Investigation of peak frequencies in the flopping regime with a two-cylinder array

The variation of the base pressure coefficient (C_p), velocity power spectra, and velocity time–frequency plots for an array of two cylinders aligned normal to the flow are presented. Power spectra of the fluctuating velocity downstream of the two-cylinder array with s/d=0.750 (where s is the spacing between the top and bottom surfaces of adjacent cylinders and d is the diameter of the cylinder) show two peaks. The corresponding Wigner–Ville frequency–time plot of the same fluctuating velocity time series shows that the peak frequency observed during a narrow wake remains constant and relatively high while the peak frequency observed during a wide wake remains constant and relatively low. The two frequency values are consistent with the peaks observed in the power spectra. Thus, during flopping, the high frequency observed in the velocity power spectra is always the peak frequency for a narrow wake and the low frequency observed in the velocity power spectra is always the peak frequency for a wide wake.     

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.     

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.     

Wake-induced vibrations of an elastically mounted cylinder located downstream of a stationary larger cylinder at low Reynolds numbers

Two-dimensional numerical simulations of flow past two unequal-sized circular cylinders in tandem arrangement are performed at low Reynolds numbers (Re). The upstream larger cylinder is stationary, while the downstream cylinder has both one (transverse-only) and two (transverse and in-line) degrees of freedom (1-dof and 2-dof, respectively). The Re, based on the free stream velocity U_∞ and the downstream cylinder diameter d, varies between 50 and 200 with a wide range of reduced velocities U_r. The diameter of the upstream cylinder is twice that of the downstream cylinder, and the center-to-center spacing is 5.5d. In general, for the 1-dof case, the calculations show that the wake-induced vibrations (WIV) of the downstream cylinder are greatly amplified when compared to the case of a single cylinder or two equal-sized cylinders. The transverse amplitudes build up to a significantly higher level within and beyond the lock-in region, and the U_r associated with the peak amplitude shifts toward a higher value. The dominant wake pattern is 2S mode for Re=50 and 100, while with the increase of Re to 150 and 200, the P+S mode can be clearly observed at some lower U_r. For the 2-dof vibrations, the transverse response characteristics are similar to those presented in the corresponding 1-dof case. The in-line responses are generally much smaller, except for several significant vibrations resulting from in-line resonance. The obvious in-line vibration may induce a C (chaotic) vortex shedding mode for higher Re (Re=200). With regard to the 2-dof motion trajectories, besides the typical figure-eight pattern, several odd patterns such as figure-double eight and single-looped trajectories are also obtained due to the wake interference effect.     

Two-dimensionality of a cantilevered-cylinder wake in the presence of an oscillating upstream cylinder

The effect of a longitudinally oscillating cylinder on the two-dimensionality of flow around a downstream cylinder is studied based on a two-point correlation measured using two hot-wires. The oscillation amplitude is A/d=0.472 and the oscillation frequency f_e/f_s=0.0372 and 0.186, where d is the cylinder diameter and f_s the frequency of natural vortex shedding from an isolated stationary cylinder. Three centre-to-centre spacing (L) ratios of the two cylinders were examined, i.e., L/d=1.8, 2.5 and 4.8, representing three typical flow regimes. The experiment was conducted at a Reynolds number (Re) of 5920, based on d and the free-stream velocity. It is found that the spanwise correlation of the flow depends on not only the oscillation but also the flow regimes. At L/d=1.8, the correlation is strongest among the three regimes, but worst in the co-shedding regime (L/d=4.8). The upstream cylinder oscillation improves the spanwise correlation of the flow in the gap of the cylinders, irrespective of regimes, especially for L/d=1.8 and 2.5, but impairs that behind the cylinders for L/d=1.8 and 2.5 due to a change in the flow regime. A theoretical analysis based on the boundary vorticity theory indicates that the oscillation increases the vorticity flux, in particular, in the spanwise direction between the cylinders, resulting in a significantly improved spanwise correlation, though this increase is negligibly small behind the downstream cylinder.     

Effect of flow diverters on free convection heat transfer from a pair of vertical arrays of isothermal cylinders

Laminar free convection heat transfer from two vertical arrays of five isothermal cylinders separated by flow diverters is studied experimentally using a Mach-Zehnder interferometer. The width of flow diverters is kept constant to two-cylinder diameters and the cylinders vertical center-to-center spacing is equal to three-cylinder diameter. Effect of the ratio of the horizontal spacing between two cylinder arrays to their diameter (S_h/D) on heat transfer from the cylinders is investigated for various Rayleigh numbers. The experiments are performed for S_h/D = 2-4, and the Rayleigh number based on the cylinder diameter ranging from 10³ to 3 × 10³. It is observed that for small S_h/D ratios, the flow diverters have a negative effect on the total rate of heat transfer from the arrays; while by increasing the horizontal center to center spacing, they tend to enhance the overall cooling rate of the array. Moreover, increasing Ra and S_h/D generally results in a higher average Nusselt number for each cylinder in the array.     

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.     

Interference effect of two equal‐sized square cylinders in tandem arrangement: With planar shear flow

Numerical simulations have been performed for flow past two equal‐sized square cylinders in tandem arrangement subjected to incoming planar shear flow. Effect of L/d ratio and the shear parameter has been studied. The range of L/d ratio (ratio of center‐to‐center distance (L) to cylinder width (d)) is varied from 2 to 7 and the non‐dimensional shear parameter (K) is varied from 0.0 to 0.4 in steps of 0.1. For all the cases the Reynolds number (Re) based on centerline velocity and cylinder width is fixed at 100. The results are compared with that of isolated square cylinder with uniform flow. Strouhal number decreases with increasing shear parameter. There are more than one shedding frequency at high shear parameters and L/d ratios. The mean drag coefficient is decreased with shear parameter and lesser than that of the single cylinder. The root mean square (RMS) value of both lift and drag coefficients is higher for the downstream cylinder for all values of shear parameter. With increasing L/d ratio, for both lift and drag, the RMS value increases and then decreases for upstream cylinder, whereas it continuously increases for the downstream cylinder. The stagnation point is moved towards the top leading edge with increasing shear. The critical L/d ratio, which is defined as the distance between two cylinders, beyond which the vortex shedding from the upstream cylinder occurs, decreases with increasing shear parameter. Copyright © 2007 John Wiley & Sons, Ltd.     

On Rayleigh scattering by a grating

The acoustic diffraction of a plane wave by a periodic row of identical cylinders of arbitrary cross section and characteristic dimension a is calculated for ka ? kd < π, where k is the wave number and d is the wavelength of the array. The reflection and transmission coefficients depend only on d, k, the angle of incidence, and the area and virtual mass of the cross section. The general results are applied to a grating of inclined flat plates.     

Experimental investigation of flow-induced vibration on isolated and tandem circular cylinders fitted with strakes

The effect of varying the geometric parameters of helical strakes on vortex-induced vibration (VIV) is investigated in this paper. The degree of oscillation attenuation or even suppression is analysed for isolated circular cylinder cases. How a cylinder fitted with strakes behaves when immersed in the wake of another cylinder in tandem arrangement is also investigated and these results are compared to those with a single straked cylinder. The experimental tests are conducted at a circulating water channel facility and the cylindrical models are mounted on a low-damping air bearing elastic base with one degree-of-freedom, restricted to oscillate in the transverse direction to the channel flow. Three strake pitches (p) and heights (h) are tested: p=5, 10, 15d, and h=0.1, 0.2, 0.25d. The mass ratio is 1.8 for all models. The Reynolds number range is from 1000 to 10 000, and the reduced velocity varies up to 21. The cases with h=0.1d strakes reduce the amplitude response when compared to the isolated plain cylinder, however the oscillation still persists. On the other hand, the cases with h=0.2, 0.25d strakes almost completely suppress VIV. Spanwise vorticity fields, obtained through stereoscopic digital particle image velocimetry (SDPIV), show an alternating vortex wake for the p=10d and h=0.1d straked cylinder. The p=10d and h=0.2d cylinder wake has separated shear layers with constant width and no roll-up close to the body. The strakes do not increase the magnitude of the out-of-plane velocity compared to the isolated plain cylinder. However, they deflect the flow in the out-of-plane direction in a controlled way, which can prevent the vortex shedding correlation along the span. In order to investigate the wake interference effect on the strake efficiency, an experimental arrangement with two cylinders in tandem is employed. The centre-to-centre distance for the tandem arrangement varies from 2 to 6. When the downstream p=10d and h=0.2d cylinder is immersed in the wake of an upstream fixed plain cylinder, it loses its effectiveness compared with the isolated case. Although the oscillations have significant amplitude, they are limited, which is a different behaviour from that of a tandem configuration with two plain cylinders. For this particular case, the amplitude response monotonically increases for all gaps, except one, a trait usually found in galloping-like oscillations. SDPIV results for the tandem arrangements show alternating vortex shedding and oscillatory wake.     

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.     

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.     

Natural convection in power-law fluids from two square cylinders in tandem arrangement at moderate Grashof numbers

In this work, free convective flow and heat transfer in power-law fluids from two heated square cylinders in tandem arrangement is studied. The governing differential equations have been solved numerically over wide ranges of Grashof number, 10 ≤ Gr ≤ 1,000, Prandtl number, 0.71 ≤ Pr ≤ 50 and power-law index, 0.4 ≤ n ≤ 1.8. In order to elucidate the extent of inter-cylinder interaction, the non-dimensional inter-cylinder spacing, L/d is varied in the range, 2 ≤ L/d ≤ 6. The results are interpreted in terms of streamline and isotherm contours in the proximity of two cylinders to gain physical insights into the nature of flow. At the next level, the distribution of the local Nusselt number along the surface of the cylinders is presented. At the minimum inter-cylinder spacing due to the intense interference, the downstream cylinder contributes much less to the overall heat transfer whereas it experiences much higher hydrodynamic drag than the upstream cylinder. Broadly, the local and average Nusselt number for both cylinders show a positive dependence on both Grashof and Prandtl numbers. Also, all else being equal, shear-thinning fluid behaviour promotes the rate of heat transfer and shear-thickening fluid behaviour impedes it. Finally, the present numerical results have been correlated by using simple forms of equations thereby enabling the estimation of Nusselt number in a new application.     

Vortex shedding from two finite circular cylinders in a staggered configuration

Wind tunnel experiments were conducted to measure the vortex shedding frequencies for two circular cylinders of finite height arranged in a staggered configuration. The cylinders were mounted normal to a ground plane and were partially immersed in a flat-plate turbulent boundary layer. The Reynolds number based on the cylinder diameter was Re_D=2.4×10⁴, the cylinder aspect ratio was AR=9, the boundary layer thickness relative to the cylinder height was δ/H=0.4, the centre-to-centre pitch ratio was varied from P/D=1.125 to 5, and the incidence angle was incremented in small steps from α=0° to 90°. The Strouhal numbers were obtained behind the upstream and downstream cylinders using hot-wire anemometry. From the behaviour of the Strouhal number data obtained at the mid-height position, the staggered configuration could be broadly classified by the pitch ratio as closely spaced (P/D<1.5), moderately spaced (1.5?P/D?3), or widely spaced (P/D>3). The closely spaced staggered finite cylinders were characterized by the same Strouhal number measured behind both cylinders, an indication of single bluff-body behaviour. Moderately spaced staggered finite cylinders were characterized by two Strouhal numbers at most incidence angles. Widely spaced staggered cylinders were characterized by a single Strouhal number for both cylinders, indicative of synchronized vortex shedding from both cylinders at all incidence angles. For selected staggered configurations representative of closely spaced, moderately spaced, or widely spaced behaviour, Strouhal number measurements were also made along the vertical lengths of the cylinders, from the ground plane to the free end. The power spectra showed that for certain cylinder arrangements, because of the influences of the cylinder–wall junction and free-end flow fields, the Strouhal numbers and flow patterns change along the cylinder.     

The near wake of sinusoidal wavy cylinders: Three-dimensional POD analyses

Three-dimensional (3D) proper orthogonal decomposition (POD) analyses are conducted to investigate the near wake of sinusoidal wavy cylinders. For a wave amplitude a/D_m = 0.152, three typical spanwise wavelengths (λ_z) of the wavy cylinder are taken into account, i.e., λ_z/D_m = 1.89, 3.79 and 6.06, where D_m is the mean diameter of the wavy cylinder, among which λ_z/D_m = 1.89 and 6.06 are the optimum wavelengths corresponding to the largest reduction/suppression of fluid forces acting on the wavy cylinder. Time- and space-resolved three-component velocities of the near wake flow, obtained from large eddy simulation (LES) at a subcritical Reynolds number Re = 3 × 10³, are used in the 3D POD analyses. Comparison is made among the wavy cylinders of the three λ_z/D_m values as well as between them and a smooth cylinder, in terms of POD modes, mode energy, mode coefficients, as well as reconstructed flow structures by lower modes. For the optimum λ_z/D_m = 1.89 and 6.06, energy associated with the first two POD modes is significantly reduced compared with that for λ_z/D_m = 3.79 and the smooth cylinder. Distinct characteristics are observed on the lower POD modes for the wavy cylinders. It is found that the first two POD modes for λ_z/D_m = 1.89 and 6.06 are linked to large-scale streamwise vortices that are additionally introduced into the near wake due to the wavy geometry. Meanwhile, POD mode 3 suggests that the wavy cylinder with the larger optimum λ_z/D_m (= 6.06) generates dominant hairpin-like and spanwise coherent structures (CSs) shedding from the saddle at a different frequency from those shedding from the node. Evolutionary development of these CSs is discussed based on reconstructed flows.     

Unsteady characteristics of low-Re flow past two tandem cylinders

This study investigated the two-dimensional flow past two tandem circular or square cylinders at Re = 100 and D / d = 4–10, where D is the center-to-center distance and d is the cylinder diameter. Numerical simulation was performed to comparably study the effect of cylinder geometry and spacing on the aerodynamic characteristics, unsteady flow patterns, time-averaged flow characteristics and flow unsteadiness. We also provided the first global linear stability analysis and sensitivity analysis on the physical problem for the potential application of flow control. The objective of this work is to quantitatively identify the effect of the cylinder geometry and spacing on the characteristic quantities. Numerical results reveal that there is wake flow transition for both geometries depending on the spacing. The characteristic quantities, including the time-averaged and fluctuating streamwise velocity and pressure coefficient, are quite similar to that of the single cylinder case for the upstream cylinder, while an entirely different variation pattern is observed for the downstream cylinder. The global linear stability analysis shows that the spatial structure of perturbation is mainly observed in the wake of the downstream cylinder for small spacing, while moves upstream with reduced size and is also observed after the upstream cylinder for large spacing. The sensitivity analysis reflects that the temporal growth rate of perturbation is the most sensitive to the near-wake flow of downstream cylinder for small spacing and upstream cylinder for large spacing.     

Passive Scalar Transport in a Turbulent Cylinder Wake in the Presence of a Downstream Cylinder

This work aims to investigate how the presence of a downstream cylinder affects the passive scalar transport in a cylinder wake. The wake was generated by two tandem brass circular cylinders of the same diameter (d). The cylinder centre-to-centre spacing L/d was 1.3, 2.5 and 4.0, respectively, covering the three typical flow regimes of this flow. The upstream cylinder was slightly heated. Measurements were conducted at x/d= 10 and Re (≡ dU _∞/ν, where U _∞ is the free-stream velocity and ν is the kinematic viscosity of fluid) = 7000. A three-wire probe consisting of an X-wire and a cold wire was used to measure the velocity and temperature fluctuations, while an X-wire provided a phase reference. The phase-averaged velocity vectors and vorticity display single vortex street behind the downstream cylinder, irrespective of the flow regimes. However, the detailed flow structure exhibits strong dependence on L/d in terms of the Strouhal number, the vortex strength and its downstream evolution. This naturally affects passive scalar transport. The coherent and incoherent heat flux vectors show significant variation for different L/d.     

Effects of aspect ratio on the drag of a wall-mounted finite-length cylinder in subcritical and critical regimes

The effect of cylinder aspect ratio (??H/d, where H is the cylinder height or length, and d is the cylinder diameter) on the drag of a wall-mounted finite-length circular cylinder in both subcritical and critical regimes is experimentally investigated. Two cases are considered: a smooth cylinder submerged in a turbulent boundary layer and a roughened cylinder immersed in a laminar uniform flow. In the former case, the Reynolds number Re _d (??U _?? d/??, with U _?? being the free-stream velocity and ?? the fluid viscosity) was varied from 2.61?×?10⁴ to 2.87?×?10⁵, and two values of H/d (2.65 and 5) were examined; in the latter case, Re _d ?=?1.24?×?10⁴?C1.73?×?10⁵ and H/d?=?3, 5 and 7. In the subcritical regime, both the drag coefficient C _D and the Strouhal number St are smaller than their counterparts for a two-dimensional cylinder and reduce monotonously with decreasing H/d. The presence of a turbulent boundary layer causes an early transition from the subcritical to critical regime and considerably enlarges the Re _d range of the critical regime. No laminar separation bubble occurs on the finite-length cylinder immersed in the turbulent boundary layer, and consequently, the discontinuity is not observed in the C _D?CRe _d and St?CRe _d curves. In the roughened cylinder case, the Re _d range of the critical regime grows gradually with decreasing H/d, while the C _D crisis becomes less obvious. In both cases, H/d has a negligible effect on the critical value of Re _d at which transition occurs from the subcritical to critical regime.     

Flow patterns and turbulence effects in large cylinder arrays

Studies on flow-induced vibrations in large tube bundles are usually focused solely on frequency analysis, without considering the flow patterns which are responsible for the fluid forces. Furthermore, investigations which involve variations in the spacing ratios do not separate transversal and longitudinal proximity effects. The purpose of this article is to separately analyze the influence of the transversal (T/D) and longitudinal (L/D) spacing ratios of a confined in-line cylinder array with five rows on the flow characteristics and to identify flow patterns. The laser Doppler anemometry technique was employed to acquire the mean velocity and its fluctuations in the transversal and longitudinal directions between the cylinder rows. Strouhal numbers and regimes reported in the literature were identified in the experiments. The same regime did not always persist along all cylinder rows for a given spacing ratio, as a result of the combined longitudinal and transversal proximity effects and also of the generation of turbulence by the array. For the smallest T/D ratio, a quasi-steady behavior associated with the biased flow pattern was noted in the experimental set-up and flip-flopping was observed in one case. Additionally, the flow characteristics in these arrays diverged from tube bundle classifications described in the literature. The behavior of the fluid forces and susceptibility to vibrations in the array were predicted based on the turbulence intensity of the incident flow of the cylinders. The results reinforced the need to extend flow pattern investigations to arrays with more cylinder rows and to consider both transversal and longitudinal proximity effects, when studying flow-induced vibrations.     

Characteristics and suppression of flow-induced vibrations of two side-by-side circular cylinders

A free-vibration experiment was conducted to examine flow-induced vibration (FIV) characteristics of two identical circular cylinders in side-by-side arrangements at spacing ratio T^⁎ (=T/D)=0.1–3.2, covering all possible flow regimes, where T is the gap spacing between the cylinders and D is the cylinder diameter. Each of the cylinders was two-dimensional, spring mounted, and allowed to vibrate independently in the cross-flow direction. Furthermore, an attempt to suppress flow-induced vibrations was undertaken by attaching flexible sheets at the rear stagnation lines of the cylinders. Based on the vibration responses of the two cylinders, four vibration patterns I, II, III and IV are identified at 0.1≤T^⁎<0.2, 0.2≤T^⁎≤0.9, 0.9<T^⁎<2.1 and 2.1≤T^⁎≤3.2, respectively. Pattern I is characterized by the two cylinders vibrating inphase^, with the maximum amplitudes occurring at the same reduced velocity Ur=10.47 almost two times that (Ur=5.25) for an isolated cylinder. Pattern II features no vibration generated for either cylinder. Pattern III exemplifies the occurrence of the maximum vibration amplitude of a cylinder at a smaller Ur and that of the other cylinder at a higher Ur compared to its counterpart in an isolated cylinder. Pattern IV represents each cylinder response resembling an isolated cylinder response; the vibrations of the two cylinders are, however, coupled inphase or antiphase. Linking maximum vibration amplitudes to fluctuating lift forces acting on fixed cylinders reveals that fluid–structure interactions between two fixed cylinders and between two elastic cylinders are not the same, even though vibration is not significant. As such, while two fixed cylinders generate narrow and wide wakes at 0.2≤T^⁎<1.7, two elastic cylinders do the same for a longer range of T^⁎ (0.2≤T^⁎<2.1). The flexible sheets effectively suppress FIV of the two cylinders in patterns III and IV, and reduce the vibration amplitude in pattern I. For the effectively controlled cases (patterns III and IV), the flexible sheet of each cylinder folds into a semicircle at the base, forming two free edges.