Determining wake flow parameters for two counterphase synchronized von Kármán vortex streets from configuration stability analysis

The problem of determining the parameters of near wake flow past a pair of cylindrical bluff bodies from one-point spectra of the velocity pulsation is solved in the limit of an inviscid incompressible flow. For this purpose, the stability of wake configuration with respect to infinitesimal perturbations of the equilibrium localization of the vortices is analyzed within the framework of a flow model of two counterphase synchronized von Kármán vortex streets. A necessary condition for the flow stability is determined.     

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.     

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.     

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.     

Numerical study of bluff body flow structures

Our recent progress in numerical studies of bluff body flow structures and a new method for the numerical analysis of near wake flow field for high Reynolds number flow are introduced. The paper consists of three parts. In part one, the evolution of wake vortex structure and variation of forces on a flat plate in harmonic oscillatory flows and in in-line steady-harmonic combined flows are presented by an improved discrete vortex method, as the Keulegan-Carpenter number (KC) varies from 2 to 40 and ratios ofU _m toU ₀ are ofO(10⁻¹),O(1) andO(10), respectively. In part 2, a domain decomposition hybrid method, combining the finite-difference and vortex methods for numerical simulation of unsteady viscous separated flow around a bluff body, is introduced. By the new method, some high resolution numerical visualization on near wake evolution behind a circular cylinder at Re=10², 10³ and 3×10³ are shown. In part 3, the mechanism and the dynamic process for the three-dimensional evolution of the Kármán vortex and vortex filaments in braid regions as well as the early features of turbulent structure in the wake behind a circular cylinder are presented numerically by the vortex dynamics method. This study was supported by the National Natural Science Foundation of China and the Laboratory for Nonlinear Mechanics, Institute of Mechanics, Chinese Academy of Sciences, as well as by the National Basic Research project “Nonlinear Science”.     

叶栅内非定常不可压流动的数值模拟

基于SMAC(SimplifiedMarkerandCell)方法推导出直接求解二维非定常、不可压N-S方程的隐式数值方法。求解的基本方程是任意曲线坐标系中以逆变速度为变量的N-S方程和椭圆型的压力Poisson方程。采用该方法,对二维叶栅非定常分离流场进行了数值模拟,叶栅表面压力的计算结果与试验结果相比比较吻合,从而验证了这种方法的可靠性。同时对叶栅非定常流场的流场结构和流动机理做了初步的探讨。在均匀来流和定常边界条件下,叶栅内部流动表现出强烈的非定常性;在小冲角和高雷诺数时,叶栅尾部产生类似卡门涡街的周期性流动。     

双圆柱尾流致涡激振动的质量比效应及其机理

双圆柱尾流激振受多种因素影响,情况复杂,质量比m*(相同体积的圆柱与流体质量的比值)对双圆柱尾流激振的影响规律尚未澄清。采用数值模拟方法,在低雷诺数下(Re=100),研究了三种质量比(m*=2,10,20)对串列双圆柱尾流致涡激振动特性和尾流流场结构的影响规律,分析了下游圆柱的升力与位移的相位差,探讨了涡激升力与能量输入的内在联系。结果表明:质量比对串列圆柱尾流致涡激振动有重要影响。随着质量比的增大,横流向最大振幅减小,并发生在较小折减速度下,振动锁定区域范围变窄;质量比越小,升力与位移之间的相位差对下游圆柱振幅的影响越显著;在较小质量比时尾流出现“2S”、不规则和平行涡街模态,而在较大质量比时只有“2S”和平行涡街模态。     

Numerical analysis of the influence of rotary rear cylinders on a nonstationary wake behind an elongated body

The influence of rotary rear cylinders on a nonstationary wake behind a rounded-off plate is analyzed numerically based on the solution of nonstationary Navier-Stokes equations on multiblock computational grids by the finite-volume method. It is shown that the von Kármán vortex trail, which develops behind the body to the point of formation of a virtually steady jet flow, substantially weakens as the rotational velocity of the cylinders increases. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 73, No. 3, pp. 606–613, May–June, 2000.     

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.     

Instabilities of flows due to rotating disks: preface

There are many flows driven by the rotation of one, or more, disks, and this paper is concerned with the instabilities of such flows, and their laminar–turbulent transition. The original, and most studied, rotating-disk flow is the von Kármán swirling flow produced by an infinite rotating disk in an otherwise still fluid. This flow shares many stability characteristics with three-dimensional boundary layers of engineering interest over aerofoils; most notably, the cross-flow instability giving rise to stationary cross-flow vortices. Various basic flows produced by rotating disks, and their stability, are reviewed, and motivations for assembling this special issue dedicated to the instabilities of rotating-disk flows are presented. The papers appearing in this special issue are discussed and related to major research themes in the field, and to one-another.     

Numerical simulation of the separated fluid flows at large Reynolds numbers

The variety of flow regimes (steady separated, periodically separated-‘Karman vortex street’, unsteady turbulent) and their characteristic peculiarities (separation and reattachment points, secondary separation, boundary layer, instability of the shear mixing layer, etc.) require the construction of effective numerical methods, which will be able to simulate adequately the considered flows. MERANGE ? SMIF–a splitting method for physical factors of incompressible fluids¹-is used for calculations of the steady and unsteady fluid flows past a circular cylinder in a wide range of Reynolds numbers (10° < Re < lo6). The finite-difference scheme for this method is of second order accuracy in the space variables, has minimal numerical viscosity and is also monotonic. Use of the Navier-Stokes equations with the corresponding transformation of Cartesian co-ordinates allows the calculations to be made by one algorithm both in a boundary layer and out of it. The method allows calculations at Re = ∞ cc and simulation of d‘Alembert’s paradox. Some results on the classical problem of the flow around a circular cylinder for a wide range of Reynolds numbers are discussed. The crisis of the total drag coefficient and the sharp rise of the Strouhal number are simulated numerically (without any turbulence models) for the critical Reynolds numbers (Re ≈ 4 × 10⁵), and are in a good agreement with experimental data.     

Rotational flow in gravity current heads

The structure of gravity currents and plumes, in an unbounded ambient, on a slope of arbitrary angle is analysed. Inviscid, rotational flow solutions in a wedge are used to study the flow near the front of a current, and used to show that the Froude number is radical2 and the angle of the front to the slope is 60 degrees. This extends the result of von Kármán (1940) to arbitrary slope angles and large internal current velocities. The predictions of the theory are briefly compared with experiments and used to explain the large negative (relative to ambient) pressures involved in avalanches.     

Edge effects in flow around a plasma actuator

We have studied the structure of flow formed in the boundary layer at the lateral edge of the discharge zone of a dielectric barrier discharge plasma actuator. It is established that a region with nonzero component of tangential velocity exists near the plasma layer boundary. At some distance downstream of the actuator, a concentrated vortex is formed with the axis aligned with the flow direction. In the presence of two closely spaced boundaries of the plasma region, a pair of counter-rotating vortices is formed. Separate microdischarges in the plasma layer also appear to be a source of similar longitudinal vortices with smaller amplitude.

     

Existence of extra vortex and twin vortex of anomalous mode in Taylor vortex flow with a small aspect ratio

Summary This experimental work on Taylor vortex flow in a gap with a small aspect ratio is concerned with two extra vortices and a twin vortex system, each of which depends on an anomalous cell of the anomalous mode. Extra vortices are smaller than other vortices such as defined cells. At any Reynolds number and aspect ratio extra vortices can be found at the corner of the end plate and inner rotating cylinder and at the corner of the end plate and outer stationary cylinder. For a one-cell flow (anomalous one-cell mode) in a symmetric system, an outer extra vortex develops and grows to the same size as the main cell, only in an aspect ratio of less than one. A twin vortex is observed to form when two vortices are aligned in the direction of the radius. There are three flow fields on the end plate; two are extra vortex flows and the other is the main cell flow. The flow direction of the anomalous cell is from the inner cylinder to the outer one, at the end plate opposite of the flow direction of the normal cell.Nomenclature R ₁ Radius of inner cylinder (2R ₁=40.19±0.006 mm) - R ₂ Radius of outer cylinder (2R ₂=60.11±0.024 mm) - R _r Radius ratio (R ₁/R ₂=0.669) - d Clearance between cylinders (R ₂–R ₁=9.96±0.025 mm) - L Height of working fluid - Aspect ratio=L/d - Rotational angular speed - Kinematic viscosity - Re Reynolds number=R ₁ d/ Other nomenclature is defined as it appears     

A dual reciprocity boundary element approach for the problems of large deflection of thin elastic plates

 A new numerical method, which is based on the dual reciprocity boundary element method, is developed for the large deflection of thin elastic plates whose behaviour is governed by von Kármán equations. In the proposed method, the nonlinear and coupled parts of von Kármán equations are transformed to a set of boundary integrals, and only are the boundary discretized into elements. Therefore, a `pure' boundary element approach for the problems of large deflection of thin elastic plates can be achieved. On the other hand, benefiting from the present method, the plate stresses can be calculated directly without integral and singularity. Several examples are given to demonstrate the efficiency and accuracy of the present method. Received 11 October 1999     

串列双圆柱静止绕流的二维数值仿真分析

利用CFX软件建立二维流场模型,采用有限体积法针对串列双圆柱的静止绕流现象进行了数值模拟计算。首先计算了雷诺数Re=200,不同间距时上下游圆柱的斯托罗哈数,并与参考文献的计算结果进行了对比,证明了该文计算的可靠性。然后分析了不同间距时上下游圆柱的升力系数和阻力系数的变化特点,得出了Re=200时双圆柱绕流的临界间距在3.375D~3.5D之间。最后通过对不同间距下流场变化的研究得出:上下游圆柱的间距小于临界间距时,上游圆柱不存在旋涡脱落;超过临界间距时,上游圆柱出现旋涡脱落;下游圆柱始终存在旋涡脱落现象。研究成果能够为计算流体力学和空气动力学技术的发展提供理论基础。     

On unsteady airfoil-vortex interaction

Summary An experimental investigation on unsteady airfoil-vortex interaction has been done. The incident vortex, to interact with a downstream airfoil (NACA 0018, chord lengthc=20 mm), is generated by a square cylinder (side lengthD=20 mm). The square cylinder and airfoil are arranged in tandem and the spacing ratioL/D of the central distance to the side length is set a constant value of 4.625. The free stream Mach numbers are varied between 0.153 and 0.750, whereas the free stream Reynolds numbers (based on the side lengthD) are varied between 0.713×10⁵ and 3.44×10⁵.It is found that as the incident vortex approaches the airfoil, the circulation and scale are decreased until it arrives at a position near the leading edge of the airfoil. During this stage, some circulation of the incident vortex is transferred to the secondary vortex generated on the airfoil opposite to the surface that the incident vortex approaches. Thus, circulation and scale of the secondary vortex are increased. However, after the incident vortex goes further downstream, no circulation of the incident vortex is transferred to the secondary vortex effectively. As the result, both of the incident vortex and secondary vortex decay due to the viscous dissipation through the interaction with the boundary layer of the airfoil. The locus of the incident vortex is deviated in such a way that it goes away from the airfoil. The streamwise position of the secondary vortex is adjusted by the incident vortex, orvice versa, so as to meet each other just behind the trailing edge of the airfoil.With 8 Figures     

Numerical Simulation of Unsteady-State Heat Transfer under Conditions of Laminar Transverse Flow past a Circular Cylinder

Two-dimensional Navier-Stokes and energy equations are used to perform a numerical calculation of the parameters of unsteady-state flow and heat transfer under conditions of laminar transverse flow of a viscous incompressible fluid past a circular cylinder and at Re = 140. The process of formation of Karman vortex street is treated, as well as the cyclic heating of the near and far wakes behind the heated cylinder. Special attention is given to analysis of the behavior of the integral characteristics of flow and heat transfer, and the distributions of pressure, friction and heat-transfer coefficients on the cylinder surface, as well as to correlations of the parameters of flow and temperature at selected points in the vicinity of the cylinder. Evaluation is made of the effect of the factor of unsteadiness on the increment of power and heat loads in the process of flow past the cylinder.