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     

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.     

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.     

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.     

Steady magnetohydrodynamic flow past a circular cylinder

The steady two-dimensional, viscous, electrically conducting flow around a circular cylinder is investigated. The flow and magnetic field are uniform and parallel at large distances from the cylinder. The equations and boundary conditions are derived for arbitrary values of R, R_mand β, where R is the Reynolds number, R_m the magnetic Reynolds number and β, the ratio of the square of the Alfvén speed to the square of the main stream speed. Because of the large number of parameters involved, the numerical solution is restricted to R = 40, R_m = 1 and infinity and 0 ? β ? 4. Also the cylinder is taken to be a perfect conductor, this avoids having to compute the magnetic field within the cylinder. The numerical computations for the non-magnetic case, i.e. β = 0, are presented and are found to be in good agreement with existing results. The effect of increasing the strength of the magnetic field (i.e. increasing β) on the drag coefficient, the size and position of the standing vortex and the increasing effect of the upstream propagation of disturbances are examined.     

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.     

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.     

Angular momentum of the fields of a few-mode fiber: I. A perturbed optical vortex

This paper presents the results of studies of the physical nature of the electrodynamic angular momentum of a stable CV ₊₁ ⁺ vortex in a few-mode fiber. It shows that the angular momentum of a CV ₊₁ ⁺ vortex can be conventionally divided into orbital and spin angular momenta. The longitudinal component of the fundamental HE ₁₁ ⁺ mode on the axis of the fiber has a pure screw dislocation with a topological charge of e=+1. The longitudinal component of a CV ₊₁ ⁺ vortex also has a pure screw dislocation on the axis of the fiber with a topological charge of e=+2. Therefore, perturbation of a CV ₊₁ ⁺ vortex by the field of the fundamental HE ₁₁ ⁺ mode removes the degeneracy of the pure screw dislocations of the longitudinal and transverse components of the field and breaks down the structural stability of the CV ₊₁ ⁺ vortex. As a result, an additional azimuthal flux of energy with an angular momentum opposite to that of the fundamental flux is induced. An analogy is drawn between the stream lines of a perturbed CV vortex and the stream lines of an inviscid liquid flowing around a rotating cylinder. Studies of the evolution of a CV vortex in a parabolic fiber show that they are structurally stable when acted on by the perturbing field of the HE ₁₁ ⁺ mode. However, perturbing a CV ₊₁ ⁺ 1 vortex of a stepped fiber with the field of the HE ₁₁ ⁺ mode destroys the structural stability of the vortex. It is found that the propagation of a circularly polarized CV vortex can be represented as a helical wavefront screwing into the medium of the fiber. The propagation of a linearly polarized vortex in free space is characterized by the translational displacement (without rotation) of a helical wavefront. Pis’ma Zh. Tekh. Fiz. 23, 74–81 (November 12, 1997)     

Theoretical and numerical results of a deterministic two-dimensional vortex method

The first part of the paper reviews results obtained in earlier work: (1) The outline of the derivation of an integral equation of Fredholm type with respect to vorticity from the Navier-Stokes equations, and (2) the analytical results for two deterministic vortex methods which are based on the corespreading model. The aim of the second part is to confirm the results of the previous analysis and to estimate the accuracy of these methods numerically. In the present paper, the model problem of a transient flow past an impulsively started circular cylinder is studied by several numerical methods. The numerical results show that (1) the Gaussian core-spreading methods are comparable with the random walk vortex method, (2) the numerical fluctuation of the deterministic methods is small, and (3) the number of panels is smaller than those in the random walk vortex method to obtain the flow with almost the same accuracy. The theoretical results in § 2–4 of the present paper are summarized from “Core-spreading vortex methods in two-dimensional viscous flows”,Computer methods in applied mechanics and engineering (in press), by Kida and Nakajima, with permission from Elsevier Science, The Boulevard, Langford Lane, Kidlington 0X5 1GB, UK. The experimental picture is transferred from “The early stage of development of the wake behind an impulsively started cylinder for 40<Re<⁴”, by R Bouard and M Coutanceau,J. Fluid Mech. (1980) 101: 583–607.     

Modeling an increase in the lift and aerodynamic efficiency of a thick Göttingen airfoil with optimum arrangement

The Reynolds equations closed using the Menter shear-stress-transfer model modified with allowance for the curvature of flow line have been numerically solved jointly with the energy equation. The obtained solution has been used to calculate subsonic flow (at M = 0.05 and 5° angle of attack) past a thick (24% chord) Göttingen airfoil with variable arrangement of a small-sized (about 10% chord) circular vortex cell with fixed distributed suction Cq = 0.007 from the surface of a central body. It is established that the optimum arrangement of the vortex cell provides a twofold decrease in the bow drag coefficient Cx, a threefold increase in the lift coefficient Cy, and an about fivefold increase in the aerodynamic efficiency at Re = 10⁵ in comparison to the smooth airfoil.

     

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”.     

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.     

An experiment on a taylor vortex flow in a gap with a small aspect ratio bifurcation of flows in an asymmetric system

Summary Both Taylor vortex flows in a symmetric or asymmetric system exhibit various patterns (cell modes). They can be classified by the process of cell formation, the number of cells and the direction of flow for the cell, into primary modes or secondary modes, and normal modes or anomalous modes. Following the previous report in which flows in a symmetric end condition were classified, in the present work, for flows in an asymmetric end condition, the Reynolds number at which a secondary mode bifurcates into another mode is experimentally investigated, and the bifurcation of the Taylor vortex flows in an asymmetric system when the Reynolds number is gradually decreased is presented in a bifurcation diagram.List of symbols R1 Radius of inner cylinder (2R1=40.19±0.006 mm) - R2 Radius of outer cylinder (2R2=60.11±0.024 mm) - D Clearance between cylinders (R2-R1=9.96±0.025 mm) - L Height of working fluid - Aspect ratio=L/D - Rotational angular speed - Kinematic viscosity - Re Reynolds number=R1D/     

The impact of cylinder vortex stabilizer on fluctuating turbulence characteristics of a cyclone separator based on Large Eddy Simulation

The main purpose of present study is to comprehensively clarify the impact of cylinder vortex stabilizer on fluctuating turbulence structure of a Stairmand cyclone separator on basis of Large Eddy Simulation. The cylinder vortex stabilizer is easy and could be applied to any existing cyclone model without any major replacement. This novel modification in cyclone body is considered to alleviate the negative effect of entrainment of particles from the ash hopper and swing of the vortex end in swirling flow. The numerical simulations were conducted based on Stairmand cyclone separator and three new models with variation of vortex stabilizer length and diameter. The results showed that the cylinder vortex stabilizer could enhance flow instability and improve fluctuating turbulence structure to some extent. It is confirmed that cylinder vortex stabilizer could significantly reduce the tangential velocity in the inner quasi-forced vortex region of the cyclones. Comparing with Stairmand cyclone, the swirling first and second peak frequency of cyclone model with vortex stabilizer (Length L/D: 6.5, diameter d/D: 0.12) have been confirmed to get considerable reduction of 11.54% and 10.86%, respectively. This modified cyclone model is comparatively better for enhancement of flow stability, providing about 18.4% maximum reduction of normalized flow angle, 24.8% of rotational kinetic energy in dust collector and 14.2% in the main body of cyclone.     

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.     

Density functional calculations for the structure of vortices in superfluid4He

The structure of a rectilinear vortex in superfluid ⁴ He at zero temperature is studied using a Density Functional method. The superfluid circulation is included via the Feynman-Onsager approximation. The energy and the density profile of a vortex are predicted for several values of the external pressure. The instability of the vortex line at negative pressure is discussed.     

Vortex ring formation for low Re numbers

The dynamics of formation and evolution of vortex rings with low Reynolds numbers created in a piston-cylinder arrangement are studied. The ratio of the piston displacement L _m to the nozzle diameter D ₀ determines the vortex size and evolution. Experiments with different conditions are presented: translation velocity of the piston and stroke ratio L _m /D ₀ for 150 < Re < 260. Measurements of the 2D velocity field were obtained with a PIV technique. The vortex circulation was computed considering a vortex identification scheme (Q criterion). The results show that there is a critical value of L _m /D ₀ above which the circulation inside the vortex cannot increase and remains constant. For the Reynolds numbers studied, we found that the limit stroke ratio is 4 ≤ L _m /D ₀ ≤ 6. As Re decreases, the vortices become “thicker”; therefore, they are able to accumulate more vorticity and increase their circulation.     

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 “A note on the flow in a trailing vortex” by K. K. Tam

Summary In a recent paper in this Journal (7, 1973, 1–6) Tam suggested that early work by Batchelor on the decay of a laminar trailing vortex was in error. Tam's claim was that the decay of axial velocity defect at the center of the vortex went asx ⁻¹ instead ofx ⁻¹ logx. The purpose of this note is to refute Tam's claim. A further term in the asymptotic expansion for the circulation in the vortex is also obtained.