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.     

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.     

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.     

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 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.     

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。     

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.     

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.     

Dynamic response of an elastic fence under wind action

Abstract

The along‐wind response of a surface‐mounted elastic fence under the action of wind was investigated numerically. In the computations, two sets of equations, one for the simulation of the unsteady turbulent flow and the other for the calculation of the dynamic motion of the fence, were solved alternatively. The resulting time‐series tip response of the fence as well as the flow fields were analyzed to examine the dynamic behaviors of the two.

Results show that the flow is unsteady and is dominated by two frequencies: one relates to the shear layer vortices and the other one is subject to vortex shedding. The resulting unsteady wind load causes the fence to vibrate. The tip deflection of the fence is periodic and is symmetric to an equilibrium position, corresponding to the average load. Although the along‐wind aerodynamic effect is not significant, the fluctuating quantities of the tip deflection, velocity and acceleration are enhanced as the fundamental frequency of the fence is near the vortex or shedding frequency of the flow due to the occurrence of resonance. In addition, when the fence is rather soft, a higher mode response can be excited, leading to significant increases in the variations of the tip velocity and acceleration.     

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     

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。     

Flows induced by the surface motions of a cylindrical sheet

Fluid flows induced by the surface stretching or shearing motion of cylindrical sheets are investigated. Steady and unsteady exact solutions of the Navier–Stokes equations are found for periodic axial shearing of an impermeable sheet and for periodic azimuthal stretching of a permeable sheet. Steady Stokes-flow solutions induced by the periodic axial stretching and the periodic azimuthal stretching of impermeable cylindrical sheets are also reported. In each case flows interior and exterior to a cylinder are considered, as well as the flow in the annulus between concentric cylinders.     

A vortex method for separated flow around an airfoil with a detached spoiler

A discrete vortex method based on no-slip condition is developed for simulating unsteady separated flows around an airfoil with a detached spoiler. For flow separated at each sharp edge, such as the spoiler tips and the trailing edge of the airfoil, a vortex sheet is used to feed discrete vortices at each time step. The length, inclination and strength of each sheet is determined by the continuity equation, the momentum principle and a Kutta pressure condition such that the flow, net force and pressure difference across the vortex sheet are all zero. The separation on the airfoil upper surface is simulated by discrete vortices shed from a fixed separation point. The flow patterns behind a detached spoiler at different time steps are obtained and compared with those of the conventional spoiler. Reasonable agreements are found between the predicted pressure distributions and experimental measurements. The computed results show that base-venting changes the flow field around the spoiler and reduces the adverse effect in lift experienced by the airfoil when the spoiler undergoes a rapid deployment.     

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.     

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.     

Simulating three-dimensional vortex motion by a vortex blob method

A three-dimensional vortex blob method was applied to calculate several vortex motions: the deformation of pseudo-elliptic vortex rings, the jet issuing from the pseudo-elliptic nozzle into flow of uniform velocity, the unsteady separated flow around a circular disk with an angle of attack, and the interaction of several vortex rings which approximately reproduced the Kolmogorov spectrum. In the first three cases, the viscous diffusion of vorticity was included. The pseudo-elliptic vortex rings experienced axis switching and split into a few deformed vortex rings. Rolling-up vortices in the pseudo-elliptic jet had a symmetric arrangement in the minor-axis plane and an antisymmetric arrangement in the major-axis plane in the developing region; further downstream, the vortices were arranged antisymmetrically in both planes. The wake behind the disk normal to the main flow reproduced the spiral and columnar modes of instability. A problem in the three-dimensional vortex method is that vorticity tends to diverge at a stage of evolution of the vortex motions. An approximate method of avoiding the divergence of vorticity is proposed.     

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”.     

Hydrodynamics numerical investigation of hoistable masts for underwater vehicles

Hoistable masts are key systems of underwater vehicles. The hoistable mast enables a underwater vehicle to penetrate the sea surface and exchange information with little risk of being detected. It is very important for researching the hydrodynamic behaviour of flow pass hoistable masts in order to reduce the production of visible, electro-optic, infrared, radar cross section wake and hydroacoustics signatures. Using the unsteady incompressible Navier-Stokes equation as the governing equation, the large eddy simulation (LES) model is implemented to investigate the shedding of vortices, the flow pattern of turbulence, the unsteady pressure fluctuation and the time history of the lift coefficient and drag coefficient of hoistable masts with various mast shapes and various arrangements in this paper. Combining the FFT, combined time-frequency transform and wavelet power spectrum analysis, the characteristics of unsteady pressure can be obtained in both time and frequency domain. It shows that the main frequency of pressure fluctuation is near the frequency of vortex shedding in time domain using the FFT method. It can be inferred from the combined time-frequency transform that the unsteady pressure fluctuation has obviously the peak value and second peak value in time domain. It could indicate that the fluctuation power varies from the fluctuation frequency through the power spectrum analysis. By the data analysis, it shows that the vortex shedding is the dominant cause of the periodically pressure fluctuation. And the interaction pattern of wake and interplay between wake and the walls of masts under different arrangements are also discussed in this paper.     

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.