Upstream Cylinder Research Articles

Effect of an upstream cylinder on the wake dynamics of two tandem cylinders with different diameters at low Reynolds numbers

This paper presents a systematic numerical study on the fluid dynamics and flow structures around a cylinder with diameter D placed in the wake of another cylinder with a smaller diameter d. Reynolds numbers of Re = 100 and 150 (based on D) are considered so the flow is physically two-dimensional. The ratios d/D and L/D vary in the ranges of 0.4–1.0 and 1.0–8.0, respectively, where L is the distance from the center of the upstream cylinder to the forward stagnation point of the downstream cylinder. The analysis focuses on how d/D and L/D influence the Strouhal number St, wake topology, and fluid forces on the downstream cylinder and links them with the flow physics. The flow is classified into the reattachment and co-shedding flow regimes, with the latter being further subdivided into the prime vortex shedding, two-layer vortex shedding, and secondary vortex shedding (SVS) modes, and the detailed aspects of the three modes are discussed based on the time-averaged flow fields. The two vortex frequencies of the downstream cylinder can be detected only in the SVS mode, and in addition to the fundamental vortex frequency f1, the shedding of the secondary vortex further results in the subharmonic frequency f2. Only when the secondary shedding length Ls* is <10 does f2 affect the downstream cylinder and lead to a pattern of alternating high- and low-amplitude peaks in the time history of the lift coefficient. A novel mechanism of secondary vortex formation is identified, and the critical spacing and the modulation of lift by f2 are also discussed.

Investigation of the steady and unsteady forces acting on a pair of circular cylinders in crossflow up to ultra-high Reynolds numbers

Measurements of the steady and unsteady forces acting on a pair of circular cylinders in crossflow are performed from subcritical up to ultra-high Reynolds numbers. The two cylinders with equal diameters d are arranged inline at two centre-to-centre distances: S/d = 2.8 and 4. The trend of the drag curve for the upstream cylinder Cd_{1}(Re) at both distances is similar to that for a single circular cylinder. The development of the drag curves Cd_{2}(Re, S/d = 2.8, 4) of the downstream cylinder is inverse to that of the upstream cylinder. For both cylinder spacing values, the drag on the downstream cylinder is negative for subcritical Reynolds numbers, increases abruptly to positive values at the beginning of the supercritical regime, and shows a significant dip at transcritical Reynolds numbers. This drag inversion indicates that the critical distance Sc decreases sharply in the supercritical Reynolds number range. For S/d = 2.8 at Rerightarrow 10^{7}, the downstream cylinder experiences once more a thrust force. The curve of the Strouhal number St(Re) of the downstream cylinder for S/d = 4 is very close to that of a single cylinder. For Reynolds numbers of Reapprox 1times10^{6} - 7times10^{6}, the Strouhal numbers have nearly equal values of Stapprox 0.22 - 0.24 for both distances. This is followed by a branching. For Rerightarrow 10^{7} and the case S/d = 2.8, the Strouhal numbers dip at St = 0.17. However, for S/d = 4, they increase up to St = 0.27. In the supercritical range, two peaks occur in the power spectra for the large distance S/d = 4. Based on a wavelet analysis, we can conclude that the low-frequency mode, which does not occur for a single cylinder, is an interference effect.Graphic abstract

The wake and force statistics of flow past tandem rectangles

A numerical investigation is performed to examine the effect of side ratios (SR), separation ratio (g*), and Reynolds number (Re) on the flow around tandem rectangles using the lattice Boltzmann method. The SR is set at 0.25, 0.5, 0.75 and 1. The g* is varied from 0.5 to 10. The Reynolds number is set at 75, 100, 125 and 150. The results reveal that the upstream cylinder has higher drag forces compared to the downstream cylinder. The results further show that in case of wide-wake shear layer reattachment flow, strongly interactive vortex shedding flow and weakly interactive vortex shedding flow regimes, a small increase in mean drag coefficient of upstream cylinder for all considered cases in this study is attributed to the reduction of wake width, which confirms the weakened influenced by the upstream cylinder. The results show that as the vortex shedding mostly occurs behind the downstream cylinder only, root-mean-square value of lift coefficient is a considerably larger for the downstream cylinder than for the upstream cylinder. The results further show that as the flow regime transition occurs the lift coefficients indicates either in-phase or anti-phase flow behavior. The numerical results are presented in detail in the form of vorticity contour, streamline, time history analysis of forces and vortex shedding frequencies.

Numerical investigation into the effect of spacing on the flow-induced vibrations of two tandem circular cylinders at subcritical Reynolds numbers

Two-degree-of-freedom (2DOF) flow-induced vibrations (FIV) for a pair of elastically mounted circular cylinders in tandem arrangement with varying centre-to-centre spacings (Sx) are numerically studied. The Reynolds number range Re=1470–10320 belongs to the subcritical flow regime. Two identical cylinders with a mass ratio of m∗=2.6 and a mass-damping parameter of m∗+Caζ=0.013 are considered in the simulation. Four spacing ratios (Sx∕D, where D is the identical diameter) ranging from 3.0 to 8.0 are employed to investigate the effect of Sx∕D on the FIV responses, hydrodynamic characteristics and wake patterns of the two cylinders. It is found that the effect of the downstream cylinder on the FIV of the upstream one becomes insignificant when Sx∕D≥4.0. Due to the unsteady wake-cylinder interactions, multi-peak responses are observed for the downstream cylinder. Dual resonance with the 2:1 in-line to cross-flow oscillation frequency ratio and figure-eight orbital trajectories is found to occur for the upstream cylinder. In contrast, the trajectories of the downstream cylinder are rather irregular because of the low frequency components in the in-line response at high reduced velocity (Vr). Both shear flow and vortex shedding may appear in the gap region depending on Sx∕D and the relative motion of the two cylinders. In general, the vortex shedding modes of the upstream cylinder are similar to those of a single cylinder. Whereas, the analyses on the wake patterns suggest that the interactions of the upstream wake with the downstream cylinder and its own wake contribute to the unsteady fluid dynamics, which is crucial to maintaining the large-amplitude vibrations of the downstream cylinder at high Vr.

Spacing effect on the two-degree-of-freedom VIV of two tandem square cylinders

Different spacing cases (L/B = 2–6) are numerically examined to identify the spacing effect on the two-degree-of-freedom vortex-induced vibration (VIV) of two tandem square cylinders at Re = 150. According to the various vibration responses, force characteristics and flow patterns, spacing cases can be divided into three different situations. At a small spacing (L/B = 2, 2.5), the upstream cylinder (UC) has no traditional lock-in region (the frequency ratio fy/fn ≈ 0.95–1.05, and the reduced velocity Vr ≈ 6), and the downstream cylinder (DC) has a narrow lock-in region. However, there is a wide soft-lock-in region (the synchronization region of fy/fn ≈ 0.85) at high reduced velocities (Vr ≈ 9.5–12) for both cylinders. In this region, both cylinders experience large-amplitude transverse vibrations, with the UC exhibiting a higher amplitude. At a moderate spacing (L/B = 3, 4), the UC does not exhibit lock-in or soft-lock-in regions, similar to a single cylinder at the same mass ratio, and the DC exhibits a relatively wide lock-in region (Vr ≈ 5.5–8) instead of a soft-lock-in region. Notably, two amplitude peaks appear within the lock-in region for the DC depending on Vr. At a large spacing (L/B = 5, 6), the amplitude of the DC is typically higher than that of a single cylinder, even within the narrow lock-in region.

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.

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.

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.

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.

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.

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 vibration of high-mass ratio isolated and tandem flexible cylinders with fixed boundary conditions

Flow-induced vibration of a flexible cylinder placed in the wake of a stationary rigid cylinder is studied, experimentally. The flexible cylinder with an aspect ratio of 47 and a mass ratio of 120 was held fixed at both ends and placed horizontally in the wake of the upstream rigid cylinder in the test-section of a subsonic wind tunnel. The dynamic response of the cylinder is studied in both the streamwise (inline) and transverse (crossflow) directions for center-to-center spacing range from 3 to 9 times the diameter of the cylinder. Amplitudes and frequencies of oscillation, as well as flow forces on the cylinder are studied in the reduced velocity range of U∗=3.3−50.3 and the Reynolds number range of Re=3,057–46,536. The dynamic response observed in this study are presumably the result of two combined phenomena of vortex-induced vibration and wake-interference galloping. Despite the high-mass ratio of the flexible cylinder, higher modes of vibrations up to the fifth mode are excited in both the crossflow and inline directions, owing to the high-flexibility of the cylinder. Both odd and even modes are excited in the crossflow and inline directions. As the separation distance between the cylinders increases, the amplitudes of oscillation increase over a wider range of reduced velocities. Spanwise trajectories of motion are studied and regions along the length of the cylinder that are excited or damped by the flow, i.e., regions with positive and negative flow force coefficient in phase with velocity, are identified.

Steady lift-force generation on a circular cylinder utilising a longitudinal vortex: Influence of geometrical parameters

A novel technique for producing a steady lift force on a circular cylinder in a uniform flow driven by the longitudinal vortex (LV) is developed. The LV forms behind the cylinder when a strip plate is located downstream in a cruciform arrangement. The upstream cylinder can stably move by itself via an aerodynamic effect of the LV-produced steady lift force. However, the effects of geometrical parameters on system performance have not been investigated. In this study, the effective parameters of the presented mechanism—the width ratio of the strip plate, W / d , and the exposed length ratio of the circular cylinder over the strip plate, l e / d —are numerically examined. An unsteady Reynolds-averaged Navier–Stokes simulation using a shear-stress-transport k–ω turbulence model is employed for this analysis. The experimental investigation in our wind tunnel laboratory is used to primarily validate the computational predictions. The distribution of the aerodynamic forces acting on the cylinder surface is continuously evaluated along the length span. Flow fields around the system are also visualised for discussion of the vortical effects. The results indicate that the proper parameters of the system needed to generate the available driving force for the moving cylinder are ( i ) a strip-plate width of 1.5 ​< ​ W/d ​< ​2.5, with W/d ​= ​2 being considered as the most suitable, and ( ii ) an optimal exposed length of the cylinder of l e ​= ​1.5 d . • Numerical results were validated with experimental data of the wind tunnel test. • Flow fields were numerically visualised providing vortical structures. • Aerodynamic-force distributions along the cylinder length were continuously investigated.

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.

New insights into numerical simulations of flow around two tandem square cylinders

Flows around tandem square cylinders at Re = 100 are numerically studied using a characteristic-based penalty operator splitting finite element method based on a multistep algorithm. The validation of the code and numerical method is performed for flows around single square cylinders. L/D effects (with L being the center-to-center distance and D being the square cylinder width) on the flow structures and parameters are investigated for 1.5 ≤ L/D ≤ 9.0. The flow structures, especially far downstream of the square cylinder, indicate six distinct flow regimes. The two-layered vortex formation (TVF) and secondary vortices formation (SVF) modes are defined, and their mechanisms are analyzed. The evolution of TVF into SVF proceeds through the combination of single and binary vortex formations. Variations in the physical flow parameters, including the coefficients of fluctuating lift (CL′), time-averaged drag (C̄D), and amplitude lift (CLA), as well as the Strouhal number and phase lag (ϕ), are analyzed for various L/D values. Obvious jumps in the flow parameters occur at both square cylinders for L/D = 4.4–4.5 because of vortex impingement. Finally, insight into the physics underlying the relationship between CL−upA, CL−up′, and ϕ is derived from the simulation results. The local maximum and minimum of CL−upA and CL−up′ occur at ϕ = 2π and 3π, respectively, corresponding to in-phase and anti-phase vortex shedding by the cylinders. The pressures on the upper and lower sides of the upstream square cylinder decrease and increase, respectively, leading to reductions in CL−upA and CL−up′ as the flow pattern changes from in-phase to anti-phase.

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 &amp;lt; 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.