Effects of a small airfoil-shaped splitter plate on vortex shedding from a square prism at subsonic Mach numbers

Summary The present study is concerned with effects of a small airfoil-shaped splitter plate (NACA 0018, chord lengthc=20 cm) on the vortex shedding from a single square prism (side lengthD=20 mm) at free-stream Mach numbers between 0.15 and 0.91 and a constant spacing ratioL/D=2.0, whereL is the central distance between the square prism and airfoil arranged in tandem.It is found that while there exist no shock waves in the flow the vortex shedding from a single square prism is retarded by the small airfoil due to the interaction with the upper and lower separating shear layers: The Strouhal number for the square prism and airfoil being arranged in tandem, is almost independent of the Mach number and takes about 0.11. This is smaller than the value of 0.13 known for a single square prism. However, as soon as shock waves appear in the flow, the Strouhal number increases suddenly and then increases with increasing the Mach number. It is inferred that the sudden increase of the Strouhal number is primarily caused by shock waves appearing above and below the vortex formation region, for the shock waves make the vortex formation region small and symmetrical with respect to the common axis of the square prism and airfoil. That means, the small airfoil causes only a secondary effect on the vortex shedding from a single square prism under the presence of shock waves in the flow.     

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     

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.     

串列双方柱干扰效应流动机理研究

为了研究建筑群体周围的流场结构,减小工程设计中由于干扰效应造成的损失,利用粒子图像测速(PIV)结合数值模拟,研究在较大雷诺数及不同间隙工况下,双方柱流场受干扰时的流动特性及流场空间结构。分析升阻力系数、涡脱频率、斯特劳哈尔数等流场特征参数,探究不同间隙对串列双方柱的影响。当Re=3.42×104时,存在临界间隙比G=4使串列双方柱流场结构发生突变,试验观察到流场中出现双稳态现象;当G<4时,下风向方柱平均阻力系数为负值,小于单方柱情况下的阻力,屏蔽效应明显,上风向方柱后方涡脱落被抑制,平均阻力系数出现了明显的降幅,最大降幅约达10%;当G>4时,上下方柱均有涡旋脱落。该结果对于工程应用具有参考意义。     

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.     

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.     

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.     

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。     

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.     

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.     

Inviscid transonic flow field analysis

This paper describes a method for analysing inviscid transonic flow. This method is based on the fact that the angle made by the streamline of the transonic flow and of the corresponding incompressible flow is usually small. By using curvilinear coordinates, the differential equation of the stream function of an inviscid compressible flow is simplified and a general solution of the equation obtained. As examples of the method, transonic solutions are given for flow through twodimensional and axisymmetric Laval nozzles of different throat wall radii together with sonic lines and iso-Mach lines. To determine the discharge coefficients of Laval nozzles, an integral relation is developed. The general behaviour of the transonic flow in the throat region is presented, and the effect of the mass discharge on the Mach number distribution in the nozzle analysed. The effects of the ratio of the specific heats on the characteristics of the flow in the throat region are discussed. For transonic flow around a circular cylinder and a sphere, sonic lines and iso-Mach lines are presented for free-stream Mach number varying from the subcritical to the supercritical, including a free-stream Mach number of one. Part of the results obtained are compared with those available in current literature. For the two-dimensional hyperbolic Laval nozzles, the iso-Mach lines are compared with those given by Cherry (1959) and Serra (1972). For, axisymmetric Laval nozzles, the discharge coefficient and the Mach number at the throatsection for various throat wall radii are compared with those given by Sauer (1944), Hall (1962), Kliegel & Levine (1969), and Klopfer & Holt (1975). The theoretical discharge coefficients are compared with the experimental results by Backet al (1975), Durham (1955), Norton & Shelton (1969) etc. For the transonic flow around a circular cylinder, the iso-Mach lines are compared with Cherry’s exact solution for the quasi-circular cylinder for.M∞ equal to 0.51. The. Mach number distributions on the surface of the circular cylinder are compared with those given by Imai (1941) forM∞ equal to 0.4, by Cherry (1947) forM∞ equal to 0.51, by Dorodnicyn (1956) forM∞ equal to 1, and by Hafez, South & Murman (1979) forM∞ equal to 0.51. The present method has a much wider scope of application, requires simpler computation and gives results with good accuracy. It is being used to analyse supercritical wings and cascades, and we expect to extend its application to the field of transonic unsteady flow.     

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。     

Finite element computation of unsteady viscous transonic flows past stationary airfoils

Results are presented for computations of unsteady viscous transonic flows past a stationary NACA0012 airfoil at various angles of attack. The Reynolds number, based on the chord-length of the airfoil, is 10,000 and the Mach number is 0.85. Stabilized finite-element formulations are employed to solve the compressible Navier-Stokes equations. The equation systems, resulting from the discretization, are solved iteratively by using the preconditioned GMRES technique. Time integration of the governing equations is carried out for large values of the non-dimensional time to understand the unsteady dynamics and long-term behavior of the flows. The results show interesting flow patterns and a complex interaction between the boundary/shear layers, shock/expansion waves and the lateral boundaries of the computational domain. For transonic flow past an airfoil at various angles of attack in a narrow channel/wind-tunnel one can observe solutions that are qualitatively different from each other. At low angles of attack an unsteady wake is observed. At moderate angles of attack the interaction between the shock system and the lateral walls becomes significant and the temporal activity in the wake decreases and eventually disappears. At high angles of attack a reflection shock is formed. Hysteresis is observed at an angle of attack 8^∘. For the flow in a domain with the lateral boundaries located far away, the unsteadiness in the flow increases with an increase in the angle of attack. Computations for a Mach 2, Re 106 flow past an airfoil at 10^∘ angle of attack compare well with numerical and experimental results from other researchers     

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.     

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.     

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.     

The formation of vortex shocks in a 3D subsonic flow behind a weak shock wave emerging from a channel

The structure of a 3D subsonic flow behind a diffracted shock wave was studied by experimental and numerical methods for the incident shock wave Mach numbers M ₀ close to unity. It is established that vortex shocks appear in the flow behind the diffracted shock wave even when M ₀ decreases to 1.04, which is much lower than the threshold Mach number obtained analytically for a 2D automodel case. The time interval from the outflow start to the local supersonic zone formation, as well as the experimentally measured time of appearance of the first vortex shock, increase with decreasing M ₀.     

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。     

微椭圆形截面斜拉索临界雷诺数区气动特性试验研究

为了研究微椭圆形截面斜拉索临界雷诺数区的气动特性,以标准圆形截面斜拉索模型和微椭圆形截面斜拉索模型为研究对象,开展了考虑截面变形和风攻角变化的风洞试验,得到了不同情况下雷诺数对模型气动力系数的影响规律,同时通过对升力时程和升力频谱分析,得到了临界雷诺数及附近区域的标准圆形截面和微椭圆形截面模型尾流旋涡脱落的变化。结果表明:微椭圆形截面模型在雷诺数亚临界区时,升力系数基本不受雷诺数的影响;在临界区时,升力系数随雷诺数逐渐增大;风攻角0°~50°时,微椭圆形截面模型升力系数最大值对应的雷诺数随风攻角同步增大;微椭圆形截面模型的升力时程在TrBL0向TrBL1阶段和TrBL1向TrBL2阶段过渡中会出现双稳态现象;微椭圆形截面变形会影响斜拉索尾流区旋涡脱落情况,进而影响不同雷诺数下的St数值变化。     

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.