Single Cylinders Research Articles

Study of coupling effects on the three-dimensional magnetohydrodynamic flows around single and tandem cylinders in duct

This work focuses on magnetohydrodynamic (MHD) flow around either single or two identical tandem circular cylinders confined in a duct under external transverse magnetic field. The influences of transverse magnetic field, inlet velocity of conducting fluid, and the distance between two cylinders arranged along the flow direction on the flow modes, vortex shedding frequency, separation angle, and drag coefficient are investigated. The simulations are conducted with the Hartmann number Ha and Reynolds number Re and are varied from 0 to 1.35 and from 100 to 200, respectively. For the MHD flow around single cylinder, the map of flow instability is set up and the relation between critical Hartmann number Hacr and Re is concluded as The coupling effect of geometry confinement and external transverse magnetic field can increase the separation angles and drag coefficients and decrease vortex shedding frequencies and lengths of reverse flow. For the tandem double cylinder cases, the spacing ratio between two cylinders L/d changes from 2 to 8. The boundary between steady regime and unsteady regime is described as, The three wake patterns are found under various magnetic fields. The nonlinear and nonmonotonous characteristics of coupling effects of Ha, Re, and L/d are summarized. The physical mechanisms of influences of MHD flow field in gap region between tandem cylinders and the existence of upstream cylinder on flow instability and wake pattern are revealed. Finally, the critical conditions corresponding to the transition from steady flow to unsteady flow are achieved with formulas.

Monte Carlo evaluation of high-gradient magnetically focused planar proton minibeams in a passive nozzle

Objective. To investigate the potential of using a single quadrupole magnet with a high magnetic field gradient to create planar minibeams suitable for clinical applications of proton minibeam radiation therapy. Approach. We performed Monte Carlo simulations involving single quadrupole Halbach cylinders in a passively scattered nozzle in clinical use for proton therapy. Pencil beams produced by the nozzle of 10–15 mm initial diameters and particle range of ∼10–20 cm in water were focused by magnets with field gradients of 225–350 T m−1 and cylinder lengths of 80–110 mm to produce very narrow elongated (planar) beamlets. The corresponding dose distributions were scored in a water phantom. Composite minibeam dose distributions composed from three beamlets were created by laterally shifting copies of the single beamlet distribution to either side of a central beamlet. Modulated beamlets (with 18–30 mm nominal central SOBP) and corresponding composite dose distributions were created in a similar manner. Collimated minibeams were also compared with beams focused using one magnet/particle range combination. Main results. The focusing magnets produced planar beamlets with minimum lateral FWHM of ∼1.1–1.6 mm. Dose distributions composed from three unmodulated beamlets showed a high degree of proximal spatial fractionation and a homogeneous target dose. Maximal peak-to-valley dose ratios (PVDR) for the unmodulated beams ranged from 32 to 324, and composite modulated beam showed maximal PVDR ranging from 32 to 102 and SOBPs with good target dose coverage. Significance. Advantages of the high-gradient magnets include the ability to focus beams with phase space parameters that reflect beams in operation today, and post-waist particle divergence allowing larger beamlet separations and thus larger PVDR. Our results suggest that high gradient quadrupole magnets could be useful to focus beams of moderate emittance in clinical proton therapy.

Interactions Between Shock Waves and Liquid Droplet Clusters: Interfacial Physics

Abstract This study quantitatively investigates the behaviors of single and multiple liquid cylinders placed in the path of a traveling normal shock wave using high-fidelity numerical simulations. The research is motivated by next-generation liquid-fueled scramjet and rotating detonation engines (RDE) where the liquid fuel interacts with shock waves and undergoes deformation, fragmentation, atomization, and vaporization before it mixes with the air and subsequently burns—the focus of this study is on the deformation and interfacial physics. The mathematical formulation to investigate this multiphase problem is based on a modified five-equation Kapila model that incorporates pressure-relaxation, viscous, and surface tension effects. A diffuse interface method is used to capture the liquid–gas interface. Two configurations are studied in this effort: (1) a single column of diameter 22 mm exposed to a shock wave traveling at Mach 2.4 and (2) a two identical cylinder system with diameters of 4.8 mm and 30 mm apart, and exposed to a shock wave moving a Mach number of 1.47. The computational results show excellent agreement with high-speed images and droplet deformation measured in the experiments. For both cases, it is found that the shock and the flow field in its wake leads to the flattening of the cylinder, followed by the formation of instability waves that are amplified by the baroclinic torque and the continuous reflections of the waves transmitted inside the liquid interior, eventually leading to ligament stripping. Based on the spatiotemporal evolution of the liquid and gaseous flowfields, time evolution of shock strength and parent droplet's mass and translation distance are also discussed.

Wave action of non-coaxial double-layer cylindrical structure

Based on the potential flow theory, the mathematical formula of the wave action of the non-coaxial double-layer cylinder structure is derived, and the effect caused by the non-coaxial of the upper and lower single cylinders is analyzed. In this paper, the water area is divided into two regions, and their respective coordinate systems are established in each region to describe the velocity potential function. The velocity potential of the two regions is linked by the matched eigenfunction expansion method (MEEM) at the interface of the two regions. The cross-sectional radius function of the interface is expressed by Fourier series. After verifying the accuracy of the mathematical formula, the effect of asymmetric structure is analyzed. The results show that when the relative angle of the two axes is 0°, the wave force on the structure can be reduced to a greater extent if the two axes are as far away as possible. At the same time, the effect of this reduction weakens with the increase of the relative angle, and even increases the wave force when α = 90°. When the lower-lawyer cylinder radius is 0.6 times the upper-lawyer cylinder radius, the effect of wave force reduction caused by the non-coaxial is the largest.

ELECTROMAGNETIC RADIATION SCATTERING BY LINEAR LOW-PARTICLE AGGREGATES OF FINITE DIELECTRIC CYLINDERS

A numerical simulation of functions of the angular distribution of the scattering intensity for dimers and thrimers of finite dielectric cylinders is made using the formalism of the volume integral equation. The function of the angular distribution of the scattering intensity dependence on the optical and geometric parameters of single finite cylinders and their mutual location is studied. It is shown that the electrodynamic interaction between the cylinders leads to a strong change of the angular distribution of intensity of the radiation scattered by this system in comparison with that for two cylinders without electrodynamic coupling.

Three Crossing Limit Cycles in a 3D-Filippov System Having a T-Singularity

Our starting point is a discontinuous piecewise linear dynamical system in [Formula: see text] with two zones that present a single invisible two-fold straight line and invariant cylinders. We broke the dynamics of this vector field to obtain a new four-parameter piecewise linear vector field with a [Formula: see text]-singularity. For this vector field, we prove that the upper bound of simple crossing limit cycles (simple CLCs) is three, and provide conditions for the existence of 1, 2, or 3 simple CLCs. We also show the occurrence of three distinct bifurcations involving such simple CLCs that are derived from a bifurcation set with two parameters: (i) a Teixeira Singularity bifurcation (TS-bifurcation); (ii) a Fold bifurcation; and (iii) a Cusp bifurcation.

Vibration, acoustic and emission characteristics of the chlorella vulgaris microalgae oil in compression ignition engine to mitigate environmental pollution

The petroleum fuel demand with high price and its exhaustion imposes a pressure to find an alternative. The fossil fuel shortage has been deteriorating over the past few years, because of the rapid increase in population. Many attempts have been made to increase the quality of biofuel with additives. In this paper, two types of nanoparticles such as carbon nanotubes (CNT) and alumina (Al2O3) in chlorella microalgae biofuel were analyzed by experimental method. The added CNT and alumina act as a catalyst that induces complete combustion with retarded emissions. In addition to above, the noise and vibration qualities are also measured. A series of test conducted using single cylinders, four stroke, naturally aspirated compression ignition diesel engine was run by using pure diesel and also different fuel blends ‘such as B10CNT50A50 Chlorella (Microalgae Biodiesel 10% + Diesel 90% + CNT 50 ppm), B20CNT50A50 (Microalgae Biodiesel 20% + Diesel 80% + CNT 50 ppm + Al2O3 50 ppm) and B30CNT50A50 (Microalgae Biodiesel 30% + Diesel 70% + CNT 50 ppm + Al2O3 50 ppm). At a constant load condition, all experimental tests were conducted at four different speeds such as 1500 rpm, 2000 rpm, 2500 rpm and 3000 rpm. The reference fuel of diesel B0 results was compared with blended fuel. From the results, it has been found that the nano additives of CNT and alumina reduced the greenhouse gas emissions of CO compared to plain diesel. Only considering the blended fuel, as the percentage of biofuel increases, the emission of nitric oxide and carbon dioxide is decreased with significant reduction in the amount of noise and vibration and also the combustion and performance qualities were also improved. The highest benefit in terms of all factors was achieved in the fuel blend of B30A50CNT50 amongst the other blends.

Flow-Induced Vibrations of Single and Multiple Heated Circular Cylinders: A Review

This study is an effort to encapsulate the fundamentals and major findings in the area of fluid-solid interaction, particularly the flow-induced vibrations (FIV). Periodic flow separation and vortex shedding stretching downstream induce dynamic fluid forces on the bluff body and results in oscillatory motion of the body. The motion is generally referred to as flow-induced vibrations. FIV is a dynamic phenomenon as the motion, or the vibration of the body is subjected to the continuously changing fluid forces. Sometimes FIV is modeled as forced vibrations to mimic the vibration response due to the fluid forces. FIV is a deep concern of engineers for the design of modern heat exchangers, particularly the shell-and-tube type, as it is the major cause for the tube failures. Effect of important parameters such as Reynolds number, spacing ratio, damping coefficient, mass ratio and reduced velocity on the vibration characteristics (such as Strouhal number, vortex shedding, vibration frequency and amplitude, etc.) is summarized. Flow over a bluff body with wakes developed has been studied widely in the past decades. Several review articles are available in the literature on the area of vortex shedding and FIV. None of them, however, discusses the cases of FIV with heat transfer. In particular systems, FIV is often coupled to heat transfer, e.g., in nuclear power plants, FIV causes wear and tear to heat exchangers, which can eventually lead to catastrophic failure. As the circular shape is the most common shape for tubes and pipes encountered in practice, this review will only focus on the FIV of circular cylinders. In this attempt, FIV of single and multiple cylinders in staggered arrangement, including tandem and side-by-side arrangement is summarized for heated and unheated cylinder(s) in the one- and two-degree of freedom. The review also synthesizes the effect of fouling on heat transfer and flow characteristics. Finally, research prospects for heated circular cylinders are also stated.

A Numerical Investigation of Turbulent Flow Over Single and Tandem Square Cylinders

This paper presents the three-dimensional flow investigations over the square cylinders placed in the tandem arrangement. Two different flow configurations were investigated in detail; one comprising of a single square cylinder and the other comprising of three square cylinders placed in a tandem arrangement with the spacing of six times the width (w) of each square cylinder. The Reynolds number based on the width of the square cylinder (w) and free stream velocity (Uo) is 22,000. The problem was solved numerically using an Unsteady Reynolds-Averaged Navier-Stokes (URANS) based model and Large Eddy Simulation (LES) based model. Strouhal Number, lift, and drag coefficients were computed for each configuration. By comparing both the models using contour plots of pressure, velocity and vorticity it is found that the LES model is more accurate to capture the turbulence around single and tandem square cylinders. In the tandem arrangement, complex periodic vortex shedding was observed in the wake of each square cylinder. The production of turbulent kinetic energy was also investigated to understand the roles of stresses during flow over the cylinders. The analysis showed that the production of turbulence by normal stresses is higher than that of shear stresses. Furthermore, it was observed that the flow over the first cylinder arranged in tandem is quite identical to that of the single square cylinder. Moreover, the upstream cylinder experienced a higher lift in comparison to the downstream cylinders.

Lattice Boltzmann method for fluid–structure interaction in compressible flow

We present a two-way coupled fluid–structure interaction scheme for rigid bodies using a two-population lattice Boltzmann formulation for compressible flows. An arbitrary Lagrangian–Eulerian formulation of the discrete Boltzmann equation on body-fitted meshes is used in combination with polynomial blending functions. The blending function approach localizes mesh deformation and allows treating multiple moving bodies with a minimal computational overhead. We validate the model with several test cases of vortex induced vibrations of single and tandem cylinders and show that it can accurately describe dynamic behavior of these systems. Finally, in the compressible regime, we demonstrate that the proposed model accurately captures complex phenomena such as transonic flutter over an airfoil.

Bound states in the continuum in strong-coupling and weak-coupling regimes under the cylinder – ring transition

Abstract Bound states in the continuum (BIC) have been at the forefront of research in optics and photonics over the past decade. It is of great interest to study the effects associated with quasi-BICs in the simplest structures, where quasi-BICs are very pronounced. An example is a dielectric cylinder, and in a number of works, quasi-BICs have been studied both in single cylinders and in structures composed of cylinders. In this work, we studied the properties of quasi-BICs during the transition from a homogeneous dielectric cylinder in an air environment to a ring with narrow walls while increasing the diameter of the inner air cylinder gradually. The results demonstrate the quasi-BIC crossover from the strong-coupling to the weak-coupling regime, which manifests itself in the transition from the avoided crossing of branches to their intersection with the quasi-BIC being preserved on only one straight branch. In the regime of strong-coupling and quasi-BIC, three waves interfere in the far-field zone: two waves corresponding to the resonant modes of the structure and the wave scattered by the structure as a whole. The validity of the Fano resonance concept is discussed since it describes the interference of only two waves under weak coupling conditions.

Investigation of the flow behaviour and local scour around single square-shaped cylinders at different positions in live-bed

Scour around non-circular cylinders has seldom been studied before. This paper aims to numerically investigate the flow behaviour and evolution of local scour around two single square-shaped piers with 90° (square pier) and 45° (diamond pier) orientation angles to the flow under steady-current and live-bed conditions. For this purpose, a coupled approach between a hydrodynamic and a morphodynamic model is developed and validated against flow and scour experimental data sets. Hydrodynamic model simulations reveal the formation of strong horseshoe vortices (HSVs) upstream of the square pier compared to the diamond pier. The scour simulation results show a faster rate of increase in the scour depth around the square pier, which leads to a deeper equilibrium scour hole. The model gives values of normalized quasi-equilibrium scour depths of Seq/wp = 1.94 and 1.00 for the square and diamond piers, respectively, where Seq is the quasi-equilibrium scour depth, and wp is the pier's projected width under steady current flow and live-bed conditions. It is discovered that the impact of other factors, such as bed material gradation, Froude number, Shields Parameter, as well as flow depth, can be as important as the shape factor in the study of equilibrium scour depth in live-bed conditions.

Flow-induced vibration suppression for a single cylinder and one-fixed-one-free tandem cylinders with double tail splitter plates

In this paper, double tail splitter plates (DTSPs) have been investigated to suppress the flow-induced vibrations (FIVs) of both an elastically mounted single circular cylinder and one-fixed-one-free tandem cylinders in a wind tunnel at Re = 4000-48000. The splitter plates length to diameter ratios, L/D, were set from 0.4 to 2.0 and the angles​ θ between them were set from 0°-90°. The amplitudes of single cylinders with DTSPs exhibit three vibration patterns: VIV (vortex-induced vibration) pattern, galloping pattern and suppressed pattern, and four patterns of vortex shedding frequencies fs can be classified. The optimal suppression efficiency is 97.6% occurred at θ = 90°, L/D = 2.0. For the one-fixed-one-free tandem arrangement cylinders, comparing to the single one, the DTSPs have a better applicability to suppress the vibration, and all the downstream cylinders present a suppressed pattern except for the case of L/D = 0.4 at θ = 0°. The best suppression efficiency is 98.4% occurred at θ = 60°, L/D = 0.8. Different from fs can be locked to multiple harmonics of natural frequencies fn, the oscillation frequencies can be only locked to the first harmonic of fn.

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.

Dynamic crystal plasticity modeling of single crystal tantalum and validation using Taylor cylinder impact tests

In this work, we extend a dislocation-density based constitutive theory for the dynamic thermomechanical behavior of crystals to body centered cubic (BCC) tantalum. Strain rate and temperature dependence of the slip resistance in the model is incorporated via an expression for the state-dependent instantaneous saturation dislocation density and a dynamic recovery fraction that affects the rate of generation of immobile dislocation density. Crystallographic slip along 111 on the {110} or {112} planes as well as their combination are examined. The Schmid stress serves as the driving force for dislocation motion and the twinning/anti-twinning sense of slip on {112} planes is accounted for by introduction of Peierls stress that depends upon this sense. The model parameters are calibrated using a two-stage Bayesian approach against experimentally generated uniaxial stress-strain compression curves at quasi-static and high strain rates over a range of temperatures. Velocity-time histories from single crystal flyer plate impact experiments were also used to parameterize this model. The calibrated model was applied to simulate previous Taylor cylinder impact experiments. Our results show that the model must include slip on {110} and {112} planes and also account for the twinning versus anti-twinning sense of slip on {112} planes, to appropriately represent the orientation dependence of the flow stress and match the deformed geometry of the single crystal Taylor cylinders.

Singularity of the Spectrum for Smooth Area-Preserving Flows in Genus Two and Translation Surfaces Well Approximated by Cylinders

We consider smooth flows preserving a smooth invariant measure, or, equivalently, locally Hamiltonian flows on compact orientable surfaces and show that, when the genus of the surface is two, almost every such locally Hamiltonian flow with two non-degenerate isomorphic saddles has singular spectrum. More in general, singularity of the spectrum holds for special flows over a full measure set of interval exchange transformations with a hyperelliptic permutation (of any number of exchanged intervals), under a roof with symmetric logarithmic singularities. The result is proved using a criterion for singularity based on tightness of Birkhoff sums with exponential tails decay. A key ingredient in the proof, which is of independent interest, is a result on translation surfaces well approximated by single cylinders. We show that for almost every translation surface in any connected component of any stratum there exists a full measure set of directions which can be well approximated by a single cylinder of area arbitrarily close to one. The result, in the special case of the stratum mathcal {H}(1,1), yields rigidity sets needed for the singularity result.

Parametric Investigation of the Flow-Sound Interaction Mechanism for Single Cylinders in Cross-Flow

Abstract Flow-excited acoustic resonance is a design concern in many industrial applications. If not treated, it may lead to excessive vibrational loads, which could subsequently result in premature structural failure of critical equipment. For the case of tube bundles in heat exchangers, several acoustic damping criteria were proposed in the literature to predict the occurrence of resonance excitation. However, these criteria, in some cases, are not reliable in differentiating between the resonant and nonresonant cases. A primary reason for that is the geometrical differences between reduced scale models and full-scale tube bundles, and their effect on the flow-sound interaction mechanism. Therefore, the effect of two geometrical aspects, namely, the duct height and the cylinder diameter, on the self-excited acoustic resonance for single cylinders in cross-flow is experimentally investigated in this work. Changing the duct height changes the natural frequency of the excited acoustic modes and the duct's acoustic damping and radiation losses. Changing the cylinder diameter changes the flow velocity at frequency coincidence, the pressure drop, and Reynolds number. It is found that increasing the duct height decreases the acoustic impedance, which makes the system more susceptible to resonance excitation. This, in turn, changes the magnitude of the acoustic pressure at resonance, even for cases where the dynamic head of the flow is kept constant. The acoustic attenuation due to visco-thermal losses is quantified theoretically using Kirchhoff's acoustical damping model, which takes into account the geometrical aspects of the different ducts. Results from the experiments are compared with the acoustic damping criteria from the literature for similar cases. It is revealed that the height of the duct is an important parameter that should be included in damping criteria proposed for tube bundles of heat exchangers, as it controls the acoustic damping and radiation losses of the system, which have been over-looked in the past.

Diameter ratio effects in the wake flow of single step cylinders

Vortex interactions behind step cylinders with diameter ratio 2 ≤ D/d ≤ 3 at Reynolds number (ReD) 150 were investigated by directly solving the three-dimensional Navier–Stokes equations. In accordance with the previous paper [C. Tian et al., “Vortex dislocation mechanisms in the near wake of a step cylinder,” J. Fluid Mech. 891, A24 (2020)], some interesting characteristics of vortex dislocations, e.g., two phase difference accumulation mechanisms, the trigger and threshold values of vortex dislocations, antisymmetric vortex interactions, and long N-cell cycles, were observed. By performing a detailed investigation of diameter ratio effects, more features of vortex dynamics were discovered. In addition to the known antisymmetric vortex interactions, a symmetric vortex interaction between neighboring N-cell cycles was observed. The long-time observations revealed an interruption of these two types of vortex interactions. By using a well-validated phase tracking method, we monitored the time trace of the phase difference accumulation process in different D/d cases from which decreasing (known) and increasing (new) phase difference tendencies were identified. Both caused the interruption of continuous symmetric or antisymmetric phenomena but through two distinct mechanisms. Meanwhile, the diameter ratio effects on the trigger and threshold values were discussed. Additionally, the likelihood of antisymmetric or symmetric vortex interactions and increasing or decreasing phase difference tendencies was analyzed. Moreover, diameter ratio effects on shedding frequencies and the extensions of three main vortex cells, i.e., S-, N-, and L-cell vortices, were described.

A new approach for handling body motion by combining a grid deformation method and an overset grids technique

A new approach for handling body motion by combining the grid deformation and the overset grids methods is proposed. The present approach can completely avoid the computational load of the dynamic overset grids method. The regions where the overset relations are composed move with the body motion, maintaining the geometrical relation to determine for the weight of the overset interpolation. The present approach is applied to the cases with 2D single and multiple cylinders with motion. The scaled-Jacobian before and after the grid deformation is examined. The values of the scaled-Jacobian maintain at least 0.35 after the grid deformation, and the velocity and vorticity contour lines are smoothly connected on the computational grids, thus, the effectiveness of the present approach is revealed. Additionally, the verification using the computational grids with three different resolutions is performed on the case with the single cylinder. The present method which combines the grid deformation and overset grids methods succeeds to reduce the CPU time approximately from 40% to 65% of the time using the dynamic overset grids method. Next, the present approach is applied to the computation of the flow around a ship with an appendage, including ship motion in regular head waves with a high Reynolds number condition. The present method reproduces the impact pressure when points on the hull surface enter the water and the difference in the peak values of the pressure at different positions. The present method succeeds in reducing the CPU time to 40% of the case using the dynamic overset grids method at the case with the ship motions in the regular waves.

Fluid flow and heat transfer around single and tandem square cylinders subjected to shear flow

Linear shear flows, forces, and heat transfer across a single and two tandem square cylinders are numerically investigated at Reynolds numbers Re = 70–150 and a Prandtl number Pr = 0.71, with the dimensionless inlet shear rate K = 0–0.2. For the two tandem cylinders, the scaled cylinder-gap spacing (S*) is varied from 1.0 to 5.0. The flow is assumed laminar and two-dimensional. The numerical method is based on a finite-volume technique. The effects of K, Re, and S* are investigated on the heat transfer topology, flow structures, and aerodynamic parameters including vortex shedding frequency, pressure coefficient, lift and drag forces, and Nusselt number. For the single cylinder, when K ≠ 0, the time-mean lift force is negative for Re = 70 and 100 but positive for Re = 150. The lift magnitude linearly increases with K. For tandem cylinders, employing three initial conditions for some S* values yields two solutions linked to hysteresis (modes I and II) in the flow, forces, and heat transfer. Hysteresis is observed for S* = 2.0–5.0 when K = 0.2 and Re = 150. Mode I turns in a smaller time- and surface-averaged Nusselt number than mode II. In general, the inlet shear has more effect on the flow around the downstream cylinder than that around the upstream cylinder.