Numerical study on bifurcations in the wake of a circular disk

Using Large-eddy simulation (LES), the dynamics in the wake of a circular disk with an aspect ratio of d/w = 5 is numerically studied. The circular disk is normal to the main flow, and Reynolds number ranges from 115 to 300. The first bifurcation is confirmed for Re = 120, leading to the steady state mode with a reflectional symmetry and a double-thread wake extending to the downstream. The Hopf bifurcation is found for Re = 152, and the planar symmetry is lost, which is different from that observed in the sphere wake; it is called the “reflectional-symmetry-breaking (RSB)” mode and the hairpin vortices in this mode are always shedding in a fixed orientation. The third bifurcation is captured for Re = 166, which is named the “standing wave (SW)” mode; the planar symmetry lost in RSB mode is recovered and the hairpin vortices are shedding in the oppositely sided orientations, unlike the ones observed in the sphere wake. The fourth bifurcation, referred to as “zigzag (ZZ)” mode, is observed for Re = 265 and the planar symmetry is lost again; the hairpin vortices are shedding in an irregular orientation and propagating in a zigzagged way; and a few small-scale structures begin to appear. Three different vortex shedding regimes are found in RSB, SW and ZZ modes, respectively. Results show that the recirculation region plays a significant role in the mode transitions, and the stagnation point of recirculation zone is conjectured to be the initial region causing the wake instability.     

Coherent structure in the turbulent wake behind a circular cylinder

A wake behind a circular cylinder at Reynolds number 850–1700 was visualized by the smoke-wire method. The observations of the How together with the results of quantitative measurements, such as various velocity correlation coefficients, illustrated the formation process of spoon-shaped large eddies in the region 90 ⩽x/d⩽ 230 attained through the deformation and rearrangement of the regular Karman vortices. A spoon vortex was likely to pair with the counterpart on the opposite side of the wake. The large-scale bulges of the turbulent and non-turbulent interface of the wake were shown to correspond to these spoon vortices.These results indicate that some coherent structures are organized by rearrangement and deformation of initially regular vortices in turbulent flow.     

Spanwise correlations in the wake of a circular cylinder and a trapezoid placed inside a circular pipe

The spanwise correlation of a circular cylinder and a trapezoidal bluff body placed inside a circular pipe in fully developed turbulent regime is studied using hotwire anemometer. The present configuration possesses complex fluid structure interaction owing to the following features: high blockage effect; low aspect ratio of the body; upstream turbulence and interaction of axisymmetric flow with a two dimensional bluff body. The spatial correlation of such configuration is seldom reported in the literature. Results are presented for Reynolds number of Re_D=1×10⁵. Three different blockage ratios (0.14, 0.19 and 0.28) are considered in the present study. Correlation coefficient is observed to improve with increase in blockage ratio. Compared to a circular cylinder, a trapezoidal bluff body possesses high correlation length. The near wall effects tend to increase the phase drift, which is reflected in low correlation coefficients close to the pipe wall. The results show that the simultaneous effect of curvature, low aspect ratio and upstream turbulence reduces the correlation coefficients significantly as compared to unconfined and confined (parallel channel) flows. The low frequency modulations with a circular cylinder are higher for lower blockage ratios. The three-dimensionality of vortex shedding for trapezoid with a blockage ratio of 0.28 was observed to be lower compared to circular cylinder and all other blockage ratios. Low frequency modulations were found to be responsible for weak vortex shedding from a circular cylinder compared to a trapezoidal bluff body. The vortex shedding is observed to be nearly two dimensional in case of a trapezoidal bluff body of blockage ratio 0.28.     

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.     

Features of the supercritical transition in the wake of a circular cylinder

The features of the wake behind a uniform circular cylinder atRe=200, which is just beyond the critical Reynolds number of 3-D transition, are investigated in detail by direct numerical simulations by solving 3-D incompressible Navier-Stokes equations using mixed spectral-spectral-element method. The high-order splitting algorithm based on the mixed stiffly stable scheme is employed in the time discretization. Due to the nonlinear evolution of the secondary instability of the wake, the spanwise modes with different wavelengths emerge. The spanwise characteristic length determines the transition features and global properties of the wake. The existence of the spanwise phase difference of the primary vortices shedding is confirmed by Fourier analysis of the time series of the spanwise vorticity and attributed to the dominant spanwise mode. The spatial energy distributions of various modes and the velocity profiles in the near wake are obtained. The numerical results indicate that the near wake is in 3-D quasi-periodic laminar state with transitional behaviors at this supercritical Reynolds number. The project supported by the State Key Fundamental Research Project of “Large Scale Scientific Computation Research” (G199903281)     

Unsteady near wake of a flat disk normal to a wall

The unsteady wake of a flat disk (diameter D) located at a distance of H from a flat plate has been experimentally investigated at a Reynolds number Re _D  = 1.3 × 10⁵. Tests have been performed for a range of gap ratio (H/D), spanning from 0.3 to 1.75. The leading edge of the flat plate is either streamlined (elliptical) or blunt (square). These configurations have been studied with PIV, high speed PIV and multi-arrayed off-set fluctuating pressure measurements. The results show a progressive increase of the complexity of the flow and of the interaction as the gap ratio decreases. For large values of H/D (1.75), the interaction is weak and the power spectral densities (PSD) exhibit a strong peak associated with the vortex shedding events (St = 0.131) – St = fD/U _∞ is the Strouhal number. For lower values of H/D (0.75), the magnitude of the wall fluctuating pressure increases significantly. A large band contribution is associated with the unsteady wake structure and turbulence. A slight increase of the shedding frequency (St = 0.145) is observed. A critical value of the gap ratio (about 0.35) has been determined. Below this critical value, a three-dimensional separated region is observed and the natural vortex shedding process is very strongly altered. These changes induce a great modification of the fluctuating pressure at the wall. Each interaction reacts in a different way to perturbed upstream conditions. In particular, the disk is an overwhelming perturbation for the lowest H/D value studied here and the relative influence of the upstream turbulence on the wall fluctuating pressure below the near wake region is moderate.     

On vortex shedding behind a circular disk

Abtract  Experiments were performed for individual realizations of the vortex shedding process behind a circular disk at Reynolds numbers of 10³–10⁵, at which periodic vortex shedding prevails in the wake. The phase differences regarding the individual vortex shedding structures detected at multiple circumferential locations in the wake were obtained by analyzing the hot-wire signals with a conditional-sampling scheme. The phase differences of vortex shedding detected at circumferential positions 90° apart show a wide scatter, but the anti-phase character is largely preserved in the individual vortex shedding process as detected at circumferential locations 180° apart. The randomness of phase differences involved in the vortex shedding process is noted to be essential in order to satisfy the axisymmetric property of the global flow. Received: 4 April 19969/Accepted: 29 January 1997     

PIV measurements of the wake behind a rotationally oscillating circular cylinder

The near-wake behind a circular cylinder undergoing rotational oscillatory motion with a relatively high forcing frequency has been investigated experimentally. Experiments were carried out varying the ratio of the forcing frequency f_f to the natural vortex shedding frequency f_n in the range of 0.0 (stationary) to 1.6 at an oscillation amplitude of θ_A=30° and Reynolds number of Re=4.14×10³. Depending on the frequency ratio (F_R=f_f /f_n), the near-wake flow could be divided into three regimes—non-lock-on (F_R=0.4), transition (F_R=0.8, 1.6) and lock-on (F_R=1.0) regimes—with markedly different flow structures. When the frequency ratio was less than 1.0 (F_R⩽1.0), the rotational oscillatory motion of the cylinder decreased the length of the vortex formation region and enhanced the mutual interaction between large-scale vortices across the wake centerline. The entrainment of ambient fluid seemed to play an important role in controlling the near-wake flow and shear-layer instability. In addition, strong vortex motion was observed throughout the near-wake region. The flow characteristics changed markedly beyond the lock-on flow regime (F_R=1.0) due to the high frequency forcing. At F_R=1.6, the high frequency forcing decreased the size of the large-scale vortices by suppressing the lateral extent of the wake. In addition, the interactions between the vortices shed from both sides of the cylinder were not so strong at this forcing frequency. As a consequence, the flow entrainment and momentum transfer into the wake center region were reduced. The turbulent kinetic energy was large in the region near the edge of the recirculation region, where the vortices shed from both sides of the cylinder cross the wake centerline for all frequency ratios except for the case of F_R=1.6. The temporally resolved quantitative flow information extracted in the present work is useful for understanding the effects of open-loop active flow control on the near-wake flow structure.     

Effect of blockage on spanwise correlation in a circular cylinder wake

A short series of experiments was conducted with the aim of assessing the possible effect of tunnel blockage on spanwise correlation lengths measured in the near-wake of a circular cylinder. The results indicate that increasing blockage acts to increase spanwise correlation. This finding has important implications for the conduct and reporting of both physical and numerical experiments on bluff-body wake flows.     

The circular disk straddling the interface of a two-phase flow

The motion is determined for a thin circular disk straddling the plane interface of an immiscible two phase creeping flow and moving parallel or perpendicular to the interface. Expressions are derived for the drag coefficient on the disk.     

Stokes flow of a rotating sphere around the axis of a circular orifice or a circular disk

This paper presents an infinite series solution to the creeping flow equations for the axisymmetric motion of a sphere of arbitrary size rotating in a quiescent fluid around the axis of a circular orifice or a circular disk whose diameters are either larger or smaller than that of the sphere. Numerical tests of the convergence are passed and the comparison with the exact solution and other computational results shows an agreement to five significant figures for the torque coefficients in both cases. The torque coefficients are obtained for the sphere located up to a position tangent to the wall plane containing either the orifice or the disk. It is concluded that the torque coefficients of the sphere and the disk are monotonically increasing with the decrease of the distance from the disk or the orifice plane in both cases.     

Translatory accelerating motion of a circular disk in a viscous fluid

The exact solution of the equation of motion of a circular disk accelerated along its axis of symmetry due to an arbitrarily applied force in an otherwise still, incompressible, viscous fluid of infinite extent is obtained. The fluid resistance considered in this paper is the Stokes-flow drag which consists of the added mass effect, steady state drag, and the effect of the history of the motion. The solutions for the velocity and displacement of the circular disk are presented in explicit forms for the cases of constant and impulsive forcing functions. The importance of the effect of the history of the motion is discussed.Nomenclature a radius of the circular disk - b one half of the thickness of the circular disk - C dimensionless form of C ₁ - C ₁ magnitude of the constant force - D fluid drag force - f(t) externally applied force - F() dimensionaless form of applied force - F ₀ initial value of F - g gravitational acceleration - H() Heaviside step function - k magnitude of impulsive force - K dimensionless form of k - M a dimensionless parameter equals to (1+37#x03C0;_s/4_f) - S displacement of disk - t time - t ₁ time of application of impulsive force - u velocity of the disk - V dimensionless velocity - V ₀ initial velocity of V - V _t terminal velocity - parameter in (13) - parameter in (13) - (t) Dirac delta function - ratio of b/a - () function given in (5) - dynamical viscosity of the fluid - kinematic viscosity of the fluid - _f fluid density - _s mass density of the circular disk - dimensionless time - _i dimensionless form of t _i - dummy variable - dummy variable     

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)     

Flow structure of wake behind a rotationally oscillating circular cylinder

Flow around a circular cylinder oscillating rotationally with a relatively high forcing frequency has been investigated experimentally. The dominant parameters affecting this experiment are the Reynolds number (Re), oscillation amplitude (θ_A), and frequency ratio F_R=f_f/f_n, where f_f is the forcing frequency and f_n is the natural frequency of vortex shedding. Experiments were carried out under conditions of Re=4.14×10³, 0°θ_A60° and 0.0F_R2.0. Rotational oscillation of the cylinder significantly modified the flow structure in the near-wake. Depending on the frequency ratio F_R, the cylinder wake showed five different flow regimes, each with a distinct wake structure. The vortex formation length and the vortex shedding frequency were greatly changed before and after the lock-on regime where vortices shed at the same frequency as the forcing frequency. The lock-on phenomenon always occurred at F_R=1.0 and the frequency range of the lock-on regime expanded with increasing oscillation amplitude θ_A. In addition, the drag coefficient was reduced when the frequency ratio F_R was less than 1.0 (F_R<1.0) while fixing the oscillation amplitude at θ_A=30°. When the oscillation amplitude θ_A was used as a control parameter at a fixed frequency ratio F_R=1.0 (lock-on regime), the drag reduction effect was observed at all oscillation amplitudes except for the case of θ_A=30°. This type of active flow control method can be used effectively in aerodynamic applications while optimizing the forcing parameters.     

On the wake of a circular cylinder with nodal and saddle attachment

Flow field of a cylinder with a mid-span curvature was experimentally investigated in a wind tunnel and a water tunnel. The azimuthal orientation of the cylinder was changed to obtain a nodal, saddle and a mixed nodal–saddle type of flow attachment. Surface flow topology suggested that the nature of the attachment strongly influenced the spanwise distributions of foci structures that play a significant role in introducing three-dimensionality in the immediate wake. Flow visualization in the water tunnel revealed that the length of a vortex formation region also followed the changes in the nature of the attachment. A symmetric shedding of vortices was observed with a saddle type of attachment. Wake mean velocity profiles showed that the velocity defect and therefore the drag of a curved cylinder was minimum for nodal, and maximum for saddle type of attachment. Nomenclature of the wake was compared with asymptotic profiles and equilibrium parameters. Approach to self-preservation, similarity and other features are discussed.     

The turbulent wake of a circular cylinder rotating about the streamwise axis

This paper presents measurements in the turbulent wake of a circular cylinder rotating with its axis normal to the free-stream velocity; in other words, the axis of rotation was parallel to the streamwise direction. All three mean velocities and six Reynolds stresses were obtained at three positions downstream of the cylinder, with and without rotation of the free-stream. Most emphasis is given to the latter results because of the better flow quality. The ratio of the circumferential velocity of the cylinder to the free-stream velocity — the swirl number — had a maximum value of 0.6. Measurements for two combinations of the free-stream and angular velocities showed the velocity deficit in the wake to be a multi-valued function of the swirl number, implying that the rotation affected the separation of the cylinder's boundary layer in a complex manner. In the turbulent wake, the rotation did not significantly alter the magnitudes of the normal stresses, but caused large changes to the shape of the profiles of the axial and cross-stream normal stresses. Eventually, the primary (cross-stream) shear stress became almost entirely positive, but there was no corresponding change to the (cross-stream) gradient of the streamwise mean velocity. Despite these alterations to the turbulence, the rotationally-activated generation terms in the Reynolds transport equations never dominated the terms that are common to the wakes of rotating and non-rotating cylinders.This work was supported by the Australian Research Council. Most of the data acquisition software was written by Mr J. J. Smith.     

Dynamic and static asymmetric response of a layered thick disk

Treated is the asymmetric static and dynamic response of a stack of layered thick disks from external load. Variables of the three-dimensional equations are separated assuming approximate simple supports along the cylindrical perimeter, yielding non-orthogonal eigenfunctions. This also couples the truncated set of radial wave numbers. Applying a radial transform to all variables eliminates radial dependence producing a diagonal eigenproblem in all coupled axial wave numbers. Comparing 3-D and 2-D asymmetric models of industrial glass disks reveals that the 3-D resonances are close to their 2-D counterparts adopting the Mindlin model. A Fourier analysis of a specific asymmetric line-load from pressure or thermal expansion produces a scale factor to static stress from a limited number of asymmetric solutions each with a different circumferential wave number.