Circular Cylinders In Tandem Arrangement Research Articles

Three-dimensional computation for flow-induced vibrations of two circular cylinders in tandem arrangement with narrow spacing

Flow-induced vibrations of two circular cylinders in tandem arrangement which are mounted in a three-dimensional flow field are investigated at a high Reynolds number of 20,000. A third-order upwind finite element scheme and the arbitrary Lagrangian–Eulerian (ALE) formulation are used to solve the three-dimensional incompressible Navier–Stokes equations. Two circular cylinders which are treated as rigid bodies are free to vibrate in both in-line and cross-flow directions. Accordingly, both cylinders are assumed as a two-degree of freedom system. The upstream cylinder is set in a smooth flow and the downstream cylinder lies in the wakes which are shed from the upstream one. Spacing S between center-to-center of the cylinders is 2D and 3D (D is the diameter of the cylinders ) less than the critical spacing. The Scruton number Sc with respect to the flow-induced vibration is given as 0.99. The excitation vibrations to the in-line direction occur in the low range of the reduced velocity because of the low Scruton number. In addition, large cross-flow amplitudes of both cylinders are observed in the high range of the reduced velocity.

Flow-Induced vibration and heat transfer enhancement in tandem cylinders: Effects of cylinder shape, corner radii, and spacing ratio

In this work, flow-induced vibration (FIV) of two heated cylinders in the tandem arrangement is numerically investigated at a Reynolds number of 150. The effect of the spacing ratio (L/D) and the corner radius (r*) is investigated by changing L/D from 2 to 4 and r* from 0 to 1, where 0 corresponds to the square cross-section and 1 to the circular cross-section. The cylinders are oriented to maintain a constant angle of attack of 45° and are allowed to vibrate in the transverse direction only. The one degree of freedom (1-DOF) motion of the cylinders is studied with varying reduced velocities (Ur = 2–10). The mass ratio (m*) of the cylinder is taken as 10, while the damping is neglected to obtain the maximum vibrational amplitude. The findings suggest that the maximum vibrational amplitude (A/D) occurs for square-shaped cylinders, while the least occurs for circular shapes. It was found that the lock-in for a single cylinder occurred at Ur = 6, irrespective of the corner radius. For tandem cylinders with L/D = 2, the lock-in region occurred at Ur = 6–8 for circular cylinders and at Ur = 8–10 for square cylinders. However, lock-in occurred at Ur = 6–8 for both square and circular tandem cylinders at L/D = 4. The vorticity patterns observed in this study include 2S, C(2S), 2P, and P + S. The flow topology, the response behavior of the cylinders, and local (Nul) and average (Nuavg) Nusselt numbers were affected by various parameters, including the corner radius, spacing ratio, reduced velocity, and the average drag coefficient. For the single cylinder, changing the shape from square to circular resulted in a 40.4% and 4.71% decrease in the maximum A/D and Nuavg, respectively. Considering the twin square cylinders in tandem with L/D = 2, the upstream and downstream cylinders experienced 3.86% and 58.0% higher A/D as compared to the single cylinder. However, increasing L/D to 4 from 2 decreased the maximum A/D for upstream and downstream square cylinders by 5.41% and 3.07%, respectively. Compared to the square cylinders at L/D = 4, the circular cylinders resulted in a 28.6% and 35.1% decrease in maximum A/D for upstream and downstream cylinders, respectively, whereas at the same time experienced 33.1% and 32.0% higher Nuavg, respectively. In conclusion, the circular cylinders in tandem arrangement give higher rates of heat transfer while experiencing lower vibration as compared to square and filleted cylinders.

Vortex-induced vibrations of two rigidly coupled circular cylinders in tandem arrangement

In this paper, we study the transverse vortex-induced vibrations (VIV) of two rigidly connected circular cylinders of equal size, arranged in a tandem configuration, by means of two-dimensional numerical computations. Results are examined for Re=250 and a fixed center-to-center separation of 2D. The dynamic response of the two-cylinder system is investigated in detail over a domain of reduced velocities ranging from Ur=2 to 8. The diverse types of branches are identified, on the basis of their distinct characteristics in the amplitude and frequency responses. Among them, the lower branch is of particular interest as it is quasi-periodic in nature, instead of the periodic regime that is well documented for the isolated cylinder case. By scrutinizing the vorticity dynamics, it reveals that this quasi-periodicity arises from the switching between two flow states, which are essentially distinguished by whether an active gap flow is present. The dynamically rich response leads to a rich variety of phase dynamics, involving phase locking, trapping, slipping and drifting; in particular, phase drifting is indicative of a forthcoming phase jump of 180° between the lift force and the displacement. It is also found that in the initial branch, the excitation of the system is driven by the pressure lift force on the rear cylinder; by contrast, in the lower branch, it is the pressure lift force on the front cylinder that acts as a source of excitation.

The influence of cylinders in tandem arrangement on unsteady aerodynamic loads

This paper presents an experimental study on the unsteady pressure loading for two circular cylinders in tandem arrangement for the Reynolds number in the subcritical regime. Experiments were conducted on two heavily instrumented cylinders, each with multiple static and dynamic pressure sensor devices positioned at various peripheral and spanwise locations, enabling extensive dynamic surface pressure, coherence, and turbulence length-scale analysis. Results show that the root-mean-squared pressure magnitude of the pressure distribution results is much larger for the rear cylinder than for the front cylinder. In the case of small spacing ratios, the surface pressure density findings show a decreased shedding frequency on both cylinders, however the critical spacing ratio shows a quick jump in shedding frequency. The lateral coherence results also revealed that beyond the critical spacing, a prominent peak at the fundamental vortex shedding frequency exists, with weaker peaks at shedding harmonics on the front and rear cylinders, resulting in smaller correlation length values than those for smaller spacing ratios. The discovery of tonal peaks and their associated flow mechanics on cylinders in tandem were reinforced by the lift and drag power spectral density as well as the higher-order spectral analysis, such as wavelet analysis and persistence spectrum.

Transient cooling of two circular cylinders arranged in Tandem an bounded by an adiabatic wall

Parametric study is carried out on the transient cooling process of two circular cylinders in tandem arrangement for a specified period of time. Transient analysis of conjugate (conduction and convection) heat dissipation from two identical cylinders is considered with various parameters. The two cylinders of same size and properties are bounded by an adiabatic flat wall from below and the cooling air is flowing normal to their axis (cross flow). The following parameters are investigated in the present study: Reynolds number, cylinders thermal properties, separation distance between the two cylinders and the cooling time. The laminar flow is considered with Reynolds number values from 50 to 500. The simulations are carried out for cooling the two cylinders made of carbon steels, plastics plexiglass and plywood. The local and average Nusselt number for both steady and transient cooling of the two cylinders are presented. The effects of the parameters are investigated and the results are presented to understand the process. It is found that increasing either the separation distance and/or the Reynolds number will increase the heat dissipation and reduce the cooling time. The results show that carbon steels cylinders need longer time of cooling compare with the plywood cylinders due to the difference in their thermal inertia.

Surface Roughness Effects on Flows Past Two Circular Cylinders in Tandem Arrangement at Co-Shedding Regime

This paper contributes by investigating surface roughness effects on temporal history of aerodynamic loads and vortex shedding frequency of two circular cylinders in tandem arrangement. The pair of cylinders is immovable; of equal outer diameter, D; and its geometry is defined by the dimensionless center-to-center pitch ratio, L/D. Thus, a distance of L/D = 4.5 is chosen to characterize the co-shedding regime, where the two shear layers of opposite signals, originated from each cylinder surface, interact generating counter-rotating vortical structures. A subcritical Reynolds number of Re = 6.5 × 104 is chosen for the test cases, which allows some comparisons with experimental results without roughness effects available in the literature. Two relative roughness heights are adopted, nominally ε/D = 0.001 and 0.007, aiming to capture the sensitivity of the applied numerical approach. Recent numerical results published in the literature have reported that the present two-dimensional model of surface roughness effects is able to capture both drag reduction and full cessation of vortex shedding for an immovable cylinder near a moving ground. That roughness model was successfully blended with a Lagrangian vortex method using sub-grid turbulence modeling. Overall, the effects of relative roughness heights on flows past two cylinders reveal changing of behavior of the vorticity dynamics, in which drag reduction, intermittence of vortex shedding, and wake destruction are identified under certain roughness effects. This kind of study is very useful for engineering conservative designs. The work is also motivated by scarcity of results previous discussing flows past cylinders in cross flow with surface roughness effects.

An Implicit Discontinuous Galerkin Chimera Method for Unsteady Laminar Flow Problems with Multiple Bodies

AbstractThe compressible Navier‐Stokes (NS) equations are spatially discretized with the discontinuous Galerkin (DG) method and an implicit backward differentiation formula of second order is used for the temporal discretization. The Chimera method is employed to realize a simple grid generation for complex technical applications consisting of multiple parts. Therefore, non‐trivial overlapping grid areas could occur in the numerical setup which require a robust implementation of the Chimera method. The flow around two circular cylinders in tandem arrangement serves as a validation case and reveals promising results for several configurations compared to reference data in literature.

직렬로 배열된 두 원형 실린더 주위를 지나는 입자가 포함된 유동

Numerical simulations are performed for particle-laden flow around two circular cylinders in tandem arrangements. The present study aims to understand the effects of cylinder spacing and particle size on particle dispersion and deposition characteristics. We consider the Reynolds number of 100 at which vortex shedding takes place, and the density ratio of particle to fluid is fixed as 1,000. For a parametric study, we vary the Stokes number from 0.1 to 10 for the center-to-center spacing of 2D, 3D, and 4D, where D is the cylinder diameter. As the spacing decreases from 4D to 2D, vortex shedding becomes weaker and lift fluctuations are reduced, agreeing well with the previous results. The dispersion pattern of particles around the cylinder changes significantly depending on the spacing. The overall deposition efficiency of the upstream cylinder is very similar to that of a single cylinder. However, the efficiency of the downstream cylinder has much smaller values with a strong dependency on the spacing. The local deposition efficiency and the deposition location are also analyzed in detail.

Numerical investigation into the effect of spacing on the flow-induced vibrations of two tandem circular cylinders at subcritical Reynolds numbers

Two-degree-of-freedom (2DOF) flow-induced vibrations (FIV) for a pair of elastically mounted circular cylinders in tandem arrangement with varying centre-to-centre spacings (Sx) are numerically studied. The Reynolds number range Re=1470–10320 belongs to the subcritical flow regime. Two identical cylinders with a mass ratio of m∗=2.6 and a mass-damping parameter of m∗+Caζ=0.013 are considered in the simulation. Four spacing ratios (Sx∕D, where D is the identical diameter) ranging from 3.0 to 8.0 are employed to investigate the effect of Sx∕D on the FIV responses, hydrodynamic characteristics and wake patterns of the two cylinders. It is found that the effect of the downstream cylinder on the FIV of the upstream one becomes insignificant when Sx∕D≥4.0. Due to the unsteady wake-cylinder interactions, multi-peak responses are observed for the downstream cylinder. Dual resonance with the 2:1 in-line to cross-flow oscillation frequency ratio and figure-eight orbital trajectories is found to occur for the upstream cylinder. In contrast, the trajectories of the downstream cylinder are rather irregular because of the low frequency components in the in-line response at high reduced velocity (Vr). Both shear flow and vortex shedding may appear in the gap region depending on Sx∕D and the relative motion of the two cylinders. In general, the vortex shedding modes of the upstream cylinder are similar to those of a single cylinder. Whereas, the analyses on the wake patterns suggest that the interactions of the upstream wake with the downstream cylinder and its own wake contribute to the unsteady fluid dynamics, which is crucial to maintaining the large-amplitude vibrations of the downstream cylinder at high Vr.

Flow and heat transfer across two inline rotating cylinders: Effects of blockage, gap spacing, Reynolds number, and rotation direction

The manipulation of the heat transfer and flow field using cylinder rotation is of a classical issue. It is of fundamental importance to study the dependence of wake and thermal topologies of two rotating cylinders in tandem arrangements. This study numerically investigates the time-resolved laminar flow, fluid forces, Strouhal number, and convective heat transfer over two isothermal co-rotating and counter-rotating circular cylinders in tandem arrangements for scaled cylinder center-to-center spacing S* = 2.5 - 6, non-dimensional rotational speed |α| ≤ 5, and Reynolds number Re = 100 - 200. How Re, S*, α and computational domain size influence the wake dynamics and thermal attributes is the focus of this study. The numerical procedure is validated against the available data in the literature for a single rotating cylinder. The influence of the blockage ratio on the single- and two-cylinder flow is determined first to decide the appropriate computational domain. It is found that rotating cylinders require a larger computational domain (blockage ratio ≈ 1%, when α> 2) than stationary cylinders (blockage ratio = 5%). The fluid forces are highly sensitive to the cylinder rotation when |α| > 2. Although both cylinders undergo the same magnitudes of time-mean drag coefficient |C¯d| or time-mean lift coefficient |C¯l| at a given |α|, the cylinder rotation shifting from co-rotation to counter-rotation reverses the direction of C¯d, i.e. repulsive for the co-rotation and attractive for the counter-rotation. On the other hand, an increase in S* from 2.5 to 6 with α = 5 results in a 43% drag reduction for either cylinder. The S*, however, has an insignificant effect on C¯l (e.g. upto 5.3% at α = 5) while Re increases both vortex shedding frequency (e.g. 16.8% at α = 1) and heat transfer (e.g. upto 73.3% at α = 1). A flow map in a three-dimensional domain of S*, α and Re is provided, distinguishing steady and unsteady flows. Four distinct flow regimes are labeled, namely steady flow, alternate coshedding (AC) flow, single rotating bluff-body (SRB) flow, and inverted-rotation (IR) flow. An increase in |α| causes a modification of the AC flow to a steady flow and then to a SRB or IR flow.

Numerical investigation on fluid forces of piggyback circular cylinders in tandem arrangement at low Reynolds numbers

Numerical simulations of flows past the piggyback circular cylinders in tandem arrangement are performed by solving the variational multiscale formulation of the incompressible Navier–Stokes equations using in-house finite element method (FEM) codes. The effects of the gap-spacing-to-diameter (G/D) and the two diameter ratio (d/D) on the flow characteristics and the reductions of the root-mean-square (RMS) drag and lift coefficients are considered for Reynolds numbers (Res) are 100 and 200. The validation shows the fluid force coefficients obtained by the in-house FEM codes are in good agreement with the results in the existing literatures. The obtained results show that, with a proper placement of the smaller cylinder ( $$d/D=0.2$$ ) behind the larger cylinder, the RMS drag and lift coefficients largely decrease compared to those of the single circular cylinder. When $$d/D=0.2$$ , the largest reductions of the RMS lift coefficient of the larger cylinder and the RMS total lift coefficient appear at $$G/D=1.2$$ as Re $$=100$$ and at $$G/D=1.0$$ as Re $$=200$$ . It is observed that the proper placement of the smaller cylinder causes the surrounding vorticity to take opposite sign with the vorticity in the outer region so as to suppress and postpone the vortex shedding in the wake, and that the different positions of the vortex shedding at two Res cause that the largest reductions of the RMS lift coefficient of the larger cylinder and the RMS total lift coefficient appear at different G/D as Re is different. When d/D varies, the variation of the RMS total lift coefficient behaves differently at two Res. It decreases with d/D increasing at Re $$=100$$ , while it no longer monotonously varies with d/D, but reaches a minimum in the considered range of d/D at Re $$=200$$ . Moreover, the larger d/D results in stronger suppression and postponement of the vortex shedding in the wake. The effects of the gap-spacing-to-diameter and the two-diameter ratio on the flow characteristics and the reductions of the root-mean-square (RMS) drag and lift coefficients are investigated by stabilized finite element method. With a proper placement of the smaller cylinder behind the larger cylinder, the RMS drag and lift coefficients are smaller than those of the single circular cylinder. The proper placement of the smaller cylinder causes the surrounding vorticity to take opposite sign with the vorticity in the outer region so as to suppress and postpone the vortex shedding in the wake.

The effect of end conditions on the flow-induced vibration of circular cylinders in tandem arrangements

The current paper reports the results of in-water experiments to study the effect of end conditions on cross flow induced vibration (FIV) of a pair of circular cylinders in a tandem arrangement. The upstream cylinder remains fixed but the downstream cylinder is elastically mounted. The single degree of freedom vibrating system has a low mass-damping parameter (m*ζ= 0.012, to 0.013). The Reynolds number ranges from 3.5 × 103 to 4 × 104. Various spacing ratios (S/D= 2, 3, 4, 5 and 6) are examined. The upper end of the oscillating cylinder is the free water surface, but the lower one remains either with or without an endplate.Based on the experimental results it is concluded that the response category, say wake induced vibration (WIV), vortex induced vibration (VIV) or transition, does not change by the presence or absence of the endplate. With the WIV category, the oscillation amplitude (A*) is predominantly higher in the absence of an endplate and the maximum amplitude (A*max) may increase as much as 100%. The maximum lift force coefficient may increase as much as 25%. In the absence of the endplate, the lift force signals contain a perceptible 3rd sub-harmonic at both low and high reduced velocities. With the VIV type of response, the maximum amplitude is less significantly affected by the end conditions.

Cross-flow vibrations of two identical elastically mounted cylinders in tandem arrangement using wind tunnel experiment

In this paper, cross-flow vibrations of two identical elastically mounted circular cylinders in tandem arrangement have been investigated in a wind channel at Reynolds number Re = 4000–42000. The spacing ratios S/D are from 1.2 to 8.0. The vibration amplitude, oscillation frequency fo and vortex shedding frequency fs are investigated. Based on the vibration characteristics, three regimes can be classified. In Regime Ⅰ (S/D ≤ 1.5), the upstream cylinder experiences galloping vibration, while the downstream cylinder undergoes fluctuating with multiple peaks; In Regime Ⅱ (1.5 < S/D ≤ 3.0), two separated vibration regions can be detected for both cylinders. In Regime Ⅲ (3.0 < S/D ≤ 8.0), the upstream cylinder presents a typical vortex-induced vibration (VIV), while the downstream cylinder displays two regions including a VIV and wake-induced galloping (WIG). A hysteresis phenomenon can be observed at S/D = 1.5 and 2.0 for different initial test conditions (‘from rest’ and ‘increasing velocity’). The effect of the initial states (fixed or elastically mounted) of the neighbouring cylinder on the other cylinder is also significant. The fs can be locked to the multiple harmonics of natural frequency fn, while the dominant fo can only be locked to the first harmonic of fn.

Buoyancy-driven flow in annular space from two circular cylinders in tandem arrangement

The two-dimensional numerical investigation is well accomplished to understand the behavior of buoyancy-driven flow in closed annular space. The studied domain consists of a pair of equal-sized circular cylinders in tandem arrangement confined in a circular enclosure which is filled with incompressible Newtonian fluid. The inner cylinders are identical in size and they are supposed to be hot with constant temperature, the outer circular enclosure is kept cold with a constant temperature. The descriptive governing equations of continuity, momentum and energy for the present problem are solved numerically using the finite-volume method. The present research studies the effects of thermal buoyancy strength, the thermophysical characteristics of the fluid, and the size of the inner cylinders on the flow patterns inside the circular domain and rate of heat transfer exchanging between the inner cylinders and fluid flow. The results showed that the studied governing parameters significantly affect the fluid flow and heat transfer rate. An increase in the diameter of inner cylinders makes the effect of buoyancy strength on fluid flow and heat transfer negligible for all values of thermo-physical parameters. Also, the average Nusselt number of each inner cylinder is computed and plotted for industrial applications.

Empirical model for Wake Induced Vibrations frequency response of cylinder with low mass ratio

The vortex-induced vibrations (VIV) of two flexible circular cylinders in tandem arrangements were studied using numerical simulations and verified by experimental data. Simulations were conducted for a constant mass ratio of 1.08, the spacing ranges of 6D to 18D, and the reduced velocities of 2.35–6.71. It is shown that the numerical results are in a good agreement with the experimental data of the amplitude and frequency of response. The features of the vibration amplitude, the dominant frequencies, the vortex structures and the fluid force acting on the cylinders are discussed. The results indicate that there is a great difference between the response of the upstream cylinder and that of the downstream cylinder. When the reduced velocity is beyond the critical reduced velocity Vr*, the dominant frequencies of the upstream cylinder and the downstream cylinder are no longer the same. And both the reduced velocity and the spacing of the cylinders have a great influence on the wake-induced vibrations (WIV) responses of the downstream cylinder. Considering these influences, an empirical model for WIV frequency response of the downstream cylinder with a low mass ratio was proposed and verified.

The predominant frequency for viscous flow past two tandem circular cylinders of different diameters at low Reynolds number

Viscous flow past two circular cylinders in tandem arrangement is numerically investigated at a typical Reynolds number of 200 which is based on the diameter of the downstream cylinder. The non-dimensional diameter of the downstream cylinder D is fixed to be 1.0, while the non-dimensional diameter of the upstream cylinder d varies from 0.1 to 1.0 with an interval of 0.1. Moreover, the minimal non-dimensional distance between the two cylinders changes from 0.1 to 4.0. The numerical results show that continuous variation of the mean drag coefficient, the lift coefficient, and the lift frequency is observed with the increase in the gap ratio for d/ D = 0.1 and 0.2. Discontinuities are found for the mean drag coefficient, the lift coefficient, and the lift frequency of the downstream cylinder with the increase in gap ratio for d/ D = 0.9 and 1.0. Multiple lift oscillating frequencies of the downstream cylinder can be detected for d/ D = 0.3–0.8 at special gap ratios. Special attention is paid on d/ D = 0.4, which is a typical example for d/ D = 0.3–0.8. The predominant lift frequency of the downstream cylinder is observed to change from fL-1 to fL-2 as the increase in the gap ratio for d/ D = 0.4, which have not been previously detected. However, the predominant drag frequency of the downstream cylinder is found always to be fD-3 in present investigation scope. Moreover, a conclusion that fD-3 = fL-1 + fL-2 can be obtained.

On the flow around two circular cylinders in tandem arrangement at high Reynolds numbers

The flows around two tandem circular cylinders in the subcritical and supercritical flow regimes are studied through three-dimensional numerical simulations. Different spacing ratios L/D (where L is the center-to-center distance between the two cylinders with D being the diameter of the cylinders) from 2.0 to 5.0 is considered. The instantaneous flow structures, pressure distributions and hydrodynamic forces on two tandem cylinders are analyzed at subcritical (Re=2.2×104) and supercritical (Re=3.0×106) Reynolds numbers. The present numerical solutions demonstrated that at the two Re, for L/D<3.5, the shear layer from the upstream cylinder reattaches on the surface of the downstream cylinder and vortex street is only formed behind the downstream cylinder, while the shear layer from the upstream cylinder rolls up alternately for L/D≥3.5, and vortex shedding occurs from both upstream and downstream cylinders. Compared with the flow characteristics at Re=2.2×104, for Re=3.0×106, the flow separation positions on the upstream cylinder move backward and the width of the wake behind the upstream cylinder becomes narrower, which leads to forward movement of the reattachment position. At the supercritical Reynolds number, the mean drag and fluctuating lift coefficients of the upstream cylinder are nearly independent of L/D while the sharp increase of force coefficients of the downstream cylinder occurs for L/D=3.5. Comparing to the case at the subcritical Reynolds number, higher vortex-shedding frequencies from the upstream and downstream cylinders are identified. It is also revealed that the slope of the best fit line for φ (the phase lag of the fluctuating lift force between two cylinders) and L/D increases at the supercritical Reynolds number. In addition, for L/D=2.5, the mean drag coefficients of the upstream cylinder decrease sharply for Re>1.0×105, while those of the downstream cylinder rise slightly with the growing Re. Moreover, the fluctuating lift coefficients of the upstream cylinder are almost independent of Re, but those of downstream cylinder drop as Re increases.

Numerical analysis of the interference between two elastically mounted cylinders in tandem subject to flows at low Reynolds numbers

Fluid-dynamic interference among cylindrical structures in arrays, frequently used in engineering, is of fundamental and practical interests since it may considerably change fluid–structure interactions and produce large fluctuating forces on structures that cause vibrations, lock-in and important motions. This paper aims to study the mutual interference between two circular cylinders in tandem arrangement, which is considered the simplest configuration of one array cylinders, elastically mounted in transversal direction and subject to a bi-dimensional uniform laminar flow at low Reynolds numbers. Both cylinders have the same diameter D, and the center-to-center spacing is equal to L = 5.25D which corresponds to co-shedding regime. The academic numerical model Ifeinco, which is based on the finite element method and uses a partitioned scheme that considers two-way interaction of fluid flow and structure, has been employed to the analysis. Combinations of upstream and downstream stationary and elastically mounted cylinders are investigated for Reynolds number range from 90 to 140. Differences of flow behaviors drag and lift forces and resonance between single cylinder and cylinders in tandem arrangement were found. Mutual and respective influences of upstream cylinder motion on the downstream cylinder and vice versa are analyzed. Results show that, in some engineering studies, the consideration of the flexibility of cylindrical structures in arrays is fundamental since it influences significantly the interference between cylinders, mainly the magnitude and direction of forces and characteristics of the resonance range, and, consequently, structural and dynamical behaviors.

Flow-induced vibration of two elastically mounted tandem cylinders in cross-flow at subcritical Reynolds numbers

A series of experimental studies on flow-induced vibration (FIV) of two identical elastically mounted circular cylinders in tandem arrangement were carried out in a low turbulence surface water channel. The Reynolds number was between 2.86 × 104–1.14 × 105. Both upstream and downstream cylinders with diameter of 8.89 cm and mass ratio of 1.343 were allowed to oscillate in the transverse direction. Four spacing ratios T/D = 1.57, 2.57, 3.57 and 4.57 (where T is the center-to-center spacing and D is the cylinder diameter) were selected. Two virtual spring-damping oscillators were used to conduct the tests and measure the position signals of two tandem circular cylinders undergoing FIV. The vibrations and fluid forces of the cylinders were analyzed and discussed to illustrate the mechanisms of interaction between the two cylinders. The experimental results indicate that the FIV characteristics of the upstream cylinder are similar to those of a single cylinder for T/D = 2.57, 3.57 and 4.57 when the reduced velocity does not exceed 12.0. Moreover, the FIV response of the upstream cylinder in the two tandem cylinder system with T/D = 1.57 is significantly different from that of the isolated cylinder. The vibration of and the fluid force on the downstream cylinder are obviously influenced by the upstream cylinder for the spacing range tested. Vortex-induced vibration (VIV)-like response features are observed for the downstream cylinder.

Large Eddy simulations of flow around tandem circular cylinders in the vicinity of a plane wall

To investigate the three-dimensional flow around free-spanning, tandem marine pipelines, Large Eddy Simulations (LES) with Smagorinsky subgrid scale model are performed using the open-source code OpenFOAM. Two circular cylinders in tandem arrangement are placed in the vicinity of a rigid, horizontal, plane wall. The cylinders are immersed in a steady current with a logarithmic boundary layer profile at an intermediate, subcritical Reynolds number (Re = 1.31 × 104). The non-dimensional distances between the cylinder centres are 2 and 5 (L/D = 2 and 5) and the gap to diameter ratios are G/D = 0.6 and 1, where gap G is the distance between the bottom of the cylinders and the wall. The present results are analysed through the values of drag and lift coefficients, as well as by the details of the flow fields in the wake of the cylinders. The results are compared with experimental results of the flow around tandem cylinders in an unlimited fluid for both L/D = 2 and 5, showing that, at chosen gaps, at L/D = 2, the flow belongs to the reattachment regime, and at L/D = 5 to the co-shedding regime. Compared with the case of a single cylinder near a plane wall, the flow around the tandem cylinders at G/D = 1 belongs to the wide gap regime, while at G/D = 0.6, tandem yields a stronger interaction with the wall than in the case of one cylinder. The presence of the wall modifies the flow in the spacing between the two cylinders, giving it some characteristics of the extended body flow regime.