Regimes of vortex shedding from an in-line oscillating circular cylinder in the uniform flow

A finite volume method for the time dependent viscous incompressible flow around an in-line oscillating circular cylinder at Reynolds number of 200, 855 is presented in this paper. The Navier-Stokes equations in a finite volume form are solved with a moving grid system, based on a time dependent coordinate transformation. To investigate the vortex-shedding characteristics behind the circular cylinder and the effects of Reynolds number and other non-dimensional parameters such as reduced amplitude and reduced frequency, several numerical schemes have been tested with different amplitude and frequency close to Sto and a harmonic at each Reynolds number. Present numerical results indicate several types of vortex shedding mode which is known mainly depending on the reduced frequency and also the reduced amplitude, which is called synchronization or lock-on.     

Induced parallel vortex shedding from a circular cylinder at Re of O(10) by using the cylinder end suction technique

In the present work, the objective is to attempt to induce parallel vortex shedding at a moderately high Reynolds number (=1.578 × 10⁴) by using the cylinder end suction method, and measure the associated aerodynamic parameters.We first measured the aerodynamic parameters of a single circular cylinder without end suction, and showed that the quantities measured are in good agreement with equivalent data in the published literature. Next, by using different amount of end suction which resulted in increasing the cylinder end velocity by 1%, 2% and 2.5%, we were able to show that the above corresponded to the situation of under suction, optimal suction and over suction, respectively. With optimal suction, we demonstrated that the end suction method works at Re = 1.578 × 10⁴. The shape of the primary vortex shed became straighter than when there is no end suction, and parameters like cylinder surface pressure distribution, drag force per unit span, as well as vortex shedding frequency all showed negligible spanwise variation. Further careful analyses showed that when compared to the naturally existing curved vortex shedding, with parallel vortex shedding the mid-span drag per unit span became slightly smaller, but the drag averaged over the cylinder span became slightly larger. For cylinder surface pressure, it was found that cylinder end effects mainly influenced the surface pressure in the angular ranges −180°  β < −60° and 60° < β  180°. Without end suction, the cylinder surface pressure in the above ranges was found to increase (become less negative) slightly with |z/d|, but such increase disappeared when optimal end suction was applied, and the cylinder surface pressure distribution became spanwise location independent. As for the vortex shedding frequency (Strouhal number), although the Strouhal number showed spanwise variation when there is no end suction and negligible spanwise variation when optimal suction was applied, the difference between the spanwise averaged Strouhal number was quite negligible. With under suction, the spanwise dependence of various aerodynamic parameters existed, but was found to be not as significant as when no end suction was applied at all. With over suction, the flow situation was found to be practically no change from the optimal suction situation.     

The evolution of starting vortex and secondary separation on an elliptic cylinder

Flow visualization was used to investigate experimentally the evolution process from symmetrical shedding to staggered shedding of the starting vortex and the phenomenon of secondary separation on an elliptic cylinder at moderate Reynolds numbers. The vortex structure of the flow separation was studied. The temporal variation of separation angle and length of wake vortex were given. The photographs and experimental results provided basis for further investigation of the complicated feature of the starting process of unsteady separated flows around an elliptic cylinder. The project supported by the National Natural Science Foundation of China.     

Vortex shedding from a circular cylinder with a slit and concave rear surface

Vortex shedding from short circular cylinders with a slit was studied using a flow visualization and amplitude spectrum analysis of a thermoanemometry probe signal. It was found that a circular cylinder with a slit and concave rear surface produces stronger vortices than other bluff cylinders but that these vortices are very vulnerable to the end wall conditions. It was established that two small splitter plates (tails) fixed directly behind the cylinder at the end walls effectively isolate the vortices shed from the cylinder from the end wall boundary layer effects. For this arrangement a perfect regularity of vortex shedding and almost constant Strouhal number were achieved in the Reynolds number test range of about 250 to 43,000.On a leave from Technical University, 60965 Poznan, Piotrowo 3, Poland.     

Numerical study on the vortex motion patterns around a rotating circular cylinder and their critical characters

A hybrid finite difference and vortex method (HFDV), based on the domain decomposition method (DDM), is used for calculating the flow around a rotating circular cylinder at Reynolds number Re=1000, 200 and the angular‐to‐rectilinear speed ratio α∈(0.5, 3.25) respectively. A fully implicit third‐order eccentric finite difference scheme is adopted in the finite difference method, and the deduced large broad band sparse matrix equations are solved by a highly efficient modified incomplete LU decomposition conjugate gradient method (MILU‐CG). The long‐time, fully developed features about the variations of the vortex patterns in the wake, as well as the drag and lift forces on the cylinder, are given. The calculated streamline contours are in good agreement with the experimentally visualized flow pictures. The existence of the critical state is confirmed again, and the single side shed vortex pattern at the critical state is shown for the first time. Also, the optimized lift‐to‐drag force ratio is obtained near the critical state. Copyright © 1999 John Wiley & Sons, Ltd.     

Vortex shedding around a near-wall circular cylinder induced by a solitary wave

This study developed a two-dimensional generalized vortex method to analyze the shedding of vortices and the hydrodynamic forces resulting from a solitary wave passing over a submerged circular cylinder placed near a flat seabed. Numerical results for validation are compared with other numerical and experimental results, and satisfactory agreement is found. A series of simulations were performed to study the effects of gap-to-diameter ratio and incident wave height on vorticity pattern as well as the forces exerted on the cylinder. The range of the heights of incident waves is from 0.3h to 0.7h, where h is the still water depth. The range of the gap-to-diameter ratios is from 0.1 to 0.8. The results indicate that the flow pattern and the pressure distribution change significantly because of the close proximity of the seabed where the vorticity flux on the seabed-side surface of the cylinder is suppressed. Placing the cylinder nearer the seabed increases the drag and the positive lift on the cylinder. When the gap-to-diameter ratio increases, the pattern of vortices changes because of the interaction between the main recirculation zone and the shear layers separated from the gap. The maxima of drag, lift and total force increase linearly with the height of the incident wave.     

Suppression of vortex shedding from a rectangular cylinder at low Reynolds numbers

Small elements of circular, square, triangular and thin-strip cross-sections are used to suppress vortex shedding from a rectangular cylinder of stream-wise to transverse scale ratio L/B=3.0 at Reynolds numbers in the range of Re=V_∞B/ν=75–130, where V_∞ is the on-coming velocity of the stream, and ν is the kinematic viscosity. The relative transverse dimension of the small element b/B is fixed at 0.2. The results of numerical simulation and visualization experiment show that, vortex shedding from both sides of the cylinder can be suppressed and the fluctuating drag and lift of the cylinder can be greatly reduced, if the element is placed in a certain region referred to as the effective zone. Comparisons at a specific Reynolds number indicate that the square element produces the largest size of the effective zone, whereas the triangular element yields the smallest. Results also show that the effective zone for the square element shrinks with increasing Re and disappears at Re>130. Independent of element cross-section shape and Reynolds number, the center of the effective zone is always at X/B=2.5–3.0 and Y/B≈1.0. The mechanism of the suppression is discussed from the view points of velocity profile stability and stress distribution.     

Simulation of vortex shedding past a square cylinder with different turbulence models

This paper presents the results of numerical simulations of vortex shedding past a free-standing square cylinder at Re_D=22 000, obtained with different turbulence models. Using wall functions, the standard k–ε model is compared with a modification suggested by Kato and Launder (Proc. 9th Symp. Turbulent Shear Flows, Kyoto, 10-4-1 (1993)). In addition, both versions are used in a two-layer approach, in which the flow close to the cylinder is computed with a locally more suitable one-equation turbulence model and only outside the viscous near-wall layer with the two mentioned high-Re model versions. To allow a comparison, the simulations are performed first using the same computational domain and boundary conditions as in previous investigations. Then results are presented that were obtained on a computational domain and with boundary conditions more suitable for a comparison with the experiments. © 1998 John Wiley & Sons, Ltd.     

The effect of air-water interface on the vortex shedding from a vertical circular cylinder

The flow past an interface piercing circular cylinder at the Reynolds number Re=2.7×10⁴ and the Froude numbers Fr=0.2 and 0.8 is investigated using large-eddy simulation. A Lagrangian dynamic subgrid-scale model and a level set based sharp interface method are used for the spatially filtered turbulence closure and the air-water interface treatment, respectively. The mean interface elevation and the rms of interface fluctuations from the simulation are in excellent agreement with the available experimental data. The organized periodic vortex shedding observed in the deep flow is attenuated and replaced by small-scale vortices at the interface. The streamwise vorticity and the outward transverse velocity generated near the edge of the separated region, which enforces the separated shear layers to deviate from each other and restrains their interaction, are primarily responsible for the devitalization of the periodic vortex shedding at the interface. The lateral gradient of the difference between the vertical and transverse Reynolds normal stresses, increasing with the Froude number, is the main source of the streamwise vorticity and the outward transverse velocity at the interface.     

A numerical exploration of secondary separation in starting flow around a flat plate by the discrete vortex model

In the present work, a further numerical simulation of the starting flow around a flat plate normal to the direction of motion in a uniform fluid has been made by means of the discrete vortex method. The secondary separation occurring at rear surface of the plate is explored, and predicted approximately using Thwait's method. The calculated results show that in the early stages of the flow secondary separation does occur. The evolution of flow field, the vortex growing process and the characteristics of secondary vortices have been described. The time dependent drag coefficients, the vorticity shed from the edges and rear surface, and the separation positions are calculated as well as the distributions of velocity and pressure on the plate. In the case of flow normal to the plate, the calculated secondary vortices are weak. Their existence will change the local velocity distributions and affect pressure distributions. However, the effect on drag coefficient is negligible.     

Suppression of lift fluctuations on a circular cylinder by inducing the symmetric vortex shedding mode

The flow around a stationary circular cylinder modified by two synthetic jets positioned at the mean separation points is numerically studied. The Reynolds number based on the free-stream velocity and the circular cylinder diameter is Re=500. The focus is to present a novel way to suppress the lift fluctuations by changing the vortex shedding mode, and thus particular attention is paid to the interactions between the synthetic jets and wake shear layers and the resulting vortex dynamics. The overall influences of both momentum coefficient and excitation frequency are discussed. In some simulated cases, the vortex lock-on phenomenon is discovered, which causes the typical Kàrmàn type vortex shedding to be converted into the symmetric shedding modes, leading to the complete suppression of lift fluctuations. In other cases, the asymmetric shedding mode still dominates the wake evolution. Detailed vortical evolution for each typical wake pattern is analyzed to reveal the control mechanism. Additionally, the control effectiveness is evaluated, indicating that the present control strategy contributes an effective way to suppress the lift fluctuations and reduce the mean drag.     

Numerical prediction of vortex shedding behind a square cylinder

It is common knowledge that flow around bluff bodies exhibits oscillatory behaviour. The aim of the present study is to compute the steady two-dimensional flow around a square cylinder at different Reynolds numbers and to determine the onset of unsteadiness through a linear stability analysis of the steady flow. Stability of the steady flow to small two-dimensional perturbations is analysed by computing the evolution of these perturbations. An analysis of various time-stepping techniques is carried out to select the most appropriate technique for predicting the growth of the perturbations and hence the stability of the flow. The critical Reynolds number is determined from the growth rate of the perturbations. Computations are then made for periodic unsteady flow at a Reynolds number above the critical value. The predicted Strouhal number agrees well with experimental data. Heat transfer from the cylinder is also studied for the unsteady laminar flow.     

Numerical modeling of the turbulent viscous-gas flow past a cylinder with a circular vortex cell in the presence of suction from the central body surface

The compressibility effect on the cylinder drag reduction due to air suction through the surface of a central body in a circular vortex cell is estimated on the basis of the solution of the steady Reynolds equations closed by the shear stress transfer model, together with the continuity, energy, and state equations.     

Application of flow suction for controlling the shedding of large-scale vortices at boundary-layer separation

A wind-tunnel study of the influence of flow suction on laminar boundary-layer separation behind a two-dimensional step on the surface is performed. Hot-wire measurements are carried out at low subsonic flow velocities. It is demonstrated that this method of flow control allows suppressing the formation of large-scale vortices determined by global stability properties of the separation region. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 4, pp. 60–65, July–August, 2006.     

Feedback control of vortex shedding from a circular cylinder by cross-flow cylinder oscillations

Feedback control of vortex shedding from a circular cylinder in a uniform flow at moderate Reynolds numbers is studied experimentally with the cylinder subjected to feedback cylinder oscillations in cross-flow direction. The cylinder oscillation is digitally phase shifted with respect to the shedding vortex and is controlled by velocity feedback from the shear layer of the cylinder wake. Possible attenuation of vortex shedding is demonstrated by hot-wire measurements of the flow field and its mechanisms are studied by simultaneous data sampling and flow visualization with the smoke wire method and a laser-sheet illumination technique. Measurement results reveal substantial reduction in the fluctuating reference velocity at the optimum phase control. Flow visualization study indicates that the shear layer roll-up and the eventual vortex formation are dynamically attenuated under the control which results in a modification of the near wake.List of symbols A amplitude of cylinder oscillation - D cylinder diameter - E _u power spectrum function for fluctuating velocity u - frequency - R radius of circular cylinder - t time - u streamwise mean velocity - u streamwise fluctuating velocity - U streamwise mean velocity of main flow - u _r mean reference velocity - u _r fluctuating reference velocity - u _rf fluctuating reference velocity after filtering - y _c cylinder displacement - x, y, z coordinates from the cylinder center (Fig. 1) - feedback coefficient - phase lag The authors would like to express thanks to Professor K. Nagaya for his advice for designing electromagnetic actuators in the present experiments.     

Unsteady characteristics of the cavity flow around a rough circular cylinder

Effects of surface roughness on the unsteady cavitating flow around a two-dimensional circular cylinder were experimentally investigated at Reynolds numbers from 1.36 × 10⁵ to 1.78 × 10⁵. Two patterns of surface roughness were investigated, a double-cut pattern and a single-cut pattern. The cavity elongates with an increase of the surface roughness, especially in supercavitating flow. However, for some roughness parameters tested, the cavity length exhibits an extreme decrease. In a particular case of the double-cut pattern, there exists the minimum cavity behind the cylinder.     

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 9×10³.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_lf. 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.     

On the hysteresis of vortex shedding in a periodically-varying flow

Efforts are made to explore the hysteresis characteristics of vortex shedding in a pipe flow, whose velocity varies periodically in time. Results obtained show that during acceleration of the flow, the vortex strength tends to be stronger, whereas during deceleration of the flow, the situation is reversed. As reconstructed from the velocity signals measured at a point in the flow field, the shed vortex arrays appear to possess uneven vortex strengths in response to periodically-varying incoming flows. Furthermore, in the hysteresis range, the streamwise spacings between the vortices appear to be unequal.