Wake Of Circular Cylinder Research Articles

Experimental investigation on coherent structures at early stage of boundary layer bypass transition induced by wake impingement

The early stage of a boundary layer bypass transition induced by the direct impingement of a circular cylinder wake is experimentally investigated in water tunnel, with the primary interest in both the evolution of coherent structures and their effects on the disturbance growth inside the boundary layer. It is found that spanwise vortices with small scale first form in the near-wall region around the leading-edge, which are either the residual of the wake rollers cut by the leading-edge or the high-order structures induced by the wake rollers. The formation of these spanwise vortices leads to the first rapid disturbance growth inside the boundary layer. On the other hand, streamwise vortices, which result from the impingement of longitudinal braids onto the leading-edge, are also observed inside the boundary layer. They lead to the three dimensional destabilization and the subsequent dispersion of spanwise vortices, and soon become the most dominant coherent structures inside the transitional boundary layer. It is suggested that the formation and evolution of these streamwise vortices contribute to the secondary disturbance growth stage and thus promote the completion of the transition process. The difference between the present transition scenario triggered by direct wake impingement and that by indirect wake-vortex inducement is further discussed.

Stratified wake of a tilted cylinder. Part 1. Suppression of a von Kármán vortex street

AbstractThis experimental and numerical study considers the two-dimensional stability of a circular cylinder wake, whose axis is tilted with respect to a stable density gradient. When the Reynolds number increases, the wake transitions from a steady flow to a periodic von Kármán vortex street as in a homogeneous fluid. However, the presence of a moderate stratification delays the appearance of the von Kármán vortex street, in agreement with the stabilization of shear flows by a density gradient. This stabilization, which does not occur for a vertical cylinder, increases with the tilt angle of the cylinder and is maximum for a horizontal cylinder. The critical Reynolds number increases when the stratification increases and diverges at a Froude number of order one for a horizontal cylinder. This critical Reynolds number can be predicted using the Richardson number based on the projection of the gravity and the density gradient in the direction of the shear, as was proposed by Candelier (J. Fluid Mech., vol. 685, pp. 191–201) for a tilted stratified jet. This picture is completely different for a strongly stratified wake since a new unstable mode appears, creating a von Kármán vortex street with a smaller Strouhal number. This surprising result is due to the presence of tilted vortices with no vertical velocity, i.e. with horizontal elliptic streamlines. This mode occurs in a band of Froude numbers which becomes smaller and smaller when the tilt angle increases, and eventually disappears for a horizontal cylinder. The presence of the tilt has thus a large impact on the structure of the wake at small Froude numbers and might need to be taken into account in geophysical flows.

S053045 球形リングを設置した円柱後流の流れの挙動に関する研究

S053045 球形リングを設置した円柱後流の流れの挙動に関する研究

Power production locality of bluff body flutter mills using fully coupled 2D direct numerical simulation

Two-dimensional, fully coupled direct numerical simulations (DNS) are conducted to examine the local energy dynamics of a flexible cantilevered plate in the wake of a two-dimensional circular cylinder. The motion of the cantilevered plate is described using a finite element formulation and a fully compressible, finite volume Navier Stokes solver is used to compute the flow field. A sharp interface level set method is employed in conjunction with a ghost fluid method to describe the immersed boundaries of the bluff body and flexible plate. DNS is first conducted to validate the numerical methodology and compared with previous studies of flexible cantilevered plates and flow over bluff bodies; excellent agreement with previous results is observed. A newly defined power production/loss geometry metric is introduced based on surface curvature and plate velocity. The metric is found to be useful for determining which sections of the plate will produce energy based on curvature and deflection rate. Scatter plots and probability measures are presented showing a high correlation between the direction of energy transfer ( i.e., to or from the plate) and the sign of the newly defined curvature-deflection-rate metric. The findings from this study suggest that a simple local geometry/kinematic based metric can be devised to aid in the development and design of flexible wind energy harvesting flutter mills.

Unsteady Characteristics of Longitudinal Vortices behind a Stepped Circular Cylinder and Nonlinier Interaction

Since a stepped circular cylinder is composed of two cylinders of different diameters, two different vortex shedding frequencies are presented in the wake. In the wake of a stepped circular cylinder, a pair of longitudinal vortices is formed behind the step. From spectral analysis, the longitudinal vortices are found to fluctuate with time at the frequency equal to the difference of the two vortex shedding frequencies. In this experiment, time variation of the flow field behind the stepped circular cylinder was investigated by phase ensemble averaging technique by means of X type hot wire anemometer. Pressure transducers are installed in the each cylinder part of different diameter, and their signals are digitally mixed and digitally filtered to produce an signal fluctuates at difference of the two vortex shedding frequencies, and it is used as reference signal of the phase ensemble averaging. From results of the experiments, velocity vector distributions in the plane perpendicular to the mean stream direction at the downstream of the stepped circular cylinder were found to vary drastically with time, and the strength of the longitudinal vortices was also found to vary periodically with time at the difference of the two vortex shedding frequencies. Furthermore, from TSC analysis of velocity signal obtained by means of I type hotwire anemometer, nonlinear interaction between two vortex shedding frequencies was detected around the longitudinal vortices.

Numerical investigation of the subcritical effects at the onset of three-dimensionality in the circular cylinder wake

The presented numerical simulations focus on the strong non-linear effects at the onset of three-dimensionality in the circular cylinder wake. The obtained numerical results shed light on the link between the linear theory and experimental observations. The latter are represented mainly by the Williamson’s Strouhal vs. Reynolds number experimental curve presenting a double discontinuity at the onset of three-dimensionality. In this paper, we show that the subcritical nature of the secondary bifurcation triggering the three-dimensionality considerably weakens the relevance of linear predictions. We first investigate the bi-stability interval of the subcritical bifurcation as a function of the spanwise periodicity of simulations. This allows us to define a non-linear marginal stability curve and to show that it predicts no preferred wavelength. The large spanwise scales and their effect on the simulated flow are then investigated in simulations with a spanwise periodicity of 31.4d and run for subcritical Reynolds numbers Re = 185, 170, and 160. It is shown that the non-linear state is chaotic and that the bi-stability interval in which it co-exists with the 2D parallel vortex shedding extends at least from Re = 170 to the linear secondary instability threshold lying between Re = 188 and Re = 189. Strouhal numbers obtained in simulations with a spanwise period close to 4d (linear preferred wavelength) tend to overestimate the Strouhal number drop. Simulations with a large spanwise period tend to put the Strouhal number closer to experimental values. Below the bi-stability interval, at Re = 160, the wake is observed to settle from the chaotic state to oblique vortex shedding.

Wake instability issues: From circular cylinders to stalled airfoils

Some recent results regarding the global dynamical behaviour of the wake of circular cylinders and airfoils with massive separation are reviewed in this paper. In order to investigate the effect of interference, the three-dimensional instability modes are analysed for the flow around two circular cylinders in tandem. In the same way, the flow around a stalled airfoil is investigated in order to provide a better understanding of the three-dimensional characteristics of wakes forming downstream of a lifting body with massive separation. These results are compared with those found for an isolated cylinder. Some fundamental differences among these flows are discussed.

Filtered POD‐based low‐dimensional modeling of the 3D turbulent flow behind a circular cylinder

AbstractLow‐dimensional models have proven essential for feedback control and estimation of flow fields. While feedback control based on global flow estimation can be very efficient, it is often difficult to estimate the flow state if structures of very different length scales are present in the flow. The conventional snapshot‐based proper orthogonal decomposition (POD), a popular method for low‐order modeling, does not separate the structures according to size, since it optimizes modes based on energy. Two methods are developed in this study to separate the structures in the flow based on size. One of them is Hybrid Filtered POD method and the second one is 3D FFT‐based Filtered POD approach performed using a fast Fourier transform (FFT)‐based spatial filtering. In both the methods, a spatial low‐pass filter is employed to precondition snapshot sets before deriving POD modes. Three‐dimensional flow data from the simulation of turbulent flow over a circular cylinder wake at Re=20000 is used to evaluate the performance of the two methods. Results show that both the FFT‐based 3D Filtered POD and Hybrid Filtered POD are able to capture the large‐scale features of the flow, such as the von Karman vortex street, while not being contaminated by small‐scale turbulent structures present in the flow. Copyright © 2010 John Wiley & Sons, Ltd.

Streamwise evolution of an inclined cylinder wake

The streamwise evolution of an inclined circular cylinder wake was investigated by measuring all three velocity and vorticity components using an eight-hotwire vorticity probe in a wind tunnel at a Reynolds number Red of 7,200 based on free stream velocity (U ∞) and cylinder diameter (d). The measurements were conducted at four different inclination angles (α), namely 0°, 15°, 30°, and 45° and at three downstream locations, i.e., x/d = 10, 20, and 40 from the cylinder. At x/d = 10, the effects of α on the three coherent vorticity components are negligibly small for α ≤ 15°. When α increases further to 45°, the maximum of coherent spanwise vorticity reduces by about 50%, while that of the streamwise vorticity increases by about 70%. Similar results are found at x/d = 20, indicating the impaired spanwise vortices and the enhancement of the three-dimensionality of the wake with increasing α. The streamwise decay rate of the coherent spanwise vorticity is smaller for a larger α. This is because the streamwise spacing between the spanwise vortices is bigger for a larger α, resulting in a weak interaction between the vortices and hence slower decaying rate in the streamwise direction. For all tested α, the coherent contribution to $$ \overline{{v^{2}}} $$ is remarkable at x/d = 10 and 20 and significantly larger than that to $$ \overline{{u^{2}}} $$ and $$ \overline{{w^{2}}}. $$ This contribution to all three Reynolds normal stresses becomes negligibly small at x/d = 40. The coherent contribution to $$ \overline{{u^{2}}} $$ and $$ \overline{{v^{2}}} $$ decays slower as moving downstream for a larger α, consistent with the slow decay of the coherent spanwise vorticity for a larger α.

Numerical investigations of lift suppression by feedback rotary oscillation of circular cylinder at low Reynolds number

This article describes a strategy of active flow control for lift force reduction of circular cylinder subjected to uniform flow at low Reynolds numbers. The flow control is realized by rotationally oscillating the circular cylinder about its axis with ω(t)=−λCL(t), where ω(t) is the dimensionless angular speed of rotation cylinder, λ is the control parameter and CL(t) is the feedback signal of lift coefficient. The study focuses on seeking optimum λ for the low Reynolds numbers of 60, 80, 100, 150, and 200. The effectiveness of the proposed flow control in suppressing lift force is examined comprehensively by a numerical model based on the finite element solution of two-dimensional Navier–Stokes equations. The dependence of lift reduction on the control parameter λ is investigated. The threshold of λ, denoted by λc, is identified for the Reynolds numbers considered in this work. The numerical results show that the present active rotary oscillation of circular cylinder is able to reduce the amplitude of lift force significantly as long as λ≤λc, at least 50% for the laminar flow regime. Meanwhile, the present active flow control does not result in the undesirable increase in the drag force. The Strouhal number is observed to decrease slightly with the increase of λ. As for a specific Reynolds number, the larger λ gives rise to the larger amount of lift reduction. The lift reduction reaches the maximum at λ=λc. The mechanism behind the present lift reduction method is revealed by comparing the flow patterns and pressure distributions near the active rotationally oscillating circular cylinder and the stationary circular cylinder. It is found that the critical value λc generally increases with Reynolds number. Two types of lift shift are observed in the numerical results for the cases with λ>λc. The first is characterized by the regular fluctuation of lift coefficient but with nonzero mean value, while the second is associated with the sustaining increase of lift coefficient. The phenomenon of lift shift is found to be related closely to the evolution of vortex pattern in the near wake of circular cylinder.

Effects of roughness elements on bypass transition induced by a circular cylinder wake

The bypass transition of flat-plate boundary layer induced by a circular cylinder wake under the influence of roughness elements is experimentally investigated. The hydrogen-bubble visualization results show that the boundary layer separation occurs upstream of the roughness, and the separated shear layer is incised by roughness to different extent, resulting in different kinds of secondary vortices formed immediately downstream of the roughness. During the evolution of the secondary vortex, two types of instabilities are observed, which are denoted as large- and small-scale instabilities, respectively, according to different spatial scale of the hairpin vortices formed afterward. A merging process of hairpin vortices is also observed when the secondary vortices undergo the small-scale instability, and a potential new transition control strategy based on the present observation is proposed.

Modulated waves in a periodically driven annular cavity

Time-periodic flows with spatio-temporal symmetry Z2 × O(2) – invariance in the spanwise direction generating the O(2) symmetry group and a half-period-reflection symmetry in the streamwise direction generating a spatio-temporal Z2 symmetry group – are of interest largely because this is the symmetry group of periodic laminar two-dimensional wakes of symmetric bodies. Such flows are the base states for various three-dimensional instabilities; the periodically shedding two-dimensional circular cylinder wake with three-dimensional modes A and B being the generic example. However, it is not easy to physically realize the ideal flows owing to the presence of end effects and finite spanwise geometries. Flows past rings are sometimes advanced as providing a relevant idealization, but in fact these have symmetry group O(2) and only approach Z2 × O(2) symmetry in the infinite aspect ratio limit. The present work examines physically realizable periodically driven annular cavity flows that possess Z2 × O(2) spatio-temporal symmetry. The flows have three distinct codimension-1 instabilities: two synchronous modes (A and B), and two manifestations of a quasi-periodic (QP) mode, either as modulated standing waves or modulated travelling waves. It is found that the curvature of the system can determine which of these modes is the first to become unstable with increasing Reynolds number, and that even in the nonlinear regime near onset of three-dimensional instabilities the dynamics are dominated by mixed modes with complicated spatio-temporal structure. Supplementary movies illustrating the spatio-temporal dynamics are available at journals.cambridge.org/flm.

Energy Harvesting from Highly Unsteady Fluid Flows using Piezoelectric Materials

In the present work we explore some aspects of energy harvesting from unsteady, turbulent fluid flow using piezoelectric generators. Turbulent flows exhibit a large degree of coherence in their spatial and temporal scales, which provides a unique opportunity for energy harvesting. The voltage generated by short, flexible piezoelectric cantilever beams placed inside turbulent boundary layers and wakes of circular cylinders at high Reynolds numbers is investigated. Matching the fluid flow’s predominant frequency with the natural frequency of the piezoelectric generator appears to maximize the piezoelectric output voltage. This voltage is also dependent on the generator’s location inside the flow field. A three-way coupled interaction simulation that takes into account the aerodynamics, structural vibration, and electrical response of the piezoelectric generator has been developed. The simulation results agree reasonably well with the experimental data paving the way of using such a tool to estimate the performance of different energy harvesting devices within unsteady flow fields.

Structural sensitivity of the secondary instability in the wake of a circular cylinder

The sensitivity of the three-dimensional secondary instability of a circular-cylinder wake to a structural perturbation of the associated linear equations is investigated. In particular, for a given flow condition, the region of maximum coupling between the velocity components is localized by using the most unstable Floquet mode and its adjoint mode. The variation of this region in time is also found by considering a structural perturbation which is impulsively applied in time at a given phase of the vortex-shedding process. The analysis is carried out for both mode A and mode B types of transition in the wake of a circular cylinder using a finite-difference code. The resulting regions identified as the core of the instability are in full agreement with the results reported in the literature and with the a posteriori checks documented here.

Interaction of circular cylinder wake with a short asymmetrically located downstream plate

This study reveals the interaction patterns of separated shear layers from a circular cylinder with a short downstream plate and their reflection on the frequency and the formation length of the vortices from the cylinder as a function of plate location relative to the cylinder. The effect of horizontal (G/D) and vertical (Z/D) distances between the cylinder and the plate on the near wake is studied via Digital Particle Image Velocimetry (DPIV) in a water channel for Reynolds numbers of 200, 400 and 750, based on the cylinder diameter D. It is shown that the interaction of wake with the plate of length D can be categorized depending on the horizontal and the vertical distances between the cylinder and the plate. For the vertical distance range of Z/D ≤ 0.7, there is a critical horizontal spacing before which the shear layers from the cylinder are inhibited to form vortices in front of the plate. Resulting elongated recirculation region between the plate and the cylinder suggests modification of the absolutely unstable near wake of free circular cylinder in favor of convective instability. Z/D = 0.9 provides a passage from Z/D ≤ 0.7 to ≥1.1 and is associated with a dominant effect on the near-wake characteristics of interaction of shear layers from the cylinder with those from the downstream plate. For Z/D ≥ 1.1, there is again, yet a smaller critical horizontal spacing after which vortices interact with decreased downstream plate interference. In this vertical separation distance range, a gap flow between the plate and the cylinder plays a determining role on the formation length and St number of vortices for small horizontal spacing values.

Wavelet analysis of the turbulent wake generated by an inclined circular cylinder

Three-dimensional velocity and vorticity characteristics in the near wake of a stationary circular cylinder at an inclination angle α in the range of 0°–45° are analysed using the wavelet multiresolution technique, where α = 0° represents the case of the cylinder in a cross-flow. This study aims to examine the dependence of the velocity and vorticity characteristics at different wavelet levels on α as compared with that obtained at α = 0°. The validity of the independence principle (IP) for vortex shedding was also examined. It was found that the IP is only applicable for α < 45°. The energy spectra for the intermediate and large-scale structures decrease in terms of their maximum energy and disperse extensively over an enlarged frequency band with the increase of α. At α = 45°, the large-scale vortex dislocations may occur because of the increase of the three-dimensionality in the wake region. The consequences of vortex dislocations in the wake region can also be seen from the results of the velocity and...

Three-dimensional vorticity measurements in the wake of a yawed circular cylinder

Using a phase-averaged technique, the dependence of the wake vortical structures on cylinder yaw angle α (=0°–45°) was investigated by measuring all three-velocity and vorticity components simultaneously using an eight-hot wire vorticity probe in the intermediate region (x/d=10) of a yawed stationary circular cylinder wake. For all yaw angles, the phase-averaged velocity and vorticity contours display apparent Kármán vortices. It is found that when α≤15°, the maximum coherent concentrations of the three vorticity components do not change with α. However, when α is increased to 45°, the maximum concentrations of the coherent transverse and spanwise vorticity components decrease by about 33% and 50%, respectively, while that of the streamwise vorticity increases by about 70%, suggesting that the strength of the Kármán vortex shed from the yawed cylinder decreases and the three dimensionality of the flow is enhanced. The maximum coherent concentrations of u and v contours decrease by more than 20% while that of w increases by 100%. Correspondingly, the coherent contributions to the velocity variances ⟨u2⟩ and ⟨v2⟩ decrease, while that of ⟨w2⟩ increases. These results may indicate the generation of the secondary axial vortices in yawed cylinder wakes when α is larger than 15°. The incoherent vorticity contours ⟨ωxr2⟩ are stretched along an axis inclining to the x-axis at an angle β in the range of 60°–25° for α=0°–45°. The magnitudes of ⟨ωxr2⟩∗ and ⟨ωyr2⟩∗ through the saddle points are comparable to the maximum concentration of the coherent spanwise vorticity ω̃z∗ at all cylinder yaw angles, supporting the previous speculation that the strength of the riblike structures in the cylinder wake is about the same as that of the spanwise structures, even in the yawed cylinder wakes.

Vortex modes in the wake of an oscillating long flexible cylinder combining POD and fuzzy clustering

A method combining proper orthogonal decomposition (POD) and Fuzzy Clustering (FC) is used as a pattern recognition technique, in order to identify vortex modes in digital particle image velocimetry (DPIV) data, obtained in the wake of a long flexible circular cylinder undergoing vortex-induced vibrations. The POD allows a low-dimensional description of the wake, so the the fuzzy c-means algorithm can be used for clustering in a reduced order problem. The output is a set of well-defined flow clusters representing the vortex patterns found in the wake. This methodology provides an alternative, easier to automate when dealing with large amounts of data, to instantaneous or phase averaged representations of vortex wakes. Phase averaging becomes difficult and tedious when applied as in this case, to wakes of bluff bodies undergoing non-periodic motions. The DPIV data were obtained at two elevations along the length of a long flexible circular cylinder model, which had an aspect ratio (length over diameter) of about 94. The experiments were carried out in a water channel with flow speeds up to 0.75 m/s, giving Reynolds numbers, based on the external diameter of the cylinder, in the range from 1,200 to 12,000. The set-up allowed changes in the fundamental natural frequencies, which resulted in reduced velocities based on that frequency (velocity divided by frequency and external diameter), up to 15. The mass ratio of the model (mass divided by mass of displaced fluid) was around 1.8.

Effect of velocity ratio on the streamwise vortex structures in the wake of a stack

The time-averaged velocity and streamwise vorticity fields within the wake of a short stack were investigated in a low-speed wind tunnel using a seven-hole pressure probe. The stack was mounted normal to a ground plane and was partially immersed in a flat-plate turbulent boundary layer. The jet-to-cross-flow velocity ratio was varied from R = 0 to 3, which covered the downwash, cross-wind-dominated and jet-dominated flow regimes. In the downwash and cross-wind-dominated flow regimes, two pairs of counter-rotating streamwise vortex structures were identified within the stack wake. The tip-vortex pair and base-vortex pair were similar to those found in the wake of a finite circular cylinder, located close to the free end and the base of the stack, respectively. In the jet-dominated flow regime, a third pair of streamwise vortex structures was observed, referred to as the jet-wake vortex pair, which occurred within the jet-wake region above the free end of the stack. The jet-wake vortex pair has the same orientation as the base vortex pair and is associated with the jet rise.

The ‘void’ structure in the wake of a self-oscillating flexible circular cylinder

We discuss the experimental vortex wake of a flexible circular cylinder undergoing vortex-induced vibration at low Reynolds number and a large cylinder aspect ratio. Hydrogen bubbles formed on the cylinder track the von Karman vortex cores. They show a characteristic ‘void’ structure. We propose a vortex skeleton model that includes a pinch-off of opposite-signed cores. Voids occurred at a node in streamwise vibration when close to an antinode in transverse cylinder vibration. A vibration model predicts the ratio of shedding frequency to natural cylinder vibration frequency necessary for void formation at specific spanwise locations.