Downstream Cylinder Research Articles

Flow-induced vibration (FIV) fatigue damage characteristics of two unequal-diameter flexible cylinders in a staggered arrangement

In offshore engineering, fatigue damage caused by flow-induced vibrations (FIVs) presents a considerable and potential threat to flexible cylindrical systems during their service lifetime. Through FIV experiments, this paper estimates and analyzes the fatigue damage of two unequal-diameter cylinders with diameter ratio d/D = 0.5 (where d and D denote the diameter of small and large cylinders) and the center-to-center spacing ratio P/d = 6 (where P denotes the center-to-center distance between two cylinders) through the S–N curve and fatigue damage accumulation methods in the DNV standard. Ten staggered configurations were studied, including two relative positions and five stagger angles (θ = 15°, 30°, 45°, 60°, and 75°). The fatigue damage evaluation results indicate that the FIV fatigue damage is highly affected by the stagger angle and relative position of the two cylinders. The FIV fatigue behavior of the two unequal-diameter cylinders is quite different from that of the two identical cylinders. When the large cylinder is located upstream, its wake shielding effect on the small cylinder is predominant at small stagger angles, so both the IL and CF fatigue damage of the downstream small cylinder is significantly suppressed, especially when Vr ≤ 16.28. But as the stagger angle is increased, the wake-induced flutter can aggravate the fatigue damage of the downstream small cylinder. Moreover, the CF fatigue damage of the large cylinder is decreased at small angles due to the vortex-shedding frequency suppression of the small cylinder and the fatigue damage of the large cylinder in the IL direction is analogous to that of the isolated cylinder and is negligibly affected by the small cylinder. When the small cylinder is located upstream, the IL FIV fatigue damage of the downstream large cylinder is approximately unaffected due to the narrow wake of the small cylinder. However, the CF fatigue damage of the large cylinder is greatly reduced at small stagger angles.

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.

Splitter plate-based flow control study for two square cylinders in tandem arrangement

A numerical study is performed to investigate the effectiveness of a splitter plate (SP) for the unsteady wake-regime control of two-dimensional tandem square cylinders (TSC) arranged with large (G/D = 6), intermediate (G/D = 4) and small (G/D = 2) gap-widths. Here, G is the center-to-center distance between the cylinders, and D is their side-length. The numerical simulations are conducted using an in-house developed FFIBLBM (flexible-forcing-immersed-boundary-lattice-Boltzmann-method) solver at Reynolds number (Re) of 100. The TSC arrangement with SP attached to either upstream or downstream cylinders is named TSC-SPU and TSC-SPD, respectively. It is found that the shear-layer characteristics, wake-regime, and flow-induced forces on TSC are highly susceptible to the G/D ratio and SP length. We observed four distinct flow patterns: VS-VS (vortex shedding-vortex shedding), QS-VS (quasi-steady-vortex shedding), S-VS (steady-vortex shedding), and S–S (steady-steady) in the wakes of TSC. Among them, the S–S flow pattern is the controlled wake-regime, with steady and stabilized vortices behind both cylinders, yielding considerably lesser drag on the TSC. Precisely, at large gap-width (G/D = 6), the TSC-SPU configuration only attains the S–S flow type for which the upstream and downstream cylinder experience 11.86% and 97.73% lesser drag, respectively, than the TSC without an attached SP. However, at intermediate gap-width (G/D = 4), both TSC-SPU and TSC-SPD generate the S–S flow type. Still, the TSC-SPU is advantageous in drag reduction, where the drag of the upstream and downstream cylinders is reduced by 1.61% and 7.26%, respectively. On the other hand, the S–S flow type is established for low gap-width (G/D = 2) with TSC-SPD setup for which the drag reduction for upstream and downstream cylinders are 1.85% and 12.76%, respectively.

Effects of variable damping on hydrokinetic energy conversion of a cylinder using wake-induced vibration

The Wake-Induced Vibration (WIV) energy converter can be used to harvest hydrokinetic energy from ocean currents. A variable damping scheme is proposed based on the idea that damping dynamically adjusts with the vibration velocity. Large damping is adopted to improve the energy conversion performance when the vibration velocity is high. Similarly, small damping is adopted to reduce the resistance of the cylinder when the vibration velocity is low. Meanwhile, since the nonlinear damping is too sensitive at higher vibration velocity, the segmental nonlinear damping model is also proposed. The research shows that (1) the variable damping model is more effective than the constant damping model to enhance the WIV response; (2) four interference regions are found according to the vortex interaction between upstream and downstream cylinders: Reattachment, Co-shedding, Wake interference, Isolated region; (3) In the Co-shedding region and Wake Interference region, the energy conversion performance of the linear variable damping is the highest. (4) the energy conversion performance of the nonlinear variable damping model is greater than that of other models in the Reattachment and Isolated Region.

On the galloping cross-flow vibration responses of three in-line square cylinders

Galloping cross-flow vibration responses of three in-line identical square cylinders are numerically studied for the mass ratio m*=2, streamwise gaps Lx=3B and 5B, reduced velocity U*=3−50, and Reynolds numbers Re = 150 in two dimensions (2-D) and 2000, where the flow is three-dimensional (3-D). Here, B is the side of the cylinder. An isolated cylinder does not gallop since the mass ratio m*=2 is less than the critical value in the Re = 150 flow, whereas for the three in-line bodies, galloping instability is triggered at the upstream cylinder due to the interference effect caused by the presence of downstream bodies. The interaction with the wake of galloping upstream cylinder promotes galloping instability for the two downstream cylinders almost immediately at Re = 150. In the three-dimensional wake at Re = 2000, downstream cylinders interact with less coherent Karman vortices shed by the galloping upstream cylinder, compared to the 2-D case. This phenomenon leads to the delayed on-set of galloping response for the first downstream cylinder, while the second one never gallops.

Flow-induced vibration of a cantilevered cylinder in the wake of another

This work presents an experimental study of the flow-induced vibration of a cantilevered circular cylinder in the wake of another cylinder, fix-supported at both ends. The diameter and spacing ratios, d/D and L/d are 0.24 – 1.0 and 1.0 – 5.5, respectively, where d and D are the diameters of the upstream and downstream cylinders, respectively, and L is the separation from the upstream cylinder center to the front stagnation point of the downstream cylinder. Measurements are performed over the reduced velocity Ur=3.8 – 68.3 (based on D and freestream velocity), with the downstream cylinder vibration, vortex shedding frequency, surface pressure distribution and flow structures simultaneously captured. The downstream cylinder accompanied by a smaller d/D and/or L/d is more susceptible to galloping vibration and hysteresis in the galloping response. The mechanism behind initiation and sustenance of galloping is unveiled. It has been found that the effective mass and damping play a key role in initiating and sustaining the vibrations. The variation in the flow structure is discussed in detail in both streamwise and spanwise directions, along with the fluid–structure interactions.

Vortex-induced vibrations of tandem diamond cylinders: A novel lock-in behavior

This paper presents a comprehensive numerical investigation of the undamped, simultaneous in-line, and transverse flow-induced vibrations of two identical diamond cylinders (of cross-stream length D) in a tandem arrangement at a low Reynolds number (= 100) in uniform flow, using a stabilized space–time finite-element formulation. The study focuses on the effects of cylinder proximity and shape, considering diamond cylinders with a mass ratio of 10 and a separation distance of 5D and varying the reduced velocity from 1 to 20. The results reveal distinct lock-in behavior for the upstream and downstream cylinders, with a low-frequency extended lock-in phenomenon observed for the downstream cylinder. The motion trajectories of both cylinders exhibit a distinctive “raindrop-shaped” pattern. Notably, the synchronization zone shows a non-zero mean lift for a narrow range of reduced velocity. The study also identifies three distinct modes of vortex arrangement in the gap region between the cylinders. Comparing the findings for tandem diamond cylinders with those for single diamond and tandem square cylinders provides further evidence of the significant impact of proximity and shape on the vibration characteristics of the cylinders.

Wake Control of Flow Past Twin Cylinders via Small Cylinders

The drag and lift force of a twin-cylinder structure are often greater than those of a single cylinder, causing serious structural safety problems. However, there are few studies on the passive control of twin cylinders. The study aimed to investigate the performance of passive drag reduction measures using small cylinders on twin cylinders at a Reynolds number of 100. The effects of small cylinder height (HD/D = 0~1.0, D is the side length of the twin cylinder) and cross-sectional shape on fluid force and flow structures were studied by direct numerical simulations. The control mechanism was analyzed using high-order dynamic mode decomposition (HODMD). The results showed that significant drag reduction occurred in the co-shedding state, particularly when the gap length of the twin cylinders L/D = 6.0. The small control cylinders with HD = 0.6, by contrast, showed the best performance in reducing the mean drag and fluctuating lift of the twin cylinders. It reduced the mean drag of the upstream cylinder (UC) by 2.58% and the downstream cylinder (DC) by more than 62.97%. The fluctuating lift coefficient for UC (DC) was also decreased by more than 70.41% (59.74%). The flow structures showed that when the flow hit UC under the action of small control cylinders, a virtual missile-like aerodynamic shape was formed at the leading edge of UC. In this way, the gap vortex consisted of two asymmetric steady vortices and the vortex length significantly increased. This was also confirmed by HODMD. The coherence modes in the gap were suppressed and thus the interaction between gap flow and wake flow was mitigated, which resulted in the fluid force reduction.

The effect of spacing on the flow-induced vibration of one-fixed-one-free tandem cylinders with a rigid splitter plate

The fluid-structure interaction mechanism of an assembly system, including a fixed upstream cylinder and a transverse oscillating downstream cylinder with a rigid splitter plate, is numerically studied at a low Reynolds number Re = 150 and mass ratio m* = 10.0. The effect of different spacing ratios (G/D = 1.5, 3.0, 5.0, and 8.0) and reduced velocities (Ur = 1.0–40.0) on the dynamic responses, hydrodynamic characteristics, and wake patterns of the downstream cylinder-plate (DCP) are analyzed in detail. The results show that, depending on the spacing ratios and the reduced velocities, different response regimes can be identified: (a) For G/D = 1.5 and 3.0, the response of the DCP presents a steady flow at low Ur where the oscillation is completely suppressed. As Ur increases, the response regime shifts to vortex-induced vibration (VIV), which is characterized by a wider lock-in bandwidth and a larger peak vibration amplitude than those of the single cylinder-plate body. (b) For G/D = 5.0 and 8.0, the response regimes consist of VIV and galloping. For the former, the upstream vortex shedding leads to a significant increase in the lift force on the DCP, and its frequency is highly synchronized with the oscillation. By contrast, multiple harmonic components of the lift force are observed in the galloping-dominated Ur range. Two prominent peaks can be identified in the power spectra. The lower peak, produced by the reattachment of the separated shear layers, is the main contributor to the oscillation. The higher peak originating from the upstream vortex shedding frequency is out of phase with the oscillation, and its contribution to the oscillation is very small.

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 shedding analysis of flows past forced-oscillation cylinder with dynamic mode decomposition

Direct numerical simulations are performed for flow past circular cylinders by the lattice Boltzmann method coupled with immersed moving boundary method. By analyzing the flows past a single cylinder at a wide range of cross-flow or in-line oscillation amplitude (0.25≤A/D≤1.5) and frequency (0.5≤fe/f0≤1.5), the results find that the vortex shedding modes inside and outside “lock-in” interval are of significant difference. The vortex shedding mode in the “unlock-in” state is 2S, but C(2S) and P + S shedding modes can be found in the lock-in state. Dynamic mode decomposition is used to analyze characteristic flow features, which shows that mode 1 is the main factor reflecting the flow field structure and mode 2 represents the vortex shedding mode in this work. The vortex shedding modes of flows past a tandem and side-by-side cross-flow double oscillating cylinders are systemically investigated. For tandem double oscillation cylinders, the results of modal decomposition suggest that the shear layer of upstream oscillating cylinder is separated behind the downstream cylinder at a space rate of L/D≤2, but separated behind the upstream cylinder at L/D≥3. Mode 2 at L/D=4 differs from other vortex shedding modes due to the strong inhibition effect by the downstream cylinder on the vortex formation of upstream cylinder. For side-by-side double oscillation cylinders, the wake of two cylinders is a single vortex street at H/D=1, a bistable flow at H/D=2 or 3, a coupled vortex street at H/D=4, and close to a single cylinder at H/D>4. The results of modal decomposition are disordered at H/D=2 due to the interaction between two cylinders and effect of gap flow.

Experimental investigation on vortex/wake-induced force of double unequal-diameter flexible cylinders in tandem

An experimental investigation on the vortex/wake-induced force of double unequal-diameter cylinders in tandem was performed. In the experiment, the upstream-to-downstream cylinder diameter ratio was 1.569, and the gap spacing ratio between the cylinder models ranged from 3 to 8. Under uniform flow with Reynolds number up to 11 328, the strains caused by the vortex/wake-induced vibrations were measured for the double flexible cylinders. Based on the measured strains, the displacements were reconstructed with the mode superposition method. Then, the vortex/wake-induced forces were obtained inversely. Subsequently, the time-varying excitation and added mass coefficients were identified by the forgetting factor least squares method. The results show that the wake-induced force coefficient and excitation coefficient of the downstream cylinder are smaller than those of the single cylinder, while the added mass coefficient becomes larger. In addition, the downstream cylinder under frequency capture can absorb a higher proportion of energy from the wake to excite larger vibration amplitudes, especially in the in-line direction.

Self-adaptive turbulence eddy simulation of flow control for drag reduction around a square cylinder with an upstream rod

The use of an upstream circular rod to control the flow around a downstream square cylinder is found to efficiently reduce the drag of the square cylinder. The complex flow characteristics and mechanism of the rod-square system in tandem arrangement as a passive flow control method for various centre-to- centre gap ratios (L/D) are investigated by numerical simulation. Turbulence modelling of the rod-square cylinder system is challenging. To select a suitable turbulence modelling, the recently developed Self-Adaptive Turbulence Eddy Simulations (SATES), as well as IDDES (Improved Delayed Detached Eddy Simulation) and SBES (Stress Blended Eddy Simulation) are first assessed for single circular and single square cylinder flow test cases. The SATES method performs best among the three models for bluff body flow simulation and is thus used in the drag flow control study. For the rod-square flow control system, the Reynolds number is 34000 based on freestream velocity U0 and the edge length of the square cylinder D. The diameter of the control rod is kept constant at d/D = 0.18. The flow characteristics and mechanism are explored in detail, varying the rod and square cylinder distance of L/D = 1.5, 2.0, 2.5and 3.0. According to the absence or presence of vortex shedding from the upstream rod cylinder, two flow patterns (pattern I and pattern II) are observed. Large drag reduction is observed for all the simulation cases the maximum drag reduction is approximately 63% with L/D = 2.0, and the minimum drag reduction approximately 53% with L/D = 3.0. The secondary lock-frequency, which presents as pattern II, is caused by the excitation of upstream vortices. It is found that the side recirculation is associated with the wake recirculation length of the square cylinder, which is similar to the elongated cylinder in the flow pattern I. The flow mechanism of suppression of the vortices from the rod can be attributed to the effective diffusion of vorticity in the separating shear layer caused by the presence of the front wall of the square cylinder.

Effects of spacing ratio on vortex-induced vibration of twin tandem diamond cylinders in a steady flow

Vortex-induced vibration of twin tandem square cylinders at an inclined angle of 45° to the fluid, i.e., twin diamond cylinders of mass ratio m* = 3, is numerically investigated at Reynolds number Re = 100 and reduced velocity Ur = 3–18. This paper focuses on the effects of cylinders' spacing ratio L* (=L/B, where L is cylinders' center-to-center spacing and B is the characteristic length) ranging from 2 to 6 on the oscillation responses of two-degree-of-freedom cylinders. The results indicate that the wake structure experiences two gap flow patterns, the reattachment and co-shedding regimes, and eight different wake modes. At a small spacing (L* = 2–3), the reattachment regime occurs for the lower or higher Ur with the approximate range of 3 and 16–18. Meanwhile, the reattachment regime mainly occurs for other ranges of Ur at L* = 2–6. The more significant oscillation of each spacing appears in the cross-flow direction, and the maximum cross-flow amplitude of the upstream cylinder is smaller than that of the downstream cylinder. Additionally, although significant cross-flow oscillations occur at small spacings (L* = 2–3) with the Ur ≈ 5–9 and 12–14, the intrinsic mechanisms are entirely different. For the cross-flow oscillation characteristics of larger spacings (L* = 4–6), they are virtually similar.

Numerical investigation on flow-induced vibrations of two tandem cylinders localized selective roughness with different natural frequencies

The characteristics of flow-induced vibrations (FIVs) of two tandem rough cylinders with different natural frequencies transversely to the flow direction are computationally investigated using two-dimensional Unsteady Reynolds-Averaged Navier-Stokes (2-D URANS) equations. Seven different sets of natural frequency ratios fn* between upstream and downstream cylinders (fn*= fn,u/fn,d =0.5, 0.707, 0.866, 1.0, 1.155, 1.414, and 2.0) are performed in the range of 30,000≤Re≤120,000, where fn,u and fn,d are the natural frequencies of the upstream and downstream cylinders, respectively. The spacing ratio is d/D=2.57 (where d is the center-to-center longitudinal spacing between two cylinders and D is the diameter). The mass ratio is m*=1.343. The characteristics of amplitude response and frequency response are analyzed in detail. According to the frequency response of the two cylinders with different natural frequency ratios, three main interactive oscillating patterns of the downstream cylinder are observed: (1) Forced oscillating pattern: the downstream cylinder oscillates forcedly with the upstream cylinder, and the dominant oscillating frequency of the downstream cylinder is equal to that of the upstream cylinder. (2) Independent oscillating pattern: the downstream cylinder oscillates independently with its own natural frequency. (3) Beat oscillating pattern: the downstream cylinder oscillates with two dominant frequencies, one is equal to the oscillating frequency of the upstream cylinder, and the other one is equal to its own natural frequency. The different natural frequencies of the cylinders suppress the vibration of the downstream cylinder at different reduced velocity ranges. The displacement time history, frequency spectrum, and vortex structures of each oscillating pattern case are also analyzed for elucidation.

Heat transfer characteristics in turbulent FIV of three circular cylinders with different isosceles-triangle arrangements

PurposeThis study aims to numerically explore the heat transfer characteristics in turbulent two-degree-of-freedom vortex-induced vibrations (VIVs) of three elastically mounted circular cylinders.Design/methodology/approachThe cylinders are at the vertices of an isosceles triangle with a base and height that are the same. The finite volume technique is used to calculate the Reynolds-averaged governing equations, whereas the structural dynamics equations are solved using the explicit integration method. Simulations are performed for three different configurations, constant mass ratio and natural frequency, as well as distinct reduced velocity values.FindingsAs a numerical challenge, the super upper branch observed in the experiment is well-captured by the current numerical simulations. According to the computation findings, the vortex-shedding around the cylinders increases flow mixing and turbulence, hence enhancing heat transfer. At most reduced velocities, the Nusselt number of downstream cylinders is greater than that of upstream cylinders due to the impact of wake-induced vibration, and the maximum heat transfer improvement of these cylinders is 21% (at Ur = 16), 23% (at Ur = 5) and 20% (at Ur = 15) in the first, second and third configurations, respectively.Originality/valueThe main novelty of this study is inspecting the thermal behavior and turbulent flow–induced vibration of three circular cylinders in the triangular arrangement.

Experimental study on the hypersonic boundary layer transition induced by tandem cylinders

The flow field structure and heat flux distribution around an isolated cylinder and tandem cylinders on a flat plate at different angles of attack (AoA) and inflow conditions are investigated in a Mach 6 low-noise wind tunnel, using nano-tracer-based planar laser scattering (NPLS) techniques and the temperature sensitive paint (TSP) technique. The results reveal that, first, at AoA = 10°, the downstream cylinder will cause a horseshoe vortex formed by the upstream cylinder, which originally propagates parallel to the downstream, to expand to both sides. Subsequently, when the number of cylinders increases, the spanwise width of the affected area is increased further. In addition, a low-heat flux region caused by the recirculation region appears behind the cylinder; downstream of the low-heat flux region, the heat flux distribution of the isolated cylinder model forms a parallel stripe structure, while in the tandem cylinder model, it resembles a “Λ-shaped” distribution. A second key finding is that, with the decrease in AoA, the region of influence of the cylinder decreases. Moreover, the “Λ-shaped” heat flux structure in the wake of the downstream tandem cylinders gradually disappears, and the stripe structure near the second cylinder is in a “shuttle-shaped” distribution. Notably, with the increase in the spacing between the two tandem cylinders, the spanwise width of the “shuttle-shaped” distribution increases. The low-heat flux area behind the second cylinder initially increases with an increase in the spacing, but when the spacing is too large, a high-heat flux stripe begins to appear in the centre of the low-heat flux region. In addition, placing a third cylinder on the wake centreline of the tandem cylinder has a slight impact on the flow, but its effect is enhanced when the third cylinder is located outside the recirculation region of the tandem cylinder.

Experimental Investigation of the Hypersonic Boundary-Layer Transition Induced by the Wall-Mounted Cylinder

The flowfield structure, heat flux distribution, and pressure fluctuations of the wall-mounted cylinder-induced hypersonic boundary-layer transition are investigated at a 10 deg angle of attack. Experiments are conducted in a Mach 6 low-noise wind tunnel using the nanotracer-based planar laser scattering (NPLS) technique, temperature-sensitive paints (TSP), and high-frequency pressure sensors. First, the streamwise and spanwise NPLS images, TSP results, and power spectral density results of isolated cylinders at different heights show that with the increase of the cylinder height , the size of the separated region and the spanwise width of the horseshoe vortex increase, and the transition moves forward. Second, the flowfield structure and wall heat flux distribution around the streamwise cylinder arrays are investigated. The results demonstrate that the downstream cylinder will destroy the development of the hairpin vortex in the upstream cylinder wake but will expand the horseshoe vortex to both sides, increasing the influence area of the cylinder.

Numerical study on flow-induced vibration of two-degree-of-freedom staggered circular cylinders at subcritical Reynolds numbers

In this study, the flow-induced vibration of two-degree-of-freedom staggered circular cylinders at subcritical Reynolds numbers is studied numerically with overset dynamic mesh. The streamwise spacing ratio Sx/D of 4 and the transverse spacing ratio Sy/D ranging from 0 to 2 are employed to explore the influence of staggered arrangement on the vibrations and fluid forces of cylinders. It is found the upstream cylinder mainly experiences the vortex-induced vibration while vortex-induced and wake-induced vibrations happen for the downstream one, which may be interfering or independent depending on the transverse spacing of cylinders. The phase lag between the displacement and fluid force of the downstream cylinder changes from 0° to 180° with the increasing of inflow velocity, which leads negative add mass and serves as the reason of wake-induced vibration. The theoretical formulae to estimate the critical velocity, fluid coefficient and vibration amplitude of wake-induced vibration are proposed and validated by the numerical simulations.

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.