Vortex Shedding Regime Research Articles

On the effects of viscoelasticity on two-dimensional vortex dynamics in the cylinder wake

The present paper represents, as far as we are aware, the first linear stability analysis for inertial flows of a viscoelastic fluid around a bluff body. Our particular interest is the effect of polymer additives on the linear stability of two-dimensional viscous flow past a confined cylinder and our investigation involves both direct numerical simulation and the solution of a generalized eigenvalue problem arising from the linearized perturbation equations. For a constant viscosity FENE-type model polymer additive is shown to have a stabilizing effect upon two-dimensional flow past a confined cylinder. In particular, our results reveal that the greater the maximum extensibility of the FENE dumbbells, the larger the value of the critical Reynolds number marking the onset of vortex shedding. Thus the stabilization brought to bear by the presence of the FENE-type dumbbells would appear to depend strongly upon the extensional properties of the polymer solution. This is in agreement with the results of the recent experimental paper of Cressman et al. [J.R. Cressman, Q. Bailey, W.I. Goldburg, Modification of a vortex street by a polymer additive, Phys. Fluids 13 (2001) 867–871] which highlight the importance of the extensional properties of high molecular weight polymers (even at low concentrations) in reducing the kinetic energy contained in the velocity fluctuations behind a cylinder. The impact of elasticity on Strouhal number, time-averaged recirculation length, drag and lift in the vortex-shedding regime are also discussed at some length.

Tuning of Strouhal number for high propulsive efficiency accurately predicts how wingbeat frequency and stroke amplitude relate and scale with size and flight speed in birds.

The wing kinematics of birds vary systematically with body size, but we still, after several decades of research, lack a clear mechanistic understanding of the aerodynamic selection pressures that shape them. Swimming and flying animals have recently been shown to cruise at Strouhal numbers (St) corresponding to a regime of vortex growth and shedding in which the propulsive efficiency of flapping foils peaks (St approximately fA/U, where f is wingbeat frequency, U is cruising speed and A approximately bsin(theta/2) is stroke amplitude, in which b is wingspan and theta is stroke angle). We show that St is a simple and accurate predictor of wingbeat frequency in birds. The Strouhal numbers of cruising birds have converged on the lower end of the range 0.2 < St < 0.4 associated with high propulsive efficiency. Stroke angle scales as theta approximately 67b-0.24, so wingbeat frequency can be predicted as f approximately St.U/bsin(33.5b-0.24), with St0.21 and St0.25 for direct and intermittent fliers, respectively. This simple aerodynamic model predicts wingbeat frequency better than any other relationship proposed to date, explaining 90% of the observed variance in a sample of 60 bird species. Avian wing kinematics therefore appear to have been tuned by natural selection for high aerodynamic efficiency: physical and physiological constraints upon wing kinematics must be reconsidered in this light.

Vortex shedding in high Reynolds number axisymmetric bluff-body wakes: Local linear instability and global bleed control

In the present work we study the large-scale helical vortex shedding regime in the wake of an axisymmetric body with a blunt trailing edge at high Reynolds numbers, both experimentally and by means of local, linear, and spatiotemporal stability analysis. In the instability analysis we take into account the detailed downstream evolution of the basic flow behind the body base. The study confirms the existence of a finite region of absolute instability for the first azimuthal number in the near field of the wake. Such instability is believed to trigger the large-scale helical vortex shedding downstream of the recirculating zone. Inhibition of vortex shedding is examined by blowing a given flow rate of fluid through the base of the slender body. The extent of the locally absolute region of the flow is calculated as a function of the bleed coefficient, Cb=qb/(πR2u∞), where qb is the bleed flow rate, R is the radius of the base, and u∞ is the incident free-stream velocity. It is shown that the basic flow becomes convectively unstable everywhere for a critical value of the bleed coefficient of Cb*∼0.13, such that no self-excited regime is expected for Cb&amp;gt;Cb*. In addition, we report experimental results of flow visualizations and hot-wire measurements for increasing values of the bleed coefficient. When a sufficient amount of base bleed is applied, flow visualizations indicate that vortex shedding is suppressed and that the mean flow becomes axisymmetric. The critical bleed coefficient predicted by linear instability analysis is shown to fall within the experimental values in the range of Reynolds numbers analyzed here.

수치 시뮬레이션을 통한 평판내 파이프라인 주위의 점성유동 연구

Numerical study was made on the flow characteristics around a circular pipeline between parallel walls. The incompressible Navier-Stokes equations were solved by using a third-order upwind differential scheme. When the distance near a wall is small enough, the vortex shedding is almost completely suppressed because of the interaction with the wall boundary layer separation. This study aims to clarify the characteristics of the vortex shedding regime as the body approaches a wall as Reynolds number varies. The feature of separated vorticity dynamics is analyzed at different conditions with particular attention to the interaction between the pipeline wake and the induced separation on the plane walls.

Flying and swimming animals cruise at a Strouhal number tuned for high power efficiency.

Dimensionless numbers are important in biomechanics because their constancy can imply dynamic similarity between systems, despite possible differences in medium or scale. A dimensionless parameter that describes the tail or wing kinematics of swimming and flying animals is the Strouhal number, St = fA/U, which divides stroke frequency (f) and amplitude (A) by forward speed (U). St is known to govern a well-defined series of vortex growth and shedding regimes for airfoils undergoing pitching and heaving motions. Propulsive efficiency is high over a narrow range of St and usually peaks within the interval 0.2 < St < 0.4 (refs 3-8). Because natural selection is likely to tune animals for high propulsive efficiency, we expect it to constrain the range of St that animals use. This seems to be true for dolphins, sharks and bony fish, which swim at 0.2 < St < 0.4. Here we show that birds, bats and insects also converge on the same narrow range of St, but only when cruising. Tuning cruise kinematics to optimize St therefore seems to be a general principle of oscillatory lift-based propulsion.

Flows past a tiny circular cylinder at high temperature ratios and slight compressible effects on the vortex shedding

The present study contributes to the numerical simulations of weak compressible effects for laminar flows around heated circular cylinders. Our aim in this work is to understand the physics of the flow around a heated cylinder and the reasons for the decrease in the frequency of vortex shedding in the wake behind the cylinder as the ratio of surface temperature to freestream temperature increases for moderate Re numbers. The previous achievements on this subject rely mainly on experimental investigations by using a “representative” or “film temperature” and therefore should be investigated more accurately by the numerical considerations. In that context, numerical experiments are carried out. A technique which was previously tested and validated on a variety of flow problems is utilized in the numerical experiments. The results show that the temperature is not a passive contaminant especially for flows with temperature ratios T*=Tw/T∞ greater than 1.1. The temperature boundary layer surrounding the wall introduces weak compressible effects on the velocity and on the pressure field especially for Re numbers below 100. As a consequence of this result, the local Ma number effects are shown on a Re–Nu curve for the laminar unsteady vortex shedding regime.

Vortex shedding in cylinder flow of shear-thinning fluids: II. Flow characteristics

A detailed experimental study on the flow characteristics of various vortex shedding regimes was carried out for the flow of non-Newtonian fluids around a cylinder. The fluids were aqueous solutions of carboxymethyl cellulose (CMC) and tylose at weight concentrations ranging from 0.1 to 0.6%, which had varying degrees of shear-thinning and elasticity. Two cylinders of 10 and 20 mm diameter were used in the experiments, defining an aspect ratio of 12 and 6 and producing blockages of 5 and 10%, respectively. The Reynolds number ( Re) ranged from 50 to 9×10 3. Shear-thinning gave rise to a decrease of the cylinder boundary-layer thickness and to a reduction of the diffusion length ( l d), which raised the Strouhal number, St. In the laminar shedding regime, a modified Strouhal number was successful at overlapping the shedding frequency variation with the Reynolds number for the various solutions. In contrast, fluid elasticity was found to increase the formation length ( l f), and this contributed to a decrease of the Strouhal number. The overall effect of shear-thinning and elasticity was an increase in the Strouhal number. The increase in polymer concentration and the corresponding increase in fluid elasticity were responsible for the reduction of the critical Reynolds number marking the sudden decrease of the formation length, Re l f . In the shear layer transition regime, the formation length and Strouhal number data collapsed onto single curves as function of a Reynolds number difference, which confirmed Coelho and Pinho (J. Non-Newtonian Fluid Mech. (2003), accepted for publication) finding that an important effect of fluid rheology was in changing the demarcations of the various flow regimes.

Effect of high rotation rates on the laminar flow around a circular cylinder

A two-dimensional numerical study on the laminar flow past a circular cylinder rotating with a constant angular velocity was carried out. The objectives were to obtain a consistent set of data for the drag and lift coefficients for a wide range of rotation rates not available in the literature and a deeper insight into the flow field and vortex development behind the cylinder. First, a wide range of Reynolds numbers (0.01⩽Re⩽45) and rotation rates (0⩽α⩽6) were considered for the steady flow regime, where α is the circumferential velocity at the cylinder surface normalized by the free-stream velocity. Furthermore, unsteady flow calculations were carried out for one characteristic Reynolds number (Re=100) in the typical two-dimensional (2D) vortex shedding regime with α varying in the range 0⩽α⩽2. Additionally, the investigations were extended to very high rotation rates (α⩽12) for which no data exist in the literature. The numerical investigations were based on a finite-volume flow solver enhanced by multi-grid acceleration and the local grid refinement technique to achieve efficient computations and accurate numerical results. The predictions show that the rotation of the cylinder suppresses the vortex development in both the steady and the unsteady flow regimes and significantly changes the flow field close to the cylinder. For very low Reynolds numbers, the drag force is not affected by rotation and the lift force is a linear function of α. For higher Re in the steady flow regime, the drag force decreases with increasing rotational velocities even leading to negative values. The lift force is almost a linear function of the rotational velocity and nearly independent of Re for low rotational speeds of α&amp;lt;2. However, for higher α values and larger Reynolds numbers (Re&amp;gt;1), a progressive increase in the lift force is observed. A very interesting phenomenon was found in the unsteady flow regime at Re=100. For low rotation rates (α⩽2) the flow exhibits the behavior known from the literature, e.g., a linear increase of the mean lift coefficient with increasing α and the suppression of vortex shedding beyond a critical α value of about αL≈1.8. However, for α≈5, an unsteady periodic flow motion was found in the wake which is characterized by a frequency much lower than that known for normal vortex shedding. The change in the flow structure also leads to a distinct change in the mean lift coefficients which exhibits a linear relation of very high rotations rates and asymptotically converges to the values known from the potential flow theory.

Instantaneous vortex-shedding behaviour in periodically varying flow

Vortex shedding behind a stationary T–shaped cylinder in a circular pipe subjected to periodically varying flow was studied at Reynolds numbers between 6.17 × 103 and 2.46 × 104, whereas the frequency ratio, Fs/Fo, ranged from 0.29 to 14.64. Fs denotes the natural vortex-shedding frequency referred to the mean flow, and Fo denotes the frequency of periodically varying flow. By adopting the Hilbert transform to analyse the velocity signals measured, the instantaneous vortex-shedding frequency was obtained. Based on this quantity, one could categorize the vortex-shedding phenomenon observed into three regimes, namely, quasi-steady vortex shedding for Fs/Fo > 4.37, hysteresis vortex shedding for Fs/Fo= 1.56-4.37 and non-interactive vortex shedding for 0.29 < Fs/Fo < 1.56. In the regime of quasi-steady vortex shedding, the instantaneous vortex-shedding frequency follows the periodically varying flow without phase lag. In the regime of hysteresis vortex shedding, the instantaneous vortex-shedding frequency lags behind the periodically varying flow. Phase lag roughly varies linearly with Fs/Fo. Further, the variations of non-dimensionalized instantaneous vortex-shedding frequencies obtained in the accelerating and decelerating portions of the periodically varying flow are found to depend on Fs/Fo and ΔU/Ū. In the regime of non-interactive vortex shedding, the vortex-shedding frequency tends to vary with the mean velocity of periodically varying flow, excluding the occurrences of primary and secondary lock-on at Fs/Fo= 0.97-1.03 and 0.495-0.514, respectively.

Flow about a circular cylinder between parallel walls

The flow about a body placed inside a channel differs from its unbounded counterpart because of the effects of wall confinement, shear in the incoming velocity profile, and separation of vorticity from the channel walls. The case of a circular cylinder placed between two parallel walls is here studied numerically with a finite element method based on the vorticity–streamfunction formulation for values of the Reynolds number consistent with a two-dimensional assumption.The transition from steady flow to a periodic vortex shedding regime has been analysed: transition is delayed as the body approaches one wall because the interaction between the cylinder wake and the wall boundary layer vorticity constrains the separating shear layer, reducing its oscillations. The results confirm previous observations of the inhibition of vortex shedding for a body placed near one wall. The unsteady vortex shedding regime changes, from a pattern similar to the von Kármán street (with some differences) when the body is in about the centre of the channel, to a single row of same-sign vortices as the body approaches one wall. The separated vortex dynamics leading to this topological modification is presented.The mean drag coefficients, once they have been normalized properly, are comparable when the cylinder is placed at different distances from one wall, down to gaps less than one cylinder diameter. At smaller gaps the body behaves similarly to a surface-mounted obstacle. The lift force is given by a repulsive component plus an attractive one. The former, well known from literature, is given by the deviation of the wake behind the body. Evidence of the latter, which is a consequence of the shear in front of the body, is given.

PERIODIC WAKES OF LOW ASPECT RATIO CYLINDERS WITH FREE HEMISPHERICAL ENDS

The wakes of circular cylinders with free hemispherical ends and of different aspect ratios (length-to-diameter ratios) are experimentally studied for moderate Reynolds numbers. This investigation is restricted to cylinders with low aspect ratios, namely less than 5, and includes the case of the sphere. The transition to nonstationarity of the flow in these cylinder wakes is the main focus of this work: the results show that the stability of wakes is strongly dependent on aspect ratio and is also affected by the free-end conditions. We characterize the frequency, amplitude and phase as well as the critical Reynolds number of the periodic vortex shedding regime.

Control of vortex shedding in an axisymmetric bluff body wake

In the present experimental study the effect of a control disc mounted at the rear of an axisymmetric blunt-based body of revolution, first studied by Mair, is investigated in the Reynolds number range 3×10 3≤ Re D ≤5×10 4 . As the distance of the control disc from the blunt base is increased, four vortex shedding regimes are identified: at small distances there is no effect, then a sharp increase of vortex shedding activity and total drag is observed, followed by an interval with reduced activity and drag and finally at large distances a regime where the flow around the main body and disc become essentially independent, i.e. where the drag forces of the two elements become additive. The near and far wake velocity fields corresponding to the different regimes are documented with time- and phase-averaged hot-wire and LDA measurements, with spectral analysis of the data and with flow visualizations of the near wake. The results are used to develop an improved understanding of the instability mechanism leading to high vortex shedding activity.

Simulation of the effects of body shape on lock-in characteristics in pulsating flow by the discrete vortex method

The viscous flow around rectangles defined by afterbody length, L, and cross-stream dimension, D, is investigated through a hybrid discrete vortex method. The side ratio, LD, varies over the range 0.4 ⩽ LD ⩽ 2.5. In the case of the square cylinder, LD = 1.0, results are presented for the variation of drag coefficient and Strouhal number with Reynolds number, Re ⩽ 1000. A good agreement with experiment is shown although for Re ⩾ 500 the calculated Strouhal number is found to be higher than experimental values. At a fixed Reynolds number, Re = 200, the variation of drag coefficient with side ratio shows Cd increasing with decreasing LD. Experimental work at higher Re predicts a drag maximum at LD ≌0.62 but such a maximum has not been determined in this study. Pulsating flows are reported for LD values of 0.62, 1.0, 2.0 and the ‘lock-in’ characteristics are shown to be highly dependent on the side ratio. In particular, with LD = 2.0, a strong regime of symmetric vortex shedding is found when the forcing frequency is more than double the natural shedding frequency value.

A NUMERICAL STUDY OF OSCILLATORY FLOW ABOUT A CIRCULAR CYLINDER FOR LOW VALUES OF BETA PARAMETER

A Hybrid Lagrangian/Eulerian Discrete Vortex Method has been used to simulate the flow around a circular cylinder in planar oscillatory flow at a value of the viscous scale parameter, β, of 76. A number of techniques are examined for estimating the forces acting on the cylinder. Surface pressure is calculated using the normal gradient of vorticity at the surface, by integrating the equation of motion along a radial line from the outer boundary of the mesh to the cylinder surface and by using Poisson’s equation. Predictions are compared with existing analytical results for low Keulegan Carpenter numbers and with recent measurements up to Keulegan Carpenter numbers of 30, made at a β of 70. These comparisons show that Wu's method, based on the generalized Blasius equation, gives accurate predictions and that surface pressure is predicted most accurately by using integration along a radial line. There is found to be good agreement between the computed and measured in-line forces across a range of KC values. Numerical flow field data is presented in the form of visualizations and, in order to be able to compare directly with visualization from experiments, passive markers are introduced into the computations. All the major vortex-shedding regimes observed in experiments at KC values up to around 30 are reproduced in the simulations.

The flow behind rings: bluff body wakes without end effects

Recent studies have demonstrated the strong influence of end effects on low-Reynoldsnumber bluff body wakes, and a number of questions remain concerning the intrinsic nature of three-dimensional phenomena in two-dimensional configurations. Some of them are answered by the present study which investigates the wake of bluff rings (i.e. bodies without ends) both experimentally and by application of the phenomenological Ginzburg–Landau model. The model turns out to be very accurate in describing qualitative and quantitative observations in a large Reynolds number interval. The experimental study of the periodic vortex shedding regime shows the existence of discrete shedding modes, in which the wake takes the form of parallel vortex rings or ‘oblique’ helical vortices, depending on initial conditions. The Strouhal number is found to decrease with growing body curvature, and a global expression for the Strouhal–Reynolds number relation, including curvature and shedding angle, is proposed, which is consistent with previous straight cylinder results. A secondary instability of the helical modes at low Reynolds numbers is discovered, and a detailed comparison with the Ginzburg–Landau model identifies it as the Eckhaus modulational instability of the spanwise structure of the near-wake formation region. It is independent of curvature and its clear observation in straight cylinder wakes is inhibited by end effects.The dynamical model is extended to higher Reynolds numbers by introducing variable parameters. In this way the instability of periodic vortex shedding which marks the beginning of the transition range is characterized as the Benjamin–Feir instability of the coupled oscillation of the near wake. It is independent of the shear layer transition to turbulence, which is known to occur at higher Reynolds numbers. The unusual shape of the Strouhal curve in this flow regime, including the discontinuity at the transition point, is qualitatively reproduced by the Ginzburg–Landau model. End effects in finite cylinder wakes are found to cause important changes in the transition behaviour also: they create a second Strouhal discontinuity, which is not observed in the present ring wake experiments.

Shallow-Water Flow past Isolated Topography. Part II: Transition to Vortex Shedding

Abstract The formation of Karman vortex streets is studied within the framework of single-layer shallow-water dynamics and in absence of surface friction and background rotation. In the first part of this study, steady numerical solutions for flow past circular topography were obtained by imposing a symmetry condition that essentially suppressed vortex shedding. In the second part, this symmetry condition is relaxed in order to study the transition into the vortex-shedding regime. This transition is due to an instability of the symmetric wake pattern. The most unstable global normal mode of this instability is derived by a numerical method. Most of the features of this mode can be understood in terms of the absolute instability theory. The mode is essentially barotropic and relies on a positive feedback between the perturbations located on the two shearlines on either side of the wake. The classical shear modes centered on a single shearline are, on the other hand, shown to be absolutely stable even thoug...

Control of vortex shedding in a two-dimensional flow past a plate.

A version of the no-feedback-control method developed by Hubler and Luscher is applied to two-dimensional open-channel flow past a plate. The control is applied in the vortex-shedding regime with the aim of reducing the effective Reynolds number, thereby suppressing the vortex shedding. The method work well not only when the flow is globally forced but also when the forcing is restricted to the boundary-layer region

A115 互違い型配置の平行二円柱における後流渦の可視化

The interacting vortex wakes of two circular cylinders in staggered arrangement are examined by visualization experiments using a towing water tank. The cylinder spacing parameters are expressed in terms of the stream-wise spacing ratio L/d (0 to 10.0) and the transverse spacing ratio T/d (0 to 4.0) for a fixed Reynolds number of 80. The point of the present study is the flow pattern analysis in various geometric arrangement of the two cylinders, covering a wide range of spacing para-meters, inclusive of the so-called bistable regime of vortex shedding, and the simultaneous measurement of Strouhal numbers corresponding to the wake frequency detected outside the near-wake region. Another point of the paper is the complicated vortex wake interaction and the subsequent wake evolution observed downstream of the leeward cylinder.

Natural convection from a horizontal cylinder at moderate grashof numbers

This chapter discusses the role of non-Newtonian flow characteristics of structured fluids—within the framework of continuum mechanics—on the hydrodynamic and convective heat and mass transport processes for bluff bodies of various shapes immersed in streaming (unconfined or confined) or quiescent fluids in different flow regimes. It focuses on the steady and laminar vortex shedding regimes of the flow over long cylinders of circular, elliptic, semicircular, square, and triangular cross sections. Within this framework, the flow invariably tends to be two-dimensional and laminar. The unconfined or free flow past a circular cylinder exhibits a rich variety of flow regimes depending upon the intrinsic nature of the flow. The simple flow is governed by the Reynolds number that is based upon the diameter of the cylinder, kinematic viscosity of the fluid, and the faraway uniform velocity. Most non-Newtonian fluids tend to be far more viscous than their Newtonian counterparts like air and water and, therefore, laminar flow conditions prevail more often in such fluids than that in Newtonian fluids like air. The chapter describes the flow regimes and fluid mechanical aspects related to circular, elliptical, semicircular, triangular, and square cylinders, together with the critical values of the Reynolds number denoting the transition from one flow regime to another. These values are strongly influenced not only by the rheological characteristics but also by the shape of the bluff body, its orientation with regard to the mean direction of flow, and its extent and type of confinement. The scaling considerations that are used to extract the pertinent dimensionless parameters which influence the detailed and macroscopic momentum and heat transfer characteristics for each shape of the bluff body have also been highlighted.