Vortex shedding and aerodynamic forces on a circular cylinder in linear shear flow at subcritical Reynolds number

Vortex shedding and aerodynamic forces on a circular cylinder in a linear shear flow with its axis normal to the plane of the velocity shear profile at subcritical Reynolds number are investigated experimentally. The shear parameter β, which is based on the velocity gradient, cylinder diameter and upstream mean velocity at the center plane of the cylinder, varies from 0 to 0.27. The Strouhal number has no significant variation with the shear parameter. The time-mean base pressure increases and the fluctuating component of the base pressure decreases significantly with increasing shear parameter. Vortex shedding is suppressed by the velocity shear. Dislocation of the stagnation point takes place and this influences the pressure distribution around the cylinder together with the velocity shear. A mean lift force arises in the shear flow due to asymmetry of the pressure distribution, and it acts from the high velocity side to the low velocity side. In addition, the lift coefficient increases and the drag coefficient decreases with increasing shear parameter.     

Vortex shedding flow behind a slowly rotating circular cylinder

This paper investigates flow past a rotating circular cylinder at 3600?Re?5000 and α?2.5. The flow parameter α is the circumferential speed at the cylinder surface normalized by the free-stream velocity of the uniform cross-flow. With particle image velocimetry (PIV), vortex shedding from the cylinder is clearly observed at α<1.9. The vortex pattern is very similar to the vortex street behind a stationary circular cylinder; but with increasing cylinder rotation speed, the wake is observed to become increasing narrower and deflected sideways. Properties of large-scale vortices developed from the shear layers and shed into the wake are investigated with the vorticity field derived from the PIV data. The vortex formation length is found to decrease with increasing α. This leads to a slow increase in vortex shedding frequency with α. At α=0.65, vortex shedding is found to synchronize with cylinder rotation, with one vortex being shed every rotation cycle of the cylinder. Vortex dynamics are studied at this value of α with the phase-locked eduction technique. It is found that although the shear layers at two different sides of the cylinder possess unequal vorticity levels, alternating vortices subsequently shed from the cylinder to join the two trains of vortices in the vortex street pattern exhibit very little difference in vortex strength.     

Vortex shedding and three-dimensional behaviour of flow past a cylinder confined in a channel

A numerical investigation of the flow past a circular cylinder centred in a two-dimensional channel of varying width is presented. For low Reynolds numbers, the flow is steady. For higher Reynolds numbers, vortices begin to shed periodically from the cylinder. In general, the Strouhal frequency of the shedding vortices increases with blockage ratio. In addition, a two-dimensional instability of the periodic vortex shedding is found, both empirically and by means of a Floquet stability analysis. The instability leads to a beating behaviour in the lift and drag coefficients of the cylinder, which occurs at a Reynolds number higher than the critical Reynolds number for the three-dimensional mode A-type instability, but lower than a Reynolds number for any mode B-type instability.     

Vortex shedding from a circular cylinder near a moving wall

Flow over a circular cylinder near a moving plane wall is simulated numerically. The influence of the moving wall on the vortex shedding from the cylinder is demonstrated and the corresponding mechanism is illustrated using instability theory. A critical gap ratio between the circular cylinder and the moving wall is defined, and a precise method for determining the critical gap ratio is proposed. The drag and lift forces and the pressure coefficient are presented as a function of the gap ratio. The scaling of the Strouhal number is discussed.     

Vortex shedding from edges including viscous effects

This paper describes results obtained by using the inviscid Cloud-in-Cell vortex method to model the vortex sheet which is shed and rolls up from a single sharp edge. There is good agreement between these results and previous (Pullin 1978) computations of the development of the sheet in impulsively started incompressible inviscid flow. The Cloud-in-Cell method has been modified to include viscous diffusion calculated by finite differences on the mesh to give a mixed Eulerian-Lagrangian Navier-Stokes solver. This method has been shown to model the diffusing free vortex and the Stokes boundary layer quite accurately. It is used to compute impulsively started flow past sharp right-angled edges and edges with small rounding. The effect of viscous diffusion on the development of the shed vortex is discussed.

The method is also used to study the effect of rounding on the vortex shedding from a right-angled edge in oscillatory flow. This problem is particularly important in determining the roll damping and hence response of certain types of ship hull in waves. It is shown that the strength and effect of the shed vortices rapidly decrease as the ratio of the edge radius to the oscillation amplitude increases, and that at larger values of this ratio the mode of shedding changes from two vortices per cycle from one edge to a more complicated mode. The computed results are compared with flow visualisation using dye and neutrally buoyant particles in water flow around an oscillating edge.     

Vortex shedding from a square cylinder in presence of a moving wall

A numerical study on the flow past a square cylinder placed parallel to a wall, which is moving at the speed of the far field has been made. Flow has been investigated in the laminar Reynolds number (based on the cylinder length) range. We have studied the flow field for different values of the cylinder to wall separation length. The governing unsteady Navier–Stokes equations are discretized through the finite volume method on a staggered grid system. A SIMPLE type of algorithm has been used to compute the discretized equations iteratively. A shear layer of negative vortex generates along the surface of the wall, which influences the vortex shedding behind the cylinder. The flow‐field is distinct from the flow in presence of a stationary wall. An alternate vortex shedding occurs for all values of gap height in the unsteady regime of the flow. The strong positive vortex pushes the negative vortex upwards in the wake. The gap flow in the undersurface of the cylinder is strong and the velocity profile overshoots. The cylinder experiences a downward force for certain values of the Reynolds number and gap height. The drag and lift are higher at lower values of the Reynolds number. Copyright © 2005 John Wiley & Sons, Ltd.     

Vortex shedding from two finite circular cylinders in a staggered configuration

Wind tunnel experiments were conducted to measure the vortex shedding frequencies for two circular cylinders of finite height arranged in a staggered configuration. The cylinders were mounted normal to a ground plane and were partially immersed in a flat-plate turbulent boundary layer. The Reynolds number based on the cylinder diameter was Re_D=2.4×10⁴, the cylinder aspect ratio was AR=9, the boundary layer thickness relative to the cylinder height was δ/H=0.4, the centre-to-centre pitch ratio was varied from P/D=1.125 to 5, and the incidence angle was incremented in small steps from α=0° to 90°. The Strouhal numbers were obtained behind the upstream and downstream cylinders using hot-wire anemometry. From the behaviour of the Strouhal number data obtained at the mid-height position, the staggered configuration could be broadly classified by the pitch ratio as closely spaced (P/D<1.5), moderately spaced (1.5?P/D?3), or widely spaced (P/D>3). The closely spaced staggered finite cylinders were characterized by the same Strouhal number measured behind both cylinders, an indication of single bluff-body behaviour. Moderately spaced staggered finite cylinders were characterized by two Strouhal numbers at most incidence angles. Widely spaced staggered cylinders were characterized by a single Strouhal number for both cylinders, indicative of synchronized vortex shedding from both cylinders at all incidence angles. For selected staggered configurations representative of closely spaced, moderately spaced, or widely spaced behaviour, Strouhal number measurements were also made along the vertical lengths of the cylinders, from the ground plane to the free end. The power spectra showed that for certain cylinder arrangements, because of the influences of the cylinder–wall junction and free-end flow fields, the Strouhal numbers and flow patterns change along 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.     

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.     

Vortex shedding in cylinder flow of shear-thinning fluids: I. Identification and demarcation of flow regimes

An experimental study on the flow of non-Newtonian fluids around a cylinder was undertaken to identify and delimit the various shedding flow regimes as a function of adequate non-dimensional numbers. The measurements of vortex shedding frequency and formation length (l_f) were carried out by laser-Doppler anemometry in Newtonian fluids and in aqueous polymer solutions of CMC and tylose. These were shear thinning and elastic at weight concentrations ranging from 0.1 to 0.6%. The 10 and 20 mm diameter cylinders (D) used in the experiments had aspect ratios of 12 and 6 and blockage ratios of 5 and 10%, respectively. The Reynolds number (Re^*) was based on a characteristic shear rate of U_∞/(2D) and ranged from 50 to 9×10³ thus encompassing the laminar shedding, the transition and shear-layer transition regimes. Increasing fluid elasticity reduced the various critical Reynolds numbers (Re_etr^*, Re_lf^*, Re_bbp^*) and narrowed the extent of the transition regime. For the 0.6% tylose solution the transition regime was even suppressed. On the other end, pseudoplasticity was found to be indirectly responsible for the observed reduction in Re_otr^*: it increases the Strouhal number which in turn increases the vortex filaments, precursors of the transition regime. Elasticity was better quantified by the elasticity number Re′/We than by the Weissenberg number. This elasticity number involves the calculation of the viscosity at a high characteristic shear rate, typical of the boundary layer, rather than at the average value (U_∞/(2D)) used for the Reynolds number, Re^*.     

Vortex shedding behind rings and discs

The wake structure of discs and bluff rings has been investigated experimentally in a wind tunnel. The rings have an inner diameter d_i, and an outer diameter d_o and are classified according to the parameter (d_o + d_i)/(d_o − d_i) = d/w. the ratio of mean diameter to ring width. As d/w → ∞ the flow approaches that around a two dimensional bluff body whereas as d/w tends to unity the body approaches a solid disc. A distinct change in the vortex shedding pattern is found around d/w = 5. Below this critical value velocity fluctuations in the wake have a weak periodic component which is 180° out of phase across a diameter of the body. Above d/w = 5. regular and coherent axisymmetric vortex ring shedding is observed with shedding occurring alternately from the inner and outer circumferences of the bluff body. Flow visualization and conditional averaging of hot-wire data are used to investigate the vortex structure.     

Vortex structures in shear flows

Large-scale vortex structures in shear flows are investigated. An effective method of describing these objects, which makes it possible to go beyond the framework of weak nonlinearity, is proposed. This is especially important in investigating spatially isolated structures. Evolution-type equations describing the shape of the vortex structures are obtained and their steady-state solutions are examined. A detailed classification of the structures in two-dimensional and cylindrical channels is given. Attention is drawn to the qualitative similarity of some of these structures to the well-known structures in real turbulent flows (wall eddies, turbulent slugs). It is established that isolated vortex structures in a pipe whose radius is fairly large as compared with their transverse dimension have kinematic characteristics similar to those of Hill vortices. The prospects of the method are discussed.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 65–75, March–April, 1989.The author wishes to thank G. S. Golitsyn for his interest and G. I. Barenblatt and V. M. Gryanik for discussing the results and offering useful advice.     

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.     

Vorticity shedding from a lentil-shaped body at large incidence in uniform flow

The 2D flow about a lentil-shaped body at high incidence in uniform stream is numerically simulated for high Reynolds numbers. The separation points are fixed on the body edges and the vorticity released through a Kutta-like condition is spatially discretized by point vortices. Their Lagrangianinviscid dynamics is described by using both aconformal mapping and aboundary elements method. The present results are in good agreement with previous calculations but still not satisfactory when compared with the experiments.The aim of the present work is to investigate the effect of different Kutta conditions and the effect of different amalgamation procedures in the far wake on global quantities such as theStrouhal number or the total shed circulation. Other remarkable effects induced either by the action of viscosity or by the rising of secondary 3D motion, may not be analyzed by the present simplified model.

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Sommario Si studia il flusso attorno ad una lente ad elevata incidenza nelle ipotesi di elevato numero di Reynolds e flusso bidimensionale. I punti di separazione sono fissati sulle estremità della lente e la produzione di vorticità da questi è realizzata con opportune condizioni di Kutta. La dinamica dei vortici è descritta con un modello Lagrangiano non viscoso. I risultati, ottenuti sia con l'uso di una trasformazione conforme che con un metodo agli elementi di contorno, sono in ottimo accordo con i risultati di precedenti simulazioni numeriche, ma non sono ancora soddisfacenti se confrontati con gli esperimenti.Si analizza in termini di grandezze globali del flusso, quali il numero di Strouhal e la circolazione totale rilasciata, l'effetto di due diverse condizioni di Kutta e dell'uso di procedure di compattazione della scia lontana. Si conclude che l'uso di diverse condizioni di Kutta produce risultati pressoché identici mentre l'utilizzo di procedure di compattazione della scia può alterare in modo significativo il numero di Strouhal del flusso. Rimangono da analizzare altre possibili cause del disaccordo con le sperimentazioni quali la diffusione viscosa e la probabile presenza di moti tridimensionali.

     

Vortex ring instability and collapse in a stably stratified fluid

Exploratory measurements of the effect of a stable continuous vertical stratification on horizontally propagating vortex rings show that the rings are subject to a stratification induced instability and subsequent collapse, which forms a well mixed intrusion. For initial ring Froude numbersF ₀=U ₀/Nd ₀=1.0–2.0, instability and collapse occurs when the ring Froude number has decreased to a value in the range 0.6–1.0.     

Vortex shedding from tapered,triangular plates: taper and aspect ratio effects

Further experiments on features of the vortex shedding from tapered flat plates normal to an airstream are described. The work extends that of Castro and Rogers (2002) and concentrates on the study of the effects of varying the spanwise aspect ratio for a fixed shape plate, by appropriate adjustment of end-plates, and of the nature of the shedding as the degree of taper becomes very large, so that the body is more like a triangular plate—e.g. an isosceles triangle—than a slightly tapered plate. With the taper ratio TR defined as the ratio of plate length to average cross-stream width, the paper concentrates on the range 0.58<TR<60. Reynolds numbers, based on the average plate width, exceed 10⁴. It is confirmed that for a small enough taper ratio the geometrical three-dimensionality is sufficiently strong that all signs of periodic vortex shedding cease. For all other cases, however, the flow at different locations along the span can vary substantially, depending on taper. There appear to be at least four different regimes, each appropriate for a different range of taper ratio. These various regimes are described.List of symbols AR Spanwise aspect ratio, W/d_av - d Local width of the plate - d_av Average width of the plate between the end-plates (or end-plate and tip or wall and tip), m - d₀ Base width of the plate (i.e. at z=0), m - f Shedding frequency, Hz - H Dimension of the tunnel cross-section normal to the plate symmetry axis, m - H_e Splitter plate height (see Fig. 1) - L Total length of plate (between base, where d=d₀, and tip, where d=0), m - L_e,L_f End plate dimensions (see Fig. 2) - St_d Local Strouhal number, fd/U - St₀ Strouhal number based on base width, fd₀/U - TR Taper ratio, L/d_av - U Measured free-stream velocity, m/s - W Spanwise distance between ends of plate - z distance along span, measured from base of plate - z =z/L - z Spanwise width of a constant-frequency cell     

Vortex shedding induced by a solitary wave propagating over a submerged vertical plate

Experimental study was conducted on the vortex shedding process induced by the interaction between a solitary wave and a submerged vertical plate. Particle image velocimetry (PIV) was used for quantitative velocity measurement while a particle tracing technique was used for qualitative flow visualization. Vortices are generated at the tip of each side of the plate. The largest vortices at each side of the plate eventually grow to the size of the water depth. Although the fluid motion under the solitary wave is only translatory, vortices are shed in both the upstream and downstream directions due to the interaction of the generated vortices as well as the vortices with the plate and the bottom. The process can be divided into four phases: the formation of a separated shear layer, the generation and shedding of vortices, the formation of a vertical jet, and the impingement of the jet onto the free surface. Similarity velocity profiles were found both in the separated shear layer and in the vertical jet.     

Vortex shedding around a heated square cylinder under the influence of buoyancy

The influence of buoyancy on vortex shedding and heat transfer from a cylinder of square cross-section exposed to a horizontal stream has been studied.Unsteady Navier-Stokes and energy equations are solved numerically using a control volume approach. Flow field has been analysed for a wide range of Reynolds number (which is based on the cross-sectional height of the cylinder) and Grashof number with Richardson number between 0 to 1. Our results show that the centerline symmetry of the wake is lost and the cylinder experiences a downwards lift when the buoyancy effect is considered. Vortex shedding suppression doesnt occur in the present case in which the cylinder is exposed to a horizontal cross-flow. Heat transfer from the cylinder increases due to increase in Reynolds number and Grashof number.