Vortex shedding suppression for laminar flow past a square cylinder near a plane wall: a two-dimensional analysis

Summary A numerical study on the uniform shear flow past a long cylinder of square cross-section placed parallel to a plane wall has been made. The cylinder is considered to be within the boundary layer of the wall. The maximum gap between the plane wall to the cylinder is taken to be 0.25 times the cylinder height. We investigated the flow when the regular vortex shedding from the cylinder is suppressed. The governing unsteady Navier-Stokes equations are discretized through the finite volume method on staggered grid system. A pressure correction based iterative algorithm, SIMPLER, has been used to compute the discretised equations iteratively. We found that the critical value of the gap height for which vortex shedding is suppressed depends on the Reynolds number, which is based on the height of the cylinder and the incident stream at the surface of the cylinder. At high Reynolds number (Re ≥ 500) however, a single row of negative vortices occurs for wall to cylinder gap height L ≥ 0.2. The shear layer that emerges from the bottom face of the cylinder reattaches to the cylinder itself at this gap hight.     

Dependence of flow characteristics of rectangular cylinders near a wall on the incident velocity

Numerically simulated results are presented for a family of rectangular cylinders with aspect ratios r ₁ (=b/a with height a and width b) ranging from 0.1 to 1.0 (square cylinder) to gain a better insight into the dependency of the aerodynamic characteristics on the operational dimensionless parameters, namely Reynolds number Re and aspect ratio r ₁. This work describes the flow from a long cylinder of rectangular cross-section placed parallel to a wall and subjected to a uniform shear flow. The flow is investigated in the laminar Reynolds number range (based on the incident stream at the cylinder upstream face and the height of the cylinder) at cylinder to wall gap height 0.5 times the cylinder height. The governing unsteady Navier?CStokes equations are solved numerically through a finite volume method on a staggered grid system using QUICK scheme for convective terms. The resulting equations are then solved by an implicit, time-marching, pressure correction-based SIMPLE algorithm for Reynolds number up to 1,000. The critical Reynolds numbers at which vortex shedding from the cylinder is started are specified for both the cases: far from the wall and near to the wall. It is reported that the vortex shedding from the rectangular cylinder of lower aspect ratio r ₁ (???0.25) becomes regular and insensitive to the Reynolds number, while the aerodynamic characteristics of the rectangular cylinders with higher aspect ratio r ₁ (???0.5) are strongly dependent on the Reynolds number.     

Temporal simulation of the wake behind a circular cylinder in the neighborhood of the critical Reynolds number

Summary The two-dimensional flow past a circular cylinder is simulated numerically using a time-dependent finite difference Galerkin method. The temporal evolution of disturbances in the wake of a circular cylinder is examined for the supercritical Reynolds numbers of 55 and 80. After the symmetry condition is relaxed, antisymmetric disturbances emerge in the wake at a pure frequency and at a well-defined exponential growth rate. The predicted critical Reynolds number of 42 is in reasonable agreement with the experimentally determined value of 46. An important aspect of this work examines the stabilizing influence a second smaller cylinder has on the formation of vortex shedding behind the main cylinder. The placement of this second cylinder is shown to completely suppress vortex shedding at a Reynolds number of 55.     

矩形柱二维尾流的稳定性研究

采用实验和数值模拟两种方法对长宽比为3∶1的矩形柱尾流进行了稳定性研究.实验发现当雷诺数接近临界值时,未加扰动的矩形柱尾流呈二维定常状态.当在柱体上游一定位置和下游靠近柱体的位置上沿垂直于来流方向施加一个宽度很小的短时脉冲射流扰动以后,扰动随时间放大,并出现旋涡脱落现象,并且这种扰动激发的旋涡脱落可以持续很长时间,不会衰减.而在下游较远处施加同样的扰动时,扰动将会衰减,不能激发出持续的旋涡脱落.数值模拟再现了上述实验结果,并且表明,当扰动强度(脉冲射流出口速度)较小时,不会出现持续的规则旋涡脱落,只有当扰动强度达到一定阈值时,旋涡脱落才能被激发.     

Effects of an airfoil and shock waves on vortex shedding process behind a square cylinder

Summary Effects of an airfoil and shock waves on vortex shedding process behind a square cylinder have been examined experimentally at a Mach number of about 0.91 and at a Reynolds number (based on the side lengthD of the square cylinder) of about 4.2×10⁵. The main experimental parameter is the spacing ratioL/D, and is varied from 1.125 to 5.5, whereL is the spacing between the square cylinder and the airfoil.It is found that similarly to the case at subcritical Mach numbers at the supercritical Mach number there exist three patterns of the flow around the square cylinder and airfoil arranged in tandem depending upon the spacing ratioL/D: In the first flow pattern with small spacing ratio, the downstream airfoil is enclosed completely in the vortex formation region of the square cylinder. In the second flow pattern, the shear layers separating from the square cylinder reattach to the airfoil. In the third flow pattern with large spacing the shear layers roll up upstream of the airfoil. The Strouhal number at the supercritical Mach number is higher than that at the subcritical Mach numbers. Shock waves hasten the vortex shedding behind the square cylinder by decreasing the area of asymmetrical part of the vortex formation region with respect to the wake axis, and let the streamwise length of the separating shear layers longer than otherwise.With 8 Figures     

Computational study of unsteady viscous flow around a transversely and longitudinally oscillating circular cylinder in a uniform flow at high reynolls numbers

A finite difference simulation method for the time dependent viscous incompressible flow around a transversely and longitudinally oscillating circular cylinder at Reynolds numbers of Re=4×10³ and 4×10⁴ is presented. The Navier-Stokes equations in finite difference form are solved on a moving grid system, based on a time dependent coordinate transformation. Solution of the vortex street development behind the cylinder is obtained when the cylinder remains stationary and also when it is oscillating. Time eholution of the flow configuration is studied by means of stream lines, pressure contours and vorticity contours. The computer results predict the lock-in phenomenon which occurs when the oscillation frequency is close to the vortex shedding frequency in the transverse mode or around double the vortex shedding frequency in the longitudinal mode. The time dependent lift and drag coefficients are obtained by the integration of the pressure and shear forces around the body. The drag, lift and the displacement relations are also discussed.     

Sand accumulation on a wall in flows around a near-wall circular cylinder

Summary The sand accumulation on a flat plate in flows around a near-wall circular cylinder has been mainly investigated by the method of numerical simulation at the sub-critical Reynolds number1200 (based on the diameter of the circular cylinder) and the gap ratio G/D (ratio of the gap between the circular cylinder and the plane wall to the diameter of the circular cylinder) 1.0, 0.5 and 0.25. The standard k− ε turbulent model and the vorticity-stream function formulation are adopted to analyze the wake characteristics. The lift and drag coefficients of the circular cylinder and the pressure pulsation on the wall are solved. The simulation of streak-lines for the flow visualization and PIV experiments are detailed carried out to analyze the sand accumulation phenomenon on the plane wall, and a possible mechanism has been proposed. Results of the numerical simulation indicate that the effect of the cylinder results in flow separation from the plane wall. Separations occur about 1 to 2 cylinder diameters behind the cylinder, where the particles in the flow near the plane wall accumulate gradually.     

圆柱绕流的流场特性及涡脱落规律研究

采用粒子图像测速技术对630、800及950三种雷诺数条件下的圆柱绕流场进行了实验,给出了圆柱下游沿流动方向4倍圆柱直径和垂直方向3倍圆柱直径区域内的速度场、涡量场以及涡脱落现象的时空演化规律.结果表明:圆柱尾流区域位于垂直方向约1.5~2.5倍圆柱直径范围内,随着雷诺数增大,这一范围呈现缩小趋势,而主流对涡的拉伸和输运能力有所增强;涡脱落频率随雷诺数增大而增大,小雷诺数时能够较为完整地捕捉到涡生成、脱落、发展和耗散过程,由于PIV采集频率的限制,大雷诺数条件下涡脱落整个过程不易被完整捕捉到.     

A comparative study on effect of plain- and wavy-wall confinement on wake characteristics of flow past circular cylinder

A first attempt is made for identifying the wake characteristics of circular cylinder confined by a wavy wall at laminar flow regime. Numerical study of flow characteristics past circular cylinder with wavy-wall confinement perpendicular to cylinder axis has been carried out in the range of Reynolds number 20–100. The finite volume-based CFD solver Ansys Fluent (Version 15.0) is used for computations. The results are presented in the form of streamline plots, mean drag co-efficient, flow separation angle and recirculation length. Wavy-wall confinement leads to highly significant changes in the cylinder wake such as the evolution of strong x-plane vortices, enhanced fluid mixing, wake suppression near the crest region and vortex stretching near the trough region on the downstream of the cylinder has been observed. Flow separation angle varies significantly along the axis of the cylinder. Increased wall shear stress on rear surface of the cylinder has also been observed. The part of vorticity magnitude as compared to strain rate has been distinguished and identified using vortex identification methods such as Q-criterion and Lambda-2 criterion.     

Experimental study on the particle accumulation phenomenon in seeded flows around a near-bottom-wall horizontal cylinder

In experiments of flows around a cylinder in a water channel, an interesting phenomenon is that a particle accumulation line obviously forms on the bottom of the channel. The present paper focuses on this phenomenon, and the formation mechanism of the particle accumulation line is in detail investigated experimentally with particle image velocimetry (PIV). The circular cylinder was set in a fully developed turbulent boundary layer with 12 gap ratios S/D ranging from 0 to 1.5 under two Reynolds numbers (1371 and 902) based on the momentum loss thickness. The possible mechanism of this phenomenon has been demonstrated with the experimental results: the separation takes place due to the interaction between the wake of the cylinder and the boundary layer of the plane wall, the gap flow separates from the wall downstream of the cylinder and causes an attachment vortex of low velocity area at about 1 to 2 cylinder diameters from the cylinder, where the particle accumulation line forms steadily.     

基于表面涡方法的单列圆柱流体诱导振动及流弹性不稳定研究

基于表面涡方法和流固耦合模型研究了Re=2.67×104时的单列圆柱流体诱导振动问题,计算了流体力、振动响应、涡脱落频率等,并给出了涡云图。计算模拟结果很好地重现了刚性单列圆柱在T/D=1.5(小间隙比)下以宽窄尾涡交替和多频为特征的非均匀流态,以及T/D=2.0的涡脱落现象。此外,该文还研究了单列弹性圆柱在T/D=1.5时的流体诱导振动以及流体弹性不稳定问题,计算了SG=1.29时圆柱列的无量纲临界速度。     

不同雷诺数下方柱绕流的数值模拟

在不同雷诺数条件下,对流体绕经方形柱体的流动进行了数值模拟,计算雷诺数分别为100,1×103,1×104和2.2×104.当Re=100时,直接采用N-S方程进行计算;当Re=1×103,1×104和2.2×104时,则引入k-ε湍流模型进行计算.应用Galerkin有限元法对控制方程进行离散和求解,利用分离时间步长法处理控制方程中的非线性项.模拟计算得出了在不同雷诺数下的卡门涡街脱落形态.方柱后尾涡的形态会随雷诺数的变化而产生一定的变化.当雷诺数较低时,尾涡会拖得比较长,随着雷诺数的增加,尾涡长度会随之缩短.计算得到了方柱的受力系数和Strouhal数.将计算结果与文献上的实验和计算结果进行了比较,两者吻合较好.     

Flow rate measurement in a pipe flow by vortex shedding

The flow rate measurement of liquid, steam, and gas is one of the most important areas of application for today’s field instrumentation. Vortex meters are used in numerous branches of industry to measure the volumetric flow by exploiting the unsteady vortex flow behind a blunt body. The classical Kármán vortex street behind a cylinder shows a decrease in Strouhal number with decreasing Reynolds number. Considering the flow behind a vortex shedding device in a pipe the Strouhal-Reynolds number dependence shows a different behaviour for turbulent flows: a decrease in Reynolds number leads to an increase in Strouhal number. This phenomenon was found in the experimental investigations as well as in the numerical results and has been confirmed theoretically by a stability analysis.     

Flow visualization studies of vortices

An actual vortex in the Kármán vortex street downstream of a circular cylinder has a core of finite dimension which increases downstream. The circulation of the vortex is nearly constant. The ratiob/a which is 0.281 according to the theory of Kármán, grows from 0.2 to 0.4 in the near wake. In the flow about a circular cylinder rotating in a uniform flow, a Kármán vortex street, Görtler-type vortices and Taylor vortices are generated at the same time. In the flow about a circular cylinder impulsively started with a constant velocity, the primary twin vortices behind the cylinder induce secondary twin vortices near the separation point. At the beginning of the motion, the separation does not occur even though a reverse flow is observed in the boundary layer. Mutual slip-through of a pair of vortex rings was achieved by increasing the Reynolds number. A vortex ring rebounds from a plane surface due to the separation of the flow on the surface induced by the vortex ring, and the secondary vortex ring is formed from the separated shear layer.     

Numerical Study on the Suppression of the Oscillating Wake of a Square Cylinder by a Traveling Wave Wall

Traveling waves generated on the side surfaces of a square cylinder are employed to suppress the oscillating wake for improving the flow behavior around a square cylinder; this method is termed the traveling wave wall (TWW) method. This study aimed to evaluate the influence of the key parameters of TWW on the control of aerodynamic forces and the oscillating wake of the flow around a square cylinder. Unsteady numerical analyses at a low Reynolds number (Re) of 100 were performed using a two-dimensional CFD simulation. First, the grid independence and time step independence tests of the simulation were conducted to verify the rationality of the solving parameter settings, and the validation of flow around the fixed square cylinder at Re =100 was carried out. Subsequently, the lift and drag coefficients and the vortex shedding modes under different combinations of three TWW control parameters, including wave velocity, wave amplitude, and wavenumber, were analyzed in detail. The results show that TWW can remarkably reduce the mean value of drag coefficient and the RMS value of the lift coefficient by more than 12% compared to the method involving a standard square cylinder. Two peaks occur in the lift coefficient spectrum, with the low frequency corresponding to the vortex shedding frequency in the wake of the flow around the square cylinder and the high frequency corresponding to the traveling wave frequency. The vorticity contours show that the alternating vortices in the wake of the square cylinder are not completely suppressed under the selected control parameters.     

自激振动圆柱体湍流场及发展变化的研究

采用雷诺平均法模拟低质量比弹性支撑的刚性圆柱体在均匀来流中的涡激振动问题,是近年来人们研究的热点。本文采用有限体积法结合SST k-ω湍流模型求解时间平均的纳维尔——斯托克斯方程(RANS),对低质量比弹性支撑的刚性圆柱体在均匀来流中横向振动的三个响应分支（初始分支、上端分支和下端分支）湍流场及其发展变化进行了研究,并与同等雷诺数下固定圆柱体的湍流场进行了对比。结果表明：三个响应分支的流体力系数、壁面压力系数、壁面切应力、流向平均速度、流向速度的脉动、横向速度的脉动、雷诺应力、湍流动能和涡量的分布均与固定圆柱体有明显差异。     

喷射方法对尾流旋涡脱落的抑制

采用数值模拟的方法研究了尾部喷射对波动来流绕圆柱流动旋涡脱落的抑制,进而研究圆柱尾流控制机理.研究流场的无量纲波频范围为0².8,来流波动的无量纲幅值为0.2,雷诺数=200.在圆柱尾部沿圆柱母线开宽度为0.04倍柱体直径的缝隙,从缝隙中射出流体对尾流进行抑制,寻找可有效抑制旋涡脱落的喷射速度范围,进而求出雷诺数=200,无量纲振幅为0.2时有效抑制范围.当喷射速度在一定范围内时,可有效抑制旋涡脱落,并且随着无量纲频率的增大,有效抑制范围逐步减小.     

小控制杆对矩形柱尾流旋涡脱落的抑制

采用小控制杆方法对主柱宽厚比B/H为2.0和3.0的两种矩形柱尾流的旋涡脱落进行了抑制实验.实验在风洞中进行,雷诺数(Re)范围为1.5×103至5.5×103,控制杆与矩形柱长度相同,两者相互平行放置.对三种不同宽度的控制杆进行了实验,小杆宽厚比分别为b/H=0.2,0.32和0.4.流动显示和热线测量结果表明:在柱体附近存在一个有效区,控制杆位于此区内时,柱体两侧的旋涡脱落被抑制.另外还存在一个单侧有效区,当控制杆位于该区内时,柱体一侧的旋涡脱落被抑制,而另一侧未被抑制,形成"单侧旋涡脱落现象".文中还研究了小杆宽厚比、矩形柱宽厚比和雷诺数对有效区和单侧有效区的影响,发现b/H增大时,有效区和单侧有效区不是扩大,而是有所缩小;当B/H增大时,有效区和单侧有效区扩大,而且有效区由一个变为两个;Re增大时,有效区和单侧有效区略有缩小.     

Suppression of the Karman vortex street and reduction in the frontal drag of a circular cylinder with two vortex cells

Numerical analysis of an unsteady-state two-dimensional incompressible flow at a Reynolds number of 40000 around a circular cylinder with two vortex cells is carried out on the basis of the finite-volume solution of the Reynolds equations closed by the Menter’s shear-stress transport model. The vortex cells are fitted with slots that ensure suction into the central channel via a fan located and through outflow of a low-pressure jet. It is shown that the suction in small-size cells intensifies the circulatory flow inside it and leads to the rearrangement of a large-scale structure of the flow around the cylinder accompanied by suppression of the Karman vortex street and a slightly symmetrical stabilization of the wake. The frontal drag of the cylinder decreases almost by three times with an optimal coefficient of the sucked air rate.