Transition phenomena in the wake of an inclined square cylinder

The division of flow regimes in a square cylinder wake at various angles of attack (α) is studied. This study provides evidence of the existence of modes A and B instabilities in the wake of an inclined square cylinder. The critical Reynolds numbers for the inception of these instability modes were identified through the determination of discontinuities in the Strouhal number versus Reynolds number curves. The spectra and time traces of wake streamwise velocity were observed to display three distinct patterns in different flow regimes. Streamwise vortices with different wavelengths at various Reynolds numbers were visualized. A PIV technique was employed to quantitatively measure the parameters of wake vortices. The wavelengths of the streamwise vortices in the modes A and B regimes were measured by using the auto-correlation method. From the present investigation, the square cylinder wake at various angles of attack undergoes a similar transition path to that of a circular cylinder, although various quantitative parameters measured which include the critical Reynolds numbers, spanwise wavelength of secondary vortices, and the circulation and vorticity of wake vortices all show an α dependence.     

Transition phenomena in the wake of a square cylinder

The transition phenomena in the wake of a square cylinder were investigated. The existence of mode A and mode B instabilities in the wake of a square cylinder was demonstrated. The critical Reynolds numbers for the inception of these instability modes were identified through the determination of discontinuities in the St–Re curves, and were found to have mean values of 160 and 204 for the onset of mode A and B instabilities, respectively. The spectra and time traces of the wake streamwise velocity component were found to display three distinct patterns in laminar, mode A and mode B flow regimes. Streamwise vortices with different wavelength at various Reynolds numbers were observed through different measures. The symmetries and evolution of the secondary vortices were observed using laser-induced-fluorescent dye. It was found that, just like the case of a circular cylinder, the secondary vortices from the top and bottom rows were out-of-phase with each other in the mode A regime, but in-phase with each other in the mode B regime. From the flow visualization, it was qualitatively proven that there is stronger interaction between braid regions in the mode B regime. At the same time, analysis of PIV measurements quantitatively demonstrated the presence of the stronger cross flow in mode B regime when compared to the mode A regime. It suggests that the in-phase symmetry of the mode B instability is the result of strong interaction between the top and bottom vortex rows. It was also observed that although the vorticity of the secondary vortices in the mode A regime was smaller, its circulation was more than twice that of mode B instability. Compared to primary vortices, the circulations of both mode A and mode B vortices were much smaller, which indicates that the secondary vortices most likely originate from the primary vortices. The wavelengths of the streamwise vortices in the mode A and B regimes were measured using the auto-correlation method, and were found to be 5.1 (±0.1)D, 1.3 (±0.1)D, and 1.1 (±0.1)D at Re=183 (mode A), 228 and 377 (both mode B), respectively. From the present investigation, mode A instability was likely to be due to the joint-effects of the deformation of primary vortex cores and the stretching of vortex sheets in the braid region. On the other hand, mode B instability was thought to originate from the “imprinting” process.     

NUMERICAL RESEARCH ON THE COHERENT STRUCTURES IN A MIXING LAYER WITH CROSS-SHEAR

The evolution of a time-developing mixing layer with cross-shear is simulated numerically using a pseudo-spectral method. The results indicate that stretching by the rollers is responsible for the formation of the streamwise vortices in a mixing layer with cross-shear. When the cross-shear is relatively strong (such as θ=20°), the co-rotating streamwise vortices related to the early spanwise Kelvin–Helmholtz instability are intensified rapidly by stretching and collapse into rib-shaped vortices, which are very similar to the ribs in a plane mixing layer. Atθ =20°, the vortex corresponding to the “quadrupole” in a plane mixing layer is also observed in the core region, and a set of streamwise vortices with signs opposite to those of the vortices containing the ribs lie at the spanwise braid region. The counterparts of the ribs, however, are of flat shape and much weaker. When θ is up to 30°, the ribs are so strong that their counterparts cannot develop. When θ is down to 10°, the symmetry of the streamwise vortices is more obvious, but the ribs do not form. Additionally, it is revealed that the introduction of the strong cross-shear results in enhanced mixing compared to a two-dimensional mixing layer.     

On the study of vortex-induced vibration of a cylinder with helical strakes

While the effect of helical strakes on suppression of Vortex-Induced Vibrations (VIV) has been studied extensively, the mechanism of VIV mitigation using helical strakes is much less well documented in the literature. In the present study, a rigid circular cylinder of diameter d=80 mm attached with three-strand helical strakes of dimensions of 10d in pitch and 0.12d in height was tested in a wind tunnel. It was found that the helical strakes can reduce VIV by about 98%. Unlike the bare cylinder, which experiences lock-in over the reduced velocity in the range of 5-8.5, the straked cylinder does not show any lock-in region. In exploring the mechanism of VIV reduction by helical strakes, measurements in stationary bare and straked cylinder wakes using both a single X-probe at four different Reynolds numbers, i.e. Re=10 240, 20 430, 30 610 and 40 800, and two X-probes with variable separations in the spanwise direction at Re=20 430 were conducted. It was found that vortices shed from the straked cylinder are weakened significantly. The dominate frequency varies by about 30% over the range of x/d=10-40 in the streamwise direction while that differs by about 37.2% of the averaged peak frequency over a length of 3.125d in the spanwise direction. The latter is supported by the phase difference between the velocity signals measured at two locations separated in the spanwise direction. The correlation length of the vortex structures in the bare cylinder wake is much larger than that obtained in the straked cylinder wake. As a result, the straked cylinder wake agrees more closely with isotropy than the bare cylinder wake. Flow visualization on the plane perpendicular to the cylinder axis at Reynolds number of about 300 reveals small-scale vortices in the shear layers of the straked cylinder wake. However, these vortices do not roll up and interact with each other to form the well-organized Karman-type vortices. Flow visualization on the plane parallel to the cylinder axis shows vortex dislocation and swirling flow, which should be responsible for the variations of the peak frequency in the streamwise as well as spanwise directions.     

Wall proximity effects on the effectiveness of upstream control rod

Two dimensional flow over a circular cylinder with an upstream control rod of same diameter is simulated in unbound condition and in wall bounded conditions. The cylinders are placed at various heights from the wall and the inter-distance between cylinders is also varied. The control rod is subjected to different rotation rates. It is found that, in unbound condition, rotating the control rod decreases the critical pitch length (S/D_cr) and increases the drag and Strouhal number of the main cylinder. In presence of plane wall, the shielding provided by the separated shear layers from the control rod in cavity regime is deteriorated due to deflection of shear layers which results in higher drag and large fluctuation of lift coefficient. However, in wake impingement regime, the binary vortices from the control rod are weakened due to diffusion of vorticity and hence, the main cylinder experiences a lower drag and small lift fluctuations than that of unbound condition. The critical height of vortex suppression (H/D_cr) is higher in cavity regime than that of wake impingement regime due to the single extended-bluff body like configuration. The rotation of control rod energizes the wall boundary layer and increases the critical height of vortex suppression. Increasing the rotational rate of control rod decreases the drag force and reduces the amplitude of lift fluctuation. Analysis of the wall shear stress distribution reveals that it suffers a sudden drop at moderate height where the normal Karman vortex shedding changes to irregular shedding consisting of single row of negative vortices. Modal structures obtained from dynamic mode decomposition (DMD) reveal that the flow structures behind the main cylinder are suppressed due to wall and the flow is dominated by the wake of control rod.     

Periodicity of large-scale coherence in turbulent boundary layers

This study examines the pronounced periodicity of large-scale coherent structures in turbulent boundary layers, which are of the order of the boundary layer thickness (δ) and reside in the logarithmic and wake regions. To this end, a series of multi-camera planar particle image velocimetry (PIV) measurements are conducted in a streamwise/spanwise and streamwise/wall-normal planes at a friction Reynolds number of Re_τ ≈ 2500. The experiments are configured to capture a large field-of-view with velocity fields that cover a streamwise extent in excess of 15δ. The resulting vector fields reveal large-scale streamwise and spanwise organisation instantaneously, which is often lost when only examining mean statistics. By extracting the dominant streamwise and spanwise Fourier modes of the large-scale motions, a clearer picture of these structural organisations and coherence is presented. A targeted inspection of these dominant modes reveal that these features remain coherent over a significant fraction of the boundary layer thickness in the wall-normal direction, but only a fraction of them have coherence that extends to the wall (wall-coherent). Further, the spatial extents and the population density of these wall-coherent and wall-incoherent modes are characterised, with the former conforming to the attached eddy arguments of Townsend (1976) and the subsequent attached eddy models. Collectively, through the evidence gathered here, we provide a conceptual picture of the representative large-scale structures in turbulent boundary layers, which are likely to have implications on the type of representative structures to be used in structure-based models for these flows.     

NEAR-WAKE FLOW STRUCTURE OF A CYLINDER WITH A HELICAL SURFACE PERTURBATION

The near-wake of a circular cylinder having a helical wire pattern about its surface is characterized using a technique of high-image-density velocimetry. Patterns of vorticity in three orthogonal planes show substantial influence of a wire having a diameter an order of magnitude smaller than the cylinder diameter. The distinctive patterns of vorticity in these three planes are associated with lack of formation of large-scale Kármán-like clusters of vorticity (ω_z) in the near-wake region of the cylinder. The instantaneous structure of the separating spanwise vorticity (ω_z) layers on either side of the cylinder involve small-scale concentrations of vorticity analogous to the well-known Kelvin–Helmholtz vortices from a smooth cylinder. Moreover, a dual vorticity layer, i.e., two adjacent layers of like vorticity (ω_z), can form from one side of the cylinder. Along the span of the cylinder, distributions of instantaneous velocity and transverse vorticity (ω_y) show a spatially periodic sequence of wake-like patterns, each of which has features in common with the very near-wake of a two-dimensional bluff body, including a large velocity defect bounded by vorticity layers with embedded small-scale vorticity concentrations. In the cross-flow plane of the wake, patterns of streamwise vorticity (ω_x) show small-scale, counter-rotating pairs of vorticity concentrations (ω_x) emanating from the inclined helical perturbation, rather than isolated concentrations of vorticity of like sign, which would indicate single streamwise vortices. All of the aforementioned patterns of small-scale vorticity concentrations are scaled according to the local wake width/local pitch of the helical wire pattern in the respective plane of observation.     

Temporal development of turbulent boundary layers with embedded streamwise vortices

The interaction of streamwise vortices with turbulent boundary layer has been investigated using large-eddy simulation. The initial conditions are a pair of counterrotating Oseen vortices with flow between them directed toward the wall (common-flow-down), superimposed on various instantaneous realizations of a turbulent boundary layer. The time development of the vortices and their interaction with the boundary layer are studied by integrating the filtered Navier-Stokes equations in time. The most important effects of the vortices on the boundary layer are the thinning of the boundary layer between vortices (downwash region) and the thickening of the boundary layer in the upwash region. The vortices first move toward the wall as a result of the self-induced velocity, and then apart from each other because of the image vortices due to the solid wall. The Reynolds stress profiles highlight the highly three-dimensional structure of the turbulent boundary layer modified by the vortices. The presence of significant turbulent activity near the vortex center and in the upwash region suggests that localized instability mechanisms in addition to the convection of turbulent energy by the secondary flow are responsible for this effect. High levels of turbulent kinetic energy and secondary stresses in the vicinity of the vortex center are also observed. The numerical results show good agreement with experimental results.This work was supported by the Office of Naval Research under Grant N00014-89-J-1638. Computer time was supplied by the San Diego Supercomputing Center.     

A bypass wake induced laminar/turbulent transition

The process of laminar to turbulent transition induced by a von Karman vortex street wake, was studied for the case of a flat plate boundary layer. The boundary layer developed under zero pressure gradient conditions. The vortex street was generated by a cylinder positioned in the free stream. An X-type hot-wire probe located in the boundary layer, measured the streamwise and normal to the wall velocity components. The measurements covered two areas; the region of transition onset and development and the region where the wake and the boundary layer merged producing a turbulent flow. The evolution of Reynolds stresses and rms-values of velocity fluctuations along the transition region are presented and discussed. From the profiles of the Reynolds stress and the mean velocity profile, a ‘negative' energy production region along the transition region, was identified. A quadrant splitting analysis was applied to the instantaneous Reynolds stress signals. The contributions of the elementary coherent structures to the total Reynolds stress were evaluated, for several x-positions of the near wall region. Distinct regions in the streamwise and normal to the wall directions were identified during the transition.     

Effect of velocity ratio on the streamwise vortex structures in the wake of a stack

The time-averaged velocity and streamwise vorticity fields within the wake of a stack were investigated in a low-speed wind tunnel using a seven-hole pressure probe. The experiments were conducted at a Reynolds number, based on the stack external diameter, of Re_D=2.3×10⁴. The stack, of aspect ratio AR=9, was mounted normal to a ground plane and was partially immersed in a flat-plate turbulent boundary layer, where the ratio of the boundary layer thickness to the stack height was δ/H≈0.5. The jet-to-cross-flow velocity ratio was varied from R=0 to 3, which covered the downwash, crosswind-dominated and jet-dominated flow regimes. In the downwash and crosswind-dominated flow regimes, two pairs of counter-rotating streamwise vortex structures were identified within the stack wake. The tip vortex pair located close to the free end of the stack, and the base vortex pair located close to the ground plane within the flat-plate boundary layer, were similar to those found in the wake of a finite circular cylinder, and were associated with the upwash and downwash flow fields within the stack wake, respectively. In the jet-dominated flow regime, a third pair of streamwise vortex structures was observed, referred to as the jet-wake vortex pair, which occurred within the jet-wake region above the free end of the stack. The jet-wake vortex pair had the same orientation as the base vortex pair and was associated with the jet rise. The peak vorticity and strength of the streamwise vortex structures were functions of the jet-to-cross-flow velocity ratio. For the tip vortex structures, their peak vorticity and strength reduced as the jet-to-cross-flow velocity ratio increased.     

Mode competition in streamwise-only vortex induced vibrations

Time-resolved Particle-Image Velocimetry (PIV) has been used to study mode competition and transient behaviour in the wake of a cylinder experiencing Vortex-Induced Vibrations (VIV) in the streamwise direction. The cylinder response regime contained two branches, occurring above and below the onset of synchronisation between the wake and the cylinder motion (lock-in). During the first branch, the wake exhibited both the S-I mode (in which two vortices are shed simultaneously per vibration cycle) and the alternate A-II mode (similar to the well known von Kármán vortex street). An extended PIV data set acquired in this region revealed mode switching between the S-I and A-II modes. A criterion based on Proper-Orthogonal Decomposition was developed to identify which mode was dominant as a function of time. The A-II mode was found to be dominant for over 90% of the instantaneous fields examined, while the S-I mode appeared to be more unstable.Symmetrically shed vortices were found to rearrange downstream into an alternate structure in which the wake was no longer synchronised to the cylinder motion. The dominant frequency of transverse velocity fluctuations was measured throughout the wake in order to study the effects of this breakdown in more detail. For the majority of the wake, the fluctuations occurred at the Strouhal frequency, while in a region in the near wake the fluctuations occurred at the frequency of the cylinder motion. It is thought that during the first response branch vortices are formed at the cylinder response frequency, but tend to quickly rearrange downstream into an alternate structure which is no longer synchronised to the cylinder motion. As a result, the fluctuating drag will be synchronised to the structural motion, and is capable of providing positive energy transfer in the apparent absence of lock-in. Finally, the spatial dependence of the frequency of velocity fluctuations throughout the wake is used to explain some of the conflicting results in the literature regarding streamwise VIV, and the implications for the general study of VIV are discussed.     

On vortex shedding from low aspect ratio dual step cylinders

A dual-step cylinder is comprised of two cylinders of different diameters. A large diameter cylinder (D) with low aspect ratio (L/D) is attached to the mid-span of a small diameter cylinder (d). The present study investigates the effect of Reynolds number (Re_D) and L/D on dual step cylinder wake development for D/d=2, 0.2≤L/D≤3, and two Reynolds numbers, Re_D=1050 and 2100. Experiments have been performed in a water flume facility utilizing flow visualization, Laser Doppler Velocimetry (LDV), and Particle Image Velocimetry (PIV). The results show that vortex shedding occurs from both the large and small diameter cylinders for 1≤L/D≤3 at Re_D=2100 and 2≤L/D≤3 at Re_D=1050. At these conditions, large cylinder vortices predominantly form vortex loops in the wake and small cylinder vortices form half-loop vortex connections. At lower aspect ratios, vortex shedding from the large cylinder ceases, with the dominant frequency in the large cylinder wake attributed to the passage of vortex filaments connecting small cylinder vortices. At these lower aspect ratios, the presence of the large cylinder induces periodic vortex dislocations. Increasing L/D increases the frequency of occurrence of vortex dislocations and decreases the dominant frequency in the large cylinder wake. The identified changes in wake topology are related to substantial variations in the location of boundary layer separation on the large cylinder, and, consequently, changes in the size of the vortex formation region. The results also show that the Reynolds number has a substantial effect on wake vortex shedding frequency, which is more profound than that expected for a uniform cylinder.     

Near-wake flow characteristics of a circular cylinder close to a wall

Flow characteristics in the near wake of a circular cylinder located close to a fully developed turbulent boundary layer are investigated experimentally using particle image velocimetry (PIV). The Reynolds number based on the cylinder diameter (D) is 1.2×10⁴ and the incident boundary layer thickness (δ) is 0.4D. Detailed velocity and vorticity fields in the wake region (0<x/D<6) are given for various gap heights (S) between the cylinder and the wall, with S/D ranging from 0.1 to 1.0. Both the ensemble-averaged (including the mean velocity vectors and Reynolds stress) and the instantaneous flow fields are strongly dependent on S/D. Results reveal that for S/D⩾0.3, the flow is characterized by the periodic, Kármán-like vortex shedding from the upper and lower sides of the cylinder. The shed vortices and their evolution are revealed by analyzing the instantaneous flow fields using various vortex identification methods, including Galilean decomposition of velocity vectors, calculation of vorticity and swirling strength. For small and intermediate gap ratios (S/D⩽0.6), the wake flow develops a distinct asymmetry about the cylinder centreline; however, some flow quantities, such as the Strouhal number and the convection velocity of the shed vortex, keep roughly constant and virtually independent of S/D.     

Measurement in a Zero-Pressure Gradient Turbulent Boundary Layer with Forced Thermal Convection

A subsonic zero-pressure gradient turbulent boundary layer developing on a uniformly heated surface at a Reynolds number in the range of 3, 560?≤?Re _θ ?≤ 5,360 was investigated. Particle-image velocimetry measurements were performed at various positions in the streamwise direction for several wind-tunnel speeds and for different wall excess temperatures to show the thermal convection effects to expand the boundary-layer thickness δ _0.99 and to enlarge the turbulence intensities in the log-law and wake region. The mean velocity profiles are found to be self-preserving. The inclination of large-scale ramp-like vortex packets increases to higher characteristic angles, i.e., the mean angles are enlarged by approximately 5–10°. Hairpin-like vortex structures originating from the near-wall region seem to undergo higher climbing rates in the wall-normal direction causing the above mentioned significant changes in the boundary-layer thickness δ _0.99 and the strongly increased distributions of turbulence intensities in the wake region of the boundary layer. Changes in the distributions of the skewness and flatness of the probability density function (PDF) of the streamwise fluctuations corroborate these findings. The two-point correlation distribution of the streamwise velocity fluctuations R _uu is increased for wall distances y/δ _0.99?=?0.1 to y/δ _0.99?=?0.75 indicating the existence of coherent structures in higher regions of the boundary layer.     

Effect of perforation on flow past a conic cylinder at $${\varvec{Re}}~=~100$$: wavy vortex and sign laws

In order to find the intrinsic physical mechanism of the original Kármán vortex wavily distorted across the span due to the introduction of three-dimensional (3-D) geometric disturbances, a flow past a peak-perforated conic shroud is numerically simulated at a Reynolds number of 100. Based on previous work by Meiburg and Lasheras (1988), the streamwise and vertical interactions with spanwise vortices are introduced and analyzed. Then vortex-shedding patterns in the near wake for different flow regimes are reinspected and illustrated from the view of these two interactions. Generally, in regime I, spanwise vortices are a little distorted due to the weak interaction. Then in regime II, spanwise vortices, even though curved obviously, are still shed synchronously with moderate streamwise and vertical interactions. But in regime III, violently wavy spanwise vortices in some vortex-shedding patterns, typically an \(\Omega \)-type vortex, are mainly attributed to the strong vertical interactions, while other cases, such as multiple vortex-shedding patterns in sub-regime III-D, are resulted from complex streamwise and vertical interactions. A special phenomenon, spacial distribution of streamwise and vertical components of vorticity with specific signs in the near wake, is analyzed based on two models of streamwise and vertical vortices in explaining physical reasons of top and bottom shear layers wavily varied across the span. Then these two models and above two interactions are unified. Finally two sign laws are summarized: the first sign law for streamwise and vertical components of vorticity is positive in the upper shear layer, but negative in the lower shear layer, while the second sign law for three vorticity components is always negative in the wake.     

Wind Impact on Single Vortices and Counterrotating Vortex Pairs in Ground Proximity

Wall-resolved large eddy simulations are employed to investigate the behaviour of wake vortices and single vortices in ground proximity at a variety of wind conditions. The six considered strengths of wind, ranging between 0.5 and 4 times the initial wake vortex descent speed, w₀, include practically and theoretically significant wind speeds. A crosswind of 0.5 w₀ may lead to windward stall posing a potential hazard to subsequently landing aircraft, whereas theoretical considerations predict that at 4 w₀ the rebound of the luff vortex is completely suppressed. The same range of wind speeds is also used to investigate the effects of headwind and diagonal wind in order to discriminate between effects of environmental turbulence increasing with wind speed and the direction of the wind shear. The study has been complemented by a number of single vortex computations in order to differentiate between effects related to the mutual interaction of the vortex pair and the individual vortices with the turbulent boundary layer flow. It is shown that vortex ascent, descent, rebound and decay characteristics are controlled by (i) the interaction of the vortices with secondary vorticity detaching from the ground, (ii) the redistribution of vorticity of the boundary layer which is altering the path of the primary vortices by mutual velocity induction, and (iii) the interaction of the vortices with the environmental turbulence.     

Vortex dynamics of a cylinder wake in proximity to a wall

Large-eddy simulations (LES) are used to investigate the modifications of wake dynamics and turbulence characteristics behind a circular cylinder placed near a wall for varying gap-to-diameter (G/D) ratios (where G signifies the gap between the wall and the cylinder, and D the cylinder diameter). The three-dimensional (3-D), time-dependent, incompressible Navier–Stokes equations with a dynamic subgrid-scale model are solved using a symmetry-preserving finite-difference scheme of second-order spatial and temporal accuracy. The immersed boundary (IB) method is employed to impose the no-slip boundary condition on the cylinder surface. Flow visualizations along with turbulence statistics are presented to gain insight into the flow structures that are due to interaction between the shear layers and the approaching boundary layer. Apart from the vortex shedding mechanism, the paper illustrates the physics involving the shear layer transition, stretching, breakdown and turbulence generation, either qualitatively or quantitatively, in the presence of a wall for a Reynolds number of Re=1440 (based on D and the inlet free-stream velocity U_∞).     

Global aerodynamic instability of twin cylinders in cross flow

This paper comprises an in-depth physical discussion of the flow-induced vibration of two circular cylinders in view of the time-mean lift force on stationary cylinders and interaction mechanisms. The gap-spacing ratio T/D is varied from 0.1 to 5 and the attack angle α from 0° to 180° where T is the gap width between the cylinders and D is the diameter of a cylinder. Mechanisms of interaction between two cylinders are discussed based on time-mean lift, fluctuating lift, flow structures and flow-induced responses. The whole regime is classified into seven interaction regimes, i.e., no interaction regime; boundary layer and cylinder interaction regime; shear-layer/wake and cylinder interaction regime; shear-layer and shear-layer interaction regime; vortex and cylinder interaction regime; vortex and shear-layer interaction regime; and vortex and vortex interaction regime. Though a single non-interfering circular cylinder does not correspond to a galloping following quasi-steady galloping theory, two circular cylinders experience violent galloping vibration due to shear-layer/wake and cylinder interaction as well as boundary layer and cylinder interaction. A larger magnitude of fluctuating lift communicates to a larger amplitude vortex excitation.     

Flow above the free end of a surface-mounted finite-height circular cylinder: A review

The wake of a surface-mounted finite-height circular cylinder and the associated vortex patterns are strongly dependent on the cylinder aspect ratio and the thickness of the boundary layer on the ground plane relative to the dimensions of the cylinder. Above a critical aspect ratio, the mean wake is characterized by streamwise tip vortex structures and Kármán vortex shedding from the sides of the cylinder. Below a critical aspect ratio, a unique mean wake structure is observed. Recent experimental studies in the literature that used phase-averaged techniques, as well as recent numerical simulations, have led to an improved physical understanding of the near-wake vortex flow patterns. However, the flow above the free end of the finite circular cylinder, and its relationship to the near wake, has not been systematically studied. The effects of aspect ratio and boundary layer thickness on the free-end flow field are also not completely understood, nor has the influence of Reynolds number on the free-end flow field been fully explored. Common features associated with the free end include separation from the leading edge, a mean recirculation zone containing a prominent cross-stream arch (or mushroom) vortex, and reattachment onto the free-surface. Other flow features that remain to be clarified include a separation bubble near the leading edge, one or two cross-stream vortices within this separation bubble, the origins of the streamwise tip or trailing vortices, and various critical points in the near-surface flow topology. This paper reviews the current understanding of the flow above the free end of a surface-mounted finite-height circular cylinder, with a focus on models of the flow field, surface oil flow visualization studies, pressure and heat flux distributions on the free-end surface, measurements of the local velocity field, and numerical simulations, found in the literature.     

TR-PIV measurement of the wake behind a grooved cylinder at low Reynolds number

A comparative study of the wakes behind cylinders with grooved and smooth surfaces was performed with a view to understand the wake characteristics associated with the adult Saguaro cacti. A low-speed recirculation water channel was established for the experiment; the Reynolds number, based on the free-stream velocity and cylinder diameter (D), was kept at Re_D=1500. State-of-the-art time-resolved particle image velocimetry (TR-PIV) was employed to measure a total of 20 480 realizations of the wake field at a frame rate of 250 Hz, enabling a comprehensive view of the time- and phase-averaged wake pattern. In comparison to the wake behind the smooth cylinder, the length of the recirculation zone behind the grooved cylinder was extended by nearly 18.2%, yet the longitudinal velocity fluctuation intensity was considerably weakened. A global view of the peaked spectrum of the longitudinal velocity component revealed that the intermediate region for the grooved cylinder, which approximately corresponds to the transition region where the shear layer vortices interact, merge and shed before the formation of the Karman-like vortex street, was much wider than that for the smooth one. The unsteady events near St=0.3-0.4 were detected in the intermediate region behind the grooved cylinder, but no such events were found in the smooth cylinder system. Although the formation of the Karman-like vortex street was delayed by about 0.6D downstream for the grooved cylinder, no prominent difference in the vortex street region was found in the far wake for both cylinders. The Proper Orthogonal Decomposition (POD) method was used extensively to decompose the vector and swirling strength fields, which gave a close-up view of the vortices in the near wake. The first two POD modes of the swirling strength clarified the spatio-temporal characteristics of the shear layer vortices behind the grooved cylinder. The small-scale vortices superimposed on the shear layers behind the grooved cylinder were found to be generated and convected downstream in the same phase, which would significantly reduce the fluctuating force on the cylinder surface.