The velocity field of the turbulent very near wake of a circular cylinder

Hot-wire measurements were conducted in the very near wake (x/d10) of a circular cylinder at a Reynolds number based on cylinder diameter, Re _d of 3900. Measurements of the streamwise velocity component with the use of single sensor hot-wire probes were found to be inaccurate for such flowfields where high flow angles are present. An X-array probe provided detailed streamwise and lateral velocity component statistics. Frequency spectra of these two velocity components are also presented. Measurements with a 4-sensor hot-wire probe confirmed that the very near wake region is dominantly two-dimensional, thus validating the accuracy of the present X-array data.This study has been funded by the NASA-Ames University Consortium Cooperative Agreement, NCC2-5003. We wish to thank Patrick Beaudan for providing us with the LES results for comparison and Parviz Moin for his interest in and encouragement of this experiment to provide validation data for the LES. We also wish to thank loseph Murray for his help with the look-up-table data reduction program.     

A large eddy simulation of the near wake of a circular cylinder

Viscous flow around a circular cylinder at a subcritical Reynolds number is investigated using a large eddy simulation (LES) coupled with the Smagorinsky subgrid-scale (SGS) model. A fractional-step method with a second-order in time and a combined finite-difference/spectral approximations are used to solve the filtered three-dimensional incompressible Navier-Stokes equations. Calculations have been performed with and without the SGS model. Turbulence statistical behaviors and flow structures in the near wake of the cylinder are studied. Some calculated results, including the lift and drag coefficients, shedding frequency, peak Reynolds stresses, and time-average velocity profile, are in good agreement with the experimental and computational data, which shows that the Smagorinsky model can reasonably predict the global features of the flow and some turbulent statistical behaviors. The project supported by the National Science Fund for Distinguished Scholars (10125210), the Special Funds for Major State Basic Research Project (G1999032801) and the National Natural Science Foundation of China (19772062)     

A study of flow properties near critical points in the near wake of a circular cylinder

By applying the phase-plane technique to velocity data in the near-wake of a circular cylinder, three types of critical points are identified. Foci and saddle points occur most frequently, but a significant number of nodes is also found. Flow topology and properties associated with these points are examined in some detail. While foci and saddle points are associated with maxima of local vorticity and strain rate respectively, nodes are associated with a strong local divergence, indicating significant local three-dimensionality. The relative probability of time delay between critical points is also discussed.     

Flow around a circular cylinder—structure of the near wake shear layer

The separated shear layer in the near wake of a circular cylinder was investigated using a single hot wire probe, with special attention given to the shear layer instability characteristics. Without end plates to force parallel vortex shedding, the critical Reynolds number for the onset of the instability was 740. The present data, together with all previously published data, show that the ratio of the instability frequency f_sl to the vortex shedding frequency f_v varies as Re^0.65, which is in agreement with the Re^0.67 dependence obtained by Prasad and Williamson [1997, J Fluid Mech 333:375–402]. However, the distribution of f_sl/f_v and the spectra of the longitudinal velocity fluctuation (u) suggest that, on either side of Re=5,000, the shear layer exhibits lower and upper subcritical regimes, in support of the observations by Norberg [1987, publication no. 87/2, Chalmers University of Technology, Sweden] and Prasad and Williamson [1997, J Fluid Mech 343:235–265]. The spectra of u provide strong evidence for the occurrence of vortex pairing in wake shear layers, suggesting that the near wake develops in a similar manner to a mixing layer.     

PIV investigation of the shear layer vortices in the near wake of a circular cylinder

Particle image velocimetry measurements are performed in the near wake of a circular cylinder at a Reynolds number of 12,500. Attention is focused on the shear layer that develops just downstream of the separation point from the cylinder surface to investigate the possible existence of a preferred spatio-temporal organization in this flow region and the possible occurrence of the vortex pairing phenomenon. Eddy structures are identified in instantaneous velocity maps in order to investigate their spatial relationships. For that purpose a vortex extraction procedure is designed, based on the wavelet transform of instantaneous maps of the swirling strength. This algorithm allows not only the detection of the vortical structures from the instantaneous velocity fields, giving access to their instantaneous location, but also the estimation of their main characteristics such as their radius, intensity and convection velocity. The vortex population detected in the shear layer is found to be of small diameter compared to that of the von Kármán vortex and of rather high intensity, in agreement with the existence of a thin shear layer. The strong flapping motion of the shear layer and its complex spatial development is also confirmed. By employing conditional analysis of the computed data and their proper scaling, the surrounding of the detected vortex cores is investigated. A preferred spatial vortex separation is detected and is shown to vary with the longitudinal distance from the origin of the shear layer, in agreement with the qualitative behavior of a turbulent plane mixing layer. Evidence of the occurrence of the vortex pairing or amalgamation mechanisms in the shear layer is also demonstrated.     

Interaction between the near wake and the cross-section variation of a circular cylinder in uniform flow

The flow around a circular cylinder with a cross-section variation is experimentally investigated. Particle Image Velocimetry (PIV) is used to scrutinize the interaction of the cylinder’s wall with its near wake. The Reynolds number based on the cylinder’s diameter and freestream velocity is 80 × 10³, corresponding to the upper subcritical flow regime. At a forcing Strouhal number of St _f = 0.02, the maximum vorticity level around the cylinder is reduced by more than 50% as compared to its uncontrolled value. The topology of the bulk flow confined between the primary vortical structure and the cylinder surface is modified resulting in substantial drag reduction.     

Symmetric vortex shedding in the near wake of a circular cylinder due to streamwise perturbations

Symmetric perturbations imposed on cylinder wakes may result in a modification of the vortex shedding mode from its natural antisymmetric, or alternating, to a symmetric one where twin vortices are simultaneously shed from both sides of the cylinder. In this paper, the symmetric mode in the wake of a circular cylinder is induced by periodic perturbations imposed on the in-flow velocity. The wake field is examined by PIV and LDV for Reynolds numbers about 1200 and for a range of perturbation frequencies between three and four times the natural shedding frequency of the unperturbed wake. In this range, a strong competition between symmetric and antisymmetric vortex shedding occurs for the perturbation amplitudes employed. The results show that symmetric formation of twin vortices occurs close to the cylinder synchronized with the oscillatory component of the flow. The symmetric mode rapidly breaks down and gives rise to an antisymmetric arrangement of vortex structures further downstream. The downstream wake may or may not be phase-locked to the imposed oscillation. The number of cycles for which the symmetric vortices persist in the near wake is a probabilistic function of the perturbation frequency and amplitude. Finally, it is shown that symmetric shedding is associated with positive energy transfer from the fluid to the cylinder due to the fluctuating drag.     

Convection velocity measurements in a cylinder wake

The convection velocity of vortices in the wake of a circular cylinder has been obtained by two different approaches. The first, implemented in a wind tunnel using an array of X-wires, consists in determining the velocity at the location of maximum spanwise vorticity. Four variants of the second method, which estimates the transit time of vortices tagged by heat or dye, were used in wind and water tunnels over a relatively large Reynolds number range. Results from the two methods are in good agreement with each other. Along the most probable vortex trajectory, there is only a small streamwise increase in the convection velocity for laminar conditions and a more substantial variation when the wake is turbulent. The convection velocity is generally greater than the local mean velocity and does not depend significantly on the Reynolds number.Nomenclature d diameter of circular cylinder - f frequency in spectrum analysis - f _v average vortex frequency - r _v vortex radius - Re Reynolds number U _o d/v - t time - Th , Th , Th _r thresholds for _zp, , and r _v respectively - U _o free stream velocity - U ₁ maximum value of (U _o – U) - U _c convection velocity of the vortex, as obtained either by Eq. (1) or Eq. (2) - U _co convection velocity used in Eq. (3) U _cd, U _cu average convection velocities of downstream and up-stream regions respectively of the vortex - U _cv the value of U _c at y = 0.5 - u, v the velocity fluctuations in x and y directions respectively - U, V mean velocity components in x and y directions respectively - U,V U = U + u, V = V + v - x, y, z co-ordinate axes, defined in Fig. 1 Greek Symbols circulation - mean velocity half-width - x spacing between two cold wires or grid spacing - ₁, ₂ temperature signals from upstream and downstream cold wires respectively - v kinematic viscosity - _c transit time for a vortex to travel a distance x - phase in the cross-spectrum of ₁ and ₂ - _z instantaneous spanwise vorticity - _zc cut-off vorticity used in determining the vortex size - _zp peak value of _z - a denotes conditional average, defined in Eq. (12) - a prime denoting rms value     

Numerical study of the effects of particles on the near wake around a circular cylinder

In this work, we investigate the dynamics of the near wake in a turbulent flow going past a circular cylinder with/without particles at a moderate Reynolds number using a direct numerical simulation method. High-order finite-deference schemes are applied to solve for the bulk fluid properties, and a Lagrangian approach is adopted to track the individual particles. The single-phase flow is analysed and validated using previous experimental data. Two converged states, U- and V-shaped, are observed in the near wake, which are consistent with the experimental results. For the two-phase flow, the addition of smaller particles shortens the length of the recirculation region and causes a V-shaped profile to form behind the circular cylinder. Furthermore, the particles increase the drag force from the circular cylinder and suppress the vortex shedding frequency. An increase in the turbulent statistics in the very near wake and a decrease in the turbulent statistics further downstream are also observed.     

Experimental study of simultaneous measurement of velocity and surface topography: in the wake of a circular cylinder at low Reynolds number

A technique to provide simultaneous measurement on both free surface topography and the velocity vector field of free surface flows is further developed and validated. Testing was performed on the topography measurement by imaging static plastic wave samples over a wide range of amplitudes. Analysis on the accuracy of the topography reconstruction, the sensitivity to noise and the dependence on spatial resolution are presented. The displacement of the free surface is insensitive to noisy input and the sensitivity shows a linear dependence with the sample spacing. Simultaneous measurements of the free surface and associated velocity field in the wake of a circular cylinder are presented for Reynolds numbers between 55 and 100.     

Streakline visualization of the structures in the near wake of a circular cylinder in sinusoidally oscillating flow

A numerical investigation of three-dimensional sinusoidally oscillating flow around a circular cylinder was conducted to examine mushroom-type structures in the near wake that are manifestations of the Honji instability. The focus of this paper is to examine the flow structure through the analysis of the streaklines in the flow. Through the use of streakline visualizations and their correlation with vorticity in the flow field, the onset and development of the mushroom-type structures is followed. The parameter value range is 0.1<KC<2.0 and β=1035, 6815, and 9956. The streakline patterns in several axial planes are examined and used to describe the various mechanisms that sustain the mushroom-type structure during the oscillatory cycle.     

Experimental investigation of a circular radially deforming cylinder near wake using an infrared technique

The present experimental study aims at developing a method to control the circular cylinder near wake by radial deformation and understand the underlying physics. Using an infra-red camera, we examine the temperature distribution of the near wake center line of a sinusoidal law radially deforming circular cylinder. From these measurements, the near wake is characterized by the length of the recirculation zone, the vortex formation zone length, the temperature fluctuation maximum intensity and the vortex street shedding frequency. For several deformations frequencies, we study the radial deformation influence on the near wake characteristics. It is noted that the wake structure is strongly affected by the deformation frequency. Among other things, we note the recirculation zone length reduction and the vortex formation zone length reduction when the radial vibrations are close to the “Lock-in” fundamental range. It is also noted that the variations of the vortex shedding frequency depend on the deformation frequency.     

Heat transfer from a line source located in the periodic laminar near wake of a circular cylinder

This experimental study is devoted to the diffusion of a passive scalar downstream a line source located in a Bénard–von Kármán street. Measurements of velocity and temperature have been performed using LDA and cold wire thermometer with a phase reference. Information on the initial evolution of mean, fluctuating velocity and temperature and associated shear-stresses and heat fluxes fields are presented for two locations of the source: ( and 1). The results show that the velocity field in the wake is strongly related to the geometric structure of vortices while the temperature field is controlled by both the time scale of rotation of the vortices and the location of the heated fluid within the vortex street.     

Simultaneous measurement of velocity and pressure in a plane jet

A new technique was developed for the simultaneous measurement of velocity and pressure in turbulent flows. To accomplish this objective, a new probe (hereafter called the combined probe) that consists of an X-type hot-wire probe and a newly devised pressure probe was developed. The pressure probe was miniaturized by the MEMS fabrication process and by using a 0.1-in. microphone as a pressure sensor for improving the spatial resolution. This pressure probe was placed between two hot-wire sensors of which the X-type hot-wire probe was composed. The pressure probe was given a hemispherical tip, like that of a pitot tube, because an earlier pressure probe with a conical tip suffered from a reduction in spatial resolution. The spatial arrangement of the pressure probe and the hot-wire probe for the combined probe was carefully determined, because there was a risk that the measurement accuracy of one probe will be influenced by disturbances caused by the other probe when the two probes were placed very close to each other. Therefore, the combined probe was arranged to engender no noticeable interference between the velocity data and the pressure data measured by their respective probes. As one application of this combined probe, simultaneous measurements of pressure and two components of instantaneous velocity were performed in a plane jet. The turbulent energy budget and the cross-correlation coefficient of velocity and pressure in the intermittent region of the plane jet were estimated. The results show that the mean streamwise velocity, velocity fluctuation, and pressure fluctuation profiles were consistent with those measured individually using the X-type hot-wire probe or pressure probe. Moreover, it was shown that the integral value of the diffusion term (which should theoretically be equal to zero) in the turbulent energy transport equation was closer to zero than previous reports (Bradbury in J Fluid Mech 23(Part 1):31–64, 1965). In addition, the time variation of the cross-correlation coefficient in the intermittent region supports the vortex structure model predicted in previous studies (Browne et?al. in J Fluid Mech 149:355–373, 1984; Tanaka et?al. JSME Int J Ser B 49(4):899–905, 2006; Sakai et?al. J Fluid Sci Technol 2(3):611–622, 2007).     

POD analysis of a finite-length cylinder near wake

The near wake of a wall-mounted finite-length square cylinder with an aspect ratio of 7 is investigated based on the proper orthogonal decomposition (POD) of the PIV data measured in three spanwise planes, i.e., z/d = 6, 3.5 and 1.0, near the cylinder free end, mid-span and fixed end (wall), respectively. The Reynolds number based on free-stream velocity (U _∞) and cylinder width (d) is 9,300. A two-dimensional (2D) square cylinder wake is also measured and analyzed at the same Reynolds number for the purpose of comparison. The structures of various POD modes show marked differences between the two flows. While the coefficients, a ₁ and a ₂, of the POD modes 1 and 2 occur within an annular area centered at a ₁ = a ₂ = 0 in the 2D wake, their counterparts are scattered all over the entire circular plane at z/d = 1.0 and 3.5 of the finite-length cylinder wake. Flow at z/d = 6 is dominated by POD mode 1, which corresponds to symmetrical vortex shedding and accounts for 54.0 % of the total turbulent kinetic energy (TKE). On the other hand, the POD modes 1 and 2, corresponding to anti-symmetrical vortex shedding, are predominant, accounting for about 45.0 % of the total TKE, at z/d = 3.5 and 1. It has been found that the flow structure may be qualitatively and quantitatively characterized by the POD coefficients. For example, at z/d = 6, a larger a ₁ corresponds to a smaller length of flow reversal zone and a stronger downwash flow. At z/d = 3.5 and 1, two typical flow modes can be identified from a ₁ and a ₂. While large a ₁ and/or a ₂ correspond to anti-symmetrical vortex shedding, as in a 2D cylinder wake, small a ₁ and a ₂ lead to symmetrical vortex shedding. Any values between the large and small a ₁ and/or a ₂ correspond to the flow structure between these two typical flow modes. As such, the probability of occurrence of a flow structure may be determined from the distribution of the POD coefficients.     

Mean and fluctuating pressure measurements over a circular cylinder in cross flow using plastic tubing

Not only can mean pressures on a surface over which a fluid flows be accurately measured using a plastic tube which connects the surface tapping points to a remote pressure transducer, but the fluctuating pressures can also, provided that the transfer function, which relates the fluctuating pressures at the opposite ends of the tubing, is known. This technique was used here to measure the mean and fluctuating pressures on the surface of a circular cylinder subject to a cross-flowing airstream in the Reynolds number range from 6.8 × 10⁴ to 9.6 × 10⁴ based on cylinder diameter. Good agreement with published results gave confidence in the technique. Received: 15 April 1998/Accepted: 19 January 2000     

The near wake structure of a square cylinder

The near wake structure of a square cross section cylinder in flow perpendicular to its length was investigated experimentally over a Reynolds number (based on cylinder width) range of 6700–43,000. The wake structure and the characteristics of the instability wave, scaling on θ at separation, were strongly dependent on the incidence angle () of the freestream velocity. The nondimensional frequency (St_θ) of the instability wave varied within the range predicted for laminar instability frequencies for flat plate wakes, jets and shear layers. For = 22.5°, the freestream velocity was accelerated over the side walls and the deflection of the streamlines (from both sides of the cylinder) towards the center line was higher compared to the streamlines for = 0°. This caused the vortices from both sides of the cylinder to merge by x/d 2, giving the mean velocity distribution typical of a wake profile. For = 0°, the vortices shed from both sides of the cylinder did not merge until x/d 4.5. The separation boundary layer for all cases was either transitional or turbulent, yet the results showed good qualitative, and for some cases even quantitative, agreement with linearized stability results for small amplitude disturbances waves in laminar separation layers.     

Flow of a particulate suspension in the wake of a circular cylinder

Measurements are reported for the average local particulate velocity and concentration distributions in the wake of a cylinder immersed in a stream containing a polydisperse aerosol. The wake centerline defects and transverse distributions were determined for both parameters. It was found that the particulate centerline defect persists a considerable distance downstream of the cylinder before fully developed conditions are satisfied. Transverse particulates and gaseous velocity distributions assume a Gaussian profile at the same point downstream. The charge-to-mass ratio throughout the wake region was equal to the free stream value for all experimental conditions and was of such a magnitude to permit the electrostatic effects to be neglected in the governing equations. Gaseous and particulate transport properties were identified in the wake.     

Effects of a splitter plate on the near wake of a circular cylinder in 2 and 3-dimensional flow configurations

 Results of flow visualization, hot wire, and base pressure measurements were conducted for an investigation of the near wake of a circular cylinder at subcritical Reynolds numbers between 2700 to 46000. A base mounted splitter plate allowed for the modification of the formation region characteristics without disrupting the normal Kármán shedding. The results provide an explanation for the non-linearity in the relationship between shedding frequency and splitter plate length and extend the previous investigations of Roshko (1954), Gerrard (1966) and Apelt et al. (1973). In addition to the nominal 2-D configurations, a sinuous trailing edge splitter plate, cylinder taper, and shear flow were incorporated to study the effects of mild 3-dimensionality. A strong spanwise coherence was found to exist in the formation region. A superposition principle was discovered which showed that certain 3-D geometry and flow configurations could be combined to produce a nominal 2-D wake. Received: 26 June 1996 / Accepted: 7 January 1997     

Comparison of two methods for direct measurement of sectional fluctuating lift on a circular cylinder

Measurements of sectional r.m.s. lift coefficients for circular cylinders under similar conditions at sub-critical Reynolds numbers using (a) multiple pressure transducers with direct on-line integration and (b) pneumatic spatial pressure averaging and only two pressure transducers gave results which are in good agreement.