Downstream Cylinder Research Articles

Empirical model for Wake Induced Vibrations frequency response of cylinder with low mass ratio

The vortex-induced vibrations (VIV) of two flexible circular cylinders in tandem arrangements were studied using numerical simulations and verified by experimental data. Simulations were conducted for a constant mass ratio of 1.08, the spacing ranges of 6D to 18D, and the reduced velocities of 2.35–6.71. It is shown that the numerical results are in a good agreement with the experimental data of the amplitude and frequency of response. The features of the vibration amplitude, the dominant frequencies, the vortex structures and the fluid force acting on the cylinders are discussed. The results indicate that there is a great difference between the response of the upstream cylinder and that of the downstream cylinder. When the reduced velocity is beyond the critical reduced velocity Vr*, the dominant frequencies of the upstream cylinder and the downstream cylinder are no longer the same. And both the reduced velocity and the spacing of the cylinders have a great influence on the wake-induced vibrations (WIV) responses of the downstream cylinder. Considering these influences, an empirical model for WIV frequency response of the downstream cylinder with a low mass ratio was proposed and verified.

Hydrodynamic characteristics of two tandem flexible cylinders undergoing flow-induced vibration

Flow-induced vibrations (FIV) of two tandem cylinders are the major concerns in many engineering fields. However, little attention is paid to the FIV mechanisms of two tandem flexible cylinders, especially for the hydrodynamic features. To investigate the FIV hydrodynamic characteristic of two tandem flexible cylinders, the fluid forces on the flexible cylinders were reconstructed by a finite element model using the response displacements acquired from model tests. Considering the coupling effect of multi-frequency vibrations, the lift coefficients, varying drag coefficients, cross-flow (CF) and in-line (IL) added mass coefficients were obtained utilizing the Forgetting Factor Least Squares (FF-LS) method. To investigate the influence of the spacing ratio T/D (where T is the center-to-center separation distance between the two cylinders and D is the cylinder diameter) on the FIV hydrodynamic features, five spacing ratios (T/D = 4.0, 6.0, 8.0, 10.0 and 16.0) were considered. The upstream cylinder and the single cylinder have CF hydrodynamic coefficients that share similar trends versus the reduced velocity, except for T/D = 4.0. The downstream cylinder may disturb the vortex shedding from the upstream cylinder, leading to the decrease in mean lift coefficients and mean varying drag coefficients on the upstream cylinder. Both the wake shielding effect and the vortex shedding effect have a significant influence on the hydrodynamic features of the downstream cylinder. Under the wake shielding effect, the mean lift coefficients and mean varying drag coefficients on the downstream cylinder are reduced, while the mean CF and IL added mass coefficients are increased. Owing to the vortex shedding effect, the mean lift coefficients and mean varying drag coefficients calculated using the local flow velocity are higher than those on the single cylinder, which increases the contribution of the adjacent modes to the vibrations.

Flow and heat transfer analysis around tandem cylinders: critical gap ratio and thermal cross-buoyancy

The focus of the current numerical investigation is to study the fluid flow and mixed convective (thermal cross-buoyancy) heat transfer of incompressible fluid across identical cylinders organized in a confined tandem configuration because of their enormous engineering and industrial applications such as heat exchange tubes, electronic cooling, twin chimney stacks, cooling tower, etc. The involved flow and energy equations are solved for different gap ratios (S/D = 2.5, 3, 3.5, 4, 5, and 5.5) with varying Richardson number (Ri = 0, 0.5, and 1) at Reynolds number Re = 100, Prandtl number Pr = 0.7 and wall confinement β = 25% by using a finite volume method-based commercial solver ANSYS Fluent. It is found that after a certain gap ratio there is a drastic change in the physical parameters and after that gap ratio the change is gradual; this gap ratio is termed as a critical gap ratio. The introduction of thermal cross-buoyancy (Ri > 0) plays a deep impact on the physical parameters, and it is to be noted that the critical spacing shifts towards a lower value with increasing Ri. The analysis of lift coefficients shows that the fluctuations in lift signal shift from zero average value at Ri = 0 towards the nonzero negative average value for the tandem cylinders at Ri > 0. The local Nusselt number shows the shift in the front stagnation point on both cylinders with increasing thermal cross-buoyancy. The drag coefficient and Nusselt number of the downstream cylinder are always less than the upstream cylinder, but the percentage increment in the physical parameters of the downstream cylinder after critical spacing is much more than its upstream counterpart.

Stationary and flow-induced vibration of two elliptic cylinders in tandem by immersed boundary-MRT lattice Boltzmann flux solver

Numerical method, combining immersed boundary method and multi-relaxation-time lattice Boltzmann flux solver, is used to carry out flow-structure interaction problems in this paper. Without dynamic mesh technique and body fitted grid re-generation, the flow-structure interaction problems can be solved by Cartesian mesh in order to simplify calculation process and save computation time. The accuracy and rationality of this method are verified by comparison of force coefficients, vibration amplitudes and flow characteristics with previous numerical results. Numerical simulations of two stationary and flow-induced vibration elliptical cylinders in tandem are carried out in laminar flow. For two stationary elliptical cylinders, the existing of downstream elliptical cylinder effectively prevents the unsteady characteristic of upstream wake at small gap spacing. With the increase of aspect ratio, the critical gap augments. After reaching the critical gap, the upstream force coefficients decrease and the downstream ones increase as aspect ratio increasing. Flow characteristic presents three regimes, including steady flow, shear layer attachment and 2S shedding vortex and 2S or C(2S) shedding vortex. For two flow-induced vibration elliptical cylinders, in comparison with stationary simulations, upstream transverse vibration responses are strengthened and downstream ones are strengthened at larger gap spacing and aspect ratio. The in-line vibration responses are both weaken, especially for downstream bluff body. Flow characteristic show different flow-regimes: (a) shear layer attachment for upstream and 2S shedding vortex for downstream; (b) 2S shedding vortex for upstream and C(2S) shedding vortex for downstream; (c) 2S shedding vortex for upstream and vortex pair presenting in the downstream wake. Greater L/D and AR, the effects of upstream wakes on downstream elliptical cylinder are more intense.

Hydrodynamic features of three equally spaced, long flexible cylinders undergoing flow-induced vibration

Abstract Three equally spaced flexible cylinders are frequently applied in many engineering fields. The flow-induced vibration (FIV) hydrodynamic features of three such cylinders are not the same as those of an isolated single one and remain unknown. In this paper, the hydrodynamic coefficients for three flexible cylinders subjected to FIV in an equilateral-triangular arrangement with a centre-to-centre spacing of 6 diameters were identified using an inverse analysis method according to the displacement response data obtained from model tests. The lift coefficient, varying drag coefficient and added mass coefficient at the dominant frequency were calculated by decomposing the cross-flow (CF) and in-line (IL) fluctuating forces. Three typical cases of an equilateral-triangular configuration (A, B, and C), which correspond to flow incidence angles of 0 ∘ , 30 ∘ , and 60 ∘ , were studied and discussed (the incidence angle is defined as the angle between the flow orientation and the line linking the centre points of one cylinder and the equilateral-triangular configuration). The hydrodynamic coefficients of the upstream cylinders are insignificantly influenced by the downstream cylinders. In contrast, the wake of the upstream cylinders impose a notable effect on the IL hydrodynamic coefficients of the downstream cylinders. Two robust frequency components ( f v , I L and f v , I L _ 1 ∕ 2 ) were observed in the IL vibrations of the downstream cylinders. The IL hydrodynamic forces at f v , I L have similar features to the classical vortex shedding forces of an isolated flexible cylinder. However, the IL hydrodynamic forces at f v , I L _ 1 ∕ 2 exhibit distinct behaviours that are closely related to the unique response characteristics in the IL direction. In addition, the IL fluctuating force coefficients and varying drag coefficients at f v , I L _ 1 ∕ 2 are relatively small and change slowly with the reduced velocity.

Three-dimensional numerical simulation on flow past three circular cylinders in an equilateral-triangular arrangement

Flow past three circular cylinders in an equilateral-triangular configuration is simulated for Reynolds numbers 200 ≤ Re ≤ 3900 and spacing ratios 1.25 ≤ L/D ≤ 4.0, where L is the center-to-center distance between each two cylinders and D is the diameter of the cylinder. Five different flow regimes are identified: proximity with deflected flow (P-D), proximity with flip-flop flow (P–F), dual vortex shedding (DV), transition between dual vortex shedding and triple vortex shedding (DV-TV), triple vortex shedding (TV). The boundary spacing ratios between the five regimes are affected by the Reynolds number. With the increase of the spacing ratio or the Reynolds number, the three-dimensionality of the wake flow becomes stronger. Mode B flow pattern with streamwise vortices is found at L/D = 1.25, 3.5 and 4.0 for Re = 1500 and L/D = 1.25 for 3900. The pressure coefficient on the surface of the downstream cylinder C3 is significantly different from that on a single cylinder, leading to significant reduction of the mean drag coefficient on C3 for all the studied spacing ratios and Reynolds numbers. The Strouhal numbers of C1 and C3 are the same and smaller than that of C2 in DV and TV regimes.

Numerical simulation of the flow past six-circular cylinders in rectangular configurations

Two-dimensional numerical simulations of the flow past six cylinders in the 2 × 3 matrix configuration and 3 × 2 matrix configuration are performed at a low Reynolds number (Re = 100) to provide a comprehensive understanding of the complicated physics for flow past multiple cylinder arrays. The spacing ratio L/D is varied from 1.25 to 7.0 (where L is the distance between the adjacent cylinder centers and D is the diameter of the cylinder). The effects of spacing ratio on the flow pattern, force coefficient, pressure distribution, and Strouhal number are investigated. The underlying flow physics for flow past six-cylinder arrays are interpreted from the view of shear layer development and force characteristics. Depending on the spacing ratio, four wake flow regimes are identified: a single bluff body flow regime (L/D = 1.25), shielding flow regime (1.5 ≤ L/D ≤ 2.5), reattachment flow regime (3.0 ≤ L/D ≤ 4.0), and co-shedding flow regime (L/D ≥ 4.5). For both configurations, regardless of L/D, the mean force coefficients on the downstream cylinders are always smaller than those of upstream cylinders, and an abrupt change of the standard deviation of the force coefficients is observed during the transition of different flow regimes. The Strouhal numbers of the six cylinders generally increase with L/D, and approach to that of a single cylinder in the co-shedding flow regime, a broadband FFT spectrum with multiple peaks is observed in the shielding and reattachment flow regimes.

Effects of surface roughness on the wake-induced instabilities of two circular cylinders

Wind tunnel tests are conducted to investigate the wake-induced vibrations (WIVs) of two circular cylinders with a centre-to-centre spacing of 4 times the diameter and attack angles varying from 0°to 20°for Reynolds numbers between 18,000 and 168,800. Two types of circular cylinders with different surface roughnesses are adopted, and the effects of the surface roughness and Reynolds number on the WIVs are examined. The results show that increasing the surface roughness of a cylinder changes the dynamic characteristic of the WIVs significantly. Two divergent types of wake-induced instability phenomena of distinct dynamic characteristics, namely oscillation trajectories, maximum amplitudes, and evolution of the vibrations, are observed. Changing the roughness of the upstream cylinder only has a smaller effect on wake-induced instabilities than changing the roughness of the downstream cylinder only. For a downstream cylinder with a rough surface, the cylinder only oscillates in a limited velocity range and exhibits “velocity-restrained vibrations” rather than divergent vibrations. Furthermore, it is found that the Reynolds number has strong effects on the wake-induced instabilities of the downstream cylinder, and the possibility that a cylinder experience instabilities is much lower at higher Reynolds numbers (Re>80,000) than at lower Reynolds numbers (Re<80,000).

The predominant frequency for viscous flow past two tandem circular cylinders of different diameters at low Reynolds number

Viscous flow past two circular cylinders in tandem arrangement is numerically investigated at a typical Reynolds number of 200 which is based on the diameter of the downstream cylinder. The non-dimensional diameter of the downstream cylinder D is fixed to be 1.0, while the non-dimensional diameter of the upstream cylinder d varies from 0.1 to 1.0 with an interval of 0.1. Moreover, the minimal non-dimensional distance between the two cylinders changes from 0.1 to 4.0. The numerical results show that continuous variation of the mean drag coefficient, the lift coefficient, and the lift frequency is observed with the increase in the gap ratio for d/ D = 0.1 and 0.2. Discontinuities are found for the mean drag coefficient, the lift coefficient, and the lift frequency of the downstream cylinder with the increase in gap ratio for d/ D = 0.9 and 1.0. Multiple lift oscillating frequencies of the downstream cylinder can be detected for d/ D = 0.3–0.8 at special gap ratios. Special attention is paid on d/ D = 0.4, which is a typical example for d/ D = 0.3–0.8. The predominant lift frequency of the downstream cylinder is observed to change from fL-1 to fL-2 as the increase in the gap ratio for d/ D = 0.4, which have not been previously detected. However, the predominant drag frequency of the downstream cylinder is found always to be fD-3 in present investigation scope. Moreover, a conclusion that fD-3 = fL-1 + fL-2 can be obtained.

Flow-induced oscillations of three tandem circular cylinders in a two-dimensional flow

Flow-induced oscillations of three identical circular cylinders, arranged in tandem configuration, are studied via two-dimensional finite element computations. Cylinders are mounted on elastic supports in the streamwise and transverse directions. Each downstream cylinder is placed at a distance of 5 diameters (5D) from its immediate upstream neighbor. Nondimensional mass ( m∗) of 2, and zero damping (ξ) are considered. Simulations are performed with the objective of understanding dynamic response of cylinders, as they are subject to wake interference, at constant Reynolds number, Re=150, and for varying reduced velocity (U∗) in the range of U∗=2−14. Similar to the behavior of an isolated cylinder at low Re, oscillation response of the upstream body exhibits initial excitation and lower lock-in regimes. However, for both the downstream cylinders, depending on their amplitude and frequency responses, the synchronization regime of U∗ can be categorized into three distinct regions: initial excitation, upper and lower lock-in regions. First downstream cylinder undergoes gradual transition between initial excitation and upper region, whereas the second downstream body exhibits this transition in two phases, which are separated by a periodic oscillation response regime. Upper lock-in region is characterized by periodic oscillations, while amplitude is modulated in the lower region. Only 2S shedding mode is observed for all the U∗ considered.

On the flow around two circular cylinders in tandem arrangement at high Reynolds numbers

The flows around two tandem circular cylinders in the subcritical and supercritical flow regimes are studied through three-dimensional numerical simulations. Different spacing ratios L/D (where L is the center-to-center distance between the two cylinders with D being the diameter of the cylinders) from 2.0 to 5.0 is considered. The instantaneous flow structures, pressure distributions and hydrodynamic forces on two tandem cylinders are analyzed at subcritical (Re=2.2×104) and supercritical (Re=3.0×106) Reynolds numbers. The present numerical solutions demonstrated that at the two Re, for L/D<3.5, the shear layer from the upstream cylinder reattaches on the surface of the downstream cylinder and vortex street is only formed behind the downstream cylinder, while the shear layer from the upstream cylinder rolls up alternately for L/D≥3.5, and vortex shedding occurs from both upstream and downstream cylinders. Compared with the flow characteristics at Re=2.2×104, for Re=3.0×106, the flow separation positions on the upstream cylinder move backward and the width of the wake behind the upstream cylinder becomes narrower, which leads to forward movement of the reattachment position. At the supercritical Reynolds number, the mean drag and fluctuating lift coefficients of the upstream cylinder are nearly independent of L/D while the sharp increase of force coefficients of the downstream cylinder occurs for L/D=3.5. Comparing to the case at the subcritical Reynolds number, higher vortex-shedding frequencies from the upstream and downstream cylinders are identified. It is also revealed that the slope of the best fit line for φ (the phase lag of the fluctuating lift force between two cylinders) and L/D increases at the supercritical Reynolds number. In addition, for L/D=2.5, the mean drag coefficients of the upstream cylinder decrease sharply for Re>1.0×105, while those of the downstream cylinder rise slightly with the growing Re. Moreover, the fluctuating lift coefficients of the upstream cylinder are almost independent of Re, but those of downstream cylinder drop as Re increases.

Quantification of wake unsteadiness for low-Re flow across two staggered cylinders

This work performs a numerical investigation on the two-dimensional flow across two circular cylinders in staggered arrangement at Re = 100. The seaparting distances between the centers of the cylinders are D/ d = 4–10 with Δ D/ d = 2 and T/ d = 0.0–2.0 with Δ T/ d = 0.5 in the streamwise and transverse directions, respectively, in which d is the cylinder diameter. Although the low- Re flow across staggered cylinders has been studied in a number of works, the authors mainly concerned about the identification and transition of various flow patterns. In this work, our objective is to quantitatively reveal the characteristics of flow unsteadiness as affected by the two separating distances. The flow unsteadiness is assessed from several aspects, including the spatial distributions and temporal variations of instantaneous flow patterns, fluctuating characteristic quantities, and fluctuating flow in the gap and in the near- and far-wake regions. To investigate the inherent instability of the flow, the global linear stability and sensitivity analysis is further carried out to demonstrate the unstable mode of perturbation growth and the critical flow patterns that destabilize the flow. The numerical results reveal that the wake flow between the two centerlines and beside the upstream cylinder is the most intensely perturbed. The flow around the downstream cylinder exhibits great fluctuation as perturbed by the destabilized shear layer of the upstream cylinder. The flow downstream of both cylinders shows multiple peak fluctuation of velocity because of the complex interactions between the destabilized shear layer and the wake vortices, resulting in the bidirectional transverse propagation of fluctuation. The stability analysis demonstrates that the unstable mode of perturbation growth is more significant in the far-wake region as the two cylinders are placed in proximity; the sensitivity analysis shows that the gap flow is crucial for the flow destabilization at small D, while the wake flow of cylinder- B is more significant for large D.

Numerical analysis of the interference between two elastically mounted cylinders in tandem subject to flows at low Reynolds numbers

Fluid-dynamic interference among cylindrical structures in arrays, frequently used in engineering, is of fundamental and practical interests since it may considerably change fluid–structure interactions and produce large fluctuating forces on structures that cause vibrations, lock-in and important motions. This paper aims to study the mutual interference between two circular cylinders in tandem arrangement, which is considered the simplest configuration of one array cylinders, elastically mounted in transversal direction and subject to a bi-dimensional uniform laminar flow at low Reynolds numbers. Both cylinders have the same diameter D, and the center-to-center spacing is equal to L = 5.25D which corresponds to co-shedding regime. The academic numerical model Ifeinco, which is based on the finite element method and uses a partitioned scheme that considers two-way interaction of fluid flow and structure, has been employed to the analysis. Combinations of upstream and downstream stationary and elastically mounted cylinders are investigated for Reynolds number range from 90 to 140. Differences of flow behaviors drag and lift forces and resonance between single cylinder and cylinders in tandem arrangement were found. Mutual and respective influences of upstream cylinder motion on the downstream cylinder and vice versa are analyzed. Results show that, in some engineering studies, the consideration of the flexibility of cylindrical structures in arrays is fundamental since it influences significantly the interference between cylinders, mainly the magnitude and direction of forces and characteristics of the resonance range, and, consequently, structural and dynamical behaviors.

Numerical investigation on interactive FIO of two-tandem cylinders for hydrokinetic energy harnessing

Flow induced oscillations (FIO) of two rough, rigid, tandem-cylinders on springs are investigated for hydrokinetic power conversion at Reynolds number 30,000 ≤ Re ≤ 120,000. Passive turbulence control (PTC) in the form of roughness strips is applied to enhance FIO and increase the power harness efficiency of the VIVACE (Vortex Induced Vibration for Aquatic Clean Energy) converter. Numerical simulations are performed using two-dimensional, Unsteady Reynolds-Averaged Navier-Stokes equations with the Spalart-Allmaras turbulence model. The center-to-center spacing ratio d/D of the two cylinders is set as 2.0 or 2.57 with mass ratio m* = 1.343, damping ratio ζ = 0.26, and stiffness K = 1,200N/m. Amplitude response, frequency response, interaction, energy harvesting, and conversion efficiency are presented and discussed. Results are compared to experimental data for validation and reveal how the interaction of two tandem cylinders may enhance the harnessed power. CFD provides complementary valuable information on visualization of wake and vortex structures. The main conclusions are: (1) In the VIV region at Re = 60,000, the amplitude response, frequency response, harnessed power, and power conversion efficiency of the upstream cylinder is the same for the two spacing ratios tested. Due to the shedding effect, the motion of the downstream cylinder for spacing ratio d/D = 2.0 is more severely suppressed than spacing ratio d/D = 2.57, which reduces the harnessed power and conversion efficiency for the downstream cylinder. (2) In the galloping region at Re = 110,000, due to the different timing of impingement of the shed vortices on the downstream cylinder, the upstream cylinder harnesses more power and has higher energy conversion efficiency for spacing ratio d/D = 2.0 than d/D = 2.57.

Steady separated flow around a pair of identical square cylinders in tandem array at low Reynolds numbers

The steady separated flow past two identical square cylinders in tandem arrangement is studied numerically. For a Reynolds number of 40, flow features are investigated for varied centre-to-centre distance, S between cylinders. The range of normalized spacing, SD is 2–30 where D denotes edge length of cylinders. Based on separation topology, four distinct flow regimes are identified. In regime I, the cylinders are closely spaced and gap between the cylinders is occupied by a pair of eddies and no wake forms behind the upstream cylinder. In regimes I and II, the cylinders are bridged by zero streamlines enveloping the gap flow. Thus, the cylinders along with the enclosed fluid, act as a single obstacle. Regime II forms as a manifestation of the first bifurcation of flow; the twin eddies in the gap split into four vortices. In regime III, the second bifurcation of flow occurs. The gap recirculation with four eddies splits; the first pair of counterrotating eddies contribute to wake of the upstream cylinder whereas the other pair adheres as a tiny vortical structure to the front part of downstream cylinder. In regime IV, separation topology is characterized by individual cylinder wakes. Four separation topologies, one corresponding to each regime, are proposed. The maximum width of the recirculation zone/wake of the upstream cylinder always exceeds the width of its downstream counterpart signifying higher drag for the former. For most of regime I, the downstream cylinder acts as a streamlined body.

Wakes of two inline cylinders at a low Reynolds number

The effect of vortex impingement on the fluid dynamics around a cylinder submerged in the wake of another of different diameters is numerically investigated at a Reynolds number Re = 200. While the diameter (D) of the downstream cylinder is fixed, impinging vortices are produced from the upstream cylinder diameter (d) varied as d/D = 0.24, 0.4, 0.6, 0.8 and 1.0, with a spacing ratio L = 5.5d, where L is the distance between the center of the upstream cylinder to the front stagnation point of the downstream cylinder. Two-dimensional simulations are carried out using the finite volume method. Fluid forces acting on the two cylinders are correlated with impinging vortices, vortex shedding, and wake structure. Different facets of wake formation, wake structure, and flow separation and their connections to fluid forces are discussed.

Numerical studies of the flow structure and aerodynamic forces on two tandem square cylinders with different chamfered-corner ratios

Three-dimensional large eddy simulations were carried out to investigate the flow over two tandem square cylinders for a fixed spacing ratio of L/D = 4 and a Reynolds number of 5.3 × 103, where L is the cylinder center-to-center distance between the cylinders and D is the cylinder width. The corners of each cylinder were chamfered with a ratio of ξ = B/D = 0%, 5%, 10%, and 15%, where B is the chamfered corner dimension. The focus is given on how ξ influences the flow structure, wake recirculation bubble, flow separation bubble, Strouhal number (St), aerodynamic force, and phase lag (ϕ) between vortex sheddings from the cylinders. With increasing ξ, the recirculation bubble length and minimum velocity in the wake of the upstream cylinder remain more or less constant and are close to those of a single cylinder, while the minimum velocity in the wake of the downstream cylinder dramatically drops between ξ = 0% and 5%. While the flow over the downstream remains attached on the side surfaces, that over the upstream cylinder forms primary and secondary side-surface bubbles on the side surface, and both shrink with increasing ξ. In addition, the leading chamfered corners are accompanied by corner bubbles that play an important role in the flow structure modification. Therefore, the time-mean drag and fluctuating lift of the upstream cylinder remarkably decrease for 0% ≤ ξ ≤ 5% and remain almost unchanged for 5% &amp;lt; ξ ≤ 15%, whereas those on the downstream cylinder diminish in the whole range of 0% ≤ ξ ≤ 15%. The Strouhal number (St) being identical for the two cylinders grows from 0.104 to 0.132 when ξ is increased from 0% to 15%. Overall, the influence of ξ on the wake structure and aerodynamics is remarkable for 0% ≤ ξ ≤ 5% because of the corner bubbles and is less for 5% &amp;lt; ξ ≤ 15%.

Wake-induced vibration of a circular cylinder at a low Reynolds number of 100

Wake-induced vibration (WIV) of a circular cylinder in the wake of a stationary bluff body at a low Reynolds number of 100 is numerically investigated in this work. Square prism, rectangular plate, and triangular prism with the same projected width as the diameter of the circular cylinder are employed as the upstream bluff body to examine the effect of obstacle’s shape on the wake interference and WIV. The downstream circular cylinder is allowed to oscillate in both inline and crossflow directions. Three spacing ratios of 2, 4, and 6 are considered in the computations that carried out for a wide range of reduced velocities (Ur = 2–20). In terms of shear layer reattachment, vortex impingement, and wake interference, three distinct flow regimes are identified for the upstream-stationary-downstream-vibrating tandem cylinders, i.e., continuous reattachment regime, alternating reattachment regime, and coshedding regime. The wake flow pattern is sensitive to the spacing ratio and the reduced velocity. Due to the vigorous streamwise response, the gap between the tandem cylinders varies over time and hence the switching of wake regime. Both the hydrodynamic forces and vibration response are tightly associated with the wake interaction. Among the three configurations, the cylinder behind a square prism possesses the largest cross-flow amplitude, while the cylinder behind a plate and that behind a triangular prism present more oscillating characteristics in the response amplitude, due mainly to the unstable and irregular vortex evolution.

Experimental study on aerodynamic characteristics of two square cylinders at various incidence angles

Wind tunnel tests are conducted to study the aerodynamic characteristics of two identical square cylinders with variations in the incidence angle at a Reynolds number of Re = 8.0 × 104. The center-to-center spacing (P) ranges from 1.25 to 5.0 times the width of the cylinders (B), and the incidence angle (α) varies from 0° to 90°. The spacing ratio significantly influences the aerodynamics. When the two cylinders are very close, they can be treated as one bluff body for which the vortex sheds only at the wake of the downstream cylinder. With an increasing spacing ratio, the flow finally separates individually from the two cylinders and creates two related vortex shedding patterns. The interference effects of the two cylinders on the aerodynamics changes with an increasing spacing ratio. According to the aerodynamics, the arrangement of two identical square cylinders can be classified by the spacing ratio into three states: closely spaced (P/B < 1.5), moderately spaced (1.5 ≤ P/B ≤ 3) and widely spaced (3 < P/B ≤ 5). The characteristics of the aerodynamics and mechanism of interference effects in the three states are discussed, considering the influence of the incidence angles.

Turbulent boundary layer perturbation by two wall-mounted cylindrical roughness elements arranged in tandem: Effects of spacing and height ratio

The perturbation of a turbulent boundary layer by two cylindrical roughness elements in close proximity was experimentally investigated in a water channel using planar particle image velocimetry. The two cylinders were arranged in tandem with center-to-center streamwise spacings of 2d, 4d, and 6d, where d is the diameter of the cylinders. The downstream cylinder had a fixed height 0.2δ, where δ is the incoming boundary layer thickness; the height of the upstream cylinder was varied to achieve upstream to downstream cylinder height ratios of 1, 0.75, and 0.5. The flow measurements were made at Reδ = 56 800 and included measurements over an isolated cylinder as a baseline case. The results highlight the effects of sheltering by an upstream cylinder on the wake of the downstream cylinder. Flow features in the wake, including the downwash, upwash, recirculation zone, velocity deficit, Reynolds shear stress, and turbulent kinetic energy (TKE), are dependent on the degree of sheltering, which is reliant on both the streamwise spacing and height ratio. Overall, sheltering results in a reduction in the downwash and size of the recirculation zone past the downstream cylinder. The magnitude and spatial distribution of the Reynolds shear stress and TKE varied significantly from those past the isolated cylinder. Depending on the streamwise spacing and height ratio, the presence of an upstream cylinder has the potential to enhance or reduce the Reynolds shear stress past the downstream cylinder. For example, the maximum Reynolds shear stress in the near wake was approximately doubled for a spacing of 2d and a height ratio of 0.5 and nearly halved for a spacing of 2d and a height ratio of 1 (relative to that past the isolated cylinder). The variations in these flow features across the 9 considered arrangements suggest changes to the wake and its vortical structures due to the presence of an upstream cylinder. The results highlight the potential of flow control through a pair of roughness elements in close proximity to achieve desired outcomes such as reduced or redistributed Reynolds shear stress and TKE, relative to the isolated cylinder.