Downstream Cylinder Research Articles

Revisiting the reattachment regime: a closer look at tandem cylinder flow at

Tandem cylinder flow comprises several different flow regimes. Within the reattachment regime, the development of the gap shear layers is of utmost importance to the flow, but has received little attention so far. Through direct numerical simulations at$Re = 10^{4}$, for a gap ratio of 3.0, we have discovered that the shear layers are significantly altered with respect to a single cylinder. These differences include early onset of separation, crossflow stabilising, delayed transition to turbulence and little meandering of the transition region. Vortex pairing in the gap shear layers is reported for the first time. The interaction between the recirculating gap flow and the shear layers was investigated. Asymmetrical, large-scale gap vortices influence the position of transition to turbulence through direct contact and through secondary flows. The occurrence of transition in the gap shear layers has consequences for both the reattachment mechanism and the development of the downstream cylinder wake. The reattachment points are unsteady with large amplitude fluctuations on a fine time scale. Reattachment is seen to be a combination of impingement and modification of the upstream shear layers, which causes a double shear layer in the downstream cylinder near-wake. Buffeting by and interaction with the gap shear layers likely cause transition to turbulence in the downstream cylinder boundary layer. This leads to significant changes in the wake topology, compared with a single-cylinder wake.

Simulation for flow across heated square cylinders

AbstractThe thermal lattice Boltzmann method is used to examine forced convection heat transfer from six inline heated square cylinders for Re = 100 at 0.5 ≤ s/d ≤ 4.0, where s is the distance between the surfaces of two cylinders and d is the cylinder size. Such a heat transfer is transient in nature for which the present work reports heat transfer regimes such as synchronous, quasiperiodic and chaotic. For 0.5 ≤ s/d ≤ 1.5 the heat transfer is synchronous, for 1.5 ≤ s/d ≤ 3.0 it is quasiperiodic and for 3.0 ≤ s/d ≤ 4.0 it is chaotic in nature at Re = 100. These regimes are confirmed through cylinder Nusselt number signals, its power spectra, and heat wake interference. The appearance of heat transfer regimes for inline heated cylinders is similar to the appearance of flow regimes for inline unheated cylinders except for the fact that transition from synchronous to quasiperiodic regime occurs at s/d = 1.5 for heat transfer and at s/d = 1.1 for flow. The synchronous heat transfer regime is characterized by a single heat wake that envelopes all cylinders while quasiperiodic heat transfer regime is characterized by the formation of thermal blobs in the gap between cylinders. A chaotic heat transfer regime is characterized by the shedding of thermal blobs and interference of thermal blobs by downstream cylinders. Regardless of spacing, the average Nusselt number encountered by cylinders is smaller than that for the isolated cylinder. The novelty of the work is that transitions occurring in the flow of heat are considered for an understanding of heat flow from bluff bodies.

Physical mechanisms behind the extreme wind pressures on two tandem square cylinders

The extreme wind pressure might lead to local or overall structural failures. The physical mechanisms behind extreme pressures on two tandem square cylinders are investigated using large-eddy simulation at a Reynolds number of 8 × 104. The spacing ratio P/B ranges from 1.1 to 5 (P: cylinders’ center distance; B: side length). The aerodynamic coefficients, flow patterns, mean and fluctuating pressure coefficients, pressure skewness and kurtosis, and instantaneous flow structures are analyzed. The extreme negative pressures are induced by the intermittent appearance of strong vortices attached to the cylinder surfaces. “Gap vortex” and “wall vortex” are responsible for the extreme pressure at the gap-sides of two cylinders in the single mode (1 < P/B < 2). “Corner vortex” would cause extreme negative pressure near the front corners of the upstream cylinder and the rear corners of both cylinders at most spacings. At the reattached (2 ≤ P/B < 4) and binary (4 ≤ P/B ≤ 5) modes, the Karman vortex released from the rear corner of the downstream cylinders leads to extreme pressure on the rear surface. As the spacing increases, the extreme pressure on non-Gaussian-pressure regions is generally strengthened but the three-dimensionality in vortex structures and instantaneous pressure distributions roughly declines.

FIV of tandem unequal-diameter flexible cylinders at different gap ratios

Studies on the flow-induced vibration (FIV) of tandem unequal-diameter flexible cylinders in a broad gap ratio range are scarce. To reveal the effect of the gap ratio on and characterize the evolution features of the cylinder FIV with hydrodynamic interference, this paper experimentally investigates the FIV of two tandem flexible cylinders with unequal diameters at different gap ratios. Both cross-flow and in-line vibrations of the cylinders are permitted. Five gap ratios (i.e., T/d = 4, 6, 8, 10, and 12) are tested with the diameter ratio (d/D) set to be 0.5, where T is the center-to-center distance, d and D are the diameters of the upstream cylinder (UC) and downstream cylinder (DC), respectively. The effective cylinder length is 2.7 m, of which 1.2 m is submerged in water, and the aspect ratios of the UC and DC are 84.375 and 168.750, respectively. Based on the strains measured by the fiber bragg grating (FBG) sensors and the modal decomposition theory, detailed analyses of the displacement and frequency response are conducted. The FIV response of the UC resembles the vortex-induced vibration (VIV), whereas the DC undergoes wake-induced vibration (WIV). Increasing the gap ratio decreases the displacement amplitude of the DC but hardly affects the dominant frequency response. This study identifies three response regions (i.e., the VIV region, the transition region, and the WIV region) for the FIV response of the DC. The dual-cylinder interaction and dual-cylinder competition induce a coupled multi-physical vibration morphology of the cylinder. The “displacement-frequency co-variation” phenomenon of the DC and the “double-frequency lock-in” phenomenon of the UC are observed in the WIV region.

Effect of acoustic waves on the flow and heat transfer around two tandem arranged cylinders

In this work, the effect of acoustic waves on vortex shedding and convective heat transfer of two tandemly arranged cylinders is investigated using experiments and numerical simulations. This paper focuses on the average Reynolds number Re = 200, the sound pressure level ranges from 127dB to145dB, and the sound frequency ranges from 100Hz to 1000Hz. Different acoustic wave frequencies and particle vibration velocity amplitudes were set as the entrance conditions. The average heat transfer in the upstream and downstream cylinders was enhanced due to the increase in the particle velocity amplitude of the fluid around the cylinder by acoustic oscillations. Moreover, with the increase in the acoustic frequency, the flow mixing is enhanced and irregular vortices appeared in the cylindrical wake. With regards to the particle velocity amplitude, the values of the Nusselt number of the two cylinders increase with the increase in particle velocity amplitude. With the increase in the particle velocity amplitude, the forced mixing and heat transfer of the gap flow between the two cylinders are enhanced. The comparison between the experimental and numerical results shows that acoustic waves can enhance convective heat transfer of two tandemly arranged cylinders in the cross-flow.

Three-dimensional transition in the wake of two tandem rotating cylinders

Three-dimensional (3-D) transition in the wake of two tandem co-rotating cylinders is studied numerically for Reynolds numbers $180\le Re\le 500$ . Infinite cylinders of equal diameter ( $D$ ) and span ( $8D$ ) are placed at streamwise gaps $Lx=2.5D$ and $7.5D$ , and rotated at rotation rates $\alpha =0$ , $0.5$ , $1$ and $2$ . For $\alpha =0$ and $Lx=7.5D$ , 3-D transition in the wake of the upstream cylinder resembles that for an isolated cylinder with the formation of Mode-A and Mode-B instabilities, whereas for the downstream cylinder, only Mode-A instability occurs in both the $Lx=2.5D$ and $7.5D$ cases with $\alpha =0$ . When the cylinders rotate at $\alpha =1$ for $Lx=7.5D$ , staggered transition takes place with the appearance of only Mode-B and only Mode-A instabilities in the near-wake regions of the upstream and downstream bodies, respectively. In the case $Lx=2.5D$ , the wake of the rotating cylinders transitions via Mode-C and Mode-D instabilities for $\alpha =0.5$ , Mode-D and Mode-D $^\prime$ for $\alpha =1$ , and Mode-C and Mode-A for $\alpha =2$ . A sudden decrease in near-wake fluctuations, accompanied by a downward jump in the force coefficients, is observed as the 3-D instability shifts from one mode to another, for $\alpha \ge 1$ and $Lx=2.5D$ . This discontinuity is caused by the formation of a pair of opposite-signed recirculation zones that mitigate each other's effects in the near-wake region.

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.

Correspondence between the number of no-slip critical points and nature of rear stagnation point of a symmetric object

For flow around an isolated object, the points of zero vorticity/shear stress located at fluid–solid interface, i.e., the separation, reattachment points inclusive of forward and rear stagnation points are refered to as no-slip critical points. The total number, n (≥2), of such points is an even number. For flow past a diamond-section object, it is shown here that a change of the value of n by 2 alters the nature of its rear stagnation point. The rear stagnation point acts as a separation point for n = 2, 6, 10, etc. and as an attachment point for n = 4, 8, 12, etc. A pair of hypothetical mean wakes is proposed and their viability discussed with reference to results available in literature. Concerning flow past two in-line diamond cylinders, the formation of an “anti-wake” at the leading edge of the downstream cylinder renders its forward stagnation point to act as a separation point, which, otherwise for an isolated object, invariably serves as an attachment point. The forebody and afterbody of a symmetric object act as independent entities in influencing the nature of no-slip stagnation points.

Numerical Investigation of Flow around Two Tandem Cylinders in the Upper Transition Reynolds Number Regime Using Modal Analysis

Flow around two tandem cylinders at Re = 3.6 × 106 for different center-to-center spacing ratio (L/D) is investigated numerically using two-dimensional (2D) Unsteady Reynolds-Averaged Navier–Stokes (URANS) equations combined with a standard k−ω SST turbulence model. The instantaneous flow structures around the cylinders, hydrodynamic forces on the cylinders and Strouhal number (St) are analyzed and discussed. Dynamic Mode Decomposition (DMD) is used to extract the spatiotemporal information of the coherent flow structures in the wake regions behind the upstream (UC) and downstream (DC) cylinders. A sparsity-promoted algorithm is implemented to select the dominant modes which contribute the most to the dynamics of the system. Based on the dominant modes, a reduced-order representation of the flows is built. A comparison of the lift and drag force–time histories, obtained by simulation results and the reduced-order representations, shows a high capability of the latter to reproduce the surrounding flow and hydrodynamic properties of the tandem cylinders at the high Reynolds number.

Numerical investigation on the effect of diameter ratio on wake induced vibrations of tandem cylinders

Numerical simulations of WIV (wake induced vibration) for tandem cylinders with different diameter ratio in the impingement regime are performed for a low Reynolds number of Re = 150 and low mass ratio of m* = 2.0. Five different diameter ratios of d/D = 1/2, 3/4, 1, 4/3, and 3/2 are examined, in order to identify the effects of diameter ratio on 2-DOF (two-degree-of-freedom) vibration responses of the cylinder in the range of 2≤Ur ≤ 14. The results show that the diameter ratio and vortex mode play important roles in the vibration amplitudes and frequencies of the downstream cylinder. The WIV can be further classified into WIEV (wake interference and enhancement vibration) and WCV (wake controlled vibration) according to two distinct mechanisms of the amplification of cross-flow vibration amplitude. As d/D ≤ 1, the vibration frequencies of the downstream cylinder are significantly pulled down and interfered by the small vortices shedding from the small upstream cylinder. Meanwhile, a wider range of lock-in and enhanced vibration amplitudes are the features for WIEV. The inline direction of the downstream cylinder have large response amplitudes in a wide range of Ur (reduced velocity) and reach to the maximum value at d/D = 1. As d/D > 1, the hydrodynamic characteristics of the downstream cylinder are mainly controlled by the larger vortices shedding from the upstream cylinder. The downstream cylinder vibrates as the vortex shedding frequency of the larger upstream cylinder and the lock-in phenomenon is absent. WCV significantly increases the risk of fatigue failure of the cylindrical structure.

Thermal flow analysis of self-driven temperature-sensitive magnetic fluid around two cylinders arranged in tandem

A temperature-sensitive magnetic fluid (TSMF) is a refrigerant that provides high heat transfer capability and pump-less long-distance heat transfer. The driving force of the self-driving TSMF is produced by the temperature difference and the magnetic field gradient. Due to this principle, expanding the heating area can improve the driving force while promoting the heat exchange efficiency between the heating body and the TSMF. This study focuses on heat flow phenomena and heat transfer around two cylinders arranged in tandem. We used the hybrid Boltzmann method to analyze the thermal flow of a self-driven TSMF and investigate the effect of distance between the two cylinders and the magnetic field magnitude of the heat transfer. The results showed that, when the magnitude of the magnetic field is small, the heat between the cylinders is not easily dissipated, which causes fluctuations in the driving force. The heat flow from the upstream cylinder has a direct effect on the downstream cylinder. A variation of the distance between the cylinders produces two different heat flow phenomena, the first type of heat flow phenomenon is characterized by the movement of heat along the central axis and the second type is the movement of heat from the trailing edge of the upstream cylinder to the trailing edge of the downstream cylinder. Compared with the first type of heat flow phenomenon, the heat transfer effect of the second type of phenomenon is significantly improved.

Effect of three tandem cylinder diameter difference on flow-induced vibrations and heat transfer

The effect of diameter differences of three tandem cylinders on flow-induced vibrations (FIVs) and convection heat transfer characteristics is investigated. The diameter reduction ratios are 0, 0.2, and 0.4, and the cylinder gap ratios are 2 and 4. The simulation is performed at Reynolds number 100, Prandtl number 0.7, reduced velocity 2 - 20, and mass ratio 2. The effect of the diameter reduction ratio on FIVs and heat transfer characteristics is observed through flow structures, oscillation amplitude, shedding frequency, correlation between lift coefficient and cylinder displacement, and Nusselt number. The flow around the downstream cylinder and the associated heat transfer depend strongly on the diameter reduction ratio. The FIV of the downstream cylinder is reduced with the increase in diameter reduction ratio. Indeed, for diameter reduction ratio 0.4 and gap ratio 2, the maximum oscillation amplitude is reduced by 48%. This is because the unequal diameter results in a weaker correlation between lift force and oscillation, modulated oscillation of cylinder, and distribution of primary shedding frequency energy to secondary frequency. At the initial and upper branches of vibration, the heat transfer from the downstream cylinder is enhanced with an increase in diameter reduction ratio due to more exposure to flow and the impingement of the gap vortices. The present flow configuration unveils reduced FIV and enhanced heat transfer, which is a desirable characteristic of multiple heated tubes for structural durability and better performance.

Numerical computations of flow around three equilateral-triangular square cylinders with rounded corners using momentum exchange-based IB-LBM at low Reynolds numbers

In this study, the flow around three square cylinders with rounded corners in equilateral-triangular arrangements were investigated using the momentum exchange-based immersed boundary-lattice Boltzmann method (IB-LBM) at low Reynolds (Re) numbers. The influences of Re number and gap ratio δ to the flow characteristics, force coefficients, and Strouhal (St) number were examined by selecting one hundred different gap ratios δ and forty different Re numbers. The wake flow patterns are divided into six distinct categories according to the gap ratio, these are single bluff-body, deflected, flip-flopping, anti-phase, anti-phase & in-phase coexist, and fully developed in-phase flow patterns. In addition, the Re number was also found to have a significant impact on the vortex shedding frequencies and flow properties. The drag coefficients, lift coefficients, and St number were calculated to demonstrate the relationship between vortex shedding properties, gap ratio, and Re numbers. The results revealed that the wake flow pattern, flow characteristics, and force coefficients depended significantly on the gap ratio and Re numbers. In addition, the power spectral density of the upstream cylinder were significantly lower than those of downstream cylinders for low gap ratios, and the mutual interference between each cylinders vanished as the gap ratio increased.

Generation mechanism of wake galloping in two staggered circular cylinders in view of hysteretic flow phenomena

A smooth cylinder placed near the wake of an upstream smooth cylinder is susceptible to galloping. This study experimentally investigated the generation mechanism of wake galloping in two staggered cylinders of equal diameter D based on the physical flow phenomena occurring in the oscillating downstream cylinder. The horizontal center-to-center distance of the two cylinders ranged from 3.0D to 3.5D and the vertical center-to-center distance was 0.3D to 0.5D. As observed, the wind velocity range in the smooth cylinder was within the subcritical Reynolds number regime, and the unsteady responses at the downstream exhibited prominent hysteresis that evolved with the reduced velocity, and ultimately, triggered wake galloping at the critical reduced velocity. In particular, this hysteretic behavior is native to certain arrangements of the two cylinders and occurs because of the interaction between the downstream cylinder and the wake of the upstream cylinder. Moreover, the hysteresis-based discussion could identify the potential wake galloping vibrations in certain arrangements that are beyond the scope of the current investigation. With the application of 12 spiral protuberances on the surface of both cylinders, the hysteresis vanished and wake galloping was suppressed.

The space effect on WIV interference between a fixed and oscillating diamond cylinder at a low Reynolds number of 100

To clarify the space effect on wake-induced vibration (WIV) of twin tandem diamond cylinders, the fixed upstream cylinder and the downstream cylinder freely oscillating in both in-line and transverse directions have been numerically investigated. The nondimensional center-to-center spacing ratio L* is varied in the range of 2–6, the Reynolds number Re is 100, the reduced velocity Ur is 3–20, and the mass ratio m* is 3. According to the wake modes and dynamic responses, the mechanism for the wake excitation of twin diamond cylinders with different spacing is further discussed. At a smaller spacing (L* = 2 and 3), the reattachment and co-shedding regimes appear with the increasing Ur, but when it comes to a larger spacing (L* = 4–6), only the co-shedding one occurs. The downstream cylinder shares a similar lock-in region at each spacing, while the corresponding flow patterns are not the same. The vortex shedding mode of the downstream cylinder within the lock-in region is 2S at L* = 2, while it is 2P at L* = 3–6. Additionally, the downstream diamond cylinder displays significant in-line and transverse oscillations at each spacing ratio, with the largest amplitude appearing at L* = 3.

Fluid–structure-coupled Koopman mode analysis of free oscillating twin-cylinders

Flow-induced vibration (FIV) of twin square cylinders in a tandem arrangement was numerically investigated at Reynolds numbers 200 and gap L/D = 2.0, 4.0, and 6.0 (D is the side length of the cylinders). Fluid-structure-coupled Koopman mode analysis method was developed to synchronously identify the coherence flow and structural modes. Then, the energy transfer between cylinders and Koopman modes was analyzed to uncover the underlying mechanism of FIV. The results showed that at L/D = 2.0 and 4.0, only soft lock-in vortex-induced vibration (VIV) was observed. The oscillating amplitude for L/D = 4.0 was much higher than that of L/D = 2.0, due to the interference effects induced by fully developed gap vortices. As L/D = 6.0, VIV and galloping coexisted. For the coherence mode, the primary flow mode induced by the vortex shedding dominated the flow field at L/D = 2.0 and 4.0. The direct mode energy dominated the energy transfer process. The upstream cylinder (UC) contributed to the negative work done and thus tended to stabilize the vibration; in contrast, the downstream cylinder (DC) exhibited the opposite behavior. In the galloping branch at L/D = 6.0, both the flow field and structural response contained three main modes: one vortex-shedding-induced mode and two vibration-induced modes. For the direct mode energy, owing to the interference effects, DC contributed to more positive work done than UC by the vibration-induced modes. The vortex-induced mode was governed by DC and afforded negative work done. Moreover, all the coupled mode energy was almost equal to zero.

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.

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.

Wake Effects on Wave-Induced Loads Acting on Cylinders in a Tripod Configuration

Comparative hydrodynamic loads caused by a focused wave acting on differently sized slender vertical cylinders placed in a wave canal were predicted at model scale using an unsteady Reynolds-averaged Navier–Stokes (URANS) solver and the Morison equation. This paper focused, first, on wake effects that need to be considered for the structural design of tripod configurations and, second, on the influence of these wake effects on wave-induced loads. For the Morison approach, flow velocities were gathered at incremental representative locations along the length of the cylinders, whereby the use of a central differencing approach obtained the associated flow accelerations. A first scenario dealt with a small- and a large-diameter cylinder, implemented individually at two immersion depths. A second scenario considered medium- and large-diameter cylinders arranged in a tripod configuration, where the upstream and downstream cylinders had the same diameter. For the single cylinder, impact loads obtained by both methods compared favorably to experimental measurements. For the tripod configuration, however, impact loads obtained by both methods differed due to the influence of wake effects. Thus, it was necessary to determine the influence of wake effects to assess the structural integrity of tripod configurations.

Numerical analysis of WIV phenomenon with two in-series cylinders: WIV suppression and energy harvesting

This numerical study aims to analyze the hydrodynamic characteristics of in-series structures with two cross-sections, as well as their power characteristics under different spacing (α) and radius (φ) ratios respectively. The results show that as the spacing ratio increases, the in-series circular/square-cylinder system displays VIV, whereas the in-series square-cylinder system can effectively suppress vibration within the interval of α = 5.3 – 5.7, 6 ≤ Ur ≤ 8 when φ = 1. It is worth noting that as the radius ratio increases, the vibration of the downstream square cylinder transits from VIV to galloping. Subsequently, the short-time Fourier transform and wavelet transform are employed to perform time-frequency analysis of different cases. In terms of energy harvesting, the in-series circular-cylinder system shows its maximum power of 48.83 mW at Ur = 9 when α = 6, φ = 1. Additionally, the power of the in-series square-cylinder system at φ = 2 is higher than that in the other two cases (φ = 1 and 3), and in these three cases, the power at α = 6 is much greater than that of the case α = 8 and 4 regardless of the radius ratio. As to conversion efficiency, the case α = 6 and φ = 2 demonstrates the optimal energy harvesting performance. Thus, flexible control of the radius ratio and spacing ratio in a special range can not only suppress vibration but also enhance energy harvesting efficiency.