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.     

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.     

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.     

Propulsive performance and vortex shedding of a foil in flapping flight

Summary. The propulsive performance and vortex shedding of an oscillating foil, which mimics biological locomotion, are investigated based on a computational fluid dynamics analysis. The objectives of this study are to investigate unsteady forces, in particular a thrust force, for the foil in pitching and plunging motion, and to deal with the relations of the propulsive performance with leading-edge vortex structure and vortex shedding in the near wake. The two-dimensional incompressible Navier–Stokes equations in the vorticity and stream-function formulation are solved by fourth-order essentially compact finite difference schemes for the space derivatives and a fourth-order Runge-Kutta scheme for the time advancement. To reveal the mechanism of the propulsive performance, the unsteady forces and the shedding of the leading- and trailing- edge vortices of the foil in the pitching and plunging motion are analyzed. Based on our calculated results, three types of the leading-edge vortex shedding, which have an effective influence on the vortex structures in the wake of the oscillating foil, are identified. The effects of some typical factors, such as the frequency and amplitude of the oscillation, the phase difference between the pitching and plunging motions, and the thickness ratio of the foil, on the vortex shedding and the unsteady forces are discussed.     

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.     

海底管道悬跨段流致振动实验研究及涡激力模型修正

对输送液体的模型管道进行了涡激振动试验研究,试验结果表明:当理论涡脱频率与管道的固有频率不一致时,作用在振荡管道上的涡激力并非简谐扰力,而是具有一定带宽的窄带随机扰力。因此,管道的涡激振动响应也是一个随机过程。当理论涡脱频率与管道的固有频率接近时,管道的涡激振动响应逼近简谐振动。试验结果也表明:作用在振荡圆柱体上的涡激力频率不仅是流速和圆柱体直径的函数,也是圆柱体固有频率的函数。     

A numerical simulation of the flow development behind a circular cylinder started from rest and a criterion for investigating unsteady separating flows

Summary The numerical solution of the Navier-Stokes equations for an unsteady compressible flow is employed to follow the development of periodic vortex shedding behind a circular cylinder starded from rest. The periodic vortex shedding is found to be a direct consequence of the interaction between the upper and lower primary vortices behind the cylinder, while the topological instability of the full saddle-point joining the vortices and the outer flow can be seen to play a predominant role in the process. A criterion based upon the rate of distortion of fluid elements and derived from the previous Lagrangian analysis of boundary-layer separation has been applied to the present study of unsteady separating flow and is found to be instrumental in revealing critical regions and surfaces in the flow where the fluid elements are extremely deformed.With 12 FiguresAt DFVLR-Institute for Theoretical Fluid Mechanics on Alexander-von-Humboldt Senior-Scientist Award.At DFVLR-Institute for Theoretical Fluid Mechanics on leave from Beijing Institute of Aeronautics and Astronautics.     

A fish perspective: detecting flow features while moving using an artificial lateral line in steady and unsteady flow

For underwater vehicles to successfully detect and navigate turbulent flows, sensing the fluid interactions that occur is required. Fish possess a unique sensory organ called the lateral line. Sensory units called neuromasts are distributed over their body, and provide fish with flow-related information. In this study, a three-dimensional fish-shaped head, instrumented with pressure sensors, was used to investigate the pressure signals for relevant hydrodynamic stimuli to an artificial lateral line system. Unsteady wakes were sensed with the objective to detect the edges of the hydrodynamic trail and then explore and characterize the periodicity of the vorticity. The investigated wakes (Kármán vortex streets) were formed behind a range of cylinder diameter sizes (2.5, 4.5 and 10 cm) and flow velocities (9.9, 19.6 and 26.1 cm s⁻¹). Results highlight that moving in the flow is advantageous to characterize the flow environment when compared with static analysis. The pressure difference from foremost to side sensors in the frontal plane provides us a useful measure of transition from steady to unsteady flow. The vortex shedding frequency (VSF) and its magnitude can be used to differentiate the source size and flow speed. Moreover, the distribution of the sensing array vertically as well as the laterally allows the Kármán vortex paired vortices to be detected in the pressure signal as twice the VSF.     

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.     

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.     

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.     

TIP4P potential for lid-driven cavity flow

Summary The TIP4P potential is used to predict the velocity profiles in the 3-D (about 100,000 molecules) liquid water lid-driven cavity flow. The vortices in the cavity are generated with the upper side wall moving with a constant speed and investigated by the leap-frog method in the field of molecular dynamics. Two kinds of problems are investigated in this paper to demonstrate the feature of the velocity profiles and traced the particle in the system, one is the cavity flow problem with square cavity and the other is with V-shape cavity. The realistic parameters of the water molecule are adopted in this research.In a very short time, from the velocity profiles it is evident that the vortices are driven by the moving top plate in all cases. And the turbulence-like phenomena are observed in the small triangular cavity when the calculating time is long enough. In addition, the vortex-like profiles in the triangular cavity are stronger and more obvious than the ones in the rectangular cavity. Therefore, the strength of vortex would be affected by the variation of the geometry. It emerges from that the dynamic transport properties like the thermal conductivity, diffusion coefficient and shear stress etc. would be varied by the variation of the geometry. Due to the application of results, the predicted phenomena can be applied on the nano-channel.     

Precessing Vortex Motion and Instability in a Rotating Column of Superfluid 3He-B

In a rotating circular cylinder of superfluid ³He-B, an evolving vortex expands longitudinally such that its end point describes a helically spiralling trajectory along the cylinder wall. The spiral motion is found to give rise to a periodically oscillating NMR signal, which is brought about by the modulation in the superfluid counterflow and its influence on the “flare-out” order parameter texture. The new NMR signal becomes observable within a narrow temperature interval close to the onset temperature of turbulence, when new vortices are continuously generated by the single-vortex instability at the cylindrical wall at a slow rate, ～1 vortex/s. We use numerical vortex filament calculations to examine the precessing motion of the evolving vortices, while they expand towards their stable state as rectilinear line vortices.     

A coupled BEM and arbitrary Lagrangian–Eulerian FEM model for the solution of two‐dimensional laminar flows in external flow fields

This paper describes a new computational model developed to solve two‐dimensional incompressible viscous flow problems in external flow fields. The model based on the Navier–Stokes equations in primitive variables is able to solve the infinite boundary value problems by extracting the boundary effects on a specified finite computational domain, using the pressure projection method. The external flow field is simulated using the boundary element method by solving a pressure Poisson equation that assumes the pressure as zero at the infinite boundary. The momentum equation of the flow motion is solved using the three‐step finite element method. The arbitrary Lagrangian–Eulerian method is incorporated into the model, to solve the moving boundary problems. The present model is applied to simulate various external flow problems like flow across circular cylinder, acceleration and deceleration of the circular cylinder moving in a still fluid and vibration of the circular cylinder induced by the vortex shedding. The simulation results are found to be very reasonable and satisfactory. Copyright © 2001 John Wiley & Sons, Ltd.     

Numerical solution of Stokes flow generated by vortices: part 2, inside an elliptical cylinder

In this second part paper, the two-dimensional flow inside an elliptical cylinder is studied in the presence of no-slip boundary conditions. For simplicity, line vortices are assumed to be parallel to the elliptical cylinder axis, all axes in the same plane. The interior boundary value problem is solved in terms of a stream function. Numerical solutions for the flow field are obtained by application of the boundary element method. The streamline patterns are sketched for a number of special cases where the elliptical cylinder is either stationary or rotating about its own axis. In particular, some interesting flow patterns are observed in the parameter space which may have potential significance in studies of various flows. We also investigate the change in streamline topologies as the parameters are varied. Eddies of various sizes and shapes appear depending on the primary vortices and their locations. The results presented may be relevant for a variety of applications including vortex mixing. The analytical closed-form expressions for the single vortex inside an elliptical cylinder and double vortices inside circular a cylinder are found.     

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.     

双矩形拱肋间的气动干扰效应研究

以某拱桥为例,通过数值模拟研究了串列双矩形拱肋的气动干扰效应,及其对两截面气动力系数的影响。在对计算模型进行验证的基础上,进一步研究了截面宽高比、间距比和来流风攻角对拱肋周围流场的影响,并结合压力云图和湍动能云图解释了气动力系数的变化规律,讨论了不同宽高比截面的漩涡脱落频率与结构自振频率之间的关系,分析了两拱肋升力时程的差异对整体扭矩可能产生的增大效应。结果表明：串列拱肋间的气动干扰效应显著。受上游截面尾流的影响,下游截面的阻力系数明显减小,其值与漩涡的形态、能量大小、移动轨迹等因素密切相关。上、下游截面的升力时程在幅值和相位上存在明显差异,导致拱肋整体的力矩增大,其效应随宽高比或间距比的增大而明显加强,随风攻角的增大而有所降低。漩涡脱落频率随宽高比的增大呈先增大后减小的趋势,而受间距比、风攻角的影响有限。对漩涡脱落频率与宽高比的变化进行多项式拟合,结合结构的模态频率可为拱肋的气动外形设计提供参考。     

行波壁抑制圆柱涡激振动的数值模拟研究

采用CFD数值模拟方法完成了圆柱绕流-涡激振动-行波壁流动控制全过程的数值模拟,重点研究行波壁流动控制方法对低雷诺数下两自由度弹性支撑单圆柱涡激振动的抑制作用。详细分析各阶段圆柱横向和流向位移、质心运动轨迹、升力和阻力系数等随频率比的变化。结果表明:行波壁圆柱的波谷处可以产生一系列稳定的随行波壁运动的小尺度旋涡,有效抑制圆柱表面分离涡的产生,达到消除圆柱绕流尾迹和抑制涡激振动的目的;在计算初始和中途启动的行波壁流动控制方法显著抑制了圆柱横向和流向振动、降低了圆柱升力系数脉动值和阻力系数均值,但阻力系数脉动值则明显增大。     

VORTEX SHEDDING FROM FIXED AND OSCILLATING RECTANGULAR PRISMS IN SHEAR FLOWS

ABSTRACT

The main focus of this paper is to study the results of experiments on six different rectangular prisms with varied side ratios, with and without forced oscillation, displaced in two shear free streams and one uniform flow. The setting of free stream shear parameters β=dU/dyxD/Uc are 0.024 and 0.032. With respect to vortex shedding phenomena, a comparison between shear flows and uniform flows is also part of the focus.

Experimental results indicate that disturbance on the two-dimensional vortex shedding of the uniform flow is caused by the longitudinal vortex of the shear flow gradient. As a result, a spanwise distribution of cells among the vortex shedding frequencies is created. Increases in the side ratios of the rectangular prisms can cause a shifting of cell boundaries toward the high-speed end. As shear parameters for the same prism increase, the cell boundaries move toward the low-speed end. During oscillation, differences arise between the vorticity structures of cells, and the vortices of each cell are more unified, with improvements in correlation.     

矩形断面抖振阻力空间分布特性试验研究

为了研究紊流作用下钝体抖振阻力的空间分布特性及流固相互作用机理,以2:1矩形断面为例,通过刚性模型测压试验研究了抖振阻力的跨向相关性及空间能量分布特性。结果表明,当紊流积分尺度与钝体特征尺寸相当时,抖振阻力的相关性高于纵向脉动风,这也许是由漩涡沿展向发生拉伸引起。而在分离点附近,来流漩涡会发生剧烈畸变,顺流向大尺度漩涡会破碎成小尺度漩涡,在此过程中能量由低频向高频的转移,并导致脉动压力的跨向相关性也会有所减弱。与迎风侧不同,背风侧脉动压力主要受钝体尾流中的紊流成分影响,其漩涡沿跨向拉伸程度可能要高于迎风侧,以致背风侧脉动压力的跨向相关性强于迎风侧。顺流向分离涡在由分离点向中部运动过程中,其高频的小尺度漩涡可能并没沿顺流向拉伸,而是直接耗散,从而导致脉动压力谱在低频保持不变,而在高频区下降。