NUMERICAL STUDY OF THE FLOW PAST A CYLINDER EXCITED TRANSVERSELY TO THE INCIDENT STREAM. PART 1: LOCK-IN ZONE,HYDRODYNAMIC FORCES AND WAKE GEOMETRY

The numerical study of the flow past a circular cylinder forced to oscillate transversely to the incident stream is presented herein, at a fixed Reynolds number equal to 106. The finite element technique was favoured for the solution of the Navier–Stokes equations, in the formulation where the stream function and the vorticity are the field variables. The cylinder oscillation frequency ranged between 0·80 and 1·20 of the natural vortex-shedding frequency, and the oscillation amplitude extended up to 50% of the cylinder diameter. Since the resolution of the characteristics of synchronized wakes is the focus of the study, the first task is the determination of the boundary of the lock-in region. The computation revealed that, when the cylinder oscillation frequency exceeds the frequency of the natural shedding of vortices, the flow is not absolutely periodic at subsequent cycles but a quasiperiodic flow pattern occurs, which creates difficulty in the determination of the lock-in boundary. The time histories of the drag and lift forces for various oscillation parameters are presented, while the vorticity contours were favoured for the numerical flow visualization. The hydrodynamic forces, the phase angle between the lift force and the cylinder displacement, and the parameters of the wake geometry when steady state was reached, are presented in cumulative diagrams. These diagrams indicate the effect of the oscillation parameters on the hydrodynamic forces and on the wake geometry.     

VORTEX SHEDDING RESONANCE FROM A ROTATIONALLY OSCILLATING CYLINDER

Vortex shedding resonance of a circular cylinder wake to a forced rotational oscillation has been investigated experimentally by measuring the velocity fluctuations in the wake, pressure distributions over the cylinder surface, and visualizing the flow field with respect to cylinder oscillations. The vortex shedding resonance occurs near the natural shedding frequency at small amplitude of cylinder oscillations, while the peak resonance frequency shifts to a lower value with an increase in oscillation amplitude. The drag and lift forces acting on the cylinder at fixed forcing Strouhal number indicate that the phase lag of fluid forces to the cylinder oscillations increases with an increase in oscillation amplitude, supporting the variation of resonance frequency with oscillation amplitude. The comparative study of the measured pressure distributions and the simultaneous flow visualizations with respect to cylinder rotation shows the mechanisms of phase lag, which is due to the strengthened vortex formation and the modification of the surface pressure distributions.     

VORTEX-INDUCED VIBRATIONS OF AN ELASTIC CIRCULAR CYLINDER

A numerical study of a uniform flow past an elastic circular cylinder using the discrete vortex method incorporating the vortex-in-cell (VIC) technique has been undertaken. The Reynolds number is kept at 200 for all calculations and the cylinder motion is modelled by a spring–damper–mass system. The fluid motion and the structural responses are solved in an iterative way so that the interactions between the fluid and the structure can be accounted for properly. Analyses of the cylinder responses, the damping, the induced forces, the vortex shedding frequency and the vortex structure in the wake have been carried out. The results show that fluid damping is responsible for a limit-cycle oscillation behaviour even when the system natural frequency is close to the vortex-shedding frequency. Reasonable agreement with previous experimental data and computational results is obtained in the comparison of the amplitude of the limit-cycle oscillations. The results further show that the cylinder oscillations could be as large as 0·57 diameter under certain flow conditions and structural properties. Finally, it is shown that a one-degree-of-freedom structural model yields results that are only in qualitative agreement with a two-degree-of-freedom model. In other words, the streamwise oscillations also have a substantial effect on the transverse vibrations and their characteristics.     

Numerical simulation of force and wake mode of an oscillating cylinder

The turbulent flow behind a circular cylinder subjected to forced oscillation is numerically studied at a Reynolds number of 5500 by using three-dimensional Large Eddy Simulations (3-D LES) technique with the Smagorinsky model. The filtered equations are discretised using the finite volume method with an O-type structured grid and a second-order accurate method in both time and space. Firstly, the main wake parameters of a stationary cylinder are examined and compared in the different grid resolutions. Secondly, a transversely oscillating cylinder with a constant amplitude in a uniform flow is investigated. The cylinder oscillation frequency ranges between 0.75 and 0.95 of the natural Kármán frequency, and the excitation amplitude is moderate, 50% of the cylinder diameter. The flow characteristics of an oscillating cylinder are numerically examined and the corresponding wake modes are captured firstly in 3-D LES at Re=5500. A transition between different wake modes is firstly investigated in a set of numerical simulations.     

A NUMERICAL SIMULATION OF VORTEX SHEDDING FROM AN OSCILLATING CIRCULAR CYLINDER

Vortex shedding from an oscillating circular cylinder is studied by numerical solutions of the two-dimensional unsteady Navier–Stokes equations. A physically consistent method is used for the reconstruction of velocity fluxes which arise from discrete equations for the mass and momentum balances. This method ensures a second-order accuracy. Two phenomena are investigated and, in both cases, the cylinder oscillation is forced. The first is the flow induced by the harmonic in-line oscillation of cylinder in water at rest. The Reynolds number is equal to 100 and the Keulegan–Carpenter number is equal to 5. A comparison of phase-averaged velocity vectors between measurements and predictions is presented. Applying the widely used model of Morison to the computed in-line force history, the drag and the inertia coefficients are calculated and compared for different grid levels. Using these to reproduce the force functions, deviations from those originally computed are revealed. The second problem is an investigation of a transversely oscillating cylinder in a uniform flow at fixed Reynolds number equal to 185. The cylinder oscillation frequency ranges between 0·80 and 1·20 of the natural vortex-shedding frequency, and the oscillation amplitude is 20% of the cylinder diameter. As the frequency of excitation of the cylinder increases relative to the inherent vortex formation frequency, the initially formed concentration of vorticity moves closer to the cylinder until a limiting position is reached. At this point, the vorticity concentration abruptly switches to the opposite side of the cylinder. This process induces distinct changes of the topology of the corresponding streamline patterns.     

Forced Convection Heat Transfer from a Finite-Height Cylinder

This paper presents a large eddy simulation of forced convection heat transfer in the flow around a surface-mounted finite-height circular cylinder. The study was carried out for a cylinder with height-to-diameter ratio of 2.5, a Reynolds number based on the cylinder diameter of 44 000 and a Prandtl number of 1. Only the surface of the cylinder is heated while the bottom wall and the inflow are kept at a lower fixed temperature. The approach flow boundary layer had a thickness of about 10% of the cylinder height. Local and averaged heat transfer coefficients are presented. The heat transfer coefficient is strongly affected by the free-end of the cylinder. As a result of the flow over the top being downwashed behind the cylinder, a vortex-shedding process does not occur in the upper part, leading to a lower value of the local heat transfer coefficient in that region. In the lower region, vortex-shedding takes place leading to higher values of the local heat transfer coefficient. The circumferentially averaged heat transfer coefficient is 20 % higher near the ground than near the top of the cylinder. The spreading and dilution of the mean temperature field in the wake of the cylinder are also discussed.     

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.     

Wake dynamics of external flow past a curved circular cylinder with the free-stream aligned to the plane of curvature

The fundamental mechanism of vortex shedding past a curved cylinder has been investigated at a Reynolds number of 100 using three-dimensional spectral/hp computations. Two different configurations are presented herein: in both cases the main component of the geometry is a circular cylinder whose centreline is a quarter of a ring and the inflow direction is parallel to the plane of curvature. In the first set of simulations the cylinder is forced to transversely oscillate at a fixed amplitude, while the oscillation frequency has been varied around the Strouhal value. Both geometries exhibit in-phase vortex shedding, with the vortex cores bent according to the body's curvature, although the wake topology is markedly different. In particular, the configuration that was found to suppress the vortex shedding in absence of forced motion exhibits now a primary instability in the near wake. A second set of simulations has been performed imposing an oscillatory roll to the curved cylinder, which is forced to rotate transversely around the axis of its bottom section. This case shows entirely different wake features from the previous one: the vortex shedding appears to be out-of-phase along the body's span, with straight cores that tend to twist after being shed and manifest a secondary spanwise instability. Further, the damping effect stemming from the transverse planar motion of the part of the cylinder parallel to the flow is no longer present, leading to a positive energy transfer from the fluid to the structure.     

Regimes of vortex shedding from an in-line oscillating circular cylinder in the uniform flow

A finite volume method for the time dependent viscous incompressible flow around an in-line oscillating circular cylinder at Reynolds number of 200, 855 is presented in this paper. The Navier-Stokes equations in a finite volume form are solved with a moving grid system, based on a time dependent coordinate transformation. To investigate the vortex-shedding characteristics behind the circular cylinder and the effects of Reynolds number and other non-dimensional parameters such as reduced amplitude and reduced frequency， several numerical schemes have been tested with different amplitude and frequency close to Sto and a harmonic at each Reynolds number. Present numerical results indicate several types of vortex shedding mode which is known mainly depending on the reduced frequency and also the reduced amplitude, which is called synchronization or lock-on.     

Resonance in flow past oscillating cylinder under subcritical conditions

Flow around an oscillating cylinder in a subcritical region are numerically studied with a lattice Boltzmann method(LBM). The effects of the Reynolds number,oscillation amplitude and frequency on the vortex wake modes and hydrodynamics forces on the cylinder surface are systematically investigated. Special attention is paid to the phenomenon of resonance induced by the cylinder oscillation. The results demonstrate that vortex shedding can be excited extensively under subcritical conditions, and the response region of vibration frequency broadens with increasing Reynolds number and oscillation amplitude. Two distinct types of vortex shedding regimes are observed. The first type of vortex shedding regime(VSR I) is excited at low frequencies close to the intrinsic frequency of flow, and the second type of vortex shedding regime(VSR II)occurs at high frequencies with the Reynolds number close to the critical value. In the VSR I, a pair of alternately rotating vortices are shed in the wake per oscillation cycle,and lock-in/synchronization occurs, while in the VSR II, two alternately rotating vortices are shed for several oscillation cycles, and the vortex shedding frequency is close to that of a stationary cylinder under the critical condition. The excitation mechanisms of the two types of vortex shedding modes are analyzed separately.     

Active Control of a Circular Cylinder Flow at Transitional Reynolds Numbers

Active and passive control of flow around a circular cylinder, at transitional Reynolds numbers was investigated experimentally by measuring cylinder surface pressures and wake velocity profiles. Two- and three-dimensional passive boundary layer tripping was considered and periodic active control using piezo-fluidic actuators was introduced from a two-dimensional slot that was nearly tangential to the cylinder surface. The slot location was varied circumferentially by rotating the cylinder and this facilitated either upstream- or downstream-directed actuation using sinusoidal or modulated wave-forms. Separation was controlled by two distinct methods, namely: by forcing laminar-turbulent transition when applied at relatively small angles (30–60°) from the forward stagnation point; and by directly forcing the separated shear-layer at larger angles. In the latter case, actuation produced the largest load changes when it was introduced at approximately 90° from the forward stagnation point. When the forcing frequency was close to the natural vortex-shedding frequency, the two frequencies “locked-in” creating clear and persistent structures. These were examined and categorized. The “lock-in” effect lowered the base pressure and increased the form-drag whereas delaying separation from the cylinder did the opposite.     

Shear layers of a circular cylinder with rotary oscillation

The behavior of the separated shear layers and the near wake of a circular cylinder with small-amplitude rotary oscillations (Ω₁ = 0.05−0.15 for f _f/f _o ≤ 1.25) were investigated experimentally at Re = 3,700. Measurements of an unforced cylinder were also made for 2,000 ≤ Re ≤ 10,000 to better understand the effects of rotary oscillations. The results show that the shear-layer vortices formed closer to the cylinder and the distance separating them was found to decrease with cylinder oscillations. The shear-layer frequency, however, increased with increasing forcing frequency f _f. The formation-region length l _f decreased significantly with increasing f _f while decreased to a lesser extent with increasing normalized oscillation amplitude Ω₁. The shear layer also diffused to a length L _d larger than that of an unforced cylinder, while the l _f-L _d-Strouhal frequency offsetting mechanism was generally maintained. The near wake was of lower momentum compared to an unforced cylinder, and the transverse velocity fluctuations associated with the unforced vortex-shedding frequency f _o always presented a local peak at f _f/f _o = 0.5, regardless of Ω₁ tested.     

隔离板对流向振荡圆柱尾流旋涡脱落的抑制

用隔离板对直径为D, 沿流向振荡的圆柱后涡脱落进行抑制. 隔离板放于圆柱尾流中心线上,控制参数包括隔离板长度L/D以及隔离板前缘到柱体振荡中心的距离G/D. 实验的雷诺数范围Re=V_∞D/v=1.01×10⁴～1.69×10⁴,柱体折减振频范围f_eD/V_∞=0～0.03, 柱体振幅固定为A/D=0.2. 风洞烟线显示和热线测量结果表明:当 G/D位于一个有效区域内时,可有效抑制振荡柱体尾流的旋涡脱落. 该有效区的大小随着隔离板板长的增大而增大, 随着Re数和圆柱振荡频率的增大而减小.     

Application of Differing Forcing Function Models on Simulated Flow Past an Oscillating Cylinder in a Uniform Low Reynolds Number Flow

A Computational Fluid Dynamics (CFD) model is presented for the uniform viscous two dimensional flow past an oscillating cylinder at low Reynolds number. Numerical simulations are made to study the effect of differing forced induced oscillation mechanisms with a large range of cylinder forcing frequencies. In the first case sinusoidal velocity slip boundary conditions are adopted for the cylinder surface to simulate cylinder oscillation. The implication suggests that no modification or additional term need to be added to the Navier-Stokes equations. In the second case this time extra body force terms which are assumed to account for velocity effects due to cylinder movement are included in the Navier-Stokes equations with the imposition of same boundary conditions. Drag and lift coefficients are extracted from present numerical results and other detailed computations of these coefficients are made at a Reynolds number of 80 and an amplitude-to diameter ratio 0.14. The results are found to be in agreement with each other at low force driving frequencies below and near lock-in. However, differences are found at higher frequencies above lock-in. Agreement are also found with experimental results at some frequency ranges.     

On the cylinder wake subjected to in-phase and out-of-phase periodic forcing

Experiments were conducted in a wind tunnel to investigate the effect of periodic forcing on the wake of a circular cylinder specially designed for independent control of the phase of forcing from slits located on opposite sides. Tests were conducted at Reynolds number (Re) of 12,000, based on diameter (D). Wake was forced at subharmonic and harmonic frequencies at constant blowing coefficient. Measurements consisted of wake pitot surveys, hotwire anemometry, and Particle Image Velocimetry. A 20% reduction in drag was achieved when the two slits operated in-phase at third harmonic. The drag reduction, however, was 18% when the two slits operated in an out-of-phase mode for the same frequency. Wake lock-in was observed for the out-of-phase forcing case. Wake power spectrum indicated the effectiveness of both types of forcing in suppressing the primary instability. This was also evident from the results of the Proper Orthogonal Decomposition of the PIV data and turbulence statistics.     

外部激励Stuart-Landau模型的数值研究

将非线性常微分方程组周期解的求解看作一个边值问题 ,运用Newton迭代构造求解这组方程的数值方法。利用上述方法求得了激励Stuart Landau方程的周期解 ,研究了圆柱振动对圆柱后Karman涡街的抑制现象 ,和振动的频率锁定现象 ,证明了激励Stuart Landau方程描写钝体尾迹动力系统的有效性     

FEEDBACK CONTROL OF VORTEX SHEDDING FROM A CIRCULAR CYLINDER BY ROTATIONAL OSCILLATIONS

The present paper describes a new active method for controlling vortex shedding from a circular cylinder in a uniform flow at medium Reynolds numbers. It uses rotary cylinder oscillations controlled by the feedback signal of a reference velocity in the cylinder wake. The effectiveness of this feedback control is evaluated by measuring the response of mean and fluctuating velocities in the cylinder wake, the spanwise correlation, the power spectrum, and the fluid forces acting on the cylinder. It is found that the velocity fluctuations and the fluid forces are both reduced by the feedback control with optimum values of the phase lag and feedback gain. The simultaneous flow visualization synchronized with the cylinder oscillation indicates the attenuation as well as the mechanisms of vortex shedding under the feedback control, which is due to the dynamic effect of cylinder oscillation on the vortex formation.     

Numerical investigation of the turbulent energy budget in the wake of freely oscillating elastically mounted cylinder at low reduced velocities

We present a numerical study of the turbulent kinetic energy budget in the wake of cylinders undergoing Vortex-Induced Vibration (VIV). We show three-dimensional Large Eddy Simulations (LES) of an elastically mounted circular cylinder in the synchronization regime at Reynolds number of Re=8000. The Immersed Boundary Method (IBM) is used to account for the presence of the cylinder. The flow field in the wake is decomposed using the triple decomposition splitting the flow variables in mean, coherent and stochastic components. The energy transfer between these scales of motions are then studied and the results of the free oscillation are compared to those of a forced oscillation. The turbulent kinetic energy budget shows that the maximum amplitude of VIV is defined by the ability of the mean flow to feed energy to the coherent structures in the wake. At amplitudes above this maximum amplitude, the energy of the coherent structures needs to be fed additionally by small scale, stochastic energy in form of backscatter to sustain its motion. Furthermore, we demonstrate that the maximum amplitude of the VIV is defined by the integral length scale of the turbulence in the wake.     

Shedding patterns of the near-wake vortices behind a circular cylinder

The unsteady incompressible Navier-Stokes equations have been accurately solved for the laminar flow past a circular cylinder in the Reynolds number range 50–200. A direct elliptic solver called the SEVP is used to rapidly advance the streamfunction in time, facilitating the overall convergence to the fully periodic or quasi-steady state. A new integral-series method is developed for the far-field streamfunction condition on a finite two-dimensional computational domain. The use of fourth-order Hermitian relations for the convection terms in the conservation-form vorticity transport equation has also contributed to the good comparison of the present results with the earlier experimental data. The vortex-shedding patterns visualized by the experimentalist are numerically reproduced here in the given Reynolds number range. Discussions that may be helpful in interpreting the behaviour of the shedding frequency are presented in the main text.     

Investigation of turbulent flow past a yawed wavy cylinder

A large eddy simulation (LES) study was conducted to investigate the three-dimensional characteristics of the turbulent flow past wavy cylinders with yaw angles from 0° to 60° at a subcritical Reynolds number of 3900. The relationships between force coefficients and vortex shedding frequency with yaw angles for both wavy cylinders and circular cylinders were investigated. Experimental measurements were also performed for the validation of the present LES results. Comparing with corresponding yawed circular cylinders at similar Reynolds number, significant differences in wake vortex patterns between wavy cylinder and circular cylinder were observed at small yaw angles. The difference in wake pattern becomes insignificant at large yaw angles. The mean drag coefficient and the Strouhal number obey the independence principle for circular cylinders at yaw angle less than 45°, while the independence principle was found to be unsuitable for yawed wavy cylinders. In general, the mean drag coefficients and the fluctuating lift coefficients of a yawed wavy cylinder are less than those of a corresponding yawed circular cylinder at the same flow condition. However, with the increase of the yaw angle, the advantageous effect of wavy cylinder on force and vibration control becomes insignificant.