Vortex Shedding Regime Research Articles

Particle capture by a circular cylinder in the vortex-shedding regime

AbstractParticle capture, whereby suspended particles contact and adhere to a solid surface (a ‘collector’), is an important mechanism for a range of environmental processes including suspension feeding by corals and ‘filtering’ by aquatic vegetation. In this paper, we use two- and three-dimensional direct numerical simulations to quantify the capture efficiency ($\eta $) of low-inertia particles by a circular cylindrical collector at intermediate Reynolds numbers in the vortex-shedding regime (i.e. for$47\lt \mathit{Re}\leq 1000$, where$\mathit{Re}$is the collector Reynolds number). We demonstrate that vortex shedding induces oscillations near the leading face of the collector which greatly affect the quantity and distribution of captured particles. Unlike in steady, low-$\mathit{Re}$flow, particles directly upstream of the collector are not the most likely to be captured. Our results demonstrate the dependence of the time-averaged capture efficiency on$\mathit{Re}$and particle size, improving the predictive capability for the capture of particles by aquatic collectors. The transition to theoretical high-Reynolds-number behaviour (i.e. $\eta \sim {\mathit{Re}}^{1/ 2} $) is complex due to comparatively rapid changes in wake conditions in this Reynolds number range.

Experimental study on the confined 3D laminar flow past a square prism with a high blockage ratio

Abstract An experimental PIV study is presented that addresses the confined 3D laminar flow behaviour past a square prism. The Reynolds number (Re), based on prism cross-section height varies between 100 and 256. The channel aspect ratio is 1/1 and the blockage ratio is 1/2.5. This geometry is representative of a passive method to enhance mixing in otherwise highly ordered laminar channel flow. It is found that the lateral walls exert a strong effect on the flow behaviour with two main consequences: (a) the onset of vortex shedding is delayed to a Re in the vicinity of 170, as opposed to the unconfined case where the critical Re is reported to be between 50 and 60 and (b) transition from the steady closed recirculation bubble regime to the vortex shedding regime is not abrupt. In particular, there is a range of Re for which the closed recirculation bubble pulsates with increasing amplitude prior to the onset of the Karman street regime. The experimental results are supported by numerical computations, and the relation of the results with the practical design of engineering systems is also discussed.

Numerical Analysis of Flow Averaging Tubes in the Vortex-Shedding Regime

This paper presents a study on flowmeters oscillatory motion when subjected to periodical, enforced vibrations induced by vortex-shedding. The proposed mathematical modelling of flow was compared to corresponding numerical simulation, in form of modal analysis. The frequencies of vortices generation and detachment were calculated for a number of flow velocities in two different flowmeter profile variants. The performed modal evaluation enabled estimating their natural frequencies, and in consequence the acquired data helped us to determine flow velocity for which the analyzed structures were prone to resonant vibrations.

Momentum and Heat Transfer from a Semi-Circular Cylinder to Power-Law Fluids in the Vortex Shedding Regime

Flow and heat transfer from a semi-circular cylinder to power-law fluids has been studied in the laminar vortex shedding regime for the range of conditions as follows: Reynolds number, 40 ≤ Re ≤ 140; Prandtl number, 0.7 ≤ Pr ≤ 50; and power-law index, 0.2 ≤ n ≤ 1.8. Extensive results are presented in terms of the streamline, vorticity and isotherm profiles, drag and lift coefficients, Strouhal number, and Nusselt number. The influence of Reynolds number, Prandtl number, and power-law index are seen to be more prominent in shear-thinning fluids (n < 1) than that in shear-thickening (n > 1) fluids. The shear-thinning fluid behavior enhances the rate of heat transfer, whereas shear-thickening fluid behavior impedes it.

Hot-Wire Calibration at Low Velocities: Revisiting the Vortex Shedding Method

The necessity to calibrate hot-wire probes against a known velocity causes problems at low velocities, due to the inherent inaccuracy of pressure transducers at low differential pressures. The vortex shedding calibration method is in this respect a recommended technique to obtain calibration data at low velocities, due to its simplicity and accuracy. However, it has mainly been applied in a low and narrow Reynolds number range known as the laminar vortex shedding regime. Here, on the other hand, we propose to utilize the irregular vortex shedding regime and show where the probe needs to be placed with respect to the cylinder in order to obtain unambiguous calibration data.

Momentum and heat transfer characteristics of a long parallelepiped submerged in power-law fluids in the laminar vortex shedding regime

The governing partial differential equations describing the flow and forced convection heat transfer characteristics of power-law fluids past a long parallelepiped at α=45° incidence have been solved numerically in the two-dimensional laminar flow regime. In particular, the major thrust of this work is to elucidate the influence of Reynolds number (Re), Prandtl number (Pr) and power-law index (n) on the detailed and macroscopic momentum and heat transfer characteristics in the laminar vortex shedding regime. The detailed features of the flow and heat transfer phenomena are visualized and analyzed in terms of the instantaneous streamlines, iso-vorticity and isotherm contours whereas the surface pressure and local Nusselt number distributions over the surface of the parallelepiped provide the next level of description of these phenomena. The gross features of the flow are captured in terms of the time-averaged drag coefficient, rms value of the lift coefficient, Strouhal number and Nusselt number. The trends seen here are qualitatively similar to that reported in the literature for a circular cylinder and a bar of square cross-section (with zero angle of incidence). Broadly, shear-thinning viscosity promotes heat transfer due to the lower effective viscosity of the fluid in the close proximity of the parallelepiped bar. As expected, shear-thickening behaviour shows the opposite effect. The ranges of the pertinent dimensionless groups spanned in this study are as follows: 0.3⩽n⩽1.8; 45⩽Re⩽120 and 0.7⩽Pr⩽80. Over this range of Reynolds number, the flow was found to be truly periodic. Finally, the numerical heat transfer results are correlated using a simple analytical form which facilitates the interpolation of the present results for the intermediate values of the parameters.

Three-dimensional numerical simulation of the wake flow of an afterbody at subsonic speeds

We numerically investigate the wake flow of an afterbody at low Reynolds number in the incompressible and compressible regimes. We found that, with increasing Reynolds number, the initially stable and axisymmetric base flow undergoes a first stationary bifurcation which breaks the axisymmetry and develops two parallel steady counter-rotating vortices. The critical Reynolds number (Recs) for the loss of the flow axisymmetry reported here is in excellent agreement with previous axisymmetric BiGlobal linear stability (BiGLS) results. As the Reynolds number increases above a second threshold, Reco, we report a second instability defined as a three-dimensional peristaltic oscillation which modulates the vortices, similar to the sphere wake, sharing many points in common with long-wavelength symmetric Crow instability. Both the critical Reynolds number for the onset of oscillation, Reco, and the Strouhal number of the time-periodic limit cycle, Stsat, are substantially shifted with respect to previous axisymmetric BiGLS predictions neglecting the first bifurcation. For slightly larger Reynolds numbers, the wake oscillations are stronger and vortices are shed close to the afterbody base. In the compressible regime, no fundamental changes are observed in the bifurcation process. It is shown that the steady state planar-symmetric solution is almost equal to the incompressible case and that the break of planar symmetry in the vortex shedding regime is retarded due to compressibility effects. Finally, we report the developments of a low frequency which depends on the afterbody aspect ratio, as well as on the Reynolds and on the Mach number, prior to the loss of the planar symmetry of the wake.

On the vortex dynamics in the wake of a finite surface-mounted square cylinder

The shedding process in the near wake of a surface-mounted, square cross-section cylinder of height-to-width aspect ratio 4 at a Reynolds number of 12,000 based on free-stream velocity and the obstacle width was investigated. The boundary layer thickness was 0.18 obstacle heights based on 99% free-stream velocity. The study is performed using planar high frame-rate particle image velocimetry synchronized with pressure measurements and hot-wire anemometry. Spatial cross-correlation, instantaneous phase relationships, and phase-averaged velocity data are reported. Two dominant vortex-shedding regimes are observed. During intervals of high-amplitude pressure fluctuations on the obstacle side faces, alternate formation and shedding of vortices is observed (regime A) similar to the von Karman process. Regime B is characterized by two co-existing vortices in the obstacle lee throughout the shedding cycle and is observed within low-amplitude pressure fluctuation intervals. Despite the coexisting vortices in the base region, opposite sign vorticity is still shed out-of-phase downstream of this vortex pair giving rise to a staggered arrangement of counter-rotating vortices downstream. While the probability of occurrence of Regime B increases toward the free end, the amplitude modulation remains coherent along the obstacle height. Conditionally phase-averaged reconstructions of the flow field are consistent with the spatial distribution of the phase relationships and their probability density function. Earlier observations are reconciled showing that the symmetric shedding of vortices is a rare occurrence.

Numerical investigation of flow around an inline square cylinder array with different spacing ratios

Flow around an inline cylinder array consisting of six square cylinders at a Reynolds number of 100 is investigated numerically by using a second-order characteristic-based split finite element algorithm in this paper. The numerical method and the code for the solution of incompressible Navier–Stokes equations are validated for the flow past a single and two tandem square cylinders, and the numerical results show a good agreement with the available literatures. The study then focuses on the effect of spacing ratio (ratio of center-to-center distance s to cylinder width d, widely ranging in s/ d = 1.5–15.0) on flow characteristics by identifying flow patterns and extracting pressure distributions, force statistics as well as wake oscillation frequencies. Numerical results showed six different flow patterns, which appeared successively with the increase of gap spacing, namely, steady wake, non-fully developed vortex street in single row and double-row, fully developed vortex street in double-row, fully developed vortex street in partially recovered single-row and fully developed multiple vortex streets. A shielding effect of the first cylinder and reducing Bernoulli effect on the rear cylinder rows work in the pressure distribution even at very large gap spacing. In the vortex shedding regime, beyond the critical spacing of wake mode transition, force statistics show a periodic variation characteristic for the last four cylinders; moreover, multiple frequency components involve in the vortex shedding oscillation behind these cylinders and the dominant frequency jumps down with the increase of the spacing. Finally, the flow fields around the critical spacing range are comprehensively analyzed to reveal the crucial mechanism behind the observed aerodynamic characteristics.

Effect of confinement on power‐law fluid flow past a circular cylinder

AbstractThe role of confinement on the flow of power‐law fluids past a cylinder confined symmetrically between two parallel walls has been investigated numerically over wide ranges of conditions as follows: power‐law index (0.4 ≤n≤ 1.8), Reynolds number (40 ≤Re≤ 140) and blockage ratio (2,4,6). For Newtonian fluids, moderate degree of confinement stabilizes the flow thereby delaying the onset of the laminar vortex shedding regime. Although similar stabilization also occurs in shear‐thickening fluids, this relationship is complex for shear‐thinning fluids. Depending upon the degree of shear‐thinning, the walls may stabilize or destabilize the flow. Extensive results are presented on streamline, vorticity contours and pressure profiles herein. The power‐law behavior exerts significant influence on the macroscopic momentum transfer characteristics also. Thus, the drag and lift coefficients and Strouhal number exhibit complex dependence on Reynolds number, blockage ratio and power‐law index. Finally, the present results are consistent with the limited data available in the literature. POLYM. ENG. SCI., 2011. © 2011 Society of Plastics Engineers

Three-dimensional numerical simulation of oscillatory flow around a circular cylinder at right and oblique attacks

Sinusoidal oscillatory flow around a circular cylinder at right and oblique attacks is investigated by three-dimensional numerical simulation. Calculations are carried out for oblique angles of α=0°, 15°, 30°, 45° and 60°, Reynolds number of 2000 and KC numbers ranging from 6.75 to 30. The oblique angle of α=0° corresponds to the right attack case. The predicted vortex shedding regimes for α=0° agree well with those found in physical experiments. It is found from the numerical simulations that when KC number is in the middle range of a vortex shedding regime (i.e. KC=10, 13, 17.5 and 26.2), the flow is in single mode. In each single mode, the number of vortices shed in each flow period is constant and the sectional hydrodynamic force in the cross-flow direction fluctuates at a unique frequency. As the KC number is close to the boundary between two vortex shedding regimes ( KC=6.75, 15, 20 and 30), the number of vortices shed from the cylinder varies from period to period and the time series of the transverse force contains more than one predominant frequencies, implying the flow switching from one mode to another. This flow mode is referred to as multi-modes. The spanwise correlation factor obtained according to the sectional transverse force is close to 1 for single-mode flows. The correlation length of multi-mode flows depends on the KC number and is generally smaller than that of single-mode flows. Comparison between the numerical results of α=0° and those of α>0° shows that the independent principle is applicable for the calculated KC number range and the oblique angle ( α≤45°). For α=60°, the maximum lift coefficient C L , max and mode-averaged lift force have distinct difference from their counterparts for α=0°.

Influence of power-law index on transitional Reynolds numbers for flow over a semi-circular cylinder

In this work, the governing partial differential equations (continuity and Cauchy’s momentum equations) describing the flow of power-law type non-Newtonian fluids across a semi-circular cylinder (oriented with its curved surface in the upstream direction) have been solved numerically. In particular, consideration has been given to the delineation of the critical Reynolds numbers denoting the onset of flow separation from the surface of the cylinder and the onset of the laminar vortex shedding regime. This information is germane to establish the scaling of the macroscopic characteristics like drag coefficient and Strouhal number on the governing parameters, namely, Reynolds number and power-law index. The present results clearly suggest that the transitional Reynolds numbers show a strong dependence on the type (shear-thinning and shear-thickening) of fluid behavior as well as on the severity of the shear-dependence of the viscosity. With reference to the behavior seen in Newtonian fluids, the flow remains not only attached to the surface up to higher Reynolds numbers, but shear-thinning behavior also delays the onset of the laminar vortex shedding regime. As expected, shear-thickening fluids, of course, display the opposite characteristics.

Three-dimensional numerical simulation of flow around a circular cylinder under combined steady and oscillatory flow

Combined steady and oscillatory flow past a circular cylinder is investigated numerically by three-dimensional Direct Numerical Simulation (DNS). The incompressible Navier-Stokes equations are solved by finite element method (FEM). The aim of this study is to investigate influence of the existence of steady current on the flow regime and hydrodynamics forces. The computational results of pure oscillatory flow past a circular cylinder agree well with the experimental data. The flow ratios (ratio of current velocity to oscillatory velocity amplitude) are 0.0, 0.2 0.5 and 1.0 in the study. The influence of the flow ratio on the vortex shedding regime and hydrodynamic forces on the cylinder are investigated numerically.

Flow past a circular cylinder between parallel walls at low Reynolds numbers

The flow about a circular cylinder placed centrally inside a channel is studied numerically with an unstructured collocated grid finite volume method based on the primitive variable formulation. The distance between the channel walls is allowed to vary to change the blockage ratio. Simulations are carried out over a range of Reynolds numbers that are consistent with the two-dimensional assumption. The study confirms that transition to vortex shedding regime is delayed when the channel walls are close to the cylinder because of the interaction between the vortices from the channel wall and cylinder wake. In the unsteady vortex shedding regime, the wake pattern is opposite to the classic Karman street in respect of the positions of the shed vortices. The cylinder drag coefficient and Strouhal number are considerably increased at smaller gaps while the root-mean-squared lift coefficient is significantly decreased. Several important flow parameters are correlated with the input parameters, namely Reynolds number and blockage ratio.

Reduced order models for wake control with a spinning cylinder

We study the formulation of reduced order models for a circular spinning cylinder in laminar vortex shedding regime. Proper orthogonal decomposition techniques based on the snapshots generated from velocity fields and a Galerkin projection are used to generate a low dimensional representation of the infinite dimensional system described by the Navier Stokes equation. This kind of problem has generally been studied numerically, without taking into consideration the constraints associated to physical experimental conditions or under the assumption that actuations do not alter significantly the time averaged velocity field. We propose a reduction technique that enables to obtain a control function based on the mean velocity field deviations from the unperturbed reference flow. This function is educed with a Gram Schmidt construction and gives rise to an extended base in which the velocity fields of the perturbed modes are expanded. The analysis allows for easy determination of a suitable model to describe a large range of the control parameter space, without needing to recalculate the coefficients that define the system for new operating conditions.

Wake structure of a transversely rotating sphere at moderate Reynolds numbers

The uniform flow past a sphere undergoing steady rotation about an axis transverse to the free stream flow was investigated numerically. The objective was to reveal the effect of sphere rotation on the characteristics of the vortical wake structure and on the forces exerted on the sphere. This was achieved by solving the time-dependent, incompressible Navier–Stokes equations, using an accurate Fourier–Chebyshev spectral collocation method. Reynolds numbers Re of 100, 250 and 300 were considered, which for a stationary sphere cover the axisymmetric steady, non-axisymmetric steady and vortex shedding regimes. The study identified wake transitions that occur over the range of non-dimensional rotational speeds Ω* = 0 to 1.00, where Ω* is the maximum velocity on the sphere surface normalized by the free stream velocity. At Re = 100, sphere rotation triggers a transition to a steady double-threaded structure. At Re = 250, the wake undergoes a transition to vortex shedding for Ω* ≥ 0.08. With an increasing rotation rate, the recirculating region is progressively reduced until a further transition to a steady double-threaded wake structure for Ω* ≥ 0.30. At Re = 300, wake shedding is suppressed for Ω* ≥ 0.50 via the same mechanism found at Re = 250. For Ω* ≥ 0.80, the wake undergoes a further transition to vortex shedding, through what appears to be a shear layer instability of the Kelvin–Helmholtz type.

Flat-Plate Interaction with the Near Wake of a Square Cylinder

B LUFF bodies are integral components of aircraft, high-speed trains, automobiles, and many forms of industrial equipment. The minimization of mean and fluctuating force levels generated by bluff bodieswhen placed in afluid streamhas the benefits of reducing drag, vibration, and radiated sound. It is therefore very important that a good understanding of the flowfield about bluff bodies be obtained to achieve these aims. This Note explores how lowReynolds number bluff-body wake interference can affect the generation of unsteady flowand force. The case chosen for study is the interaction of a square cylinder and an infinitely thin flat plate. A rigid square cylinder is one of the most basic forms of a bluff body and when placed in a uniform fluid stream has been shown to exhibit strong vortex shedding, resulting in fluctuating forces and the radiation of sound in the form of an aeolian tone. Previous fluid dynamic experimental studies [1,2] exhibit this strong vortex shedding over a wide range of Reynolds number (10–10). Numerical studies investigating the fluid dynamics [3–6] also confirm this behavior. Despite the wealth of experimental data available for circular cylinders, experimental or numerical data for square cylinders are rare. Available studies include the work of Inoue [7], who performs a numerical simulation of compressible flow about a square cylinder at Re 150. Zhou et al. [8] use an upstream plate to suppress fluctuating lift on a square cylinder. They find that there is an optimal position and size for the upstream plate for effective lift suppression. Studies concerning the control of noise from a circular cylinder are more common. Recent numerical studies [9,10] investigate the use of a splitter plate attached to the base of a circular cylinder. These studies show that vortex shedding can disappear once the splitter plate achieves a certain length. Numerical solutions of the compressible unsteady Navier–Stokes equations for tandem square cylinders [11] show that significant force and noise reduction can occur if the cylinders are placed at a critical spacing in a region in which vortex shedding from the upstream cylinder is suppressed. If this separation distance is increased, the force and noise increase rapidly, due to the reestablishment of upstream vortex shedding and the associated vortex impingement on the downstream cylinder. Other work includes the experimental time-resolved force measurements of tandem bluff bodies by Sakamoto et al. [12] and Alam and Zhou [13], which were used to investigate the phase difference between the aerodynamic forces of each body in the vortex-shedding regime (i.e., the interbody spacing was such that vortex shedding was allowed to occur from each body). In each case, the phase varied linearly with separation distance. Further, Alam and Zhou developed a theoretical model based on the convective properties of isolated bluff-body wakes that agrees reasonably with experimental results. This Note will consider the case of an infinitely thin flat plate placed in the near wake of a square cylinder at a Reynolds number of Re 150. To the author’s knowledge, there have been no previous investigations of the interaction of a thin flat plate with the near wake of a square cylinder. The Note is structured as follows. After outlining the numerical approach (Sec. II), a solution of the incompressible Navier–Stokes equations for the single square cylinder case is presented and validated against available experimental and numerical results (Sec. III). A second solution is then presented that includes the downstream plate (Sec. IV), and the flow and force results are analyzed. The Note concludes with a summary of the key results.

Numerical Study on Heat Transfer and Fluid Flow Past a Circular Cylinder in the Vicinity of a Plane Wall

This article describes a numerical study on heat transfer and fluid flow for unsteady, incompressible, Newtonian fluid past a circular cylinder in the vicinity of a plane wall. Finite difference implicit method, based on vorticity-stream function formulation with uniform inlet flow conditions, is employed for unsteady state computations for Reynolds numbers in the range 20–200, consistent with a two-dimensional assumption and gap ratios (ratio of distance of the cylinder from the wall to the diameter of the cylinder) in the range between 0.1 and 2.5. With these flow parameters, vortex-shedding and its subsequent effect on heat transfer from the cylinder in the vicinity of a plane wall is investigated. The change of unsteady vortex-shedding regime from two rows of vortices of opposite-sign to single row vortices of same-sign as the cylinder approaches the plane wall can also be viewed from the time-evolution of the average Nusselt number. The vortex-shedding is found to be completely suppressed when the cylinder is located below a critical gap-ratio. The present study shows that a critical gap-ratio is to be maintained to achieve effective heat transfer from the cylinder.

Control of Vortex Shedding From a Bluff Body Using Imposed Magnetic Field

The two-dimensional incompressible laminar viscous flow of a conducting fluid past a square cylinder placed centrally in a channel subjected to an imposed transverse magnetic field has been simulated to study the effect of a magnetic field on vortex shedding from a bluff body at different Reynolds numbers varying from 50 to 250. The present staggered grid finite difference simulation shows that for a steady flow the separated zone behind the cylinder is reduced as the magnetic field strength is increased. For flows in the periodic vortex shedding and unsteady wake regime an imposed transverse magnetic field is found to have a considerable effect on the flow characteristics with marginal increase in Strouhal number and a marked drop in the unsteady lift amplitude indicating a reduction in the strength of the shed vortices. It has further been observed, that it is possible to completely eliminate the periodic vortex shedding at the higher Reynolds numbers and to establish a steady flow if a sufficiently strong magnetic field is imposed. The necessary strength of the magnetic field, however, depends on the flow Reynolds number and increases with the increase in Reynolds number. This paper describes the algorithm in detail and presents important results that show the effect of the magnetic field on the separated wake and on the periodic vortex shedding process.

The influence of temperature gradient on the Strouhal–Reynolds number relationship for water and air

This paper focuses on the wake flow behind a heated circular cylinder in the laminar vortex shedding regime. The phenomenon of vortex shedding from a bluff body is an interesting scientific and engineering problem. Acquisition of reliable experimental data is considered an indispensable step toward a deeper physical understanding of the topic. An experimental study of the wake flow behind a heated cylinder in the forced convection regime is performed using water as the working fluid. Firstly, qualitative visualization experiments were performed and the parallel vortex shedding mode was adjusted. Next, hot-wire anemometry was used for St–Re data acquisition. Data analysis confirmed the so-called thermal effect in water: cylinder heating increases the vortex shedding frequency and destabilizes the wake flow. The effective temperature concept was used and the St–Re data were successfully transformed to the St–Re eff curve. Furthermore, a comparison with air as the working fluid was discussed (cylinder heating decreases the vortex shedding frequency in air, thus stabilizing the wake flow). The formula to determine the effective temperature in water was experimentally derived from the present data, while the data and formula for air is already known. The relationship between the Strouhal number and the effective Reynolds number for water and air is represented by the same, universal formula: St = 0.2660 - 1.0160 Re eff - 0.5 , where Re eff is calculated at the effective temperature. Finally, the measurement results were compared to the thermodynamic St–Re equation derived by Maršík et al. [F. Maršík, Z. Trávníček, R.H. Yen., A.-B. Wang, Fluid dynamics concept for the critical Reynolds number of a heated/cooled cylinder in laminar crossflow, in preparation]. A satisfactory agreement between the derived equation and experimental data for both fluids (water and air) was achieved.