Flow around four cylinders arranged in a square configuration

This paper presents an experimental study of the flow around four circular cylinders arranged in a square configuration. The Reynolds number was fixed at Re=8000, the pitch-to-diameter ratio between adjacent cylinders was varied from P/D=2 to 5 and the incidence angle was changed from α=0° (in-line square configuration) to 45° (diamond configuration) at an interval of 7.5°. The flow field was measured using digital Particle Image Velocimetry (PIV) to examine the vortex shedding characteristics of the cylinders, together with direct measurement of fluid dynamic forces (lift and drag) on each cylinder using a piezoelectric load cell. Depending on the pitch ratio, the flow could be broadly classified as shielding regime (P/D≤2), shear layer reattachment regime (2.5≤P/D≤3.5) and vortex impinging regime (P/D≥4). However, this classification is valid only in the case that the cylinder array is arranged nearly in-line with the free stream (α≈0°), because the flow is also sensitive to α. As α increases from 0° to 45°, each cylinder experiences a transition of vortex shedding pattern from a one-frequency mode to a two-frequency mode. The flow interference among the cylinders is complicated, which could be non-synchronous, quasi-periodic or synchronized with a definite phase relationship with other cylinders depending on the combined value of α and P/D. The change in vortex pattern is also reflected by some integral parameters of the flow such as force coefficients, power spectra and Strouhal numbers.     

Strouhal numbers,forces and flow structures around two tandem cylinders of different diameters

This paper presents a detailed investigation of Strouhal numbers, forces and flow structures in the wake of two tandem cylinders of different diameters. While the downstream cylinder diameter, D, was fixed at 25 mm, the upstream cylinder diameter, d, was varied from 0.24D to D. The spacing between the cylinders was 5.5d, at which vortices were shed from both cylinders. Two distinct vortex frequencies were detected behind the downstream cylinder for the first time for two tandem cylinders of the same diameter. The two vortex frequencies remained for d/D=1.0–0.4. One was the same as detected in the gap of the cylinders, and the other was of relatively low frequency and was ascribed to vortex shedding from the downstream cylinder. While the former, if normalized, declined progressively from 0.196 to 0.173, the latter increased from 0.12 to 0.203 with decreasing d/D from 1 to 0.24. The flow structure around the two cylinders is examined in the context of the observed Strouhal numbers. The time-averaged drag on the downstream cylinder also climbed with decreasing d/D, though the fluctuating forces dropped because vortices impinging upon the downstream cylinder decreased in scale with decreasing d/D.     

Dependence of flow classification on the Reynolds number for a two-cylinder wake

This work aims to investigate the dependence of flow classification on the Reynolds number (Re) for the wake of two staggered cylinders. The Re examined ranges from 1.5×10³ to 2.0×10⁴. The pitch ratio, P^⁎=P/d examined is 1.2–6.0 (d is the cylinder diameter), and angle (α) is 0–90°, where P is the center-to-center spacing between two cylinders and α is the angle between the incident flow and the line through the cylinder centers. Two single hotwires were used to measure simultaneously the fluctuating streamwise velocities (u) in the vortex streets generated by the two cylinders. The power spectral density functions and the Strouhal numbers were then obtained from the u signals, based on which the flow structure pattern or mode could be determined. Over two hundred configurations of two staggered cylinders have been examined for each Re. It is found that Re has an appreciable effect on the dependence of the flow mode on P^⁎ and α. The observation is connected to the Re effect on the generic features of a two-cylinder wake such as flow separation, boundary layer thickness, gap flow deflection and vortex formation length.     

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.     

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.     

A numerical investigation of the flow over a pair of identical square cylinders in a tandem arrangement

This paper describes a numerical study of the two‐dimensional and three‐dimensional unsteady flow over two square cylinders arranged in an in‐line configuration for Reynolds numbers from 40 to 1000 and a gap spacing of 4D, where D is the cross‐sectional dimension of the cylinders. The effect of the cylinder spacing, in the range G = 0.3D to 12D, was also studied for selected Reynolds numbers, that is, Re = 130, 150 and 500. An incompressible finite volume code with a collocated grid arrangement was employed to carry out the flow simulations. Instantaneous and time‐averaged and spanwise‐averaged vorticity, pressure, and streamlines are computed and compared for different Reynolds numbers and gap spacings. The time averaged global quantities such as the Strouhal number, the mean and the RMS values of the drag force, the base suction pressure, the lift force and the pressure coefficient are also calculated and compared with the results of a single cylinder. Three major regimes are distinguished according to the normalized gap spacing between cylinders, that is, the single slender‐body regime (G < 0.5), the reattach regime (G < 4) and co‐shedding or binary vortex regime (G ≥4). Hysteresis with different vortex patterns is observed in a certain range of the gap spacings and also for the onset of the vortex shedding. Copyright © 2011 John Wiley & Sons, Ltd.     

FLOW PERIODICITY AND ACOUSTIC RESONANCE IN PARALLEL TRIANGLE TUBE BUNDLES

Parallel triangle tube arrays with pitch ratios in the range of 1·2–4·2 have been tested at Reynolds numbers up to 9×10⁴to investigate the vorticity shedding and acoustic resonance mechanisms. Three different components of flow periodicities have been observed. The flow periodicity with the highest Strouhal number (S₃) is the weakest component. It is caused by a shear-layer instability in small pitch ratio arrays and at low Reynolds numbers. The S₂component is associated with small-scale vortex shedding at the first row. The third component has the lowest Strouhal number (S₁) and is the strongest. It is generated by large-scale, alternating vortex shedding at deeper rows, and it becomes dominant at all rows at high Reynolds numbers. For tube arrays with pitch ratios less than 3·4, the onset of acoustic resonances could not be related to the natural flow periodicities mentioned above. This behaviour is in contrast with that of normal triangle arrays, but similar to the acoustic behaviour of in-line arrays. Strouhal number charts for the natural flow periodicities and for the onset of acoustic resonances have been developed.     

Flow-excited acoustic resonance of two side-by-side cylinders in cross-flow

The aeroacoustic response of two side-by-side circular cylinders in cross-flow is investigated experimentally. In order to investigate the effect of the gap between the cylinders on the acoustic resonance mechanism, six spacing ratios between the cylinders, in the range of T/D=1.25–3, have been investigated, where D is the diameter of the cylinders and T the centre-to-centre distance between them. Special attention is given to the intermediate spacing ratio range, which exhibits bistable flow regimes in the absence of resonance. During the tests, the acoustic cross-modes of the duct housing the cylinders are self-excited. For the intermediate spacing ratios, T/D=1.25, 1.35, 1.46 and 1.75, two distinct vortex-shedding frequencies at the off-resonance conditions are observed. These are associated with the wide and narrow wakes of the cylinders, as described in the literature. In this case, acoustic resonances occur at a Strouhal number, which is between those observed before the onset of resonance. The acoustic resonance synchronizes vortex shedding in the two wakes and thereby eliminates the bistable flow phenomenon. For large spacing ratios, T/D=2.5 and 3, vortex shedding occurs at a single Strouhal number at which the acoustic resonance is excited.     

Passive control of wake flow by two small control cylinders at Reynolds number 80

Passive control of the wake behind a circular cylinder in uniform flow is studied by numerical simulation at Re_D=80. Two small control cylinders are placed symmetrically along the separating shear layers at various stream locations. In the present study, the detailed flow mechanisms that lead to a significant reduction in the fluctuating lift but maintain the shedding vortex street are clearly revealed. When the stream locations lie within 0.8≤X_C/D≤3.0, the alternate shedding vortex street remains behind the control cylinders. In this case, the symmetric standing eddies immediately behind the main cylinder and the downstream delay of the shedding vortex street are the two primary mechanisms that lead to a 70–80% reduction of the fluctuating lift on the main cylinder. Furthermore, the total drag of all the cylinders still has a maximum 5% reduction. This benefit is primarily attributed to the significant reduction of the pressure drag on the main cylinder. Within X_C/D>3.0, the symmetry of the standing eddy breaks down and the staggered vortex street is similar to that behind a single cylinder at the same Reynolds number. In the latter case, the mean pressure drag and the fluctuating lift coefficients on the main cylinder will recover to the values of a single cylinder.     

FLUID BEHAVIOUR OF SIDE-BY-SIDE CIRCULAR CYLINDERS IN STEADY CROSS-FLOW

The flow field for two and three circular cylinders of equal diameter D arranged in a side-by-side configuration in steady cross-flow was investigated using flow visualization, hot-film anemometry and particle image velocimetry (PIV), for centre-to-centre pitch ratios from T/D=1·0 to 6·0, and Reynolds numbers from Re=500 to 3000. For two-cylinder arrangements, three basic flow patterns were observed: single bluff-body vortex shedding at small T/D , biased flow with synchronized vortex shedding at intermediateT /D , and symmetric flow with synchronized vortex shedding at larger T/D . For three-cylinder arrangements, either single bluff-body behaviour or an asymmetric biased flow pattern could be observed at smallT /D , whereas a symmetric-biased flow pattern was found at intermediate T/D . Instantaneous representations of the in-plane vorticity field obtained from the PIV technique revealed some variation in these basic flow patterns at given T/D and Re.     

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.     

Free-stream turbulence effects on vortex-induced vibration of two side-by-side elastic cylinders

The effect of free-stream turbulence on vortex-induced vibration of two side-by-side elastic cylinders in a cross-flow was investigated experimentally. A turbulence generation grid was used to generate turbulent incoming flow with turbulence intensity around 10%. Cylinder displacements in the transverse direction at cylinder mid-span were measured in the reduced velocity range 1.45<U_r0<12.08, corresponding to a range of Reynolds number (Re), based on the mean free-stream velocity and the diameter of the cylinder, between Re=5000–41 000. The focus of the study is on the regime of biased gap flow, where two cylinders with pitch ratio (T/D) varying from 1.17 to 1.90 are considered. Results show that the free-stream turbulence effect is to enhance the vortex-induced force, thus to restore the large-amplitude vibration associated with the lock-in resonance. However, the enhancement is significant at a different Strouhal number (St) for different pitch ratios. When the spacing between two cylinders is relatively small (1.17<T/D<1.50), the enhancement is significant at St≈0.1. When the spacing is increased, the Strouhal number at which the enhancement is significant shifts to St≈0.16. This enlarges the range of reduced velocity to be concerned. An energy analysis showed that free-stream turbulence feeds energy to the cylinder at multiple frequencies of vortex shedding. Therefore, the lock-in region is still of main concern when the approach flow is turbulent.     

Identification of flow regimes around two staggered square cylinders by a numerical study

The flow over two square cylinders in staggered arrangement is simulated numerically at a fixed Reynolds number (\(Re =150\)) for different gap spacing between cylinders from 0.1 to 6 times a cylinder side to understand the flow structures. The non-inclined square cylinders are located on a line with a staggered angle of \(45^{\circ }\) to the oncoming velocity vector. All numerical simulations are carried out with a finite-volume code based on a collocated grid arrangement. The effects of vortex shedding on the various features of the flow field are numerically visualized using different flow contours such as \(\lambda _{2}\) criterion, vorticity, pressure and magnitudes of velocity to distinguish the distinctive flow patterns. By changing the gap spacing between cylinders, five different flow regimes are identified and classified as single body, periodic gap flow, aperiodic, modulated periodic and synchronized vortex shedding regimes. This study revealed that the observed multiple frequencies in global forces of the downstream cylinder in the modulated periodic regime are more properly associated with differences in vortex shedding frequencies of individual cylinders than individual shear layers reported in some previous works; particularly, both shear layers from the downstream cylinder often shed vortices at the same multiple frequencies. The maximum Strouhal number for the upstream cylinder is also identified at \({G}^{*}=1\) for aperiodic flow pattern. Furthermore, for most cases studied, the downstream cylinder experiences larger drag force than the upstream cylinder.     

Force coefficients and Strouhal numbers of three circular cylinders subjected to a cross-flow

In this paper, wind tunnel experiments were conducted to measure the mean force coefficients and Strouhal numbers for three circular cylinders of equal diameters in an equilateral-triangular arrangement when subjected to a cross-flow. These experiments were carried out at five subcritical Reynolds numbers ranging from 1.26 × 10⁴ to 6.08 × 10⁴. The pressure distributions on the surface of the cylinders were measured using pressure transducers. Furthermore, the hot-wire anemometer was employed to measure the vortex shedding frequencies behind each cylinder. Six spacing ratios (l/d) varying from 1.5 to 4 were investigated. It is observed that for l/d > 2, the upstream cylinder experiences a lower mean drag coefficient compared with the downstream cylinders. The minimum values of the drag coefficient for the downstream cylinders occur at l/d = 1.5 and l/d = 2, because there is no vortex shedding from the foregoing cylinders. Also, the value of the pressure coefficient behind the upstream cylinder reduces by increasing l/d. Moreover, by decreasing the value of l/d, the Strouhal number for the upstream cylinder increases. It can be concluded that the flow pattern and aerodynamic coefficients are basically dependent on l/d; in other words, decreasing l/d results in an increase in the effects of the flow interference between the cylinders.     

Large eddy simulation of cross-flow through a staggered tube bundle at subcritical Reynolds number

The Large Eddy Simulation (LES) technique is used to study the vortex shedding characteristics inside a staggered tube array consisting of six rows with intermediate spacings (S_L/D×S_T/D=1.6×3.6) at the subcritical Reynolds number of 8600 (based on the gap velocity). The filtered equations are discretised using the finite volume method in an unstructured, collocated grid arrangement with second-order accurate methods in space and time. The predictions of mean velocities and Reynolds stresses are in very good agreement with detailed LDA measurements performed in 17 stations along the depth of the array. The sizes of the recirculation zones behind the cylinders in the first and third row also compare favourably with available correlations. Two distinct and independent shedding frequencies are detected behind the first two rows, but the high-frequency component vanishes in the downstream rows. The corresponding Strouhal numbers agree well with measurements available in the literature for similar tube spacings. The lift coefficient as well as instantaneous flow patterns of the whole array are also examined.     

Time-averaged topological flow patterns and their influence on vortex shedding of a square cylinder in crossflow at incidence

Flow characteristics around the square cylinder and their influence on the wake properties are studied. Time-averaged flow patterns on the surfaces of square cylinder in a cross-stream at incidence are experimentally probed by surface-oil flow technique and analyzed by flow topology for Reynolds numbers between 3.9×10⁴ and 9.4×10⁴ as the incidence angle changes from 0° to 45°. Vortex shedding characteristics are measured by a single-wire hot-wire anemometer for Reynolds numbers between 5×10³ and 1.2×10⁵. The effects of topological flow patterns on the wake properties then are revealed and discussed. Flows around the square cylinder are identified as three categories: the subcritical, supercritical, and wedge flows according to the prominently different features of the topological flow patterns. The Strouhal number of vortex shedding, turbulence in the wake, and wake width present drastically different behaviors in different characteristic flow regimes. A critical incidence angle of 15° separates the subcritical and supercritical regimes. At the critical incidence angle the wake width and shear-layer turbulence present minimum values. The minimum wake width appearing at the critical incidence angle, which leads to the maximum Strouhal number, is due to the reattachment of one of the separated boundary layer to the lateral face of the square cylinder. If the Strouhal numbers are calculated based on the wake width instead of the cross-stream projection width of cylinder, the data in the subcritical and supercritical regimes are well correlated into two groups, which would approach constants at high Reynolds numbers.     

The effects of surface injection through a perforated square cylinder on some aerodynamic parameters

The surface pressure distribution and the vortex shedding frequency were investigated for the flow around perforated horizontal and diagonal square cylinders with surface injection through various surfaces. For this purpose, surface pressure measurements on each square cylinder (horizontal and diagonal) and vortex shedding frequency measurements in the wake region were performed at three different Reynolds numbers in a wind tunnel. The parameters considered were injection coefficient, position of perforated surface (i.e., top, rear, top-rear and all), pressure coefficient, drag coefficient, and the Strouhal number. The results showed that pressure coefficient distribution, drag coefficient, and the Strouhal number were influenced by the position of the perforated surface and by the injection coefficient. The surface injections through the top-rear, rear and all surfaces of a diagonal square cylinder reduce the drag coefficient for the all Reynolds numbers, while the injection through all surfaces only reduces the drag coefficient of a horizontal square cylinder. The other aerodynamic parameter Strouhal number can also be controlled by injection through certain surfaces of a horizontal square cylinder.     

Thermal study of an array of inline horizontal cylinders below a nearly adiabatic ceiling

Steady state two-dimensional free convection heat transfer from a horizontal, isothermal cylinder in a horizontal array of cylinders consists of three isothermal cylinders, located underneath a nearly adiabatic ceiling is studied experimentally. A Mach–Zehnder interferometer is used to determine thermal field and smoke test is made to visualize flow field. Effects of the cylinders spacing to its diameter (S/D), and cylinder distance from ceiling to its diameter (L/D) on heat transfer from the centered cylinder are investigated for Rayleigh numbers from 1500 to 6000. Experiments are performed for an inline array configuration of horizontal cylinders of diameters D = 13 mm. Results indicate that due to the nearly adiabatic ceiling and neighboring cylinders, thermal plume resulted from the centered cylinder separates from cylinder surface even for high L/D values and forming recirculation regions. By decreasing the space ratio S/D, the recirculation flow strength increases. Also, by decreasing S/D, boundary layers of neighboring cylinders combine and form a developing flow between cylinders. The strength of developing flow depends on the cylinders Rayleigh number and S/D ratio. Due to the developing flow between cylinders, the vortex flow on the top of the centered cylinder appears for all L/D ratios and this vortex influences the value of local Nusselt number distribution around the cylinder.Variation of average Nusselt number of the centered cylinder depends highly on L/D and the trend with S/D depends on the value of Rayleigh number.     

Vortex shedding and acoustic resonance of single and tandem finned cylinders

The effect of fins on vortex shedding and acoustic resonance is investigated for isolated and two tandem cylinders exposed to cross-flow in a rectangular duct. Three spacing ratios between the tandem cylinders (S/D_e=1.5, 2 and 3) are tested for a Reynolds number range from 1.6×10⁴ to 1.1×10⁵. Measurements of sound pressure as well as mean and fluctuating velocities are performed for bare and finned cylinders with three different fin densities. The effect of fins on the sound pressure generated before the onset of acoustic resonance as well as during the pre-coincidence and coincidence resonance is found to be rather complex and depends on the spacing ratio between cylinders, the fin density and the nature of the flow-sound interaction mechanism.For isolated cylinders, the fins reduce the strength of vortex shedding only slightly, but strongly attenuate the radiated sound before and during the occurrence of acoustic resonance. This suggests that the influence of the fins on correlation length is stronger than on velocity fluctuations. In contrast to isolated cylinders, the fins in the tandem cylinder case enhance the vortex shedding process at off-resonant conditions, except for the large spacing case which exhibits a reversed effect at high Reynolds numbers. Regarding the acoustic resonance of the tandem cylinders, the fins promote the onset of the coincidence resonance, but increasing the fin density drastically weakens the intensity of this resonance. The fins are also found to suppress the pre-coincidence resonance for the tandem cylinders with small spacing ratios (S/D_e=1.5, 2 and 2), but for the largest spacing case (S/D_e=3), they are found to have minor effects on the sound pressure and the lock-in range of the pre-coincidence resonance.     

TANDEM CYLINDERS IN IMPULSIVELY STARTED FLOW

The impulsively started flow field for circular cylinders of equal diameter arranged in tandem was investigated using flow visualization and particle image velocimetry (PIV), over a longitudinal pitch ratio range ofL /D=1·0–3·0, and for Reynolds numbers from Re=1200–3800. The PIV technique was used to obtain a time history of the instantaneous in-plane vorticity field from the moment of impulsive start, from which the spatial and temporal development of the flow was studied. Measurements of vortex strength and vortex position relative to the cylinders were obtained from these data. Three types of fluid behaviour were identified based on L/D: single bluff-body behaviour when the cylinders are in contact, constrained streamwise growth and lateral expansion of the gap recirculation zones at small and intermediate L/D, and independent formation of recirculation zones similar to a single impulsively started circular cylinder at larger L/D.