Tandem Cylinders Research Articles

Flow-induced vibrations of a twistable two-tandem cylinder system across varied gap ratios

This paper presents a simulation study on the flow-induced vibrations (FIVs) of a two-tandem cylinder system with three degrees of freedom, encompassing in-flow, cross-flow, and torsional motions at a Reynolds number of 150. We specifically focus on investigating the impact of gap ratios (G*) between the cylinders, considering values of 0.5, 2, and 3. The ratio of torsional natural frequency to translational natural frequency was maintained at 12.5, while the mass ratio between the cylinder system and the fluid was set to 2. Our findings reveal a notable sensitivity of the FIV responses to the gap ratio between the cylinders. It was observed that the cylinder system's vibrations can undergo locking phenomena at both the translational and torsional natural frequencies, with maximal cross-flow amplitudes occurring within the torsional locked region. Particularly, at G* = 0.5, the maximal cross-flow amplitude reached approximately 21.4 times that of the cylinder system without torsional vibration, posing potential risks of fatigue failure in offshore equipment. Conversely, at G* = 2, an unusual ultra-low frequency was detected in the in-flow vibration. This phenomenon significantly magnified the FIV of the cylinder system, despite the absence of frequency locking. Furthermore, at G* = 3, we observed an expanded range of vibrations with ultra-low frequency compared to G* = 2. Our analysis identified the differential development speed of the shear layers around the upstream and downstream cylinders as a key factor contributing to varying vortex shedding frequencies. This discrepancy led to periodic changes in the vortex shedding mode of the cylinder system over time, thereby introducing low-frequency components into the flow-induced vibration. These insights deepen our understanding of the complex dynamics governing the FIV of tandem cylinder systems, which holds implications for the design and maintenance of offshore structures.

On the Spanwise Periodicity within the Gap between Two Different-Sized Tandem Circular Cylinders at Re = 3900

Although the spanwise periodicity within the gap between two tandem circular cylinders has been observed by some researchers, there is a lack of systematic research on the properties of this periodicity. For the spanwise periodicity within the gap, this study aims to ascertain its characteristics, its influences on the flow field, and its variation trend with increasing spacing ratio. By numerically simulating the flow around two tandem circular cylinders with a diameter ratio of d/D = 0.6 and seventeen spacing ratios (L/D = 1.00~6.00) at Re = 3900, this study shows four flow regimes: Reattachment Flow (L/D = 1.00~3.15), Bi-stable Flow (L/D = 3.24), Intermittent Lock-in Co-shedding (L/D = 3.30~3.50), and Subharmonic Lock-in Co-shedding (L/D = 4.00~6.00). Further, depending on the spanwise periodicity length of the time-averaged flow structures (i.e., Pz) within the gap, Reattachment Flow is, for the first time, subdivided into three new sub-flow regimes: Small-scale Periodic Reattachment (L/D = 1.00~1.50, Pz/D = (0, 4]), Large-scale Periodic Reattachment (L/D = 2.00~2.25, Pz/D > 4) and Non-periodic Reattachment (L/D = 2.50~3.15, no spanwise periodicity). The formation mechanisms are elaborated by analyzing the combined effect of both the L/D value and the spanwise-averaged time-averaged reattachment angle of the downstream cylinder. Moreover, this study proves that the newly defined Small-scale Periodic Reattachment and Large-scale Periodic Reattachment are responsible for the pronounced asymmetry of the flow along the transverse direction within the gap. In addition, detailed flow properties and statistical parameters are provided for each flow regime, such as velocity, vorticity, force coefficient, separation/reattachment angle, Strouhal number, and Q-criterion.

Wake Structures and Hydrodynamic Characteristics of Flows around Two Near-Wall Cylinders in Tandem and Parallel Arrangements

To clarify the hydrodynamic interference characteristics of flows around multiple cylinders under the wall effect, the two-dimensional (2D) flows around the near-wall single, two tandem and parallel cylinders are simulated under different gap ratios (0.15 ≤ G/D ≤ 3.0) and spacing ratios (1.5 ≤ T/D ≤ 4.0) at a Reynolds number of Re = 6300. We also examine the wake patterns, the force coefficients, and the vortex-shedding frequency with emphases on the wall effect and effects of the two-cylinder interference. A critical wall gap of G/D = 0.6 is identified in the single-cylinder case where the wall can exert significant influences. The two near-wall tandem cylinders exhibit three wake states: stretching mode, attachment mode, and impinging mode. The force coefficients on the upstream cylinder are significantly affected by the wall for G/D ≤ 0.6. The downstream cylinder is mainly influenced by the upstream cylinder. For G/D > 0.6, the force coefficients on the two cylinders exhibit a similar variation trend. In the parallel arrangement, the two cylinders exhibit four wake states in different G/D and T/D ranges: double stretching mode, hetero-vortex scale mode, unilateral vortex mode, and free vortex mode. Moreover, the two parallel cylinders in the hetero-vortex scale or free vortex mode have two states: synchronous in-phase state and synchronous out-of-phase state. The mean drag coefficients on the two cylinders decrease, while the mean lift coefficients exhibit opposite variation trends, as the T/D grows.

The onset of instability and bifurcations in the transitional wake of two tandem square cylinders

Unsteady three-dimensional simulations are performed to elucidate the hidden transitional flow dynamics and Hopf bifurcations along the topological corelines of the created von Kármán streets behind a pair of square cylinders positioned in tandem. Our simulations provide significant new insight into the three-dimensional wake evolution and governing flow physics. We explain how pressure, velocity, and vorticity fluctuation along the Kármán vortex corelines in the increasingly unstable wake amplify, facilitating the growth of various modal instability patterns. The existing knowledge of wake transition through the intertwining of modes A, B, and C instabilities and associated linear stability analysis helped to gain some insight into the overall wake feature. The current study explains how exactly the transitional disturbances physically spread behind a pair of inline and tandem cylinders through the self-excited spanwise-periodic oscillation of the wake and created a sequence of variable length scaled Hopf bifurcations and their swapping for varied gaps between the cylinders and Reynolds number. The growth of a slow mode of the spectral frequency at the bifurcation points seemed crucial in initiating the near-transitional flow irregularity.

Flow-induced vibration of two tandem square cylinders at low Reynolds number: transitions among vortex-induced vibration, biased oscillation and galloping

The flow-induced vibrations (FIVs) of two identical tandem square cylinders with mass ratio m* = 3.5 at Reynolds number Re = 150 are investigated through two-dimensional direct numerical simulation (DNS) and linear stability analysis over a parameter range of spacing ratio 1.5 ≤ L* ≤ 5 and reduced velocity 3 ≤ Ur ≤ 34. Three kinds of FIV responses, namely vortex-induced vibration (VIV), biased oscillation (BO) and galloping (GA), are identified. The FIVs are then further classified into the branches of initial VIV (IV), resonant VIV (RV and RV′), flutter-induced VIV (FV), desynchronized VIV (DV), VIV developing from GA (GV), transitional state between VIV and GA (TR), BO and GA based on the characteristics of the vibration responses. The transitions among different FIV branches are examined by combining the DNS with linear stability analysis, where the transition boundaries among the VIV, BO and GA branches over the concerned parameters are identified on the branch maps. The transition from IV to RV or RV′ is found to be related to the unstable wake mode, while the FV, transiting from RV or RV′, is induced by the unstable structural factor in the wake-structure mode. The structural instability is considered as the physical origin of GA, whereas the mode competition between unstable wake and structure leads to DV, GV and TR, and thus delays the appearance of GA. The transition from DV to BO with biased equilibrium position, accompanied by the even-order harmonic frequencies, is essentially induced by the symmetry breaking bifurcation.

Near-Field Aeroacoustic Shape Optimization at Low Reynolds Numbers

We investigate the feasibility of gradient-free aeroacoustic shape optimization using the flux reconstruction (FR) approach to study two-dimensional flow at low Reynolds numbers. The overall sound pressure level (OASPL) is computed via the direct acoustic approach, and optimization is performed using the gradient-free mesh adaptive direct search (MADS) algorithm. The proposed framework is assessed across three problems. First, flow over an open cavity is investigated at a Reynolds number of Re=1500 and freestream Mach number of M∞=0.15, resulting in a 7.9 dB noise reduction. The second case considers tandem cylinders at Re=200 and M∞=0.2, achieving a 16.5 dB noise reduction by optimizing the distance between the cylinders and their diameter ratio. Finally, a NACA0012 airfoil is optimized at Re=10,000 and M∞=0.2 to reduce trailing edge noise. The airfoil’s shape is optimized to generate a new four-digit NACA airfoil at an appropriate angle of attack to reduce OASPL while maintaining the baseline time-averaged lift coefficient and preventing an increase in the baseline time-averaged drag coefficient. The optimized airfoil is silent at 0 dB and the drag coefficient is decreased by 24.95%. These results demonstrate the feasibility of shape optimization using MADS and FR for aeroacoustic design.

Spacing Ratio Effects on the Evolution of the Flow Structure of Two Tandem Circular Cylinders in Proximity to a Wall

The flow around two tandem circular cylinders in proximity to a wall is investigated using particle image velocimetry (PIV) for Re = 2 × 103. The spacing ratios L/D are 1, 2, and 5, and the gap ratios G/D are 0.3, 0.6, and 1. The proper orthogonal decomposition (POD) method and λci vortex identification method are used to investigate the evolution of flow structure, and the influences of L/D and G/D on flow physics are shown. At L/D = 2 and G/D = 0.3, a “pairing” process occurs between the wall shear layer and the upstream cylinder’s lower shear layer, resulting in a small separation bubble behind the upstream cylinder. At L/D = 1, the Strouhal number (St) increases with decreasing G/D. At three gap ratios, the St gradually decreases as L/D increases. At G/D = 0.3, there is nearly a 49.98% decrease from St = 0.3295 at L/D = 1 to St = 0.1648 at L/D = 5, which is larger than the reductions in cases of G/D = 0.6 and G/D = 1. The effects of L/D on the evolution of flow structure at G/D = 0.6 are revealed in detail. At L/D = 1, the vortex shedding resembles that of the single cylinder. As L/D increases to 2, a squarish flow structure is formed between two cylinders, and a small secondary vortex is formed due to induction of the lower shear layer of the upstream cylinder. At L/D = 5, there is a vortex merging process between the upper wake vortices of the upstream and downstream cylinders, and the lower wake vortex of the upstream cylinder directly impinges the downstream cylinder. In addition, the shear layers and wake vortices of the upstream cylinder interact with the wake of the downstream cylinder as L/D increases, resulting in reductions in velocity fluctuations, and the production and turbulent diffusion of turbulent kinetic energy are decreased behind the downstream cylinder.

Suppression of wake-induced galloping of tandem cylinders by helical strakes

Helical strakes as a classic passive control method for vortex-induced vibration (VIV), have been extensively studied, but wake-induced galloping (WIG) control of three tandem cylinders has received no previous attention. The current wind tunnel experimental study tries to fill this gap in the context of mechanical science. WIG of three tandem cylinders considering different structures of helical strakes is modeled and investigated. Helical strakes with varying heights G, pitches P, and cross-sectional shapes (square “S”, involute “I”, and D-shaped “D”) are first designed. Wind tunnel tests are conducted to experimentally study the dynamics responses of tandem cylinders (m*ξ = 0.09) at different spacings, and three vibration modes are obtained. This study delves into the characterization and quantification of the impact of various parameters of helical strakes on WIG of three tandem cylinders. These aspects, scarcely addressed in existing research, are thoroughly explored through statistical analysis, focusing on vibration amplitude, vibration frequency, and wavelet analysis. It is found that helical strakes can effectively suppress the multi-frequency vibration instability of bare cylinders. For wind speeds below 6 m/s, the "S" helical strakes achieves a vibration suppression efficiency of up to 665 %; Three-dimensional computational fluid dynamics (3D-CFD) demonstrate the coupling effect in the flow field, revealing that the "S" helical strakes has a greater impact on boundary layer formation than the "D" helical strakes; Reducing the pitch of the helical strakes can enhance the disturbance ability of the spanwise position, thereby increasing its suppression effect. This work improves vibration reduction and sheds light on how the helical strakes' cross-section controls vibrations in the tandem cylinders.

Characterizing vibrations and associated wake structures of tandem square cylinders at different angles of incidence

Finite element computations were conducted to investigate the transverse vibrations of three identical tandem square cylinders and the associated wake patterns at a Reynolds number Re = 150. The reduced velocities ranged from U*=3 to 20, and the angles of incidence were set at α=0°, 22.5°, and 45°. The streamwise gaps for these three α were Lx=5H, 3.8H, and 3.5H, respectively, where H represents the projected dimension of the cylinder normal to the freestream. The mass ratio of the cylinders was fixed at m*=2, and damping was neglected to allow the cylinders to attain maximum amplitudes. In the presence of primary vortices being shed from all three cylinders, the upstream cylinder at α=22.5° and 45° exhibits three distinct vibration regimes: initial excitation and upper and lower response regions. On the other hand, due to interaction with the upstream vortices, the two downstream cylinders display four response regions. In the case of α=0°, the dynamic response of the upstream cylinder appears in only two regimes, but with a higher peak amplitude compared to α=22.5° and 45°. Vibration and shedding frequencies closely synchronize with the natural frequency of the spring-mass system in the second regime, leading to high amplitude oscillations for the most upstream cylinder with α=22.5° and 45°. The third response regime for the two downstream cylinders is associated with the lock-in phenomenon. In α=0° and 22.5° configurations, the shedding mode is 2S in all response regimes, while at α=45°, the shedding mode shifts to P + S during the second regime. Up to the second regime, lift and vortex forces are in-phase with the cylinder's oscillation for α=0° and 22.5°, but they go out of phase beyond that. In the case of α=45°, although lift remains in-phase with the displacement in the second regime, the vortex force is found to be out of phase. This study is expected to enhance the understanding of fluid–structure interaction phenomena involved in multiple structures and can aid in the design of stable structures in civil engineering, offshore engineering, and development of energy harvesting devices.

Wake of two tandem square cylinders

The wake of two tandem square cylinders of identical width (d) is experimentally studied, with a view to understanding the dependence of the flow structure, aerodynamics forces and Strouhal number on the centre-to-centre spacing ratio L/d and Reynolds number Re, where L is the distance between the cylinder centres. Extensive measurements are carried out, using hot-wire, particle imaging velocimetry, laser-induced fluorescence flow visualization, surface-oil-flow visualization and surface pressure scanning techniques, for L/d = 1.0 ~ 5.0 and Re ≡ U∞d/ν = 2.8 × (103 ~ 104), where U∞ is the free-stream velocity and ν is the kinematic viscosity of the fluid. The flow is classified into four regimes, i.e. the extended-body (L/d ≤ 1.5–2.0), reattachment (1.5–2.0 < L/d < 2.7–3.2), co-shedding (L/d ≥ 3.0–3.4) and transition (2.7 ≤ L/d ≤ 3.3) where both reattachment and co-shedding phenomena may take place. The mean drag and fluctuating drag and lift exhibit distinct features for different flow regimes, which is fully consistent with the proposed flow classification. Comparison is made between this flow and the wake of two tandem circular cylinders, which provides valuable insight into the profound effect of the flow separation point and the presence of sharp corners on the flow development and classification.

Wake-induced vibration of an elastic plate submerged in the wake of tandem circular cylinders

This paper investigates the dynamic responses of an elastic plate submerged in the wake of tandem circular cylinders. The examined Reynolds numbers (Re) are set between 50 and 200. The gap spacing between the centers of the cylinders is kept constant at L* = L/D = 4.0, which is identical with the gap spacing between the center of the downstream cylinder and the front tip of the plate. The length of the plate is also L* = 4.0 to be consistent with the literature data. The flow field is analyzed, and the imposed forces on the structures are studied using two-way fluid–structural interaction (FSI). Initially, the mathematical equations of the FSI model are formulated in detail. Due to the interaction of the fluid and structure, the dynamic response of the system is analyzed. The variations in vortex shedding frequency are derived by employing two rational functions. The phase difference between lift forces is evaluated. In addition, the results of dynamic response of the plate due to FSI and wake-induced vibration are presented.

Flow-induced Vibration of Two Tandem Oscillating Square Cylinders in Reattachment Regime

To improve our understanding of structural stability, two vibrating tandem square cylinders is numerically investigated in the present study. In reattachment regime (L* = 2), mass ratios (m* = 3), Reynolds numbers (Re = 100) are considered. Different branches are identified. For the first cylinder, the maximum A* is about 0.10, which is one-third of a single cylinder. For the second cylinder, the maximum A* is about 0.42, which is 1.45 times of a single cylinder. Wake mode is observed, and the existence of the second cylinder restrains the vortex shedding from the first cylinder.

Flow around single and two tandem rectangular cylinders with various single-side fairings

The shape of single-side wind fairing, which is the longitudinal triangular prism that tailors the outer side of a bridge deck, is key to the aerodynamic performances of double streamlined box girders used in long-span bridges. Uniform flow past single and double 4:1 rectangular cylinders with various single-side fairings are investigated using large-eddy simulation at a Reynolds number of 1.1 × 104. Various fairing nose angles and heights are compared. The wind loading and flow characteristics of the cylinders are discussed. The upstream fairing shows a larger reduction of mean drag and fluctuating lift on double cylinders than on a single cylinder. The fairing nose angle has a stronger influence on the wind loading than the nose height. By adding the fairing, sharpening the fairing nose, or lifting the fairing nose, the lateral recirculation zones are shortened while the rear recirculation zone barely changes, leading to different influences on the surface pressure. The upstream fairing is effective in reducing the vertical range and complexity of vortex structures around single and double cylinders.

POD-LSTM model for predicting pressure time series on structures

A novel method for predicting wind pressure time series on structures is proposed by combining long short-term memory network (LSTM) with proper orthogonal decomposition (POD). POD-LSTM predicts the pressure time series on any circumferential locations of a structure using data from limited pressure taps. The wind tunnel test data of pressure on a single square cylinder and the downstream cylinder of two tandem square cylinders is utilized to evaluate the performances of POD-LSTM, LSTM, and POD-BPNN (back-propagation neural network). Results of pressure time series, aerodynamic parameters, and pressure moments are presented. POD-LSTM takes advantage of LSTM in time series prediction and POD in extracting essential features, resulting in a better performance than POD-BPNN and LSTM. The similarity of pressure on nearby taps affects the accuracy of POD-LSTM. A larger error is observed at the rear corners of a single cylinder where intermittent flow reattachment occurs. The predicted results for mean and fluctuating pressure coefficients are satisfactory, but POD-LSTM underestimates the absolute value of skewness and kurtosis at structural surfaces where the non-Gaussian property of pressure is significant. Compared with the uniform flow condition, the prediction accuracy decreases when the structure is in the wake of upstream structures.

Experimental Investigations on the Wake‐Induced Vibration of an Electromagnetic Energy‐Harvesting System

The wake energy of an electromagnetic harvesting device is derived from the phenomena of wake‐induced vibration (WIV). Experiments were conducted to determine the effects of the Reynolds number, the resistance of the circuit, and the distance between two concentric circular cylinders on the wake energy of the flow. The mechanism of the diaphragm energy harvester (DEH) consists of a single and tandem circular cylinders, which were examined separately. An elastic diaphragm with a magnet was also mounted in the wake of the cylinders. The Reynolds number varies between 2000 and 5000. The converter transforms the wake energy of the flow into electricity due to the vibration of the cylinder in a magnetic field. This research fills a critical gap in the literature by investigating the energy performance of a DEH under the wake‐induced vibration of two fixed circular bluff bodies, demonstrating for the first time the feasibility of capturing vortex energy through the wake in the presence of a diaphragm. This unique approach distinguishes our work in the field of electromagnetic energy‐harvesting devices, showcasing the potential for practical applications in renewable energy generation. The test results indicate that increasing the Reynolds number enhances the converter’s power output. Additionally, it has been observed that two critical distances are significant for the output voltage: the gap between the tandem cylinders (L∗) and the distance between the edge of the diaphragm and the center of the cylinder (X∗). The voltage output of tandem cylinders suggests that an optimal cylinder spacing falls within the range of 4 ≤ L∗ < 5.

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.

Near-moving-wall flows past three tandem elliptical cylinders at low Reynolds number of 150

Dynamic flows past three tandem elliptic cylinders of equal spacing in parallel arrangement with a moving wall are numerically conducted by the lattice Boltzmann method. The gap ratio (G/D, where G and D are the gap between the wall surface and cylinder center and major axis, respectively) from 0.6 to 2.5 and spacing ratio (L/D, where L is the distance of two adjacent cylinder centers) from 1.5 to 10 are examined at Reynolds number of Re = 150 (based on D). The desired analysis correlates variations of hydrodynamic coefficients, wake structures, and spectral analysis in wide space of G/D and L/D with underlying fluid mechanics. The flow is highly adjustable in G/D−L/D space, dividing into six distinct regimes: overshoot, continuous reattachment, alternative reattachment, wavy, meandering, and coshedding, which are spatially classified into four modes because of flow interference, namely, shear layer, primary, two-layered, and secondary vortex shedding modes. The transition between adjacent modes defines three boundaries. The first boundary always occurs behind the middle or downstream cylinder, whereas the second and third boundaries occur between the upstream and middle cylinders and the downstream cylinder wake. Due to the near-wall flow interference, the hydrodynamic coefficients are highly changeable in L/D−G/D space, signifying the crucially lower drag coefficient of the middle and downstream cylinders than that of a single cylinder. A small G/D determines the increase in lift coefficient of the upstream cylinder as a result of the ground effect, while the shadowing effect of the upstream cylinder induces identical Strouhal numbers of the middle and downstream cylinders.

Investigation of the flow topology evolution between two tandem cylinders using a discontinuous Galerkin method

Investigation of the flow topology evolution between two tandem cylinders using a discontinuous Galerkin method

Investigation of the flow topology evolution between two tandem cylinders using a discontinuous Galerkin method

Investigation of the flow topology evolution between two tandem cylinders using a discontinuous Galerkin method

Feel the force: From local surface pressure measurement to flow reconstruction in fluid–structure interaction

Drawing inspiration from the lateral lines of fish, the inference of flow characteristics via surface-based data has drawn considerable attention. The current approaches often rely on analytical methods tailored exclusively for potential flows or utilize black-box machine learning algorithms to estimate a specific set of flow parameters. In contrast to a black-box machine learning approach, we demonstrate that it is possible to identify certain modes of fluid flow and then reconstruct the entire flow field from these modes. We use dynamic mode decomposition to parametrize complex, dynamic features across the entire flow field. We then leverage deep neural networks to infer the dynamic modes of the pressure and velocity fields within a large, unsteady flow domain, employing solely a time series of pressure measurements collected on the surface of an immersed obstacle. Our methodology is successfully demonstrated to diverse fluid–structure interaction scenarios, including cases with both free oscillations in the wake of a cylinder and forced oscillations of tandem cylinders, demonstrating its versatility and robustness.