Steady forces on a cylinder with oblique vortex shedding

We present a curious situation of a fluid-flow wherein the body experiences non-fluctuating fluid-flow force despite being associated with an unsteady flow comprising of sustained vortex shedding. The flow past a circular cylinder at Re=100 is investigated. It is shown that the spatio-temporal periodicity of the oblique vortex shedding results in constant-in-time force experienced by a cylinder placed in uniform flow. On the contrary, parallel vortex shedding leads to fluid force that fluctuates with time. It is found that, both, the parallel and oblique shedding are linearly unstable eigenmodes of the Re=100 steady flow past a cylinder.     

Free v/s forced vibrations of a cylinder at low Re

Free vibrations of a circular cylinder of low non-dimensional mass are investigated at low Reynolds numbers. Computations are carried out for 5% blockage. Lock-in is observed for a range of Re and is accompanied with hysteresis at both lower as well as higher Re ends of the synchronisation/lock-in region. It is well known that the lock-in regime for free vibrations depends on the non-dimensional mass of the oscillator. The results from the present computations are compared with the data for forced vibrations from Koopmann (Journal of Fluid Mechanics, 28, 501–512, 1967) on a Y _max/D vs. f* plot, where Y _max is the maximum oscillation amplitude and f* is the ratio of cylinder vibration frequency to the vortex shedding frequency for a stationary cylinder. Good agreement is observed for the critical amplitude needed for onset of synchronisation between the forced and free vibrations. The results from the free vibrations are compared to the predictions from the linear oscillator model by assuming that the forces on the cylinder are unaffected as a result of vibrations. It is found that, for low mass oscillators, the modification of vortex shedding frequency and lift coefficient due to cylinder oscillations leads to the enhancement of the lock-in regime.     

利用O型环抑制圆柱绕法流涡脱落的数值研究

圆柱绕流涡脱落诱发较大的振动和声,如何有效地抑制值得关注.利用大涡模拟技术求解了Navier-Stokes方程,得到了涡脱落频率,升力脉动幅值及平均阻力系数.计算表明二维模拟不能体现流动基本特征,三维计算与实验吻合较好.为了抑制涡脱落,在直径为D的圆柱表面装入间距为1D,直径为0.0167D的O型环.通过升力、速度谱分析以及柱向横截面流场分析可知,在光滑圆柱外表面加入O型环能诱发流体边界层分离,有效地抑制涡脱落现象,升力脉动和观测点速度脉动幅值几乎完全消失,阻力系数也略微降低,适合在实际工程中采用.     

Three-dimensional numerical simulation of vortex-induced vibration of an elastically mounted rigid circular cylinder in steady current

Vortex-induced vibration (VIV) of an elastically mounted rigid circular cylinder in steady current is investigated by solving the three-dimensional Navier–Stokes equations. The cylinder is allowed to vibrate only in the cross-flow direction. The aim of this study is to investigate the variation of the vortex shedding flow in the axial direction of the cylinder and to study the transition of the flow from two-dimensional (2D) to three-dimensional (3D) for VIV of a cylinder. Simulations are carried out for a constant mass ratio of 2, the Reynolds numbers ranging from 150 to 1000 and the reduced velocities ranging from 2 to 12. The three-dimensionality of the flow is found to be the strongest in the upper branch of the VIV response and weakest in the initial branch. The 2S and 2P vortex shedding modes are found to coexist along the cylinder span in the upper branch, leading to strong variations of the lift coefficient in the axial direction of the cylinder. The difference between the flow transition from 2D to 3D in the VIV lock-in regime and that in the wake of a stationary cylinder is identified. The transition mode B found in the wake of a stationary cylinder is also found in the wake of a vibrating cylinder. The critical Reynolds number for flow transition from 2D to 3D of a cylinder undergoing cross-flow VIV at a reduced velocity of 6 is found to be greater than that for a stationary cylinder. For a constant reduced velocity of 6, the wake flow changes from 2D to 3D as the Reynolds number is increased from 250 to 300. Some 2D numerical simulations are performed and it is found that the 2D Navier–Stokes (NS) equations are not able to predict the VIV in the turbulent flow regime, while the 2D Reynolds-averaged Navier–Stokes (RANS) equations improve the results.     

Numerical investigation on vortex-induced vibration of an elastically mounted circular cylinder at low Reynolds number using the fictitious domain method

A direct numerical simulation of two-dimensional (2D) flow past an elastically mounted circular cylinder at low Reynolds number using the fictitious domain method had been undertaken. The cylinder motion was modelled by a two degree-of-freedom mass–spring–damper system. The computing code was verified against a benchmark problem in which flow past a stationary circular cylinder is simulated. Then, analyses of vortex-induced vibration (VIV) responses, drag and lift forces and the phase and vortex structures were carried out. Results show that the cylinder's non-dimensional cross-flow response amplitude reaches its summit of 0.572 in the ‘lock-in’ regime. The ‘2S’, instead of the ‘2P’, vortex shedding mode is dominated in the ‘lower’ branch for this 2D low-Re VIV. A secondary oscillation is observed in the lift force when ‘lock-in’ occurs. It is shown that this secondary component changes the phase, offset the energy input by the primary component and thus reduces the cylinder responses. Effects of the Skop–Griffin parameter on cylinder responses were also investigated.     

Roughness and turbulence intensity effects on the induced flow oscillation of a single cylinder

The effects of the surface roughness and the turbulence intensity on the dynamic characteristics of the flow induced oscillations of an elastically supported single circular cylinder in a cross flow in the vortex shedding and fluid elastic regions were experimentally investigated. The results of these experiments indicate that, for the vortex shedding region, increasing the surface roughness results in a reduction of the amplitude of oscillation, while in the fluid elastic region, increasing the surface roughness tends to enhance the oscillations. A similar trend for the dynamic response of the cylinder in the vortex shedding region was also observed when the free stream turbulence intensity was varied, while in the fluid elastic region variations in the free stream turbulence intensity were observed to have no drastic effect on the dynamic response of the cylinder.     

Roughness and turbulence intensity effects on the induced flow oscillation of a single cylinder

The effects of the surface roughness and the turbulence intensity on the dynamic characteristics of the flow induced oscillations of an elastically supported single circular cylinder in a cross flow in the vortex shedding and fluid elastic regions were experimentally investigated. The results of these experiments indicate that, for the vortex shedding region, increasing the surface roughness results in a reduction of the amplitude of oscillation, while in the fluid elastic region, increasing the surface roughness tends to enhance the oscillations. A similar trend for the dynamic response of the cylinder in the vortex shedding region was also observed when the free stream turbulence intensity was varied, while in the fluid elastic region variations in the free stream turbulence intensity were observed to have no drastic effect on the dynamic response of the cylinder.     

Vortex shedding from a circular cylinder with a slit and concave rear surface

Vortex shedding from short circular cylinders with a slit was studied using a flow visualization and amplitude spectrum analysis of a thermoanemometry probe signal. It was found that a circular cylinder with a slit and concave rear surface produces stronger vortices than other bluff cylinders but that these vortices are very vulnerable to the end wall conditions. It was established that two small splitter plates (tails) fixed directly behind the cylinder at the end walls effectively isolate the vortices shed from the cylinder from the end wall boundary layer effects. For this arrangement a perfect regularity of vortex shedding and almost constant Strouhal number were achieved in the Reynolds number test range of about 250 to 43,000.On a leave from Technical University, 60965 Poznan, Piotrowo 3, Poland.     

湍流涡致振动频率特性

用数值模拟方法对固定圆柱湍流涡脱落频率与弹性圆柱湍流涡致振动频率特性进行了研究,湍流计算模型采用标准κ-ε模型,压力泊松方程提法基于非交错网格系统.研究结果表明:固定圆柱湍流绕流涡脱落频率基本不随雷诺数而变,对于同一固有频率弹性圆柱,涡振频率基本不随雷诺数而变;对于某一固定雷诺数流动涡振频率在一定范围内与系统固有频率有关.     

On the origin of wake-induced vibration in two tandem circular cylinders at low Reynolds number

We numerically investigate flow-induced vibrations of circular cylinders arranged in a tandem configuration at low Reynolds number. Results on the coupled force dynamics are presented for an isolated cylinder and a pair of rigid cylinders in a tandem configuration where the downstream cylinder is elastically mounted and free to vibrate transversely. Contrary to turbulent flows at high Reynolds number, low frequency component with respect to shedding frequency is absent in laminar flows. Appearance and disappearance of the vorticity regions due to reverse flow on the aft part of the vibrating cylinder is characterized by a higher harmonic in transverse load, which is nearly three times of the shedding frequency. We next analyze the significance of pressure and viscous forces in the composition of lift and their phase relations with respect to the structural velocity. For both the isolated and tandem vibrating cylinders, the pressure force supplies energy to the moving cylinder, whereas the viscous force dissipates the energy. Close to the excitation frequency ratio of one, the ratio of transverse viscous force to pressure force is found to be maximum. In addition, movement of stagnation point plays a major role on the force dynamics of both configurations. In the case of isolated cylinder, displacement of the stagnation point is nearly in-phase with the velocity. During vortex-body interaction, the phase difference between the transverse pressure force and velocity and the location of stagnation point determines the loads acting on the cylinder. When the transverse pressure force is in-phase with velocity, the stagnation point moves to higher suction region of the cylinder. In the case of the tandem cylinder arrangement, upstream vortex shifts the stagnation point on the downstream cylinder to the low suction region. Thus a larger lift force is observed for the downstream cylinder as compared to the vibrating isolated cylinder. Phase difference between the transverse load and the velocity of the downstream cylinder determines the extent of upstream wake interaction with the downstream cylinder. When the cylinder velocity is in-phase with the transverse pressure load component, interaction of wake vortex with the downstream cylinder is lower compared to other cases considered in this study. We extend our parametric study of tandem cylinders for the longitudinal center-to-center spacing ranging from 4 to 10 diameter.     

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.     

The variation in the maximum loading of a circular cylinder impacted by a 2D vortex with time of impact

Direct numerical simulation is used to study the loading of a rigid, circular cylinder impacted by a 2D vortex. The vortex travels within a stream of fluid characterized by Reynolds number of 150. Vortex impact occurs at twenty-five different times within one vortex shedding cycle. Substantial variation is observed in the maximum values of the drag and lift force coefficients. This variation is due to interaction between the impinging vortex and those attached to the cylinder. As the radius of the impinging vortex is increased from one to three times the cylinder’s diameter, the variation in maximum force coefficients with time of impact decreases. The variation decreases because the larger vortex alters the flow field and vortex shedding cycle prior to impacting the cylinder. For structures impacted by a vortex similar in size, significant under-prediction of the maximum loading may occur if variation in loading with vortex impact time is not considered.     

Hydrodynamics of flow over a transversely oscillating circular cylinder beneath a free surface

In this paper, hydrodynamic force coefficients and wake vortex structures of uniform flow over a transversely oscillating circular cylinder beneath a free surface were numerically investigated by an adaptive Cartesian cut-cell/level-set method. At a fixed Reynolds number, 100, a series of simulations covering three Froude numbers, two submergence depths, and three oscillation amplitudes were performed over a wide range of oscillation frequency. Results show that, for a deeply submerged cylinder with sufficiently large oscillation amplitudes, both the lift amplitude jump and the lift phase sharp drop exist, not accompanied by significant changes of vortex shedding timing. The near-cylinder vortex structure changes when the lift amplitude jump occurs. For a cylinder oscillating beneath a free surface, larger oscillation amplitude or submergence depth causes higher time-averaged drag for frequency ratio (=oscillation frequency/natural vortex shedding frequency) greater than 1.25. All near-free-surface cases exhibit negative time-averaged lift the magnitude of which increases with decreasing submergence depth. In contrast to a deeply submerged cylinder, occurrences of beating in the temporal variation of lift are fewer for a cylinder oscillating beneath a free surface, especially for small submergence depth. For the highest Froude number investigated, the lift frequency is locked to the cylinder oscillation frequency for frequency ratios higher than one. The vortex shedding mode tends to be double-row for deep and single-row for shallow submergence. Proximity to the free surface would change or destroy the near-cylinder vortex structure characteristic of deep-submergence cases. The lift amplitude jump is smoother for smaller submergence depth. Similar to deep-submergence cases, the vortex shedding frequency is not necessarily the same as the primary-mode frequency of the lift coefficient. The frequency of the induced free surface wave is exactly the cylinder oscillation frequency. The trends of wave length variation with the Froude number and frequency ratio agree with those predicted by the linear theory of small-amplitude free surface waves.     

不同控制角下附加圆柱对圆柱涡激振动影响

在弹性支撑的圆柱周围布置直径更小圆柱会影响剪切层发展以及旋涡脱落,进而改变其涡激振动状态.通过不同的布置形式和附加小圆柱个数可以实现对圆柱涡激振动的促进或抑制.激励更大幅值的振动可以更好地将水流动能转化为可利用的机械能或电能,抑制其振动则可以实现对海洋平台等结构物的保护.采用基于迭代的嵌入式浸入边界法对前侧对称布置两个小圆柱的圆柱涡激振动进行数值模拟研究,系统仅做横向振动,其中基于主圆柱直径的雷诺数为100,质量比为2.0,折合流速为3~11.小圆柱与主圆柱的直径比为0.125,间隙比为0.125.结果表明,在研究的控制角范围内(30°~90°),附加小圆柱可以很大程度上改变圆柱涡激振动的状态.当控制角较小(30°)时,附加小圆柱对主圆柱的振动起抑制作用;当控制角为45°~60°时,圆柱的振动分为涡振和弛振两个阶段,在弛振阶段,圆柱振幅随折合流速增加而持续增加;当控制角较大(75°~90°)时,附加小圆柱的促进作用随着控制角增加而减小.进一步地,结合一个周期内不同时刻旋涡脱落以及圆周压强分布,解释了附加小圆柱对主圆柱涡激振动的作用机制.应用能量系数对圆柱系统的进一步分析发现,弛振阶段由流体传递到主圆柱的能量系数随折合流速的增加逐渐下降,旋涡结构的改变是产生这种变化的直接原因.      

Numerical simulation of two-degree-of-freedom vortex-induced vibration of a circular cylinder close to a plane boundary

Two-degree-of-freedom vortex-induced vibrations (VIV) of a circular cylinder close to a plane boundary are investigated numerically. The Reynolds-Averaged Navier-Stokes (RANS) equations are solved using the Arbitrary Lagrangian Eulerian (ALE) scheme with a k-ω turbulence model closure. The numerical model is validated against experimental data of VIV of a cylinder in uniform flow and VIV of a cylinder close to a plane boundary at low mass ratios. The numerical results of the vibration mode, vibration amplitude and frequency agree well with the experimental data. VIV of a circular cylinder close to a plane boundary is simulated with a mass ratio of 2.6 and gap ratios of e/D=0.002 and 0.3 (gap ratio is defined as the ratio of gap between the cylinder and the bed (e) to cylinder diameter (D)). Simulations are carried out for reduced velocities ranging from 1 to 15 and Reynolds numbers ranging from 1000 to 15 000. It is found that vortex-induced vibrations occur even if the initial gap ratio is as small as e/D=0.002, although reported research indicated that vortex shedding behind a fixed circular cylinder is suppressed at small gap ratios (e/D<0.3 or 0.2). It was also found that vibration amplitudes are dependant on the bouncing back coefficient when the cylinder hits the plane boundary. Three vortex shedding modes are identified according to the numerical results: (i) single-vortex mode where the vortices are only shed from the top of the cylinder; (ii) vortex-shedding-after-bounce-back mode; (iii) vortex-shedding-before-bounce-back mode. It was found that the vortex shedding mode depends on the reduced velocity.     

Flow above the free end of a surface-mounted finite-height circular cylinder: A review

The wake of a surface-mounted finite-height circular cylinder and the associated vortex patterns are strongly dependent on the cylinder aspect ratio and the thickness of the boundary layer on the ground plane relative to the dimensions of the cylinder. Above a critical aspect ratio, the mean wake is characterized by streamwise tip vortex structures and Kármán vortex shedding from the sides of the cylinder. Below a critical aspect ratio, a unique mean wake structure is observed. Recent experimental studies in the literature that used phase-averaged techniques, as well as recent numerical simulations, have led to an improved physical understanding of the near-wake vortex flow patterns. However, the flow above the free end of the finite circular cylinder, and its relationship to the near wake, has not been systematically studied. The effects of aspect ratio and boundary layer thickness on the free-end flow field are also not completely understood, nor has the influence of Reynolds number on the free-end flow field been fully explored. Common features associated with the free end include separation from the leading edge, a mean recirculation zone containing a prominent cross-stream arch (or mushroom) vortex, and reattachment onto the free-surface. Other flow features that remain to be clarified include a separation bubble near the leading edge, one or two cross-stream vortices within this separation bubble, the origins of the streamwise tip or trailing vortices, and various critical points in the near-surface flow topology. This paper reviews the current understanding of the flow above the free end of a surface-mounted finite-height circular cylinder, with a focus on models of the flow field, surface oil flow visualization studies, pressure and heat flux distributions on the free-end surface, measurements of the local velocity field, and numerical simulations, found in the literature.     

Wake modes of a cylinder undergoing free streamwise vortex-induced vibrations

Simultaneous measurements of the response of a circular cylinder experiencing vortex-induced vibrations (VIVs) in the streamwise direction and the resulting wake field were performed for a range of reduced velocities using time-resolved Particle-Image Velocimetry in the Reynolds number range 450–3700. The dominant vortex shedding mode was identified using phase-averaged vorticity fields. The cylinder response amplitude was characterised by two response branches, separated by a low amplitude region at resonance, as has been previously reported in the literature. During the first response branch the wake exhibited not only the symmetric S-I mode, but also the alternate A-II mode at slightly higher reduced velocities. For both modes, the vortices were observed to be shed at the cylinder response frequency, but rearranged downstream into a more stable structure in which the velocity fluctuations were no longer synchronised to the cylinder motion. A special case of the A-II mode, referred to as the SA mode, was found to dominate in the second response branch and the low amplitude region, while the far wake and the cylinder motion were synchronised (lock-in). A change in the timing of the vortex shedding with respect to the cylinder motion was observed between the low amplitude region and the second response branch. This is likely to correspond to a change in the fluid forcing and levels of excitation, and may explain the variation in the cylinder amplitude observed in this region. Lock-in and the second response branch were found to coincide with a contraction of the wake and an increase in strength of the shed vortices. This work reveals the inherent differences between the extensively studied case of transverse-only VIV and the streamwise-only case, which is crucial if the wealth of information available on transverse VIV is to be extended to the more practical two degree-of-freedom case.     

Numerical study of the suppression mechanism of vortex-induced vibration by symmetric Lorentz forces

In this paper, the electro-magnetic control of vortex-induced vibration (VIV) of a circular cylinder is investigated numerically based on the stream function–vorticity equations in the exponential–polar coordinates attached on the moving cylinder for Re=150. The effects of the instantaneous wake geometries and the corresponding cylinder motion on the hydrodynamic forces for one entire period of vortex shedding are discussed using a drag–lift phase diagram. The drag–lift diagram is composed of the upper and lower closed curves due to the contributions of the vortex shedding but is magnified, translated and turned under the action of the cylinder motion. The Lorentz force for controlling the vibration cylinder is classified into the field Lorentz force and the wall Lorentz force. The symmetric field Lorentz force will symmetrize the flow passing over the cylinder and decreases the lift oscillation, which, in turn, suppresses the VIV, whereas the wall Lorentz force has no effect on the lift. The cylinder vibration increases as the work performed by the lift dominates the energy transfer. Otherwise, the cylinder vibration decreases. If the net transferred energy per motion is equal to zero, the cylinder will vibrate steadily or be fixed.     

A finite element formulation for global linear stability analysis of a nominally two‐dimensional base flow

A stabilized finite element method, to carry out the linear stability analysis of a two‐dimensional base flow to three‐dimensional perturbations that are periodic along span, is presented. The resulting equations for the time evolution of the disturbance requires a solution to the generalized eigenvalue problem. The analysis is global in nature and is also applicable to non‐parallel flows. Equal‐order‐interpolation functions for velocity and pressure are utilized. Stabilization terms are added to the Galerkin formulation to admit the use of equal‐order‐interpolation functions and to eliminate node‐to‐node oscillations that might arise in advection‐dominated flows. The proposed formulation is tested on two flow problems. First, the mode transitions in the circular Couette flow are investigated. Two scenarios are considered. In the first one, the outer cylinder is at rest, while the inner one spins. Two linearly unstable modes are identified. The primary mode is real and represents the axisymmetric Taylor vortices. The second mode is complex and consists of spiral vortices. For the counter‐rotating cylinders, the primary transition is via the appearance of spiral vortices. Excellent agreement with results from earlier studies is observed. The formulation is also utilized to investigate the parallel and oblique modes of vortex shedding past a cylinder for the Re = 100 flow. It is found that the flow is associated with a large number of unstable oblique shedding modes. The parallel mode of vortex shedding is a special case of this family of modes and is associated with the largest growth rate. Copyright © 2014 John Wiley & Sons, Ltd.     

Vortex-induced oscillations at low Reynolds numbers: Hysteresis and vortex-shedding modes

Results are presented for the numerical simulation of vortex-induced vibrations (VIVs) of a cylinder at low Reynolds numbers (Re). A stabilized space–time finite-element formulation is utilized to solve the incompressible flow equations in primitive variables. The cylinder, of low nondimensional mass (m^*=10), is free to vibrate in, both, the transverse and in-line directions. To investigate the effect of Re and reduced natural frequency, F_n, two sets of computations are carried out. In the first set of computations the Reynolds number is fixed (=100) and the reduced velocity (U^*=1/F_n) is varied. Hysteresis, in the response of the cylinder, is observed at the low- as well as high-end of the range of reduced velocity for synchronization/lock-in. In the second set of computations, the effect of Reynolds number (50Re500) is investigated for a fixed reduced velocity (U^*=4.92). The effect of the Reynolds number is found to be very significant for VIVs. While the vortex-shedding mode at low Re is 2S (two single vortices shed per cycle), at Re300 and larger, the P+S mode of vortex shedding (a single vortex and one pair of counter-rotating vortices are released in each cycle of shedding) is observed. This is the first time that the P+S mode has been observed for a cylinder undergoing free vibrations. This change of vortex-shedding mode is hysteretic in nature and results in a very large increase in the amplitude of in-line oscillations. Since the flow ceases to remain two-dimensional beyond Re200, it remains to be seen whether the P+S mode of shedding can actually be observed in reality for free vibrations.