Downstream Cylinder Research Articles

Modelling of wake-induced vibrations of tandem cylinders with a nonlinear wake-deficit oscillator

For a pair of elastically mounted circular cylinders in a tandem configuration, the downstream cylinder may experience the wake-induced vibration (WIV) due to the hydrodynamic excitation associated with the wake behind the upstream cylinder. In addition to WIV, the downstream cylinder may also be simultaneously subject to the vortex-induced vibration (VIV) due to the vortex shedding in its own wake. This nonlinear coupled wake-vortex interaction can result in a sustained large-amplitude response depending on the cylinder spacing. In this study, a new nonlinear wake-deficit oscillator model for predicting the combined WIV-VIV responses in the cross-flow direction of the downstream cylinder is presented. While the upstream stationary or oscillating cylinder is placed in a uniform steady flow, the downstream cylinder is subject to a non-uniform unsteady flow with a space–time varying velocity being modified by the wake deficit or shielding effect. The total cross-flow hydrodynamic force on the downstream cylinder is modelled as a combination of the wake-induced transverse force and the combined vortex-induced lift and drag forces. The wake-induced force is approximated using a wake deficit theory based on a linearised boundary layer equation. The vortex-induced force is modelled using the van der Pol oscillator which incorporates the wake-deficit flow velocity, relative flow-cylinder velocities and dynamically staggered positions between the two interfering cylinders. These empirical hydrodynamic force equations are nonlinearly coupled, simulating the wake-vortex interaction leading to the combined WIV-VIV responses depending on the fluid–structure parameters. By focusing on the wake interference regime, the wake profiles and hydrodynamic forces are calibrated and validated, introducing new empirical coefficients and functions. The downstream cylinder responses and oscillation frequencies are predicted and compared with relevant experimental data by accounting for the important effects of cylinder spacing ratio, reduced flow velocity and Reynolds number in a subcritical flow regime. The wake stiffness characterisation is also presented, providing an analytical formulation related to the dynamic wake profile. Several key features associated with WIV response amplitudes and frequencies are highlighted and discussed using the calibrated wake-deficit oscillator. The present concept and model can be further improved to account for the effects of in-line response and arbitrarily staggered arrangement as well as the application of multiple long flexible cylinders with multi modal responses.

Effects of nondimensional distance between two square cylinders on the dissipation characteristics of the complex flow

In this paper, effects of nondimensional distance between two square cylinders on the dissipation characteristics of the complex flow are investigated. The viscosity entropy generation rates around two serial square cylinders and the lift coefficient are analyzed to fully reveal the statistical features of the flow dissipation. Numerical results mainly show that the major viscosity entropy generation rate appears in the shear intersection region of the main flow and local stationary vortex. The viscosity entropy generation rate increases with increasing nondimensional distance ([Formula: see text]). The increasing slope of the viscosity entropy generation rate at a range of [Formula: see text] is greater than that of [Formula: see text]. It is also found that the viscosity entropy generation rate is kept as a constant when the nondimensional distance [Formula: see text] is greater than 5. At [Formula: see text], the effect of downstream square cylinder becomes negligible on the viscosity entropy generation rate. The fluctuating amplitude increases with increasing the nondimensional distance [Formula: see text]. The high-frequency peak is ascribed to the strong vortex shedding around the downstream square cylinder, and the low-frequency peak is ascribed to the weak vortex shedding around the up square cylinder at [Formula: see text]. Although our focus is mainly on the complex flow around two square cylinders, this work demonstrates the viscosity entropy generation rate with increasing nondimensional distance, which provides nice physical insight into understanding the local flow dissipation characteristics around the two serial square cylinders.

Wake-induced instabilities of parallel circular cylinders with tandem and staggered arrangements

When two circular cylinders are closely arranged in parallel, the downstream cylinder frequently exhibits wake-induced vibrations (WIVs). This study investigates the classifications of WIVs in various arrangements of cylinders by considering the generation mechanisms of WIVs through a series of wind tunnel tests. The generation mechanisms are defined through flutter and time-history analyses using the quasi-steady theory. Finally, this study suggests a classification map of the arrangements with four types of generation mechanisms: vertical flutter, anti-phase coupled flutter, in-phase coupled flutter (quasi-steady applicable), and in-phase coupled flutter (quasi-steady inapplicable). Vertical flutter occurs in closely staggered cylinders and tandem cylinders with a horizontal center distance measuring 2.5–9.5 times the cylinder diameter. A key parameter for distinguishing coupled flutter is the contribution of the aerodynamic coupling terms. Furthermore, for closely staggered cylinders, two types of vibrations occur, depending on the reduced wind velocity. The arrangement of the two cylinders is slightly changed because of the static displacement of the downstream cylinder depending on the wind velocity, resulting in a change in the generation mechanism. The results pertaining to the generation mechanisms effectively explain the WIV responses of the two cylinders in various arrangements.

Interactions between Tandem Cylinders in an Open Channel: Impact on Mean and Turbulent Flow Characteristics

The flow hydrodynamics around a single cylinder differ significantly from the flow fields around two cylinders in a tandem or side-by-side arrangement. In this study, the experimental results on the mean and turbulence characteristics of flow generated by a pair of cylinders placed in tandem in an open-channel flume are presented. An acoustic Doppler velocimeter (ADV) was used to measure the instantaneous three-dimensional velocity components. This study investigated the effect of cylinder spacing at 3D, 6D, and 9D (center to center) distances on the mean and turbulent flow profiles and the distribution of near-bed shear stress behind the tandem cylinders in the plane of symmetry, where D is the cylinder diameter. The results revealed that the downstream cylinder influenced the flow development between cylinders (i.e., midstream) with 3D, 6D, and 9D spacing. However, the downstream cylinder controlled the flow recirculation length midstream for the 3D distance and showed zero interruption in the 6D and 9D distances. The peak of the turbulent metrics generally occurred near the end of the recirculation zone in all scenarios.

Numerical investigation of breaking wave loads on the downstream inclined cylinder under shelter effect from the upstream vertical cylinder

ABSTRACT Breaking waves interaction with two tandem cylinders are numerically studied using Computational Fluid Dynamic (CFD) software OpenFOAM. The effects of transverse inclined angles of the downstream cylinder and separation distances between two cylinders on breaking wave loads and free surface elevations are investigated. The interface between air and water phases is captured by the Volume of Fluid (VOF) method. The Shear Stress Transport turbulence model is employed to solve the incompressible Reynolds-Averaged Navier-Stokes (RANS) equations. The present numerical model is validated against published experimental data by examining the horizontal breaking wave loads and free surface elevations of breaking waves past a vertical cylinder and an inclined cylinder. In the present incident wave conditions, the breaking wave force on the downstream cylinder decreases first and then increases with the transverse inclined angle varying from to , while it shows an opposite trend versus the distance between cylinders. The maximum breaking wave load on the downstream cylinder occurs when the it is installed vertically with a separation distance of four times diameter.

Flow-induced cross-flow vibrations of long flexible cylinder with an upstream wake interference

Flow-induced vibration (FIV) of a flexible cylinder with an upstream wake interference at a subcritical Reynolds number is numerically investigated in this study. Two cylinders are installed in a tandem arrangement with the tandem separation between the cylinder centers set at 5.0 diameters. The downstream cylinder is flexible and placed in the wake of the stationary rigid upstream cylinder. A quasi-three-dimensional fluid-structure interaction (FSI) numerical methodology that couples the strip theory-based Lagrangian discrete vortex method with the finite-element method (FEM) for structural dynamics is developed to simulate the FIV response of the flexible cylinder with the upstream wake interference. The vortex-induced vibration (VIV) of an identical isolated cylinder is also numerically simulated as a contrast. This numerical study characterizes the dynamic response of the cylinder FIV with the upstream wake interference and sheds light on the FSI mechanisms responsible for the structural dynamic response. With the upstream wake interference, the cylinder FIV response shows two features distinct from the isolated VIV response: the vibration of large amplitude during the modal resonance branch transition and the extension of the modal resonance branch. The hydrodynamic coefficients database is constructed by the rigid cylinder forced vibration experiment to help explain the FSI properties of the FIV dynamic response. The lower added mass coefficient for the FIV with the upstream wake interference than the VIV of the isolated cylinder guarantees the synchronization between the vortex shedding frequency and the “true” natural frequency of the structure persisting to higher reduced velocity in a certain modal resonance response branch. The excitation coefficient distribution indicates that the cylinder FIV with the upstream wake interference reaches higher amplitude at high reduced velocity, instead of ceasing resonance as the isolated cylinder. The numerical wake visualization is shown and used to explain the correlation between the distribution of hydrodynamic coefficients along the cylinder span and the wake vortex mode. It is found that the upstream wake interference effect is strongly correlated with the vortex–structure interaction pattern between the upstream wake vortices and the downstream motion. When the upstream vortex impinges on the downstream cylinder and splits into subvortices, the effect of the upstream wake interference acting on the downstream cylinder reduces. When the downstream cylinder enters the gap between the upstream vortices over the entire vibration process, the upstream wake has a stronger interference effect on the downstream FIV response.

STUDY ON THE SPECTRUM CHARACTERISTICS OF VORTEX-INDUCED VIBRATION OF THREE TANDEM CIRCULAR CYLINDERS

The numerical computation of vortex-induced vibration of three circular cylinders in a tandem arrangement with two degrees of freedom has been carried out. The effects of Reynolds number, natural frequency ratio and reduced velocity on the dynamic response and spectral characteristics of three tandem cylinders were analyzed. The results indicate that the Reynolds number and natural frequency ratio have little influence on the amplitude and fluid force coefficient of the upstream cylinder. The frequency locked region of the midstream cylinder increases with the increasing of Reynolds number. The dynamic response of the midstream cylinder is greatly affected by the wake of the upstream cylinder, whereas the effect of natural frequency ratio is small. Meanwhile, when the reduced velocity is small, Reynolds number and natural frequency ratio have great influence on the fluid force coefficient. In addition, the amplitude and the fluid force coefficient of the downstream cylinder are greatly affected by Reynolds number and natural frequency ratio. Reynolds number, natural frequency ratio and reduced velocity have great influence on the main peak amplitude, spectrum component and fluctuation of fluid force coefficients PSD curve. The fluctuation of the PSD curve becomes intense, giving rise to the movement trajectory of cylinder from 8 shape to irregular shape. As natural frequency ratio increases to 2.0, the P$+$S mode is found in the wake of the upstream cylinder, which leads to the occurrence of asymmetric motion, and the equality of main peaks of the PSD curve of the lift and drag coefficients. Finally, the variation of average power value of excitation load with reduced velocity is similar to that of corresponding structural dynamic response. In the same reduced velocity range, the strength of structural vibration response is directly proportional to the average power value of displacement. When analyzing the power spectral density of lift coefficient in different intervals, the vibration frequency ratio has more influence on the structural vibration response.

Aerodynamic wake oscillator for modeling flow-induced vibration of tandem cylinders with short spans

The tandem cylinders immersed in an oncoming flow undergo violent flow-induced vibration (FIV). The cylinders with short spans, in the specific conditions of airflow and mass damping, experience the galloping-like but self-limited vibration. It promotes a coupling instability, controlled by the shear layers and wake vortices. The peculiar behavior of FIV for tandem cylinders is the interference between transverse galloping and vortex-induced vibration (VIV), which lacks a modeling approach through classical theories. Based on the quasi-steady assumptions, a mathematical model including two semicoupled structural oscillators and a reduced wake oscillator was established to simulate the vibration responses. A nonlinear aerodynamic damping coefficient and an empirical interfered force were introduced to the model, revealing the unexplored interference mechanism between two cylinders with short spans. The model with calibrated parameters can reproduce the nonlinear and bifurcated vibration responses of cylinders, providing a quantitative agreement with the experimental data. Although the model only works for high Scruton numbers and loses high fidelity in predicting the vibration amplitudes of the downstream cylinder in several cases, the vital velocity thresholds, amplitude-velocity trends and maximum amplitudes can be precisely obtained. This model is conducive to preacquiring the FIV responses of tandem industrial structures, including steel stacks, bladeless wind turbines, low-power energy-harvesting devices, etc.

An LBM-based investigation of thermal buoyancy and arrangement angle on flow characteristics and heat transfer over four heated square cylinders

In this work, the effects of thermal buoyancy and rotation angle on the hydrodynamics and mixed convection heat transfer characteristics over four heated identical square cylinders placed in a parallel horizontal channel are numerically studied. For the flow field, the Lattice Boltzmann method (LBM) with multiple relaxation time collision operator (MRT) is implemented and the Bhatnagar-Gross-Ktook collision operator (BGK) is adopted for the thermal field simulation. The distance between two adjacent square cylinders is fixed for a parametric study and a uniform velocity is imposed at the inlet region. Ranges of the influence parameters are defined as: α = 45°, 90°, 120°; 50 ≤ Re ≤ 150; 0 ≤ Ri ≤ 0.5. Several flow and heat transfer parameters including the time-averaged lift/drag coefficients, the global time-averaged Nusselt number and the distributions of local Nusselt number are analyzed, respectively. The vorticity and isotherm patterns are also plotted to illustrate the visual disturbance of the thermal buoyancy and the rotation angle on the flow and thermal fields. Numerical results show that the flow and thermal patterns for all arrangements become disordered and nonsystematic with the introduction of thermal buoyancy, and the thermal pattern for the downstream cylinders has an upward drift in the wake region. The time-averaged lift coefficient for each square cylinder is relatively sensitive to the influence parameters and the arrangement, and it is always less than zero when the Richardson number is not equal to zero. The global time-averaged Nusselt number is directly proportional to the Reynolds number and Richardson number, and the local Nusselt numbers on the front and rear faces for each square cylinder reach a maximum and minimum, respectively. It is also observed that the distribution of local Nusselt number for all rotation angles is intensively affected by the thermal buoyancy.

Effect of surface curvature on destabilization and unsteadiness of low-Re flow across two tandem elliptic cylinders

This work performed a direct simulation investigation on two-dimensional flow across two tandem elliptic cylinders at Re = 100. The cylinders are placed with a center-to-center distance D/ d = 2-10 where d is the diameter, and the minor-to-major axis ratio, denoted as aspect ratio AR, varies as AR = 0.25-1.00. The objective of this study is to quantitatively identify the effect of surface curvature of the cylinders, as represented by AR, and the separating distance on the destabilization and unsteadiness of flow. Numerical results reveal that the local surface curvature at the ends of major axis of the cylinder has substantial influence on the separation and detachment of boundary layer flow on the leeward side of the upstream cylinder, determines the characteristics of gap flow, perturbs the flow around the downstream cylinder, and finally produces various patterns of wake flow. As AR increases, the gap flow tends to be stabilized for small separating distance and even quasi-steady flow for the AR = 0.75 and 1.00 cylinders at D/ d = 2; the wake flow after the downstream cylinder also gets less unstable and only sheds in the far-wake region. The non-uniformity of time-averaged pressure coefficient around the downstream cylinder is reduced but the fluctuating amplitude increases, while the flow around the upstream cylinder is quite close to that of the single cylinder case.

Single-step deep reinforcement learning for open-loop control of laminar and turbulent flows

We introduce single-step proximal policy optimization, a deep reinforcement learning algorithm for situations where neural network optimization does not depend on state. Optimization is examined with open-loop control problems of laminar and turbulent flows (Re up to a few ${10}^{4}$). For turbulent flow past a square cylinder, the approach reduces drag by 30% by finding the best placement of a small control cylinder, in agreement with existing experimental data. For turbulent flow past a fluidic pinball, drag is reduced by 60% by using boat tailing actuation made up of a slowly rotating front cylinder and two oppositely rotating downstream cylinders, matching existing machine learning results.

Flow-induced vibration on isolated and tandem elliptic cylinders with varying reduced velocities: A lattice Boltzmann flux solver study with immersed boundary method

Numerical simulations of flow-induced vibration on isolated and tandem elliptic cylinders with varying reduced velocities are carried out. Immersed boundary multi-relaxation-time lattice Boltzmann flux solver is used as numerical solution method so that the solution procedure can be conducted in a Cartesian grid. The accuracy and rationality of this method are verified by comparison with previous numerical results. For vortex-induced vibration on isolated elliptical cylinder, numerical simulations are conducted for different aspect ratio (0.7 ≤AR≤ 1.5) and reduced velocities (4.0 ≤Ur≤ 10.0). Vibration response mainly contains desynchronization regime, initial branch and lower branch. When reduced velocity drives to lower branch, transverse amplitude reach to the peak value and double vortex street is formed in the wake. For flow-induced vibration on two elliptical cylinders in a tandem arrangement, numerical simulations are conducted for different aspect ratio (0.7 ≤AR≤ 1.5) and reduced velocities (3.0 ≤Ur≤ 10.0) at gap spacing L/D= 3 and 6. Vibration and flow characteristics are more complex compared with a single elliptical cylinder. The beginnings of entering into lock-in region are delayed for both bluff bodies and vibration response of downstream elliptical cylinder is enhanced by coupling interaction at higher reduced velocity. The flow and vibration characteristics of upstream elliptical cylinder are close to that of single elliptical cylinder at larger gap spacing. The tandem system is beneficial to gain more energy for higher reduced velocity. When downstream elliptical cylinder drives into lower branch, the transverse amplitude is the largest and double vortex street is formed in the wake region.

A novel V-shaped layout method for VIV hydrokinetic energy converters inspired by geese flying in a V-Formation

A novel bio-inspired V-shaped layout is proposed to enhance energy conversion performance for VIV hydrokinetic energy converters. The layout method is inspired by wild geese flying in a V-formation. In this paper, 2-dimensional RANS equations with the SST k-ω turbulence model are used to simulate the VIV responses at various distances. The numerical method is verified by comparing with experiments. Two-cylinder and five-cylinder V-shaped layout are investigated separately to analyze multi-cylinder interactions. The main conclusions are: (1) The VIV response of the upstream cylinder is suppressed due to the blockage effect when at small distance. (2) The energy recovery area of downstream cylinders is identified and located on the edge of the wake. (3) In the energy recovery area, the enhancement mechanism of this novel layout is the upstream and downstream vortices coalesce, resulting in a significant increase in lift force on the downstream cylinder. (4) The converted power of downstream cylinders in the energy recovery area is increased by up to 6.3%–8.4%. Future work is directed to optimize the distance among the cylinders for optimal energy conversion.

Aerodynamic Characteristics of Coupled Twin Circular Bridge Hangers with Near Wake Interference

Much work has been devoted to the investigation and understanding of the flow-induced vibrations of twin cylinders vibrating individually (e.g., vortex-induced vibration and wake-induced galloping), but little has been devoted to coupled twin cylinders with synchronous galloping. The primary objective of this work is to investigate the aerodynamic forcing characteristics of coupled twin cylinders in cross flow and explore their effects on synchronous galloping. Pressure measurements were performed on a stationary section model of twin cylinders with various cylinder center-to-center distances from 2.5 to 11 diameters. Pressure distributions, reduced frequencies and total aerodynamic forces of the cylinders are analyzed. The results show that the flow around twin cylinders shows two typical patterns with different spacing, and the critical spacing for the two patterns at wind incidence angles of 0° and 9° is in the range of 3.8D~4.3D and 3.5D~3.8D, respectively. For cylinder spacings below the critical value, vortex shedding of the upstream cylinder is suppressed by the downstream cylinder. In particular, at wind incidence angles of 9°, the wake flow of the upstream cylinder flows rapidly near the top edge and impacts on the inlet edge of the downstream cylinder, which causes a negative and positive pressure region, respectively. As a result, the total lift force of twin cylinders comes to a peak while the total drag force jumps to a higher value. Moreover, there is a sharp drop of total lift coefficient for α = 9–12°, indicating the potential galloping instability. Finally, numerical simulations were performed for the visualization of the two flow patterns.

Numerical investigation of unsteady flow across tandem square cylinders near a moving wall at Re = 100

Flow across tandem square cylinders placed close to a plane moving wall, has been studied extensively for various cylinder inter-spacing ratio (0.5≤S/D≤8) and cylinder-to-wall gap ratio values (0.1≤G/D≤4) at a fixed value of Reynolds number, Re = 100. Numerical experiments are performed using the computational package ANSYS FLUENT®. Results indicate that unsteady flow past tandem cylinders relies primarily on the presence of a moving wall. Exhaustive details on the effects of varying S/D and G/D values on the onset and suppression of vortex shedding behind the tandem cylinders are given. A detailed description of the underlying flow physics is provided through instantaneous vorticity and streamline contours. Forces such as the lift and drag acting on the cylinders are reasoned qualitatively through time-averaged pressure, lift, and drag coefficient plots. A remark on existence and suppression of flow unsteadiness is given through Strouhal number variation. A rigorous comparison of the present flow field with flow past an isolated square cylinder, square cylinder near a moving wall, and unbounded tandem cylinders is given. Overall, unlike the lift, drag coefficient values happen to be highest for single cylinder case, followed by the upstream cylinder, and they are least for the downstream cylinder.

Hydrokinetic Energy Conversion by Flow-Induced Oscillation of Two Tandem Cylinders of Different Stiffness

Abstract The vortex-induced vibration for aquatic clean energy (VIVACE) converter harnesses hydrokinetic energy by enhancing flow-induced oscillations (FIOs) of elastically supported rigid cylinders in a river, tide, or ocean current. The harnessing power depends on the intensity of the oscillation, which is a consequence of the flow–structure interaction. The inflow condition for the downstream (second) cylinder is slowed down and perturbed by the upstream (first) cylinder, due to the shielding effect. Therefore, the optimal structural parameters, i.e., stiffness and damping ratio, for the second cylinder may be different from the first cylinder, in terms of energy harnessing. To improve the performance of the VIVACE converter, a series of experiments are conducted in a recirculating water channel, with various stiffness combinations of two cylinders in tandem. Results show that the stiffness of the second cylinder, K2, does not affect the energy harnessing power in vortex-induced vibration (VIV) occurring at low speeds, because the oscillation of the downstream cylinder in this velocity range is completely dominated by the wake of the upstream cylinder. K2 has a great influence on the harnessing power at higher velocities in the transition region from VIV to galloping and in galloping. Changing K2 onsets and enhances galloping at lower flow velocity and harnesses up to 110% more energy than the case of K1 = K2.

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

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

Wake structure characteristics of three tandem circular cylinders at a low Reynolds number of 160

This paper reports the results of a numerical investigation into the flow around three isodiametric circular cylinders placed in an in-line configuration with identical spacing and the associated wake structures. The effect of spacing ratio (L/D, where L is the center-to-center spacing between two adjacent cylinders and D is the cylinder diameter) ranging from 1.5D to 10D with increment of 0.5D is examined at a low Reynolds number of 160. The results indicate that the wake structure experiences three evolutions as L/D increases, exhibiting four combined flow patterns: the overshoot, continuous reattachment-alternate reattachment (CR-AR), quasi-co-shedding (QCS), and co-shedding-co-shedding regimes. More than one frequency participates in the lift fluctuation for all three cylinders in the latter three patterns, signifying the wake interference. The evolution of the flow regime results in the variations of drag and lift coefficients, the alteration of pressure distribution around the cylinders' surface, and the switching of the phase lags of fluctuating lifts as well as the modification of vortex shedding characteristics, including the vortex formation location, wake width, and shedding frequencies. Particularly, the fluid forces and Strouhal number for the upstream and middle cylinders present a jump in the transition from the CR-AR to QCS regimes, while the fluid forces are reduced for the downstream cylinder. Furthermore, the transition from two layered vortices to the secondary vortex street is observed at 3.5 < L/D ≤ 6.5, where the downstream cylinder is sandwiched between the two shear layers detached from the middle cylinder, and two same-sign vortices in the same layer merge into a new vortex in the far wake.

A fluid–structure interaction simulation on the wake-induced vibration of tandem cylinders with pivoted rotational motion

This paper predicts the wake-induced vibration of tandem cylinders with pivoted rotational or translational motion using the fluid–structure interaction technique. Large eddy simulation using a dynamic Smagorinsky subgrid-scale model is applied for the turbulent flow. Structural computation is applied to obtain the displacement of the downstream cylinder in the cross-flow direction. Conditions such as damping ratio, natural frequency, and mass ratio of pivoted rotational motion are the same as those of translational motion. The computational conditions are Re=3790, 8470 and 15 160, corresponding to U*=5.0, 11.2 and 20.0, respectively. The unsteady characteristics of lift, drag, and cross-flow motion of tandem cylinders are investigated. Distributions of pressure, λ2 criterion, vorticity, and streakline are also investigated. Finally, the energy harvesting capability of the pendulum system is compared with the translation system.

Numerical studies of laminar flow over two tandem elliptical cylinders using Ramanujan approximation

This paper studies a laminar flow over tandem elliptical cylinders at Re = 200. While the aspect ratio (AR) of the upstream cylinder varies from AR = $$a_{1}$$ / $$b_{1}$$ = 0.25 to 2.00, the aspect ratio of the downstream cylinder is kept constant at AR = 1.00 (e.g., $$a_{2}$$ / $$b_{2}$$ = 1). This range of AR covers the most important practical cross sections of elliptical cylinders, including normal elliptic cylinder (with 90° incidence) and parallel elliptic cylinders (with 0° incidence). Although the spacing ratio between the centers of the cylinders is kept constant at $$L^{*}$$ = 4 $$D_{2}$$ , the gap ratio (G* = G/ $$D_{2}$$ ) between the surfaces of the cylinders is varied due to the alteration of AR of the upstream cylinder. Unlike the previously published studies, which estimated the hydraulic diameter of the elliptical cylinder, in this paper, the precise hydraulic diameter is evaluated and used to analyze the wake instabilities and the variation of the imposed pressure as well as forces coefficients on the cylinders. The results reveal that with the estimation of the hydraulic diameter of the elliptic cylinder, the maximum error of 178% has arisen, which significantly affects forces (lift and drag) coefficients. It was found that the phase lag between the sinusoidal lift coefficients of the cylinders varies and it reaches a minimum at AR = 1.5 and it slightly increases once AR = 2.0. Besides, the amplitude of the fluctuating drag coefficient is larger for the upstream cylinder as compared with that of the downstream cylinder. Besides, it is found that the minimum St = 0.065 occurs at AR = 0.25, and it is regularly increased to the maximum value of St = 0.211 at AR = 1.75. A parabolic equation is deduced with high accuracy and a reasonable error of less than 1.8% to show the relationship between St and AR.