Co-shedding Regime Research Articles

Aerodynamic force characteristics and flow field mechanism of multiple square cylinders in a tandem arrangement

Wind tunnel tests and large eddy simulations were employed to obtain the aerodynamic coefficients and flow fields of two and three tandem square cylinders across various spacing ratios. The spacing ratio L/D, defined as the ratio of the center-to-center spacing between adjacent square cylinders to their width, ranges from 1.2 to 8. By analyzing these results, the aerodynamic force characteristics and their generation mechanism of the three tandem square cylinders at a high Reynolds number (Re = 3.2 × 104) were revealed. By comparing the results of the two and three tandem square cylinders, the effect of adding a third square cylinder behind the two tandem square cylinders on its aerodynamic characteristics was clarified. The results show that unlike the two tandem square cylinders, the three tandem square cylinders exhibit two critical spacing ratios, (L/D)cr1 = 2.5–3 and (L/D)cr2 = 3.5–4, respectively. Based on these two critical spacing ratios, the flow around the three tandem square cylinders is identified as single blunt body, reattachment, and co-shedding regimes. In the single blunt body and reattachment regimes, the addition of a third square cylinder behind significantly alters the flow around the two tandem square cylinders, leading to reduced mean drag coefficients, fluctuating lift coefficients, and Strouhal numbers, along with an increased critical spacing ratio. In the co-shedding regime, this addition has little effect on the flow.

Numerical investigation on flow transition of two tandem circular cylinders in an X arrangement: Effects of spacing ratio and transverse inclination angle

This paper reports on a numerical study of the effects of five spacing ratios (L/D = 3–5) and eight transverse inclination angles (α = 0°–30°) on force coefficients and wake patterns of two tandem circular cylinders in an X arrangement, at a subcritical Reynolds number Re = 3900. It also addresses the mutual wake interference between the cylinders and the critical parameters determining the flow transition (FT) from the reattachment to the co-shedding regime. The main findings are: (1) the FT from the reattachment to the co-shedding regimes was identified for the considered range of L/D and α. The flow transition induces a sharp rise in force coefficients, especially for the downstream cylinder. FT can be triggered by the critical spacing ratio (L/D)c at different α, as well as excited by the critical transverse inclination angle αc at different L/D. (2) When α = 0° (i.e., two tandem vertical cylinders), FT occurs at (L/D)c = 4.5–5. As α increases to 5°, 15°, and 25°, (L/D)c gradually drops to 4–4.5, 3.5–4, and 3–3.5, respectively. From another perspective, with fixed spacing ratios of L/D = 3.5, 4, and 4.5, FT appears at αc = 20°–25°, 12.5°–15°, and 0°–5°, respectively. Additionally, in the case of L/D = 3 and 5, the flow pattern, respectively, remains in the reattachment and co-shedding regimes. (3) The formation of the co-shedding regime requires sufficient gap space between two crossing cylinders. A nondimensional center spacing ratio on the top view between the cylinders (CS*top view), was proposed to reflect the variation of gap space. The critical value of CS*top view to excite FT falls within the range of 3.5–5, which is a function of α and L/D. The mathematical expression of (CS*top view) points to the predominant role of L/D on the FT when compared with α. In addition, it also accounts for the fact that the transverse inclination angle has an inverse effect on the critical value of the spacing ratio and vice versa. These findings provide new insight into understanding the flow transition and wake interference of two crossing cylinders in an X arrangement.

The effect of transverse inclination angle on hydrodynamic characteristics of two tandem circular cylinders in an X arrangement

A numerical investigation of the flow around two stationary circular cylinders in an X arrangement, with a Reynolds number of Re = 3900 and a spacing ratio of L/D = 4.0, is conducted using Large-Eddy Simulation. Eight different transverse inclination angles (α = 0°–30°) are considered to investigate their effects on several aspects, including the time-averaged drag coefficient (Cd-ave), root-mean-square lift coefficient (Cl-rms), Strouhal number (St), instantaneous flow structure, and time-averaged pressure distribution. The numerical results demonstrate that when the inclination angle exceeds a critical value of αc = 12.5°–15°, the flow pattern in the gap between two cylinders transitions from the reattachment regime to the co-shedding regime. This flow transition indicates that the wake vortex periodically detaches from the upstream cylinder and impinges on the downstream cylinder, resulting in a sharp increase in force coefficients, especially for the downstream one. When compared with α = 15°–30°, the force coefficients for both cylinders at α = 0°–12.5° are reduced, which is favorable to the structural stability. Furthermore, an increase in α leads to a monotonic rise in Cd-ave for the downstream cylinder. This can be primarily attributed to the amplified pressure coefficient on the front face of the downstream cylinder, which is caused by the reduced shielding effect from the upstream one.

Applying reinforcement learning to mitigate wake-induced lift fluctuation of a wall-confined circular cylinder in tandem configuration

The flow around two tandem circular cylinders leads to significant lift fluctuation in the downstream cylinder owing to periodic vortex shedding. To address such research issues, we present herein a numerical study that uses deep reinforcement learning to perform active flow control (AFC) on two tandem cylinders with a low Reynolds number of 100, where the actuator causes the rotation of the downstream cylinder. First, the cylinder center spacing ratio L* varies from 1.5 to 9.0, and the variation of L* leads to the quasi-steady reattachment regime (L*≤3.5) and the co-shedding regime (L*≥4.0). The fluctuating lift of the downstream cylinder is maximum when L*=4.5. Next, we train an optimal AFC strategy that suppresses 75% of the lift fluctuation in the downstream cylinder. This approach differs from using direct-opposition control to change the vortex-shedding frequency or strength, as reported in previous studies. This strategy modifies the phase difference between the lift fluctuations of the two cylinders by delaying the merging with the upstream cylinder wake and accelerating the formation of recirculating bubbles after the vortex merging. With the new phase difference, the effect of the additional lift from the upstream cylinder is significantly mitigated. The results of the dynamic mode decomposition show that the vortices surrounding the downstream cylinder in mode 1 that contribute to the lift fluctuation are weakened. To the best of our knowledge, this investigation can provide new ideas and physical insights into the problem of AFC under disturbed incoming flow.

Vortex-induced vibration of two tandem square cylinders with different restraint conditions

The present work investigates the vortex-induced vibration of twin square cylinders at Re = 150 with three restraint conditions. (Ⅰ) the upstream cylinder (UC) is free to oscillate while the downstream cylinder (DC) is fixed; (Ⅱ) both cylinders are free to oscillate, and (Ⅲ) the UC is fixed while the DC is free to oscillate. The centre-to-centre distance between the cylinders is fixed as 4.0B, and the mass ratio of the cylinder is m* = 3. The computations are performed for the reduced velocity ranging from 1 to 15 under each restraint condition. The flow dynamics are described by the two-dimensional incompressible Navier-Stokes equations and solved numerically using the Ansys Fluent CFD code (based on the finite volume method and SIMPLEC algorithm. It is found that whether the DC oscillates, the UC will exhibit the soft-lock-in phenomenon within the co-shedding regime. At high reduced velocities, the UC re-shows the soft-lock-in phenomenon when the DC is fixed. Whether the UC oscillates, the DC will exhibit the soft-lock-in phenomenon within the reattachment regime. For Case-Ⅱ, the strong vortex falling off the leeward side of the UC leads to a sharp decrease in distance between the two cylinders, and the DC exhibits the soft-lock-in phenomenon again.

Cross flow over two heated cylinders in tandem arrangements at subcritical Reynolds number using large eddy simulations

This study analyses the heat transfer and flow characteristics of cross-flow over two heated infinite cylinders in a tandem (in-line) configuration. Non-isothermal Large Eddy Simulations (LES) using the dynamic Smagorinsky model were conducted at a fixed Reynolds number of 3,000 (based on the free stream velocity and the cylinder diameter). A range of cylinder gap ratios (1.0≤L/D≤5.0) was investigated (in increments of 0.25) with two different Prandtl numbers Pr=0.1 and 1.0. Results show that the flow structures vary according to the order of the patterns: (i) Extended body regime: without attachment for low L/D (1.0-1.25) where cylinders behave as a single bluff body with top–bottom vortex shedding, (ii) Shear layer reattachment regime: with reattachment for moderate L/D (1.5-3.75) where the detached shear layer from the upstream cylinder reattaches to the downstream cylinder, and (iii) Co-shedding regime: for high gap ratios (3.75≤L/D≤5.0) a phenomenon called “jumping”, where the two cylinders behave as isolated bluff bodies. Furthermore, it was observed that the average Nusselt number of both cylinders experience a drastic variation at a critical spacing ratio (between 3.75≤L/D≤4.0). For L/D≤3.0, the average Nusselt number of the upstream cylinder was found to be higher than that of the downstream one. However, for spacing ratios L/D>3.0, the average Nusselt number was similar for both cylinders. For the downstream cylinder, the maximum Nusselt number was located at the separation angle and was found to be independent of the spacing ratio.

Receptivity-orientated drag reduction of twin cylinders by steady leading-edge suction control based on adjoint method

This study investigates the drag reduction of two tandem square cylinders under steady suction control at Reynolds numbers 50–200. The position where the suction flow should be placed is determined by using a receptivity analysis based on the adjoint method, and we investigate how control affects the fluid force and flow structures. High-order dynamic mode decomposition (HODMD) is applied to analyze the dynamic coherence modes and uncover the underlying control mechanism. The adjoint modes show that the regions of maximum receptivity to momentum forcing are localized on each side of the up-cylinder (UC) near the leading edge (LE). Thus, the suction flow is placed on the LE. The drag can be significantly reduced at wide gap distances, especially for the co-shedding regime. Under suction flow control, the separation is suppressed near the LE, and the gap vortices are no longer fed by the vorticity generated by the separated shear layer; they only result from the trailing-edge separation, which weakens and shrinks. Subsequently, the interaction between the gap flow and the down-cylinder (DC) is weakened, which reduces the drag and lift forces. The decrease in drag exceeds 66.4% for the UC and reaches 81.6% for the DC. The fluctuating reduction in the lift for the UC (DC) exceeds 59.0% (75.7%). HODMD results show that, as the suction flow velocity increases, the LE suction flow modifies the local time-averaged modes rather than the global mode energy. Conversely, the dynamic mode energy decreases significantly, whereas the mode shape remains unchanged except for a phase shift.

Heat transfer and wake-induced vibrations of heated tandem cylinders with two degrees of freedom: Effect of spacing ratio

The heat transfer and wake-induced vibrations of a cylinder of circular cross section in the wake of another identical cylinder are numerically studied in this work at a Reynolds number (Re) = 100. The reduced velocities (Ur) are varied in the range of 2–14. The downstream cylinder is allowed to oscillate in two degrees of freedom, i.e., in the transverse as well as in the streamwise direction. The mass ratio (m*) is taken as 10, while the structural damping is ignored to get the maximum amplitude of vibration. The spacing ratio (L/D) between the cylinders is varied from 1.5 to 6, covering the major regimes, i.e., single body, reattachment, and co-shedding. The coefficients of lift (CL) and drag (CD), vibrational amplitudes of the cylinder, the Nusselt number (Nu), the Strouhal number (St), and vortex shedding patterns are studied. The results are discussed with the help of lift-displacement phase plots, cylinder trajectory plots, and vorticity and temperature contours. The lock-in condition at Ur = 8 is observed for all values of L/D, whereas the lock-in zone is the widest for the co-shedding regime at L/D = 6. By increasing L/D from 1.5 to 2.5 at Ur = 8, the CL of the downstream cylinder increases by 43%, whereas the CL of the upstream cylinder decreases by 61%. The downstream cylinder experiences lower drag as compared to the upstream cylinder and stationary isolated cylinder. A maximum decrease in the average drag coefficient of 107%, as compared to the stationary isolated cylinder, was observed for the downstream cylinder at L/D = 1.5 and Ur = 2, leading to the negative drag. Mostly, the 2S and C(2S) vortex shedding pattern is observed, whereas a steady flow and chaotic pattern emerged in a few cases. The results reveal that with increasing L/D, the average Nu for both the upstream and downstream cylinders increases as the effect of each cylinder on the other diminishes.

Vortex-induced vibration of two rigidly coupled tandem square cylinders at a low Reynolds number

Vortex-induced vibration of two rigidly coupled tandem square cylinders with center spacing L = 4B was numerically investigated at a Reynolds number of Re = 150. Both 2 degrees of freedom (DOF)-C (translational vibration) and 3DOF-C (translational and rotational vibration) cases are considered and compared with the case of no rigid connection. The results reveal that the onset of the synchronization region for rigidly coupled cylinders is earlier than that without connection. Compared with the latter, the upstream cylinder with rigid connection displays a lower transverse amplitude within the synchronization region and a higher one outside the region. The transverse amplitude of the downstream cylinder with 2DOF-C is generally lower than that without connection. In contrast, the vibration of the downstream cylinder with 3DOF-C is higher than that without connection, except for the high reduced velocity, in which the maximum transverse amplitude increases by 20%. The synchronization region of the twin uncoupled cylinders appears within the reattachment and co-shedding regimes, while that of the twin coupled cylinders only appears within the co-shedding regime. Although the synchronization region with a similar flow pattern appears within the co-shedding regime in these three cases, it shows different vibration characteristics.

Spacing effect on the vortex-induced vibrations of near-wall flexible cylinders in the tandem arrangement

The vibration responses and flow dynamics in the vortex-induced vibrations of two near-wall flexible cylinders in the tandem arrangement are investigated through three-dimensional direct numerical simulations with the spacing ratio s/D =1.5–6 (D = diameter of the cylinder), gap ratio G/D = 0.8, cylinder length of 25D, and Reynolds number of 500. The in-line (IL) and crossflow (CF) vibrations are predominated by the first-order mode along the span. The upstream cylinder oscillates at a higher CF amplitude than the downstream one, and the maximum IL and CF vibration amplitudes of the tandem cylinders are both smaller than those of the single cylinder. The dominant frequencies of IL and CF oscillation are identical for the tandem cylinders, and they are larger than that of the single cylinder. The smaller mean drag and larger rms drag occur on the downstream cylinder than in the upstream counterpart. The difference between the spanwise rms lift of the two cylinders reduces as the s/D increases. Different flow types are observed along the flexible cylinders: at s/D = 1.5–2, an “extended-body regime” and a “reattachment regime” are excited near the two-ends and the middle regions along the span, respectively; at s/D = 3, a reattachment regime and a “co-shedding regime” appear; at s/D = 4–6, the co-shedding regime is observed but with different vorticities related to the vibration amplitudes. At s/D = 3, the wall proximity induces multi-frequencies in both the IL and CF oscillations, compared to single-frequency oscillations in wall-free conditions. The lower IL and higher CF vibration amplitudes are excited in the near-wall conditions. Weak “2S” and the typical 2S vortex shedding patterns are observed in the near-wall and wall-free conditions, respectively.

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.

Wake evolution and vortex structure characteristics of flow over two tandem semi-circular cylinders with flat surfaces facing each other

This paper reports the results of a numerical investigation into the flow over two tandem semi-circular cylinders with flat surfaces facing each other and the associated wake flow characteristics. The effect of spacing ratio (L/D, L is the in-line spacing between two flat surfaces and D is the diameter of cylinders) ranging from 1 to 16 is examined in a low Reynolds number range of Re = 60–180. Five flow patterns are identified including the over-shoot, continuous reattachment, alternate reattachment, quasi-co-shedding, and co-shedding regimes. The difference between quasi-co-shedding and co-shedding regimes depends on the origin of the vortices shed from the downstream cylinder. Unlike the vortices generated due to the roll-up of shear layers detached from both upstream and downstream cylinders in the co-shedding regime, the vortices shed from the downstream cylinder come from upstream instead of the roll-up of shear layers for the quasi-co-shedding regime. The wake flow characteristics are discussed in terms of the vortex formation and shedding, wake structure and evolution, boundary layer separation and shear layer development, the occurrence of secondary vortex street, and the associated migrating vortex modes. The variations of hydrodynamic coefficients and Strouhal number are associated with the flow regime transition. When the alternate reattachment and quasi-co-shedding regimes emerge, a small pair of peaks of the root-mean-squared streamwise flow velocity (u*rms) fixedly occurs at the two corners of the downstream cylinder, illustrating the strong velocity fluctuation caused by vortices impingement and the secondary separation. Three types of vortex street are observed in the wake, where the secondary vortex street region is further divided into three parts in terms of the vortex structure, including S + P (a single vortex and a pair of vortices are formed per cycle in the secondary vortex street), P (a pair of vortices is formed per cycle in the secondary vortex street), and 2S (two vortices in opposite directions are formed per cycle in the secondary vortex street) modes. Two partitions in Re–L/D map (Re and L/D as the vertical and horizontal ordinates, respectively) are proposed in this work for the flow regime as well as the vortex street.

Flow-induced vibrations of a pair of in-line square cylinders

Flow-induced bidirectional vibrations of two in-line square cylinders of same size and mass ratio (=10) are analyzed at Reynolds number, Re = 100. The cylinders are located in the co-shedding regime, i.e., they are separated by a normalized center-to-center spacing of 5. The reduced speed, U*, is varied from 3 to 15 keeping Re constant. The upstream and downstream cylinders display identical frequency characteristics with U*. Accordingly, the cylinders share identical decomposition of dynamic response. The response is composed of the desynchronization regimes and lower branch; an initial branch does not exist. The vibrations are hysteretic at the lock-in boundaries whereas for a single square oscillator, hysteresis is identified only near the onset of lock-in. Hysteresis in the solutions for U*=7 within the lower branch is reflected in the wake mode of the rear cylinder whereas for the upstream cylinder, wake mode remains identical. The vortex-induced vibration (VIV) of the upstream cylinder is qualitatively similar to that of an isolated square oscillator. Despite the range of lock-in of the cylinders being identical, the VIV of the downstream cylinder departs significantly from its upstream counterpart. The shear layers separated from the front cylinder impinge on the rear cylinder and alter its flow field. The rear cylinder executes high amplitude VIV over the entire lower branch. The symmetry of the drag-lift phase diagrams does not necessarily translate to symmetric phase plots of in-line and cross-stream response. The drag and in-line response of the cylinders are out of phase throughout.

Two-degree-of-freedom flow-induced vibration of two rigidly coupled tandem cylinders of unequal diameters

This paper reports the results of a numerical investigation in to the two-degree-of-freedom (2-DOF) flow-induced vibration (FIV) of two rigidly coupled tandem cylinders of unequal diameters at a low Reynolds number of 150. Three typical center-to-center spacing ratios of L/D = 1.5, 3.75 and 6.0 are examined in the reduced velocity range of Ur = 3–12. For the rigidly coupled tandem cylinders, three typical flow regimes are observed including extended-body regime, reattachment regime and co-shedding regime. The occurrence of flow regime transition is associated with the spacing ratio (L/D) and the reduced velocity (Ur). Accordingly, the flow regime is illustrated in the L/D–Ur diagram. The hydrodynamic forces of both cylinders are significantly reduced in the extended-body regime, resulting in an excellent suppression of FIV. In contrast, both the hydrodynamic forces and response amplitudes are augmented at L/D = 3.75 and L/D = 6.0 as compared with those at L/D = 1.5. Furthermore, the cross-flow amplitude is even larger than that of an isolated cylinder at Ur ≥ 8 with the associated response frequency deviating from the Strouhal curve. The transition of flow regime affects the phase angle of the upstream cylinder. As a greater lift force exerted on the downstream cylinder and the corresponding phase difference with the vibration displacement is either close to 0° or about 180°, the downstream cylinder dominates the movement of the rigidly coupled cylinders in the majority of an oscillating cycle.

Numerical study of wake and aerodynamic forces on a twin-box bridge deck with different gap ratios

Two-dimensional Delayed Detached Eddy Simulation (DDES) was carried out to investigate the uniform flow over a twin-box bridge deck (TBBD) with various gap ratios of L/C=5.1%, 12.8%, 25.6%, 38.5%, 73.3% and 108.2% (L: the gap-width between two girders, C: the chord length of a single girder) at Reynolds number, Re=4x104. The aerodynamic coefficients of the prototype deck with gap ratio of 73.3% obtained from the present simulation were compared with the previous experimental and numerical data for different attack angles to validate the present numerical method. Particular attention is devoted to the fluctuating pressure distribution and forces, shear layer reattachment position, wake velocity and flow pattern in order to understand the effects of gap ratio on dynamic flow interaction with the twin-box bridge deck. The flow structure is sensitive to the gap, thus a change in L/C thus leads to single-side shedding regime at L/C󖼩.6%, and co-shedding regime at L/C󖼳.8% distinguished by drastic changes in flow structure and vortex shedding. The gap-ratio-dependent Strouhal number gradually increases from 0.12 to 0.27, though the domain frequencies of vortices shedding from two girders are identical. The mean and fluctuating pressure distributions is significantly influenced by the flow pattern, and thus the fluctuating lift force on two girders increases or decreases with increasing of L/C in the single-side shedding and co-shedding regime, respectively. In addition, the flow mechanisms for the variation in aerodynamic performance with respect to gap ratios are discussed in detail.

Numerical investigation on two degree-of-freedom flow-induced vibration of three tandem cylinders

Numerical simulations of two-degree-of-freedom flow-induced vibration of three elastically mounted tandem cylinders are performed for a low Reynolds number of Re = 150. The spacing ratio L/D is varied from 2 to 5, where L is the center-to-center between the cylinders and D is the cylinder diameter, and the reduced velocity Vr is varied from 3 to 14. The results show a typical vortex-induced vibration response of the upstream cylinder, except for those at L/D=2, where the response amplitudes are about twice those of the single cylinder. Both the midstream and downstream cylinders have large response amplitudes at all the examined spacing ratios. Depending on the flow interferences among three cylinders, the large amplitudes at high reduced velocities are contributed to the gap flow mechanism in the proximity regime and wake-induced vibration mechanism in the co-shedding regime, respectively. The periodic beating phenomenon occurs on both the midstream and downstream cylinders and the range of Vr for beating phenomenon increases with L/D. Depending on the spacing ratios and reduced velocities, six different flow regimes are identified: single bluff body flow, alternating shear layer reattachment flow, deflected gap flow, two parallel vortex streets with co-shedding flow, chaotic wake and 2S wake flow.

On the wake interference effects for flow around tandem bodies

The present study investigates the wake interference effects for flow around two tandem cylinders under the effect of gap spacing ranging from 0.5 to 10. The flow Reynolds number is fixed at 150, and lattice Boltzmann method is used as a numerical tool for this study. The results show that three different regimes exist depending on gap spacing and flow structure mechanism around cylinders: single cylinder body regime, reattachment regime and co-shedding regime. The results also show that in a particular regime multiple flow patterns may coexist and affect the behavior of fluid forces. This study reveals that there exists a critical value of spacing which alters the fluid flow characteristics abruptly. The drag coefficient of second cylinder is negative until critical spacing and becomes positive after that. It is found that when spacing crosses the critical value, both cylinders start shedding vortices and the drag coefficient oscillates. The wake interference effect is found to be dominant at small spacing values which weakens with increment in spacing between cylinders.

Wake adjustment and vortex-induced vibration of a circular cylinder with a C-shaped plate at a low Reynolds number of 100

The vortex-induced vibration (VIV) of a circular cylinder with a C-shaped plate arranged in its wake at a low Reynolds number of 100 is numerically investigated in this work using the direct numerical simulation. Four typical streamwise spacing ratios of 1.5, 3, 4.5, and 6 are examined in the computations that were carried out for the range of reduced velocities (Ur = 2–12). In terms of shear layer reattachment, wake interference, and vortex shedding, five flow regimes are identified, i.e., the extended-body regime, the front-face reattachment regime, the shear-layer combination regime, the one-row co-shedding regime, and the two-row co-shedding regime. The wake regime is sensitive to the spacing ratio and the reduced velocity. The switching of the flow regime occurs at the transition between the initial VIV branch and the lower VIV branch, accompanying a phase jump of 180°. Furthermore, the shift of the wake regime leads to the prominent fluctuation of the response amplitude. Among the five regimes, the two-row co-shedding regime has the maximum wake width, resulting in the maximum amplitude. In contrast, the shear layers are elongated in the extended-body regime and hence the prolongation of the vortex formation length, contributing to the suppression of VIV. The best suppression is achieved by placing the C-shaped plate behind the cylinder with a spacing of 1.5D, and the reductions in the lift force and the cross-flow amplitude reach 85.5% and 94.5%, respectively.

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.

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.