is not clear why the flow is unstable to such a mode. Furthermore, there appears to be some support for the suggestion that vortex dislocations may be a feature of the flow for Re at least up to 30×103, as evidenced by the work of Norberg (1994).

A study of three-dimensional aspects of vortex shedding from a bluff body with a mild geometric disturbance

Experiments have been carried out to study the three-dimensional characteristics of vortex shedding from a half-ellipse shape with a blunt trailing edge. In order to control the occurrence of vortex dislocations, the trailing edges of the models used were constructed with a series of periodic waves across their spans. Flow visualization was carried out in a water tunnel at a Reynolds number of 2500, based on trailing-edge thickness. A number of shedding modes were observed and the sequence of mode transitions recorded. Quantitative data were obtained from wind tunnel measurements performed at a Reynolds number of 40000. Two shedding frequencies were recorded with the higher frequency occurring at spanwise positions coinciding with minima in the chord. At these same positions the base pressure was lowest and the vortex formation length longest. Arguments are put forward to explain these observations. It is shown that the concept of a universal Strouhal number holds, even when the flow is three-dimensional. The spanwise variation in time-average base pressure is predicted using the estimated amount of time the flow spends at the two shedding frequencies.