Flow structure around two finite circular cylinders located in an atmospheric boundary layer: side-by-side arrangement

The flow structure around the free-end region of two adjacent finite circular cylinders embedded in an atmospheric boundary layer (ABL) was investigated experimentally. The experiments were carried out in a closed-return-type subsonic wind tunnel, in which two finite cylinders with an aspect ratio of 6 were mounted vertically on a flat plate in a side-by-side arrangement. The Reynolds number based on the cylinder diameter was about Re=2×10⁴. Systems with gap ratios (i.e., center-to-center distance/cylinder diameter) in the range 1.0–2.0 were investigated. A hot-wire anemometer was employed to measure the wake velocity, and the mean pressure distribution on the cylinder surface was also measured. The flow past two finite cylinders was found to have a complicated three-dimensional wake structure in the region near the free ends. As the gap ratio increases, regular vortex-shedding becomes dominant, but the length of the vortex formation region decreases. The pressure distribution and flow structure around two cylinders were found to differ substantially from the behavior of a two-dimensional circular cylinder due to mutual interference. The three-dimensional flow structure seems to originate from the strong entrainment of irrotational fluids caused by the downwash counter-rotating vortices separated from the finite cylinder (FC) free ends.     

Vortex-shedding from single and tandem cylinders in the presence of applied sound

A single cylinder and two tandem cylinder configurations with longitudinal pitch ratios L/D=1.75 and 2.5 were rigidly mounted in an open circuit wind tunnel and a standing acoustic pressure wave was imposed so that the acoustic particle velocity was normal to both the cylinder axis and the mean flow velocity. The effect of sound on the vortex-shedding was investigated for various amplitudes by means of pressure taps on the cylinders and wake hot-wire probes. These tests show that applied sound can entrain and shift the natural vortex-shedding frequency to the frequency of excitation and produce nonlinearities in the wake. The lock-in envelope for the tandem cylinders is considerably larger than for the single cylinder. The lock-in range for the smaller tandem cylinder spacing was broader still than either the single cylinder, or the L/D=2.5 tandem cylinder case. The pressure and hot-wire measurements show for the single cylinder, and tandem cylinder configuration with pitch ratio L/D=2.5, that there was a phase jump near the coincidence of the vortex-shedding frequency and the excitation frequency, while there was no jump for the pitch ratio of 1.75. As well, the applied sound field was also noted to induce vortex-shedding in the gap for the L/D=2.5 case, while no vortex-shedding was noted for the smaller pitch ratio.     

Surface flow pattern and local mass transfer on the free-end surface of a finite circular cylinder

 Relation between the surface flow pattern and the local mass transfer characteristic on the free end surface of a finite circular cylinder mounted on a flat plate was investigated using the oil surface flow visualization and the naphthalene sublimation technique. The aspect ratio [the ratio of the cylinder length to the cylinder diameter (H/D)] was 1.25 and the Reynolds number based on the diameter was 1.48 × 10⁵. Several kinds of critical points on the free-end surface were identified by the visualization and the mass transfer measurement around those critical points through the naphthalene sublimation technique was then performed to investigate the relation between the flow and mass transfer. The free-end surface flow was topologically characterized by the presence of a saddle point and two focal points in the fore-half portion of the surface and two nodes and a saddle point in the rear-half portion. It was found that the rate of mass transfer was largest in the vicinity of the nodes in the rear-half of the free-end surface. Received on 26 April 2000     

Large eddy simulations of flow interference between two unequal sized square cylinders

A uniform flow past two unequal sized square cylinders arranged in a side-by-side pattern and at a Reynolds number of 50,000 has been investigated using large eddy simulation (LES) technique. The modelling of sub-grid scales of turbulence is done using the Smagorinsky model. The effect of the transverse gap ratio (T/D) on the flow characteristics has been studied. Numerical simulations are carried out for five different transverse gap ratios (T/D), namely 1.120, 1.250, 1.375, 1.750 and 2.500. Results in terms of the aerodynamic forces, Strouhal number, mean base pressure coefficient, streamlines, vorticity, surface pressure distribution, normal and shear stresses are presented. A shift in the stagnation point for the small square cylinder from the centre of its front face towards its gap side is seen at smaller T/D ratios. The presence of a jet-like flow seen in the gap side is more pronounced at T/D = 1.12. A biased gap side flow towards the near wake of the small square cylinder is seen at smaller T/D ratios. No interference effect is seen at T/D = 2.5. The flow behaviour is similar to that of the isolated square cylinder at this gap ratio.     

Influence of wall proximity on vortex shedding from a square cylinder

Mean and fluctuating surface pressure data are presented for a square cylinder of side length D placed near a solid wall at Re _D=18,900. One oncoming boundary layer thickness, d=0.5 D was used. Measurements were made for cylinder to wall gap heights, S, from S/ D=0.07 to 1.6. Four gap-dependent flow regimes were found. For S/ D>0.9, the flow and the vortex shedding strength are similar to the no-wall case. Below the critical gap height of 0.3 D, periodic activity is fully suppressed in the near wake region. In between, for 0.3< S/ D<0.9, the wall exerts a greater influence on the flow. For 0.6< S/ D<0.9, the mean drag and the strength of the shed vortices decrease as the gap is reduced, while the mean lift towards the wall increases. Evidence is presented that for S/ D>0.6 the influence of the viscous wall flow in the gap is not dominant and that, consequently, inviscid flow theory can describe changes in the mean lift as S/ D decreases. For 0.3< S/ D<0.6, the flow reattaches intermittently on the bottom face of the cylinder and viscous effects become important. Below the gap height of 0.4 D, periodic activity cannot be observed on the cylinder.     

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.     

An experimental investigation of flow past a dual step cylinder

Flow development in the wake of a dual step cylinder has been investigated experimentally using Laser Doppler Velocimetry and flow visualization. The dual step cylinder model is comprised of a large diameter cylinder (D) mounted at the mid-span of a small diameter cylinder (d). The experiments have been performed for a Reynolds number (Re _D ) of 1,050, a diameter ratio (D/d) of 2, and a range of large cylinder aspect ratios (L/D). The results show that the flow development is highly dependent on L/D. The following four distinct flow regimes can be identified based on vortex dynamics in the wake of the large cylinder: (1) for L/D ≥ 15, three vortex shedding cells form in the wake of the large cylinder, one central cell bounded by two cells of lower frequency, (2) for 8 < L/D ≤ 14, a single vortex shedding cell forms in the wake of the large cylinder, (3) for 2 < L/D ≤ 6, vortex shedding from the large cylinder is highly three-dimensional. When spanwise vortices are shed, they deform substantially and attain a hairpin shape in the near wake, (4) for 0.2 ≤ L/D ≤ 1, the large cylinder induces vortex dislocations between small cylinder vortices. The results show that for Regimes I to III, on the average, the frequency of vortex shedding in the large cylinder wake decreases with L/D, which is accompanied by a decrease in coherence of the shed vortices. In Regime IV, small cylinder vortices connect across the large cylinder wake, but these connections are interrupted by vortex dislocations. With decreasing L/D, the frequency of dislocations decreases and the dominant frequency in the large cylinder wake increases toward the small cylinder shedding frequency.     

Turbulent wake and vortex shedding for a stack partially immersed in a turbulent boundary layer

The effect of the jet-to-cross-flow velocity ratio, R, on the turbulent wake and Kármán vortex shedding for a cylindrical stack of aspect ratio AR=9 was investigated in a low-speed wind tunnel using thermal anemometry. The cross-flow Reynolds number was Re_D=2.3×10⁴, the jet Reynolds number ranged from Re_d=7.6×10³ to 4.7×10⁴, and R was varied from 0 to 3. The stack was partially immersed in a flat-plate turbulent boundary layer, with a boundary layer thickness-to-stack-height ratio of δ/H=0.5 at the location of the stack. From the behaviour of the turbulent wake and the vortex shedding, the flow around the stack could be classified into three regimes depending on the value of R, which were the downwash (R<0.7), cross-wind-dominated (0.7R<1.5), and jet-dominated (R1.5) flow regimes. Each flow regime had a distinct structure to the mean velocity (streamwise and wall-normal directions), turbulence intensity (streamwise and wall-normal directions), and Reynolds shear stress fields, as well as the variation of the Strouhal number and the power spectrum along the stack height.     

Interaction of circular cylinder wake with a short asymmetrically located downstream plate

This study reveals the interaction patterns of separated shear layers from a circular cylinder with a short downstream plate and their reflection on the frequency and the formation length of the vortices from the cylinder as a function of plate location relative to the cylinder. The effect of horizontal (G/D) and vertical (Z/D) distances between the cylinder and the plate on the near wake is studied via Digital Particle Image Velocimetry (DPIV) in a water channel for Reynolds numbers of 200, 400 and 750, based on the cylinder diameter D. It is shown that the interaction of wake with the plate of length D can be categorized depending on the horizontal and the vertical distances between the cylinder and the plate. For the vertical distance range of Z/D ≤ 0.7, there is a critical horizontal spacing before which the shear layers from the cylinder are inhibited to form vortices in front of the plate. Resulting elongated recirculation region between the plate and the cylinder suggests modification of the absolutely unstable near wake of free circular cylinder in favor of convective instability. Z/D = 0.9 provides a passage from Z/D ≤ 0.7 to ≥1.1 and is associated with a dominant effect on the near-wake characteristics of interaction of shear layers from the cylinder with those from the downstream plate. For Z/D ≥ 1.1, there is again, yet a smaller critical horizontal spacing after which vortices interact with decreased downstream plate interference. In this vertical separation distance range, a gap flow between the plate and the cylinder plays a determining role on the formation length and St number of vortices for small horizontal spacing values.     

Near-wake flow structure of elliptic cylinders close to a free surface: effect of cylinder aspect ratio

The flow fields behind elliptic cylinders adjacent to a free surface were investigated experimentally in a circulating water channel. A range of cylinder aspect ratios (AR=2, 3, 4) were considered, while the cross-sectional area of the elliptical cylinder was kept constant. The main objective of this study was to investigate the effect of cylinder aspect ratio and a free surface on the flow structure in the near-wake behind elliptic cylinders. For each elliptic cylinder, the flow structure was analyzed for various values of the submergence depth of the cylinder beneath the free surface. The flow fields were measured using a single-frame double-exposure PIV (Particle Image Velocimetry) system. For each experimental condition, 350 instantaneous velocity fields were obtained and ensemble-averaged to obtain the mean velocity field and spatial distribution of the mean vorticity statistics. The results show that near-wake can be classified into three typical flow patterns: formation of a Coanda flow, generation of substantial jet-like flow, and attachment of this jet flow to the free surface. The general flow structure observed behind the elliptic cylinders resembles the structure previously reported for a circular cylinder submerged near a free surface. However, the wake width and the angle of downward deflection of the shear layer developed from the lower surface of the elliptic cylinder differ from those observed for a circular cylinder. These trends are enhanced as cylinder aspect ratio is increased. In addition, the free surface distortion is also discussed in the paper.     

Cross-flow past a pair of nearly in-line cylinders with the upstream cylinder subjected to a transverse harmonic oscillation

An experimental investigation is presented for the cross-flow past a pair of staggered circular cylinders, with the upstream cylinder subject to forced harmonic oscillation transverse to the flow direction. Experiments were conducted in a water tunnel with Reynolds numbers, based on upstream velocity, U, and cylinder diameter, D, in the range 1440⩽Re⩽1680. The longitudinal separation between cylinder centres is L/D=2.0, with a transverse separation (for the mean position of the upstream cylinder) of T/D=0.17; the magnitude of the harmonic oscillation is 0.44D peak-to-peak and the nondimensional frequency range of the excitation is 0.05⩽f_eD/U⩽0.44. Flow visualization of the wake-formation region and hot-film measurements of the wake spectra are used to investigate the wake-formation process. An earlier study showed that stationary cylinders in this nearly in-line configuration straddle two very different flow regimes, the so-called shear-layer reattachment (SLR) and induced separation (IS) regimes. The present study, demonstrates that oscillation of the upstream cylinder causes considerable modification of the flow patterns around the cylinders. In particular, the wake experiences strong periodicities at the frequency of the oscillating cylinder; in addition to the usual fundamental lock-in, both sub- and superharmonic resonances are obtained. It is also observed that, although the flow exhibits regions of SLR and IS for excitation frequencies below the fundamental lock-in, for frequencies above the lock-in range the flow no longer resembles either of these flow regimes and vortices are formed in the gap between the cylinders.     

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.     

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.     

Momentum and heat transport in a finite-length cylinder wake

This paper reports an experimental study of turbulent momentum and heat transport in the wake of a wall-mounted finite-length square cylinder, with its length-to-width ratio L/d = 3–7. The cylinder was slightly heated so that heat produced could be considered as a passive scalar. A moveable three-wire probe (a combination of an X-wire and a cold wire) was used to measure velocity and temperature fluctuations at a Reynolds number of 7,300 based on d and the free-stream velocity. Measurements were performed at 10 and 20d downstream of the cylinder at various spanwise locations. Results indicate that L/d has a pronounced effect on Reynolds stresses, temperature variance and heat fluxes. The downwash flow from the free end of the cylinder acts to suppress spanwise vortices and, along with the upwash flow from the cylinder base, makes the finite-length cylinder wake highly three-dimensional. Reynolds stresses, especially the lateral normal stress, are significantly reduced as a result of suppressed spanwise vortices at a small L/d. The downwash flow acts to separate the two rows of spanwise vortices further apart from the wake centerline, resulting in a twin-peak distribution in temperature variance. While the downwash flow entrains high-speed fluid into the wake, responsible for a small deficit in the time-averaged streamwise velocity near the free end, it does not alter appreciably the distribution of time-averaged temperature. It has been found that the downwash flow gives rise to a counter-gradient transport of momentum about the central region of the wake near the free end of the cylinder, though such a counter-gradient transport does not occur for heat transport.     

GROUND EFFECT OF FLOW AROUND AN ELLIPTIC CYLINDER IN A TURBULENT BOUNDARY LAYER

The flow characteristics around an elliptic cylinder with an axis ratio of AR=2 located near a flat plate were investigated experimentally. The elliptic cylinder was embedded in a turbulent boundary layer whose thickness is larger than the cylinder height. For comparison, the same experiment was carried out for a circular cylinder having the same vertical height. The Reynolds number based on the height of the cylinder cross-section was 14000. The pressure distributions on the cylinder surface and on the flat plate were measured for various gap distances between the cylinder and the plate. The wake velocity profiles behind the cylinder were measured using hot-wire anemometry. In the near-wake region, the vortices are shed regularly only when the gap ratio is greater than the critical value of G/B=0·4. The critical gap ratio is larger than that of a circular cylinder. The variation of surface pressure distributions on the elliptic cylinder with respect to the gap ratio is much smaller than that on the circular cylinder. This trend is more evident on the upper surface than the lower one. The surface pressures on the flat plate recover faster than those for the case of the circular cylinder at downstream locations. As the gap ratio increases, the drag coefficient of the cylinder itself increases, but the lift coefficient decreases. For all gap ratios tested in this study, the drag coefficient of the elliptic cylinder is about half that of the circular cylinder. The ground effect of the cylinder at small gap ratio constrains the flow passing through the gap, and restricts the vortex shedding from the cylinder, especially in the lower side of the cylinder wake. This constraint effect is more severe for the elliptic cylinder, compared to the circular cylinder. The wake region behind the elliptic cylinder is relatively small and the velocity profiles tend to approach rapidly to those of a flat plate boundary layer     

An immersed interface method for flow past circular cylinder in the vicinity of a plane moving wall

Two‐dimensional flows past a stationary circular cylinder near a plane boundary are numerically simulated using an immersed interface method with second‐order accuracy. Instead of a fixed wall, a moving wall with no‐slip boundary is considered to avoid the complex involvement of the boundary layer and to focus only on the shear‐free wall proximity effects for investigating the force dynamics and flow fields. To analyze the convergence and accuracy of our implementation, numerical studies have been first performed on a simple test problem of rotational flow, where the second order of convergence is confirmed through numerical experiments and an optimal range of relative grid‐match ratio of Lagrangian to Eulerian grid sizes has been recommended. By comparing the force quantities and the Strouhal number, the accuracy of this method has been demonstrated on the flow past a stationary isolated cylinder. The cylinder is then put in proximity to the wall to investigate the shear‐free wall proximity effects in the low Reynolds number regime (20≤Re≤200). The gap ratio, e/D, where e denotes the gap between the cylinder and the moving wall and D denotes the diameter of the cylinder, is taken from 0.10 to 2.00 to determine the critical gap ratio, (e/D)_critical, for the alternate vortex shedding, where the fluid forces, flow fields and the streamwise velocity profiles are studied. One of the key findings is that the (e/D)_critical for the alternate vortex shedding decreases as the Reynolds number increases. We also find that, in this low Reynolds number regime, the mean drag coefficient increases and peaks at e/D = 0.5 with the increase of e/D and keeps decreasing gently from e/D = 0.5 to e/D = 2.0, while the mean lift coefficient decreases monotonically with the increase of e/D. New correlations are then proposed for computing force coefficients as a function of Re and e/D for a cylinder in the vicinity of a moving plane wall. Copyright © 2015 John Wiley & Sons, Ltd.     

The Unsteady Wake of a Circular Cylinder near a Free Surface

The behaviour of the wake Strouhal number for flow past a cylinder close to a free surface at both low and moderate Froude numbers is investigated numerically. For the low Froude number case (i.e., gravity-dominated), the results obtained are similar to those for flow past a cylinder close to an adjacent no-slip boundary. As the distance between the wall and the cylinder is reduced, the Strouhal number, as measured from the time varying lift, increases to a maximum at a gap ratio of 0.70. Further gap reduction leads to a rapid decrease in the Strouhal number, with shedding finally ceasing altogether at gap ratios below 0.16. The agreement between the results for a free surface and a no-slip boundary suggests that the mechanism behind the suppression of vortex shedding is common. For flow at a fixed gap ratio and a moderate Froude number, two distinctly different wake states are observed with the flow passing over the cylinder tending to switch from a state of attachment to the free surface, to one of separation from it, and then back again in a pseudo-periodic fashion. Even though there is a significant difference in Reynolds number, the predicted numerical two-dimensional behaviour is found to compare favourably with the experimental observations at higher Reynolds number.     

The effect of a wake-mounted splitter plate on the flow around a surface-mounted finite-height circular cylinder

The influence of a wake-mounted splitter plate on the flow around a surface-mounted circular cylinder of finite height was investigated experimentally using a low-speed wind tunnel. The experiments were conducted at a Reynolds number of Re=7.4×10⁴ for cylinder aspect ratios of AR=9, 7, 5 and 3. The thickness of the boundary layer on the ground plane relative to the cylinder diameter was δ/D=1.5. The splitter plates were mounted on the wake centreline with negligible gap between the base of the cylinder and the leading edge of the plate. The lengths of the splitter plates, relative to the cylinder diameter, ranged from L/D=1 to 7, and the plate height was always equal to the cylinder height. Measurements of the mean drag force coefficient were obtained with a force balance, and measurements of the vortex shedding frequency were obtained with a single-component hot-wire probe situated in the wake of the cylinder–plate combination. Compared to the well-studied case involving an infinite circular cylinder, the splitter plate was found to be a less effective drag-reduction device for finite circular cylinders. Significant reduction in the mean drag coefficient was realized only for the finite circular cylinder of AR=9 with intermediate-length splitter plates of L/D=1–3. The mean drag coefficients of the other cylinders were almost unchanged. In terms of its effect on vortex shedding, a splitter plate of sufficient length was able to suppress Kármán vortex shedding for all of the finite circular cylinders tested. For AR=9, vortex shedding suppression occurred for L/D≥5, which is similar to the case of the infinite circular cylinder. For the smaller-aspect-ratio cylinders, however, the splitter plate was more effective than what occurs for the infinite circular cylinder: for AR=3, vortex shedding suppression occurred for all of the splitter plates tested (L/D≥1); for AR=5 and 7, vortex shedding suppression occurred for L/D≥1.5.     

A numerical investigation of the effects of the spanwise length on the 3-D wake of a circular cylinder

The numerical prediction of vortex-induced vibrations has been the focus of numerous investigations to date using tools such as computational fluid dynamics. In particular, the flow around a circular cylinder has raised much attention as it is present in critical engineering problems such as marine cables or risers. Limitations due to the computational cost imposed by the solution of a large number of equations have resulted in the study of mostly 2-D flows with only a few exceptions. The discrepancies found between experimental data and 2-D numerical simulations suggested that 3-D instabilities occurred in the wake of the cylinder that affect substantially the characteristics of the flow. The few 3-D numerical solutions available in the literature confirmed such a hypothesis. In the present investigation the effect of the spanwise extension of the solution domain on the 3-D wake of a circular cylinder is investigated for various Reynolds numbers between 40 and 1000. By assessing the minimum spanwise extension required to predict accurately the flow around a circular cylinder, the infinitely long cylinder is reduced to a finite length cylinder, thus making numerical solution an effective way of investigating flows around circular cylinders. Results are presented for three different spanwise extensions, namely πD/2, πD and 2πD. The analysis of the force coefficients obtained for the various Reynolds numbers together with a visualization of the three-dimensionalities in the wake of the cylinder allowed for a comparison between the effects of the three spanwise extensions. Furthermore, by showing the different modes of vortex shedding present in the wake and by analysing the streamwise components of the vorticity, it was possible to estimate the spanwise wavelengths at the various Reynolds numbers and to demonstrate that a finite spanwise extension is sufficient to accurately predict the flow past an infinitely long circular cylinder.     

Low Reynolds number flow over a square cylinder with a detached flat plate

A numerical study of the alteration of a square cylinder wake using a detached downstream thin flat plate is presented. The wake is generated by a uniform flow of Reynolds number 150 based on the side length of the cylinder, D. The sensitivity of the near wake structure to the downstream position of the plate is investigated by varying the gap distance (G) along the wake centerline in the range 0 ⩽ G ⩽ 7D for a constant plate length of L = D. A critical gap distance is observed to occur at G_c ≈ 2.3D that indicates the existence of two flow regimes. Regime I is characterised by vortex formation occurring downstream of the gap while for regime II, formation occurs within the gap. By varying the plate length and gap distance, a condition is found where significant unsteady total lift reduction can occur. The root mean square lift reduction is limited by an unsteady stall process on the plate.