Two-degree-of-freedom vortex induced vibration of low-mass horizontal circular cylinder near a free surface at low Reynolds number

Two-degree-of-freedom vortex induced vibration (VIV) of a low-mass zero-damping circular cylinder horizontally placed near a free surface at Re = 100 was numerically studied with an adaptive Cartesian cut-cell/level-set method. Two Froude numbers and various normalized submergence depths were considered. The results reveal that the Froude number affects the critical normalized submergence depth and possible physical mechanisms are proposed. The in-line vibration amplitude cannot be neglected. Proximity to a free surface strengthens and suppresses the VIV for low and high Froude numbers, respectively; increases the occurrence of amplitude modulation; and in general enhances the magnitude of the time-averaged lift coefficient, which is always negative. The phase lag of the transverse displacement behind the lift coefficient jumps at some reduced velocity, which strongly depends on the Froude number and normalized submergence depth. Regular trajectories exist only in cases with a small vibration amplitude or a large normalized submergence depth. The vortex structures in any case with large transverse amplitude basically originate from the alternative vortex shedding with the negative vortex weaker than the positive one. For the higher Froude number, an extra free surface positive vortex interacts with the vortices from the cylinder surface. The vibration frequency deviates from the natural structure frequency in fluids in the large-amplitude regime.     

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.     

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.     

Flow-induced vibrations of a tethered circular cylinder

One of the most basic examples of fluid-structure interaction is provided by a tethered body in a fluid flow. The tendency of a tethered buoy to oscillate when excited by waves is a well-known phenomenon; however, it has only recently been found that a submerged buoy will act in a similar fashion when exposed to a uniform flow at moderate Reynolds numbers, with a transverse peak-to-peak amplitude of approximately two diameters over a wide range of velocities. This paper presents results for the related problem of two-dimensional simulations of the flow past a tethered cylinder. The coupled Navier–Stokes equations and the equations of motion of the cylinder are solved using a spectral-element method. The response of the tethered cylinder system was found to be strongly influenced by the mean layover angle as this parameter determined if the oscillations would be dominated by in-line oscillations, transverse oscillations or a combination of the two. Three branches of oscillation are noted, an in-line branch, a transition branch and a transverse branch. Within the transition branch, the cylinder oscillates at the shedding frequency and modulates the drag force such that the drag signal is dominated by the lift frequency. It is found that the mean amplitude response is greatest at high reduced velocities, i.e., when the cylinder is oscillating predominantly transverse to the fluid flow. Furthermore, the oscillation frequency is synchronized to the vortex shedding frequency of a stationary cylinder, except at very high reduced velocities. Visualizations of the pressure and vorticity in the wake reveal the mechanisms behind the motion of the cylinder.     

流向振荡圆柱绕流的格子Boltzmann方法模拟

用一种新近发展起来的格子Boltzmann方法(LBM)在相对较小的雷诺数(Re \le 200)条件下模拟了不可压缩的流向振荡圆柱绕流问题, 考查了涡脱落模态和升阻力特性. 通过模拟, 在近尾流区发现了实验研究中已经发现的对称/反对称的涡脱落模态, 包括有些传统数值方法未发现的模态. 研究了频率锁定区域的范围及其与振幅的关系, 发现振幅越大, 发生锁定的频率区域越宽. 此外还对升阻力进行了定量意义的模拟,研究了振荡频率和振幅与升阻力的关系.      

基于浸入边界算法的振动钝体绕流模拟研究

传统CFD方法在振动钝体绕流计算中常借助动网格技术,网格再生任务繁重。针对于此,本文利用可在静止网格中计算动边界绕流问题的浸入边界算法(IBM),编写数值模拟程序,分别对竖向强迫正弦振动方柱(Re=UD/v=103、振幅恒定、振动频率变化)以及桥梁断面(Re=UB/v=7.5×103、振幅、振动频率均变化)展开气动特性和流场特征结构分析。初步研究结果表明,振幅恒定为方柱高度的14%时,其涡脱锁定区长度为0.06~0.2,锁定区后端(Stc0.2)振动方柱涡脱频率回归静止涡脱频率;不同振幅下的桥梁断面阻力系数均在静止涡脱频率处产生峰值,桥梁断面升力系数则在此处均出现归零效应,且振幅越大,归零效应愈明显。     

流向振荡柱体尾流控制研究进展

详细介绍了近几年采用尾部喷射、隔离板和小窄条控制件等3 种方法对流向振荡柱体绕流旋涡脱落的抑制情况. 在研究范围内存在非锁频和3种锁频旋涡脱落模式. 风洞实验表明, 尾部喷射对这4 种模式都有抑制效果,窄条控制件对非锁频和2种锁频模式具有抑制效果, 而隔离板仅对非锁频和1 种锁频模式有效. 在不同流动和振荡条件下找出了每种方法的有效控制区, 研究了减阻和减少脉动力的效果, 并探讨了控制机理.      

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     

Frequency effects on lift and drag for flow past an oscillating cylinder

A transversely oscillating cylinder in a uniform flow is modeled to investigate frequency effects of flow-induced wake on lift and drag of the cylinder. Specifically, verified unsteady fluid dynamic simulations using an immersed-boundary method in a fixed Cartesian grid predict the flow structure around the cylinder and reveal how the integration of surface pressure and shear distributions provides lift and drag on the oscillating cylinder. In this study, frequency ranges to be considered are both near and away from the natural frequency of wake vortex shedding. Subsequently, the effects of frequency lock-in, superposition and demultiplication on lift and drag are discussed based on the spectral analysis of time histories of lift and drag.     

单窄条控制件对横向振荡柱体尾流 2P模式 旋涡脱落的改变

横向强迫振荡柱体尾流控制是柱体涡激振动控制的基础,在海洋、土木等工程中具有重要意义. 横向强迫振荡柱体尾流中存在一种锁频旋涡脱落模式,即在一个振荡周期内柱体上、下侧各脱落旋转方向相反的一对涡,称为2P模式. 本文将相对宽度b/D=0.32的窄条控制件置于横向强迫振荡柱体下游,对振幅比A/D=1.25, 无量纲振频f_e D/V_∞=0.22,雷诺数Re=1 200的2P模式旋涡脱落进行干扰,并通过改变控制件位置,研究旋涡的变化规律. 采用二维大涡模拟和实验验证方法进行研究,在控制件位置范围0.8≤X/D≤3.2, 0.4≤Y/D≤3.2内,得到了2P, 2S, P+S和另外6种新发现的旋涡脱落模式,并对各模式旋涡的形成过程作了详细描述. 在控制件位置平面上给出了各旋涡模式的存在区域,画出了旋涡脱落强度的等值线图,并发现在一个相当大的区域内,旋涡脱落强 度可减小一半以上,尾流变窄. 发现柱体大幅振荡引起的横向剪切流在旋涡生成中起关键作用. 探讨了控制件对横向剪切流的影响,分析了控制件在每种旋涡模式形成中的作用机制.      

The Unsteady Wake of a Circular Cylinder near a Free Surface

The behaviour of the wake Strouhal number for flow past a cylinder close to a free surface at both low and moderate Froude numbers is investigated numerically. For the low Froude number case (i.e., gravity-dominated), the results obtained are similar to those for flow past a cylinder close to an adjacent no-slip boundary. As the distance between the wall and the cylinder is reduced, the Strouhal number, as measured from the time varying lift, increases to a maximum at a gap ratio of 0.70. Further gap reduction leads to a rapid decrease in the Strouhal number, with shedding finally ceasing altogether at gap ratios below 0.16. The agreement between the results for a free surface and a no-slip boundary suggests that the mechanism behind the suppression of vortex shedding is common. For flow at a fixed gap ratio and a moderate Froude number, two distinctly different wake states are observed with the flow passing over the cylinder tending to switch from a state of attachment to the free surface, to one of separation from it, and then back again in a pseudo-periodic fashion. Even though there is a significant difference in Reynolds number, the predicted numerical two-dimensional behaviour is found to compare favourably with the experimental observations at higher Reynolds number.     

A numerical study on the flow patterns of two oscillating cylinders

Flow around two oscillating cylinders in a side-by-side arrangement at Reynolds number (Re)=185 is simulated using the immersed boundary method. The purpose of this study is to investigate the combined effects of the gap between the two cylinders and their oscillation in the flow. The cylinders oscillate transversely to a uniform cross-flow with a prescribed sinusoidal function in the opposite direction, with the oscillation amplitude equal to 20% of the cylinder diameter. The gap between the two cylinders and the oscillating frequency are chosen as major variables for the parametric study to investigate their influence on the flow pattern. The ratio of mean gap distance between the two oscillating cylinders to the cylinder diameter is chosen to be 0.6, 1.0, 1.4, and 1.8, and the ratio of oscillating frequencies to the natural vortex shedding frequency of a fixed cylinder is 0.8, 1.0, and 1.2. Wake patterns and the drag and lift coefficients are described and compared with those from a single oscillating cylinder and two stationary cylinders. The wake patterns of two oscillating cylinders can be explained by flow mechanisms of two stationary cylinders, a single oscillating cylinder, and their combinations, and are in agreement with classifications of flow over two stationary cylinders presented in previous studies. In the case of two oscillating cylinders, the modulation phenomenon appears from a lower excitation frequency than in a single oscillating cylinder. Generally, oscillating cylinders have higher drag and root-mean-square (r.m.s.) values of drag coefficients than stationary cylinders.     

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.     

FREE SURFACE WAVE INTERACTION WITH A HORIZONTAL CYLINDER

Classes of vortex formation from a horizontal cylinder adjacent to an undulating free-surface wave are characterized using high-image-density particle image velocimetry. Instantaneous representations of the velocity field, streamline topology and vorticity patterns yield insight into the origin of unsteady loading of the cylinder. For sufficiently deep submergence of the cylinder, the orbital nature of the wave motion results in multiple sites of vortex development, i.e., onset of vorticity concentrations, along the surface of the cylinder, followed by distinctive types of shedding from the cylinder. All of these concentrations of vorticity then exhibit orbital motion about the cylinder. Their contributions to the instantaneous values of the force coefficients are assessed by calculating moments of vorticity. It is shown that large contributions to the moments and their rate of change with time can occur for those vorticity concentrations having relatively small amplitude orbital trajectories. In a limiting case, collision with the surface of the cylinder can occur. Such vortex–cylinder interactions exhibit abrupt changes in the streamline topology during the wave cycle, including abrupt switching of the location of saddle points in the wave. The effect of nominal depth of submergence of the cylinder is characterized in terms of the time history of patterns of vorticity generated from the cylinder and the free surface. Generally speaking, generic types of vorticity concentrations are formed from the cylinder during the cycle of the wave motion for all values of submergence. The proximity of the free surface, however, can exert a remarkable influence on the initial formation, the eventual strength, and the subsequent motion of concentrations of vorticity. For sufficiently shallow submergence, large-scale vortex formation from the upper surface of the cylinder is inhibited and, in contrast, that from the lower surface of the cylinder is intensified. Moreover, decreasing the depth of submergence retards the orbital migration of previously shed concentrations of vorticity about 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.     

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.     

Interactions between a rectangular cylinder and a free-surface flow

The salient features of the interaction between a free-surface flow and a cylinder of rectangular cross-section are investigated and discussed. Laboratory-scale experiments are performed in a water channel under various flow conditions and elevations of the cylinder above the channel floor. The flow field is characterized on the basis of time-averaged and fluctuating local velocity measurements. Dynamic loadings on the cylinder are measured by two water-insulated dynamometers placed inside the cylinder structure. Starting from frequency and spectral analyses of the force signals, insights on the relationship between force dominant frequencies and the Strouhal number of the vortex shedding phenomenon are provided. Experimental results highlight the strong influence of the asymmetric configuration imposed by the two different boundary conditions (free surface and channel floor) on (i) the mean force coefficients and (ii) the vortex shedding frequencies. We provide an analysis of the nature of the dependence of average force coefficients on relevant dimensionless groups, i.e., the Reynolds number, normalized flow depth and cylinder submersion.     

Controlled oscillations of a cylinder: a new wake state

The wake states resulting from the controlled oscillation of a cylinder transverse to the free stream are presented. A new wake state is revealed by instantaneous measurements of the total and vortex lift phases, and the phase-referenced, quantitative wake structure. This “intermediate wake state” occurs at oscillation frequencies between the previously observed low- and high-frequency states. It cannot be deduced from classical, time-averaged representations of the loading on the cylinder.     

Influence of slip on vortex-induced motion of a superhydrophobic cylinder

The partial slip boundary condition produced by a superhydrophobic surface in the Cassie state has been shown capable of reducing skin friction drag as well as influencing the flow around coated bodies including cylinders and spheres. In this paper, we investigated how the changes in vortex shedding and separation previously observed on superhydrophobic cylinders affects the rms lift force and the resulting oscillations induced on an elastically mounted cylinder. Two hydrophobic polytetrafluoroethylene cylinders were studied. The first was smooth and the second was roughened to make it superhydrophobic and to induce slip. The presence of slip was found to decrease rms lift and amplitude of the oscillating cylinder by up to 15% with no measurable impact on drag or the natural frequency of the elastically mounted system. We show that the observed reductions are a direct result of reduced fluid forcing on the superhydrophobic cylinder.     

Free surface waves in equilibrium with a vortex

Finite amplitude solitary waves of uniform depth which interact with a stationary point vortex are considered. Waves both with and without a submerged obstacle are computed. The method of solution is collocation of Bernoulli's equation at a finite number of points on the free surface coupled with equations for equilibrium of a point vortex. The stream function and vortex location are found by computing a conformal map of the flow domain to an infinite strip. For a given obstacle the solutions are parametrized with respect to Froude number and vortex circulation. When no obstacle is present there are two families of solutions, in one of which the amplitude of the wave increases by increasing the circulation, while in the other amplitude increases by decreasing the circulation. Beyond a certain critical Froude number the maximum amplitude wave has a sharp crest with an angle of 120 degrees. Similar behavior is observed for the flow past a submerged obstacle except that there is a critical Froude number below which there is no solution at all.