Wake Of Circular Cylinder Research Articles

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.

An Exploratory Analysis of the Transient and Long-Term Behavior of Small Three-Dimensional Perturbations in the Circular Cylinder Wake

An initial-value problem (IVP) for arbitrary small three-dimensional vorticity perturbations imposed on a free shear flow is considered. The viscous perturbation equations are then combined in terms of the vorticity and velocity, and are solved by means of a combined Laplace‐Fourier transform in the plane normal to the basic flow. The perturbations can be uniform or damped along the mean flow direction. This treatment allows for a simplification of the governing equations such that it is possible to observe long transients, which can last hundreds time scales. This result would not be possible over an acceptable lapse of time by carrying out a direct numerical integration of the linearized Navier‐Stokes equations. The exploration is done with respect to physical inputs as the angle of obliquity, the symmetry of the perturbation, and the streamwise damping rate. The base flow is an intermediate section of the growing two-dimensional circular cylinder wake where the entrainment process is still active. Two Reynolds numbers of the order of the critical value for the onset of the first instability are considered. The early transient evolution offers very different scenarios for which we present a summary for particular cases. For example, for amplified perturbations, we have observed two kinds of transients, namely (1) a monotone amplification and (2) a sequence of growth‐decrease‐final growth. In the latter case, if the initial condition is an asymmetric oblique or longitudinal perturbation, the transient clearly

Twenty years of experimental and direct numerical simulation access to the velocity gradient tensor: What have we learned about turbulence?

Twenty years ago there was no experimental access to the velocity gradient tensor for turbulent flows. Without such access, knowledge of fundamental and defining properties of turbulence, such as vorticity dissipation, and strain rates and helicity, could not be studied in the laboratory. Although a few direct simulations at very low Reynolds numbers had been performed, most of these did not focus on properties of the small scales of turbulence defined by the velocity gradient tensor. In 1987 the results of the development and first successful use of a multisensor hot-wire probe for simultaneous measurements of all the components of the velocity gradient tensor in a turbulent boundary layer were published by Balint et al. [Advances in Turbulence: Proceedings of the First European Turbulence Conference (Springer-Verlag, New York, 1987), p. 456]. That same year measurements of all but one of the terms in the velocity gradient tensor were carried out, although not simultaneously, in the self-preserving region of a turbulent circular cylinder wake by Browne et al. [J. Fluid Mech. 179, 307 (1987)], and the first direct numerical simulation (DNS) of a turbulent channel flow was successfully carried out and reported by Kim et al. [J. Fluid Mech. 177, 133 (1987)], including statistics of the vorticity field. Also in that year a DNS of homogeneous shear flow by Rogers and Moin [J. Fluid Mech. 176, 33 (1987)] was published in which the authors examined the structure of the vorticity field. Additionally, Ashurst et al. [Phys. Fluids 30, 2343 (1987)] examined the alignment of the vorticity and strainrate fields using this homogeneous shear flow data as well as the DNS of isotropic turbulence of Kerr [J. Fluid Mech. 153, 31 (1985)] who had initiated such studies. Furthermore, Metcalfe et al. [J. Fluid Mech. 184, 207 (1987)] published results from their direct simulation of a temporally developing planar mixing layer in which they examined coherent vortical states resulting from secondary instabilities. Since then several experimentalists have used multisensor hot-wire probes of increasing complexity in turbulent boundary layers, wakes, jets, mixing layers, and grid flows. Numerous computationalists have employed DNS in a wide variety of turbulent flows at ever increasing Reynolds numbers. Particle image velocimetry and other optical methods have been rapidly developed and advanced during these two decades which have provided other means of access to these fundamental properties of turbulence. This paper reviews highlights of these remarkable developments and points out some of the most important things we have learned about turbulence as a result.

Feedback control of a circular cylinder wake with rotational oscillation

A new feedback control algorithm for controlling vortex shedding from a circular cylinder in a uniform flow is proposed and tested. The lift coefficient (CL) is employed as a feedback signal and the control forcing is given by a rotational oscillation of the cylinder. A fractional form of the transfer function for the controller is designed, into which the interaction of the phase and magnitude of the controller is fully incorporated. In the proposed feedback control algorithm, the main emphasis is placed on controlling the phase of the feedback signal. When the feedback control forcing is imposed ‘out of phase’ with the response (i.e. outside the range of lock-on), the response is significantly reduced. In contrast, the response is increased when the feedback forcing is imposed in an ‘in phase’ manner. The effect of the feedback signal phase is ascertained by calculations using the Van der Pol oscillator, and the feedback control process is analyzed in terms of energy transfer between an actuator and an oscillator. Based on the analysis, the proposed feedback control method is applied to the wake behind a circular cylinder. The mechanism by which CL is reduced is delineated by examining the vortex formation modes as a function of the forcing phase.

Low-dimensional modelling of a transient cylinder wake using double proper orthogonal decomposition

For the systematic development of feedback flow controllers, a numerical model that captures the dynamic behaviour of the flow field to be controlled is required. This poses a particular challenge for flow fields where the dynamic behaviour is nonlinear, and the governing equations cannot easily be solved in closed form. This has led to many versions of low-dimensional modelling techniques, which we extend in this work to represent better the impact of actuation on the flow. For the benchmark problem of a circular cylinder wake in the laminar regime, we introduce a novel extension to the proper orthogonal decomposition (POD) procedure that facilitates mode construction from transient data sets. We demonstrate the performance of this new decomposition by applying it to a data set from the development of the limit cycle oscillation of a circular cylinder wake simulation as well as an ensemble of transient forced simulation results. The modes obtained from this decomposition, which we refer to as the double POD (DPOD) method, correctly track the changes of the spatial modes both during the evolution of the limit cycle and when forcing is applied by transverse translation of the cylinder. The mode amplitudes, which are obtained by projecting the original data sets onto the truncated DPOD modes, can be used to construct a dynamic mathematical model of the wake that accurately predicts the wake flow dynamics within the lock-in region at low forcing amplitudes. This low-dimensional model, derived using nonlinear artificial neural network based system identification methods, is robust and accurate and can be used to simulate the dynamic behaviour of the wake flow. We demonstrate this ability not just for unforced and open-loop forced data, but also for a feedback-controlled simulation that leads to a 90% reduction in lift fluctuations. This indicates the possibility of constructing accurate dynamic low-dimensional models for feedback control by using unforced and transient forced data only.

Flow structure behind two staggered circular cylinders. Part 1. Downstream evolution and classification

Flow structures, Strouhal numbers and their downstream evolutions in the wake of two-staggered circular cylinders are investigated at Re=7000 using hot-wire, flow-visualization and particle-image velocimetry techniques. The cylinder centre-to-centre pitch, P, ranges from 1.2d to 4.0d (d is the cylinder diameter) and the angle (α) between the incident flow and the line through the cylinder centres is 0° ~ 90°. Four distinct flow structures are identified at x/d ≥ 10 (x is the downstream distance from the mid-point between the cylinders), i.e. two single-street modes (S-I and S-II) and two twin-street modes (T-I and T-II), based on Strouhal numbers, flow topology and their downstream evolution. Mode S-I is further divided into two different types, i.e. S-Ia and S-Ib, in view of their distinct vortex strengths. Mode S-Ia occurs at P/d ≤ 1.2. The pair of cylinders behaves like one single body, and shear layers separated from the free-stream sides of the cylinders roll up, forming one street of alternately arranged vortices. The street is comparable to that behind an isolated cylinder in terms of the topology and strength of vortices. Mode S-Ib occurs at α ≤ 10° and P/d > 1.5. Shear layers separated from the upstream cylinder reattach on or roll up to form vortices before reaching the downstream cylinder, resulting in postponed flow separation from the downstream cylinder. A single vortex street thus formed is characterized by significantly weakened vortices, compared with Mode S-Ia. Mode S-II is identified at P/d=1.2~2.5 and α>20° or 1.5≤P/d≤4.0 and 10° < α≤20°, where both cylinders generate vortices, with vortex shedding from the upstream cylinder at a much higher frequency than from the downstream, producing two streets of different widths and vortex strengths at x/d≤5.0. The two streets interact vigorously, resulting in a single street of the lower-frequency vortices at x/d≥10. The vortices generated by the downstream cylinder are significantly stronger than those, originating from the upstream cylinder, in the other row. Mode T-I occurs at P/d≥2.5 and α=20°~88°; the two cylinders produce two streets of different vortex strengths and frequencies, both persisting beyond x/d=10. At P/d≥2.5 and α≥88°, the two cylinders generate two coupled streets, mostly anti-phased, of the same vortex strength and frequency (St≈0.21), which is referred to as Mode T-II. The connection of the four modes with their distinct initial conditions, i.e. interactions between shear layers around the two cylinders, is discussed.

Optimal control of the cylinder wake in the laminar regime by trust-region methods and POD reduced-order models

In this paper, optimal control theory is used to minimize the total mean drag for a circular cylinder wake flow in the laminar regime ( Re = 200 ). The control parameters are the amplitude and the frequency of the time-harmonic cylinder rotation. In order to reduce the size of the discretized optimality system, a proper orthogonal decomposition (POD) reduced-order model (ROM) is derived to be used as state equation. We then propose to employ the trust-region proper orthogonal decomposition (TRPOD) approach, originally introduced by Fahl [M. Fahl, Trust-region methods for flow control based on reduced order modeling, Ph.D. Thesis, Trier University, 2000], to update the reduced-order models during the optimization process. A lot of computational work is saved because the optimization process is now based only on low-fidelity models. A particular care was taken to derive a POD ROM for the pressure and velocity fields with an appropriate balance between model accuracy and robustness. The key enablers are the extension of the POD basis functions to the pressure data, the use of calibration methods for the POD ROM and the addition in the POD expansion of several non-equilibrium modes to describe various operating conditions. When the TRPOD algorithm is applied to the wake flow configuration, this approach converges to the minimum predicted by an open-loop control approach and leads to a relative mean drag reduction of 30% at reduced cost.

Global frequency selection in the observed time-mean wakes of circular cylinders

Observations have been made of the time-mean velocity profile at midspan in the near-wake of circular cylinders at moderate Reynolds numbers between 600 and 4600, well beyond the Reynolds number of approximately 200 at which the wake becomes three-dimensional. The measured profiles are found to be represented quite accurately by a family of function profiles with known linear instability characteristics. The complex instability frequency is then determined as a function of wake position, using the function profiles. In general, the near wake undergoes a transition from convective to absolute instability; the distance downstream to the point of transition is found to increase over the Reynolds number range investigated. The emergence of a significant region of convective instability is consistent with the known appearance of Bloor–Gerrard vortices. The selected frequency of the wake instability is determined by the saddle-point criterion; the Strouhal numbers for Bénard–von Kármán vortex shedding are found to compare well with the values in the literature.

Experimental and numerical modelling of the three-dimensional incompressible flow behaviour in the near wake of circular cylinders

An experimental investigation was carried out to study the structure of the flow field around three-dimensional circular cylinders. The study of the flow field around an obstacle was performed in a wind tunnel using a particle image velocimetry (PIV) system. The flow of a fluid around an obstacle with a different velocity to the oncoming flow was examined. The results showed the dependence of the flow structure around the obstacle on its Reynolds number, and the spacing between a pair of obstacles. Detailed quantitative information of turbulence parameters in the vicinity of the obstacle was attained. Extensive wind tunnel experimental results are presented and compared with numerical simulation. A three-dimensional numerical model with Reynolds stress model (RSM) turbulence and a non-uniform grid system were used to examine the effects of a single cylinder and two cylinders in tandem on the flow. The principal objective was to analyse three-dimensional flow past a single cylinder and two circular cylinders placed in tandem by combining the application of a PIV experimental technique and an RSM turbulence model. For the case of two cylinders in tandem, the flow patterns are characterized in the gap region as a function of the distance between the cylinders. A good level of agreement was found between the experimental results of flow and numerical simulation.

D16 円柱近傍後流のスパン方向特性に及ぼす端部層流境界層の影響(流体工学I)

D16 円柱近傍後流のスパン方向特性に及ぼす端部層流境界層の影響(流体工学I)

Numerical Computation of a New Vortex (A Cooled Vortex Street) and its Generation Mechanism in a Cooled Circular Cylinder Wake at Low Reynolds Number

A strongly cooled, circular cylinder wake with an upward main stream of air at low Reynolds number Re, i.e., 15 ≦ Re ≦ 44, is analyzed numerically, and is elucidated as follows. (1) A new vortex street, i.e., a “cooled vortex street,” is discovered, develops in the range of computed Re, i.e., 15 ≦ Re ≦ 44, has strong asymmetry, and is extremely different from the Karman vortex. (2) The vortex street occurring in the cooled wake is either the Karman vortex street or the cooled vortex street. No vortex street except these vortex streets ever occurs in a wake. (3) The critical Reynolds number Rec, i.e., the minimum Re occurring in the Karman vortex street by cooling a cylinder, is nearly 24. When the isothermal wake is cooled weakly, the Karman vortex street certainly develops at Re > 24, but never occurs at any cooling rate at Re < 24. The generation mechanism of the cooled vortex street is elucidated by employing the computed vorticity and temperature distributions as follows. (1) With an extreme increase in the cooling rate, the wake vorticity is generated strongly by the temperature gradient, the absolute value of vorticity in shear layers becomes extremely large, and the shear layers are elongated remarkably. The angle between shear layers and the wake width increase remarkably. (2) As a result, shear layers roll up considerably, and their tips reach the midplane alternately. Extremely large-scale vorticity-concentrated tips are generated, and move to the downstream. Thus a stable wake, i.e., the cooled vortex street, is generated. That is, the stable rolling of shear layers is realized only in the Karman and the cooled vortex streets.

Effect of buoyancy on the wakes of circular and square cylinders: a schlieren-interferometric study

Wakes behind heated cylinders, circular, and square have been experimentally investigated at low-Reynolds numbers. The electrically heated cylinder is mounted in a vertical airflow facility such that buoyancy aids the inertia of main flow. The operating parameters, i.e., Reynolds number and Richardson number are varied to examine flow behavior over a range of experimental conditions from forced to mixed convection regime. Laser schlieren-interferometry has been used for visualization and analysis of flow structures. Complete vortex shedding sequence has been recorded using a high-speed camera. The results on detailed dynamical characteristics of vortical structures, i.e., their size, shape and phase, Strouhal number, power spectra, convection velocity, phase shift, vortex inception length, and fluctuations are reported. On heating, alteration of organized (coherent) structures with respect to shape, size and their movement is readily perceived from instantaneous Schlieren images before they reduce to a steady plume. For both cylinders, Strouhal number shows a slow increase with an increase in Richardson number. At a critical value, there is complete disappearance of vortex shedding and a drop in Strouhal number to zero. The corresponding spectra evolve from being highly peaked at the vortex shedding frequency to a broadband appearance when vortex shedding is suppressed. The geometry of vortex structures transforms to a slender shape before shedding is suppressed. At this heating level, absence of multiple peaks in power spectra at cylinder centerline indicates absence of interaction between opposite shear layers. The convection velocity of vortices increases in stream wise direction to an asymptotic value and its variation is a function of Richardson number. The convection speed abruptly falls to zero at critical Richardson number. The phase difference of shed vortices between upstream and downstream location increases with an increase in Richardson number. Velocity profiles show an increase in fluid speed and beyond the critical point, buoyancy forces add enough momentum to cancel momentum deficit due to the cylinder. Overall, the combined effect of temperature gradient on the separating shear layer velocity profile in near field and vortical structures interaction in far field influences wake instability of a heated cylinder.

Low Reynolds number instabilities and transitions in bluff body wakes

The circular cylinder has been the generic geometry employed to understand many aspects of flows around bluff bodies, including the transition to a turbulent wake flow. The FLAIR group has been interested in the types and orders of instabilities and transitions for a range of bluff body flows. In this paper, variations of the flow from the generic case of a fixed circular cylinder are considered: contraction to a thin plate whilst preserving elliptical profile; elongation of cylinders with elliptical leading edge and square trailing edge: contraction of tori from large major radius to a sphere; and transverse oscillation of a circular cylinder. For elongated cylinders with streamlined leading edges, the analogs of the instability modes for a circular cylinder become unstable in the reverse order. As well, the analogue of mode B has a significantly increased relative spanwise wavelength and appears to have a different near-wake structure. At the other extreme, for a normal flat plate, the wake first becomes unstable to a non-periodic mode that appears distinct from either of the dominant circular cylinder wake modes. For tori, which have a local geometry approaching a two-dimensional circular cylinder for large aspect ratios, the sequence of transitions with increasing Reynolds number is a strong function of aspect ratio. For intermediate aspect ratios, the first occurring wake instability mode is a subharmonic mode. In the case of transversely oscillating cylinders, it is shown that when the two-dimensional wake is in the 2S configuration, modes A, B and QP are present, similar in nature and symmetry structure to the modes of the same names for a fixed cylinder. However, increasing the amplitude of oscillation sees the critical Reynolds number for mode A increase significantly, to the point where mode B becomes critical before mode A. For higher Reynolds numbers, the two-dimensional wake loses its spatio-temporal symmetry and takes on the P + S configuration. With the onset of this configuration, modes A, B and QP cease to exist. It is shown that two new three-dimensional modes (SL and SS) arise from this base flow. The variety of transition modes and order of transition for these different cases may have implications for the route to wake turbulence for such bodies, distinct from that found for a fixed circular cylinder.

Numerical Computation for Buoyancy Effect on Three-Dimensionality and Vortex Dislocation in Heated Wake with Vertical Mainstream

For a heated circular cylinder wake with a vertical mainstream of air at Reynolds number 300 and Richardson number 0.3, the time-dependent three-dimensionality leading to the vortex dislocation is analyzed by direct numerical simulation (DNS). Time-series images of 3-D streaklines are obtained. The computed results are compared with those in the isothermal wake. The three-dimensionality and vortex dislocation in the heated wake are discussed, and the positive buoyancy effects are revealed. Buoyancy effects are as follows: (1) an increase of the upward velocity u in the whole wake (Effect I); (2) activation of three-dimensionality in the nearwake (Effect II); (3) suppression of the Karman vortex street in the farwake (Effect III); (4) suppression of the three-dimensionality and vortex dislocation in the farwake (Effect IV). Effect IV is more dominant than Effect III. Because of buoyancy, the vortex dislocation is more suppressed than the Karman vortex street. Because of Effect II, the nearwake dominant frequency f p of spanwise velocity w is increased to 2f wake and 5f wake . Because of Effect IV, Λ d and Λ v in the farwake are increased to Λ d fallingdotseqΛ v = 3 (Mode-A*). Here f wake is the wake frequency, and Λ v and Λ d are the spanwise wavelengths of ω x , ω y , and vortex dislocation normalized by the cylinder diameter.

402 異形円柱の伴流特性(流体力学I)

402 異形円柱の伴流特性(流体力学I)

318 ノズル内の小円柱後流による二次元噴流の拡散制御 : 制御条件におけるレイノルズ数の影響(2)(OS3-4 噴流,後流,せん断流の構造・普遍的特性(噴流2),OS3噴流,後流,せん断流の構造・普遍的特性)

318 ノズル内の小円柱後流による二次元噴流の拡散制御 : 制御条件におけるレイノルズ数の影響(2)(OS3-4 噴流,後流,せん断流の構造・普遍的特性(噴流2),OS3噴流,後流,せん断流の構造・普遍的特性)

318 ノズル内の小円柱後流による二次元噴流の拡散制御 : 制御条件におけるレイノルズ数の影響(1)(OS3-4 噴流,後流,せん断流の構造・普遍的特性(噴流2),OS3噴流,後流,せん断流の構造・普遍的特性)

318 ノズル内の小円柱後流による二次元噴流の拡散制御 : 制御条件におけるレイノルズ数の影響(1)(OS3-4 噴流,後流,せん断流の構造・普遍的特性(噴流2),OS3噴流,後流,せん断流の構造・普遍的特性)

On the power required to control the circular cylinder wake by rotary oscillations

In this Brief Communication, we determine an approximate relation that gives the mean time power required to control the wake flow downstream from a circular cylinder. The control law is the sinusoidal tangential velocity imposed on whole or part of the cylinder surface. The mean control power thus depends on four parameters: the amplitude and the Strouhal number of forcing, the control angle that defines the controlled upstream part of the cylinder, and the Reynolds number. This relation indicates that the control power grows like the square of the forcing amplitude, like the square root of the forcing Strouhal number, linearly with the control angle and varies like the inverse of the square root of the Reynolds number. We show that the values obtained with this approximate relation are in very good agreement with the corresponding values given numerically. Finally, the energetic efficiency of the control is discussed. We claimed that the most energetically efficient control law corresponds a priori to low forcing amplitudes applied to a restricted upstream part of the cylinder for relatively high values of the Reynolds number.

Turbulent wake of a finite circular cylinder of small aspect ratio

Abstract The turbulent wake of a finite circular cylinder mounted normal to a wall and partially immersed in a turbulent boundary layer was studied experimentally using two-component thermal anemometry in a low-speed wind tunnel. Four circular cylinders of aspect ratios AR=9, 7, 5, and 3 were tested at a Reynolds number of Re D = 6 × 1 0 4 . The cylinders were either completely or partially immersed in the wall boundary layer, where the boundary layer thickness relative to the cylinder diameter was δ / D = 3.0 . A similar turbulent wake structure (mean velocity, turbulence intensity, and Reynolds shear stress distributions) was found for cylinders of AR=9, 7, and 5, while a distinctly different turbulent wake structure was found for the cylinder of AR=3. This was consistent with the results of a previous study that focused on the time-averaged streamwise vortex structures in the wake.