Numerical simulation of flow around a square cylinder in uniform-shear flow

This paper presents results obtained from a numerical simulation of a two-dimensional (2-D) incompressible linear shear flow over a square cylinder. Numerical simulations are performed, using the lattice Boltzmann method, in the ranges of 50⩽Re⩽200 and 0⩽K⩽0.5, where Re and K are the Reynolds number and the shear rate, respectively. The effect of the shear rate on the frequency of vortex shedding from the cylinder, and the lift and drag forces exerted on the cylinder are quantified together with the flow patterns around the cylinder. The present results show that vortex structure behind the cylinder is strongly dependant on both the shear rate and Reynolds number. When Re=50, a small K can disturb the steady state and cause an alternative vortex shedding with uneven intensity. In contrast, a large value of K will suppress the vortex shedding from the cylinder. When Re>50, the differences in the strength and size of vortices shed from the upper and lower sides of the cylinder become more pronounced as K increases. Vortex shedding disappears when K is larger than a critical value, which depends on Re. The flow patterns around the cylinder for different Re tend towards self-similarity with increasing K. The lift and drag forces exerted on the cylinder, in general, decrease with increasing K. Unlike a shear flow past a circular cylinder, the vortex shedding frequency past a square cylinder decreases with increasing the shear rate. A significant reduction of the drag force occurs in the range 0.15<K<0.3.     

Vortex shedding and aerodynamic forces on a circular cylinder in linear shear flow at subcritical Reynolds number

Vortex shedding and aerodynamic forces on a circular cylinder in a linear shear flow with its axis normal to the plane of the velocity shear profile at subcritical Reynolds number are investigated experimentally. The shear parameter β, which is based on the velocity gradient, cylinder diameter and upstream mean velocity at the center plane of the cylinder, varies from 0 to 0.27. The Strouhal number has no significant variation with the shear parameter. The time-mean base pressure increases and the fluctuating component of the base pressure decreases significantly with increasing shear parameter. Vortex shedding is suppressed by the velocity shear. Dislocation of the stagnation point takes place and this influences the pressure distribution around the cylinder together with the velocity shear. A mean lift force arises in the shear flow due to asymmetry of the pressure distribution, and it acts from the high velocity side to the low velocity side. In addition, the lift coefficient increases and the drag coefficient decreases with increasing shear parameter.     

Passive control of wake flow by two small control cylinders at Reynolds number 80

Passive control of the wake behind a circular cylinder in uniform flow is studied by numerical simulation at Re_D=80. Two small control cylinders are placed symmetrically along the separating shear layers at various stream locations. In the present study, the detailed flow mechanisms that lead to a significant reduction in the fluctuating lift but maintain the shedding vortex street are clearly revealed. When the stream locations lie within 0.8≤X_C/D≤3.0, the alternate shedding vortex street remains behind the control cylinders. In this case, the symmetric standing eddies immediately behind the main cylinder and the downstream delay of the shedding vortex street are the two primary mechanisms that lead to a 70–80% reduction of the fluctuating lift on the main cylinder. Furthermore, the total drag of all the cylinders still has a maximum 5% reduction. This benefit is primarily attributed to the significant reduction of the pressure drag on the main cylinder. Within X_C/D>3.0, the symmetry of the standing eddy breaks down and the staggered vortex street is similar to that behind a single cylinder at the same Reynolds number. In the latter case, the mean pressure drag and the fluctuating lift coefficients on the main cylinder will recover to the values of a single cylinder.     

Numerical simulation of shear effect on vortex shedding behind a square cylinder

This paper is concerned with the numerical simulation of the flow structure around a square cylinder in a uniform shear flow. The calculations were conducted by solving the unsteady 2D Navier–Stokes equations with a finite difference method. The effect of the shear parameter K of the approaching flow on the vortex-shedding Strouhal number and the force coefficients acting on the square cylinder is investigated in the range K=0·0–0·25 at various Reynolds numbers from 500 to 1500. The computational results are compared with some existing experimental data and previous studies. The effect of shear rate on the Strouhal number and the force acting on the cylinder has a tendency to reduce the oscillation. The Strouhal number, mean drag and amplitude of the fluctuating force tend to decrease as the shear rate increases, but show no significant change at low shear rate. Increasing the Reynolds number decreases the Strouhal number and increases the force acting on the cylinder. At high shear rate the shedding frequencies of the fluctuating drag and lift coefficients are identical. © 1997 John Wiley & Sons, Ltd.     

Wall proximity effects on the effectiveness of upstream control rod

Two dimensional flow over a circular cylinder with an upstream control rod of same diameter is simulated in unbound condition and in wall bounded conditions. The cylinders are placed at various heights from the wall and the inter-distance between cylinders is also varied. The control rod is subjected to different rotation rates. It is found that, in unbound condition, rotating the control rod decreases the critical pitch length (S/D_cr) and increases the drag and Strouhal number of the main cylinder. In presence of plane wall, the shielding provided by the separated shear layers from the control rod in cavity regime is deteriorated due to deflection of shear layers which results in higher drag and large fluctuation of lift coefficient. However, in wake impingement regime, the binary vortices from the control rod are weakened due to diffusion of vorticity and hence, the main cylinder experiences a lower drag and small lift fluctuations than that of unbound condition. The critical height of vortex suppression (H/D_cr) is higher in cavity regime than that of wake impingement regime due to the single extended-bluff body like configuration. The rotation of control rod energizes the wall boundary layer and increases the critical height of vortex suppression. Increasing the rotational rate of control rod decreases the drag force and reduces the amplitude of lift fluctuation. Analysis of the wall shear stress distribution reveals that it suffers a sudden drop at moderate height where the normal Karman vortex shedding changes to irregular shedding consisting of single row of negative vortices. Modal structures obtained from dynamic mode decomposition (DMD) reveal that the flow structures behind the main cylinder are suppressed due to wall and the flow is dominated by the wake of control rod.     

A numerical investigation of the flow over a pair of identical square cylinders in a tandem arrangement

This paper describes a numerical study of the two‐dimensional and three‐dimensional unsteady flow over two square cylinders arranged in an in‐line configuration for Reynolds numbers from 40 to 1000 and a gap spacing of 4D, where D is the cross‐sectional dimension of the cylinders. The effect of the cylinder spacing, in the range G = 0.3D to 12D, was also studied for selected Reynolds numbers, that is, Re = 130, 150 and 500. An incompressible finite volume code with a collocated grid arrangement was employed to carry out the flow simulations. Instantaneous and time‐averaged and spanwise‐averaged vorticity, pressure, and streamlines are computed and compared for different Reynolds numbers and gap spacings. The time averaged global quantities such as the Strouhal number, the mean and the RMS values of the drag force, the base suction pressure, the lift force and the pressure coefficient are also calculated and compared with the results of a single cylinder. Three major regimes are distinguished according to the normalized gap spacing between cylinders, that is, the single slender‐body regime (G < 0.5), the reattach regime (G < 4) and co‐shedding or binary vortex regime (G ≥4). Hysteresis with different vortex patterns is observed in a certain range of the gap spacings and also for the onset of the vortex shedding. Copyright © 2011 John Wiley & Sons, Ltd.     

基于浸入边界-格子Boltzmann通量求解法的椭圆柱流动特性分析

基于浸入边界-格子Boltzmann通量求解法,开展了雷诺数Re=100不同几何参数下单椭圆柱及串列双椭圆柱绕流流场与受力特性对比研究。结果表明,随长短轴比值的增加,单椭圆柱绕流阻力系数先减小后缓慢上升,最大升力系数则随长短轴比值的增大而减小;尾迹流动状态从周期性脱落涡到稳定对称涡。间距是影响串列圆柱及椭圆柱流场流动状态的主要因素,间距较小时,串列圆柱绕流呈周期性脱落涡状态,而椭圆柱则为稳定流动;随着间距增加,上下游圆柱及椭圆柱尾迹均出现卡门涡街现象,且串列椭圆柱临界间距大于串列圆柱。串列椭圆柱阻力的变化规律与圆柱的基本相同,上游平均阻力大于下游阻力;上游椭圆柱阻力随着间距的变大先减小,下游随间距的变大而增加,当间距达到临界间距时上下游阻力跃升,随后出现小幅度波动再逐渐增加,并趋近于相同长短轴比值下单柱体绕流的阻力。     

带有柔性薄板三维方柱流固耦合的数值模拟研究

采用双向流固耦合方法,对带有柔性薄板三维方柱的流场变化特性进行了研究。通过对比单方柱,分析了带有柔性薄板三维方柱阻力系数、升力系数以及斯特劳哈尔数的变化规律。研究表明,在方柱尾流区域附加一柔性薄板可以使其阻力系数降低34.6%,同时其变化幅值大大减小;其升力系数的均方根减小84.8%,流场脉动大幅度减小;斯特劳哈尔数降低79.5%。研究结果表明,在三维方柱后设置柔性薄板可有效抑制涡脱落,从而改善三维方柱的尾流特性。     

Numerical simulation of Reynolds number effects on velocity shear flow around a circular cylinder

Three-dimensional Direct Numerical Simulation (DNS) and Large Eddy Simulation (LES) are performed to investigate the shear effects on flow around a circular cylinder at Reynolds numbers of Re=60–1000. The shear parameter, β, which is based on the velocity gradient, cylinder diameter and upstream mean velocity at the center plane of the cylinder, varies from 0 to 0.30. Variations of Strouhal number, drag and lift coefficients, and unsteady wake structures with shear parameter are studied, along with their dependence on Reynolds number. The presented simulation provides detailed information for the flow field around a circular cylinder in shear flow. This study shows that the Strouhal number exhibits no significant variation with shear parameter. The stagnation point moves to the high-velocity side almost linearly with shear parameter, and this result mainly influences the aerodynamic forces acting on a circular cylinder in shear flow. Both the Reynolds number and shear parameter influence the movement of the stagnation point and separation point. Mode A wake instability is suppressed into parallel vortex shedding mode at a certain shear parameter. The lift force increases with increasing shear parameter and acts from the high-velocity side to the low-velocity side. In addition, a simple method to estimate the lift force coefficient in shear flow is provided.     

Force coefficients and Strouhal numbers of three circular cylinders subjected to a cross-flow

In this paper, wind tunnel experiments were conducted to measure the mean force coefficients and Strouhal numbers for three circular cylinders of equal diameters in an equilateral-triangular arrangement when subjected to a cross-flow. These experiments were carried out at five subcritical Reynolds numbers ranging from 1.26 × 10⁴ to 6.08 × 10⁴. The pressure distributions on the surface of the cylinders were measured using pressure transducers. Furthermore, the hot-wire anemometer was employed to measure the vortex shedding frequencies behind each cylinder. Six spacing ratios (l/d) varying from 1.5 to 4 were investigated. It is observed that for l/d > 2, the upstream cylinder experiences a lower mean drag coefficient compared with the downstream cylinders. The minimum values of the drag coefficient for the downstream cylinders occur at l/d = 1.5 and l/d = 2, because there is no vortex shedding from the foregoing cylinders. Also, the value of the pressure coefficient behind the upstream cylinder reduces by increasing l/d. Moreover, by decreasing the value of l/d, the Strouhal number for the upstream cylinder increases. It can be concluded that the flow pattern and aerodynamic coefficients are basically dependent on l/d; in other words, decreasing l/d results in an increase in the effects of the flow interference between the cylinders.     

Forced‐convection heat transfer from tandem square cylinders in cross flow at low Reynolds numbers

This paper presents the results of a numerical study on the flow characteristics and heat transfer over two equal square cylinders in a tandem arrangement. Spacing between the cylinders is five widths of the cylinder and the Reynolds number ranges from 1 to 200, Pr=0.71. Both steady and unsteady incompressible laminar flow in the 2D regime are performed with a finite volume code based on the SIMPLEC algorithm and non‐staggered grid. A study of the effects of spatial resolution and blockage on the results is provided. In this study, the instantaneous and mean streamlines, vorticity and isotherm patterns for different Reynolds numbers are presented and discussed. In addition, the global quantities such as pressure and viscous drag coefficients, RMS lift and drag coefficients, recirculation length, Strouhal number and Nusselt number are determined and discussed for various Reynolds numbers. Copyright © 2008 John Wiley & Sons, Ltd.     

Flow around four cylinders arranged in a square configuration

This paper presents an experimental study of the flow around four circular cylinders arranged in a square configuration. The Reynolds number was fixed at Re=8000, the pitch-to-diameter ratio between adjacent cylinders was varied from P/D=2 to 5 and the incidence angle was changed from α=0° (in-line square configuration) to 45° (diamond configuration) at an interval of 7.5°. The flow field was measured using digital Particle Image Velocimetry (PIV) to examine the vortex shedding characteristics of the cylinders, together with direct measurement of fluid dynamic forces (lift and drag) on each cylinder using a piezoelectric load cell. Depending on the pitch ratio, the flow could be broadly classified as shielding regime (P/D≤2), shear layer reattachment regime (2.5≤P/D≤3.5) and vortex impinging regime (P/D≥4). However, this classification is valid only in the case that the cylinder array is arranged nearly in-line with the free stream (α≈0°), because the flow is also sensitive to α. As α increases from 0° to 45°, each cylinder experiences a transition of vortex shedding pattern from a one-frequency mode to a two-frequency mode. The flow interference among the cylinders is complicated, which could be non-synchronous, quasi-periodic or synchronized with a definite phase relationship with other cylinders depending on the combined value of α and P/D. The change in vortex pattern is also reflected by some integral parameters of the flow such as force coefficients, power spectra and Strouhal numbers.     

Influence of inlet shear on the 3-D flow past a square cylinder at moderate Reynolds number

Unsteady three-dimensional (3-D) numerical simulations of linear shear flow past a square cylinder at moderate Reynolds number (Re=200) are performed. The shear parameter (K) considered in this study is varied as 0.0, 0.1, and 0.2. For the uniform flow (K=0.0) case, the chosen Re falls in the transition Reynolds number range. The low frequency force pulsations of square cylinder transition phenomena are observed to decrease with increasing shear parameter. The evolution of streamwise vortical structures indicates a mode A spanwise instability in the uniform flow. Unlike in uniform flow, mixed mode A and mode B spanwise instability is observed in the case of a shear flow. The autocorrelation function of the lift and the drag coefficients is improved for any particular separation distance with increasing K.     

串列双锥柱绕流流动特性的大涡模拟研究

利用大涡模拟研究了雷诺数Re = 3900下串列双锥柱在间距比L/D_m = 2 ~ 10下的升阻力特性及三维流动结构. 研究发现: 上游锥柱在后方形成的两个展向不对称回流区, 使其后方压力分布不对称. 上游锥柱发展的上洗、下洗和侧面剪切层作用在下游锥柱的附着点位置不同是上游和下游锥柱时均阻力系数和脉动升力系数变化的主要原因, 串列双锥柱间流动结构随间距比变化可分为三种状态: 剪切层包裹状态, 过渡状态及尾流撞击状态. 剪切层包裹状态. 上游锥柱的自由端主导来流在下游锥柱迎风面影响范围广, 上游锥柱剪切层完全包裹住下游锥柱, 从而抑制下游锥柱后方回流区形成, 导致下游锥柱时均阻力系数降低; 尾流撞击状态; 上游锥柱尾流得到充分发展, 其回流区大小随间距比增大不再发生变化, 上游锥柱尾流出现周期性脱落, 撞击在下游锥柱表面, 从而使脉动升力系数大幅增加, 最大脉动升力系数较单直圆柱提升约20.7倍; 过渡状态, 此时时均阻力系数和脉动升力系数均会较剪切层包裹状态增加. 该研究可以为风力俘能结构群列阵布局提供理论支持.      

Fluid forces on a square cylinder in oscillating flows with non‐zero‐mean velocities

The unsteady forces on a square cylinder in sinusoidally oscillating flows with non‐zero‐mean velocities are investigated numerically by using a weakly compressible‐flow method with three‐dimensional large eddy simulations. The major parameters in the analysis are Keulegan–Carpenter number (KC) and the ratio between the amplitude and the mean velocities of the approaching flow (A_R). By varying the values of KC and A_R the resulting drag and lift of the cylinders are analyzed systematically at two selected approaching‐flow attack angles (0 and 22.5^°). In the case of the non‐zero attack angle, results show that both the drag and lift histories can be adequately described by Morison equations. However, Morison equations fail to correctly describing the lift history as the attack angle is zero. In addition, when the ratio of A_R/KC is near the Strouhal number of the bluff‐body flow, the resulting drag is promoted due to the occurrence of resonance. Based on the results of systematic analyses, finally, the mean and inertia force coefficients at the two selected attack angles are presented as functions of KC and A_R based on the Morison relationships. Copyright © 2008 John Wiley & Sons, Ltd.     

Identification of flow regimes around two staggered square cylinders by a numerical study

The flow over two square cylinders in staggered arrangement is simulated numerically at a fixed Reynolds number (\(Re =150\)) for different gap spacing between cylinders from 0.1 to 6 times a cylinder side to understand the flow structures. The non-inclined square cylinders are located on a line with a staggered angle of \(45^{\circ }\) to the oncoming velocity vector. All numerical simulations are carried out with a finite-volume code based on a collocated grid arrangement. The effects of vortex shedding on the various features of the flow field are numerically visualized using different flow contours such as \(\lambda _{2}\) criterion, vorticity, pressure and magnitudes of velocity to distinguish the distinctive flow patterns. By changing the gap spacing between cylinders, five different flow regimes are identified and classified as single body, periodic gap flow, aperiodic, modulated periodic and synchronized vortex shedding regimes. This study revealed that the observed multiple frequencies in global forces of the downstream cylinder in the modulated periodic regime are more properly associated with differences in vortex shedding frequencies of individual cylinders than individual shear layers reported in some previous works; particularly, both shear layers from the downstream cylinder often shed vortices at the same multiple frequencies. The maximum Strouhal number for the upstream cylinder is also identified at \({G}^{*}=1\) for aperiodic flow pattern. Furthermore, for most cases studied, the downstream cylinder experiences larger drag force than the upstream cylinder.     

圆角化对方柱气动性能影响的流场机理

方形截面柱体的圆角化处理是常用的流动控制方法,但其流场作用机理尚未被澄清.采用大涡模拟方法,在雷诺数为2.2$\times$10$^{4}$时,考虑风攻角的影响,对均匀流作用下的标准方柱和圆角方柱的气动性能和流场特性进行了研究,定量分析了圆角化气动措施和风攻角变化对分离泡特性的影响规律,从流场角度澄清了圆角化气动措施对方柱气动性能的影响机理.研究表明:与标准方柱相比,圆角方柱的表面风压、气动力和涡脱强度呈整体下降的趋势,但圆角方柱的斯特劳哈尔数更高;圆角方柱的"分离泡流态'发生在更小的风攻角范围内,分离泡的出现会进一步造成方柱的尾流变窄,涡脱强度减弱;随着风攻角的增大,分离泡的长度会逐渐减小直至消失,分离泡的中心会逐渐向方柱前角(迎风向)和方柱壁面移动;与标准方柱相比,圆角方柱的气流发生初次分离的位置向下游移动,分离后的剪切层更贴近方柱,因而更易发生再附现象;方柱尾流宽度的减小和涡脱强度的减弱是导致圆角方柱气动力减小和斯特劳哈尔数增大的主要原因.      

Numerical simulation with a TVD–FVM method for circular cylinder wake control by a fairing

A water drop-shaped fairing is applied to control the wake behind a circular cylinder and to suppress the formation of Karman vortex street in this paper. The results are evaluated using high resolution CFD technique. A finite-volume total variation diminishing (TVD) approach based upon the recently proposed elemental velocity vector transformation (EVVT) method, which aims at solving the incompressible turbulent flow for irregular boundary conditions with renormalization group (RNG) turbulence model, is used to simulate the flow field around circular cylinder systems. The calculations are carried out with cylinder systems with and without fairings, while the fairings have different top shape angles within the range of $30°~90°$. The Reynolds number ranges from 1000 to 50 000. It is shown that the simulation results of present numerical method reaches good agreement with the available experimental and numerical simulation data of typical circular cylinder flow and a fixed fairing cylinder system flow. Compared with bare cylinder, the faired bluff structures can obviously reduce the lift and drag forces and alter the vortex shedding frequency. Overall, the mean drag coefficient can be reduced up to about (10–31)% and the RMS lift coefficient can be reduced up to (30–99)% for all faired systems at given Reynolds numbers. The influence of Reynolds number and attack angles on the flow field characters of bare cylinder and faired cylinders is also discussed. The faired structures with shape angles within $30°~45°$under zero-attack-angle-inflow case are considered as the optimal structures, with which the mean drag coefficient and the RMS lift coefficient can be reduced up to (26–31)% and (98–99)%, respectively. Considering the influence of attack angles on lift and drag coefficients reduction, 75° shaped faired structure may be taken as a proper option.     

The effect of a wake-mounted splitter plate on the flow around a surface-mounted finite-height circular cylinder

The influence of a wake-mounted splitter plate on the flow around a surface-mounted circular cylinder of finite height was investigated experimentally using a low-speed wind tunnel. The experiments were conducted at a Reynolds number of Re=7.4×10⁴ for cylinder aspect ratios of AR=9, 7, 5 and 3. The thickness of the boundary layer on the ground plane relative to the cylinder diameter was δ/D=1.5. The splitter plates were mounted on the wake centreline with negligible gap between the base of the cylinder and the leading edge of the plate. The lengths of the splitter plates, relative to the cylinder diameter, ranged from L/D=1 to 7, and the plate height was always equal to the cylinder height. Measurements of the mean drag force coefficient were obtained with a force balance, and measurements of the vortex shedding frequency were obtained with a single-component hot-wire probe situated in the wake of the cylinder–plate combination. Compared to the well-studied case involving an infinite circular cylinder, the splitter plate was found to be a less effective drag-reduction device for finite circular cylinders. Significant reduction in the mean drag coefficient was realized only for the finite circular cylinder of AR=9 with intermediate-length splitter plates of L/D=1–3. The mean drag coefficients of the other cylinders were almost unchanged. In terms of its effect on vortex shedding, a splitter plate of sufficient length was able to suppress Kármán vortex shedding for all of the finite circular cylinders tested. For AR=9, vortex shedding suppression occurred for L/D≥5, which is similar to the case of the infinite circular cylinder. For the smaller-aspect-ratio cylinders, however, the splitter plate was more effective than what occurs for the infinite circular cylinder: for AR=3, vortex shedding suppression occurred for all of the splitter plates tested (L/D≥1); for AR=5 and 7, vortex shedding suppression occurred for L/D≥1.5.     

Flow about yawed,stranded cables

The development of a steady lift force on a stranded cable, which is yawed with respect to a flow, is a unique characteristic of a cable when compared to a circular cylinder. Comparisons of lift and normal drag coefficients and wake characteristics were made between stranded cable models and the cylinder. These were based upon surface pressure and hot-wire measurements and flow visualization studies conducted in a low speed wind tunnel on rigid cables and cylinders. The models were yawed to four different yaw angles and tested within the Reynolds number range of 5,000 and 50,000. Pressure profiles for the yawed cables indicated that the lift force is directed towards the side where the primary strands are more nearly aligned with the flow. The pressure profiles also indicated that the lift force is generated by asymmetric separation. The small scale irregularities associated with wires within individual strands also appeared to have an effect on the cable's lift and drag characteristics. Results show that cables have significantly different shedding characteristics and near-wake shear layer structure when compared to the circular cylinder. For the flow regime tested, the Strouhal number showed no dependence on Reynolds number nor spanwise position along the cable.List of symbols C _dn normal drag coefficient - C _l lift coefficient - C _p pressure coefficient - D actual diameter, based on circumscribing circle for the cable - f _v shedding frequency - L/D length to actual diameter ratio - ppd peak-to-peak distance, unit span - Re Reynolds number based on actual diameter - S Strouhal number, - V free stream velocity - cable angle - azimuthal angle