Shear flow past a square cylinder near a wall

A numerical study on the wake behind a square cylinder placed parallel to a wall has been made. The cylinder is considered to be within the boundary layer of the wall, so that the outside flow is taken to be due to uniform shear. Flow has been investigated in the laminar Reynolds number (based on the cylinder height) range. The interaction of wall boundary layer on the vortex shedding at Reynolds number up to 1400.0 has been investigated for cylinder to wall gap height 0.5 and 0.25 times the cylinder height. The gap flow between the cylinder and wall during a period of vortex shedding has been obtained. The governing unsteady Navier–Stokes equations are discretised through the finite volume method on staggered grid system. An algorithm SIMPLE has been used to compute the discretised equations iteratively. Our results show that at the gap height 0.5 times the cylinder height the vortex shedding occurs at a Strouhal number greater than for an isolated cylinder. Vortex shedding suppression occurs and wake becomes steady up to a certain value of Reynolds number at gap height 0.25 time the cylinder height. At higher Reynolds number the formation of a single row of negative vortices behind the cylinder when it is in close proximity to wall is noteworthy. Due to the shear, the drag experienced by the cylinder is found to decrease with the reduction of gap height.     

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.     

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.     

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     

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.     

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.     

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.     

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。     

倒角切角对方柱气动性能影响的大涡模拟研究

倒角和切角措施对方柱的气动力及流场影响很大,常作为方柱流动控制的手段,采用大涡模拟方法,以雷诺数22000的方柱为研究对象,考虑了角部措施(角部变化率10%)的影响,对均匀流场下标准方柱、倒角和切角方柱周围流场及气动性能进行了模拟研究。通过将标准方柱大涡模拟结果与相关文献的试验和数值模拟结果对比,验证了该方法及参数取值的有效性;研究分析了倒角和切角措施对方柱风压分布和气动力的影响,并着重从时均流场和瞬态流场角度分析了角部处理措施对方柱气动性能的影响机理。结果表明,倒角和切角措施对方柱表面风压分布和气动力均有一定影响,其中对方柱表面流动分离区的风压系数影响更为显著。采用角部处理措施后,方柱前缘角区的流动分离受到影响,分离剪切层扩散角更小,侧面的分离涡更贴近壁面,从而在方柱侧面形成再附,尾流变窄,旋涡脱落频率成分更为复杂,使得方柱的平均阻力系数更小,气动力脉动强度更弱,旋涡脱落频率更高、强度更弱。     

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.     

On the interaction of a vortex pair and a vortex ring with a flat shield

The approximate method of calculation of nonstationary flow in the interaction of a vortex pair and a vortex ring with a parallel and respectively perpendicular flat shield is presented. It is shown that these primary vortices induce transverse wall flow on the shield in the ideal-fluid approximation; in this flow, with allowance for the fluid’s viscosity, a boundary layer is generated which represents vortex flow with sign opposite to that of the primary vortices. Boundary-layer separations occur on the portion of the shield with a positive longitudinal pressure gradient. Secondary flows interact with the primary ones due to which the flow is rearranged; the transverse displacement of the initial vortex pair with a loop-shaped trajectory of its motion is observed in the plane problem, whereas the formation of ascending flow along the axis of the vortex ring is observed in the axisymmetric problem. The effect found in the latter case in laminar and turbulent regimes of flow is confirmed for the laminar regime by experiment and by the data of numerical simulation of Navier–Stokes and Reynolds equations.     

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.     

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.     

Numerical simulation of planar shear flow passing a rotating cylinder at low Reynolds numbers

Two-dimensional shear flow over a rotating circular cylinder is investigated using lattice Boltzmann method. Simulations are performed at a fixed blockage ratio (B = 0.1) while the Reynolds number, nondimensional shear rate (K) and absolute rotational speed range as 80 ≤ Re ≤ 180, 0 ≤ K ≤ 0.2 and −2 ≤ β ≤ 2, respectively. To verify the simulation, the results are compared to previous experimental and numerical data. Quantitative information about the flow variables such as drag and lift coefficients, pressure coefficient and vorticity distributions on the cylinders is highlighted. It is found that, generally, with the increment in |β|, the absolute value of time average lift coefficient increases and time average drag coefficient decreases, and beyond a certain magnitude of β, the vortex shedding vanishes. It is also revealed that the drag coefficient decreases as the Reynolds number increases while the effect of the Reynolds number on lift is almost negligible. At the end, correlations for drag and lift coefficients ([`(C<sub>D</sub> )] ,[`(C_L )]){(\overline {C_D } ,\overline {C_L })} are extracted from the numerical data.     

Vortex motion in the early stages of unsteady flow around a circular cylinder

In this paper, processes in the early stages of vortex motion and the development of flow structure behind an impulsively-started circular cylinder at high Reynolds number are investigated by combining the discrete vortex model with boundary layer theory, considering the separation of incoming flow boundary layer and rear shear layer in the recirculating flow region. The development of flow structure and vortex motion, particularly the formation and development of secondary vortex and a pair of secondary vortices and their effect on the flow field are calculated. The results clearly show that the flow structure and vortices motion went through a series of complicated processes before the symmetric main vortices change into asymmetric: development of main vortices induces secondary vortices; growth of the secondary vortices causes the main vortex sheets to break off and causes the symmetric main vortices to become “free” vortices, while a pair of secondary vortices is formed; then the vortex sheets, after breaking off, gradually extend downstream and the structure of a pair of secondary vortices becomes relaxed. These features of vortex motion look very much like the observed features in some available flow field visualizations. The action of the secondary vortices causes the main vortex sheets to break off and converts the main vortices into free vortices. This should be the immediate cause leading to the instability of the motion of the symmetric main vortices. The flow field structure such as the separation position of boundary layer and rear shear layer, the unsteady pressure distributions and the drag coefficient are calculated. Comparison with other results or experiments is also made. This work was presented at the First Asian Congress of Fluid Mechanics, Bangalore in December 1980.     

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.     

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.     

An unstructured finite volume projection method for pulsatile flows through an asymmetric stenosis

An unstructured finite volume method coupled with a fractional-step projection method is developed for the numerical solution of the incompressible Navier–Stokes equations. Based on the use of the proposed method, numerical investigations are performed for a pulsatile flow through a stenotic channel. The geometry of the stenotic segment is assumed to be asymmetric, which can mimic the deformations in the diseased arteries. The numerical results reveal that for the pulsatile flow, the Womersley and Reynolds numbers have a great influence on the vortex generation and the wall shear stress distributions. The size and number of vortices depend largely on the Womersley number but less on the Reynolds.     

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.     

Effect of the blockage ratio on the flow in a channel with a built-in square cylinder

The structures wakes behind a square cylinder in a laminar channel flow is conducted numerically. The Strouhal number, drag and lift coefficients were studied in a periodic flow for different blockage ratios =1/4, 1/6 and 1/8 at Reynolds number ranging from 62 to 300. The governing equations are solved by using control volume finite element method (CVFEM) adapted to the staggered grid. The SIMPLER algorithm is used for the velocity-pressure coupling. The critical Reynolds numbers corresponding to the onset of vortex shedding and its change from simple periodic to complex periodic motion are established. A discussion about the effect of the blockage ratio on the Strouhal number, the time-averaged drag coefficient and the amplitude of the lift coefficient is also presented.