基于浸入边界-格子Boltzmann通量求解法的椭圆柱流动特性分析

基于浸入边界-格子Boltzmann通量求解法,开展了雷诺数Re=100不同几何参数下单椭圆柱及串列双椭圆柱绕流流场与受力特性对比研究。结果表明,随长短轴比值的增加,单椭圆柱绕流阻力系数先减小后缓慢上升,最大升力系数则随长短轴比值的增大而减小;尾迹流动状态从周期性脱落涡到稳定对称涡。间距是影响串列圆柱及椭圆柱流场流动状态的主要因素,间距较小时,串列圆柱绕流呈周期性脱落涡状态,而椭圆柱则为稳定流动;随着间距增加,上下游圆柱及椭圆柱尾迹均出现卡门涡街现象,且串列椭圆柱临界间距大于串列圆柱。串列椭圆柱阻力的变化规律与圆柱的基本相同,上游平均阻力大于下游阻力;上游椭圆柱阻力随着间距的变大先减小,下游随间距的变大而增加,当间距达到临界间距时上下游阻力跃升,随后出现小幅度波动再逐渐增加,并趋近于相同长短轴比值下单柱体绕流的阻力。     

串列双锥柱绕流流动特性的大涡模拟研究

利用大涡模拟研究了雷诺数Re = 3900下串列双锥柱在间距比L/D_m = 2 ~ 10下的升阻力特性及三维流动结构. 研究发现: 上游锥柱在后方形成的两个展向不对称回流区, 使其后方压力分布不对称. 上游锥柱发展的上洗、下洗和侧面剪切层作用在下游锥柱的附着点位置不同是上游和下游锥柱时均阻力系数和脉动升力系数变化的主要原因, 串列双锥柱间流动结构随间距比变化可分为三种状态: 剪切层包裹状态, 过渡状态及尾流撞击状态. 剪切层包裹状态. 上游锥柱的自由端主导来流在下游锥柱迎风面影响范围广, 上游锥柱剪切层完全包裹住下游锥柱, 从而抑制下游锥柱后方回流区形成, 导致下游锥柱时均阻力系数降低; 尾流撞击状态; 上游锥柱尾流得到充分发展, 其回流区大小随间距比增大不再发生变化, 上游锥柱尾流出现周期性脱落, 撞击在下游锥柱表面, 从而使脉动升力系数大幅增加, 最大脉动升力系数较单直圆柱提升约20.7倍; 过渡状态, 此时时均阻力系数和脉动升力系数均会较剪切层包裹状态增加. 该研究可以为风力俘能结构群列阵布局提供理论支持.      

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.     

低雷诺数下串列三圆柱涡激振动中的弛振现象及其影响因素

对间距比为1.2和雷诺数为100的串列三圆柱涡激振动进行数值模拟, 发现在某个折合流速之后, 三圆柱的响应均呈现为随着折合流速增大而增大的弛振现象, 平衡位置偏移、低频振动以及旋涡脱落与圆柱运动之间的时机三个因素共同决定了弛振现象的出现. 进一步的研究发现, 串列三圆柱的弛振现象仅出现在质量比不大于2.0和雷诺数不大于100的工况下. 当质量比较大时, 串列三圆柱的平衡位置固定不变, 且圆柱的振动不规律, 使得旋涡脱落与圆柱运动的时机处于变化之中. 当雷诺数较高时, 最上游圆柱的平衡位置在折合流速较大时回到初始位置, 不再参与对圆柱振动的调节, 使得圆柱的振动响应不再规律, 旋涡脱落与圆柱运动的时机也一直处于变化之中.      

Numerical predictions of low Reynolds number flows over two tandem circular cylinders

Flows over two tandem cylinders were analysed using the newly developed collocated unstructured computational fluid dynamics (CUCFD) code, which is capable of handling complex geometries. A Reynolds number of 100, based on cylinder diameter, was used to ensure that the flow remained laminar. The validity of the code was tested through comparisons with benchmark solutions for flow in a lid‐friven cavity and flow around a single cylinder. For the tandem cylinder flow, also mesh convergence was demonstrated, to within a couple of percent for the RMS lift coefficient. The mean and fluctuating lift and drag coefficients were recorded for centre‐to‐centre cylinder spacings between 2 and 10 diameters. A critical cylinder spacing was found between 3.75 and 4 diameters. The fluctuating forces jumped appreciably at the critical spacing. It was found that there exists only one reattachment and one separation point on the downstream cylinder for spacings greater than the critical spacing. The mean and the fluctuating surface pressure distributions were compared as a function of the cylinder spacing. The mean and the fluctuating pressures were significantly different between the upstream and the downstream cylinders. These pressures also differed with the cylinder spacing. Copyright © 2004 John Wiley & Sons, Ltd.     

虚拟边界法研究正交双圆柱及串列双圆球绕流

把Goldstein等人提出的虚拟边界法推广到三维情况,研究了 Re=150时不同间距下正交双圆柱绕流,和Re=250时不同间距下串列双 圆球绕流流场. 对于正交双圆柱绕流,当间距比大于3,下游圆柱对上游圆柱尾流的影响只 限定在下游圆柱的尾流所扫过的范围之内;当间距比小于等于3,下游圆柱对上游圆柱尾流 的影响扩大,下游圆柱尾流扫过区上下出现两排三维流向二次涡结构. 对于串列圆球绕流, 研究发现,在小间距比(L/D≈ 1.5)的情况下,由于上下游圆球尾流区的相互抑 制消除了压力不稳定性,整个流场呈现稳 态轴对称特征;间距比为2.0时,周向压力梯度诱发出流体的周向输运,流场呈现稳态非对 称性,但流场中存在特定的对称面;间距比增大到2.5后,绕流场开始周期振荡,原有的对 称面依旧存在;在间距比3.5时下游圆球下表面的涡结构强度有所减弱,导致占优频率发生 交替;间距比增至7.0时,整个流场恢复稳态特征,两圆球尾部同时出现双线涡,这时流场 对称面的位置发生了变动.     

Global aerodynamic instability of twin cylinders in cross flow

This paper comprises an in-depth physical discussion of the flow-induced vibration of two circular cylinders in view of the time-mean lift force on stationary cylinders and interaction mechanisms. The gap-spacing ratio T/D is varied from 0.1 to 5 and the attack angle α from 0° to 180° where T is the gap width between the cylinders and D is the diameter of a cylinder. Mechanisms of interaction between two cylinders are discussed based on time-mean lift, fluctuating lift, flow structures and flow-induced responses. The whole regime is classified into seven interaction regimes, i.e., no interaction regime; boundary layer and cylinder interaction regime; shear-layer/wake and cylinder interaction regime; shear-layer and shear-layer interaction regime; vortex and cylinder interaction regime; vortex and shear-layer interaction regime; and vortex and vortex interaction regime. Though a single non-interfering circular cylinder does not correspond to a galloping following quasi-steady galloping theory, two circular cylinders experience violent galloping vibration due to shear-layer/wake and cylinder interaction as well as boundary layer and cylinder interaction. A larger magnitude of fluctuating lift communicates to a larger amplitude vortex excitation.     

Strouhal numbers,forces and flow structures around two tandem cylinders of different diameters

This paper presents a detailed investigation of Strouhal numbers, forces and flow structures in the wake of two tandem cylinders of different diameters. While the downstream cylinder diameter, D, was fixed at 25 mm, the upstream cylinder diameter, d, was varied from 0.24D to D. The spacing between the cylinders was 5.5d, at which vortices were shed from both cylinders. Two distinct vortex frequencies were detected behind the downstream cylinder for the first time for two tandem cylinders of the same diameter. The two vortex frequencies remained for d/D=1.0–0.4. One was the same as detected in the gap of the cylinders, and the other was of relatively low frequency and was ascribed to vortex shedding from the downstream cylinder. While the former, if normalized, declined progressively from 0.196 to 0.173, the latter increased from 0.12 to 0.203 with decreasing d/D from 1 to 0.24. The flow structure around the two cylinders is examined in the context of the observed Strouhal numbers. The time-averaged drag on the downstream cylinder also climbed with decreasing d/D, though the fluctuating forces dropped because vortices impinging upon the downstream cylinder decreased in scale with decreasing d/D.     

Coherent and turbulent processes in the bistable regime around a tandem of cylinders including reattached flow dynamics by means of high-speed PIV

The turbulent flow around two cylinders in tandem at the sub-critical Reynolds number range of order of 10⁵ and pitch to diameter ratio of 3.7 is investigated by using time-resolved Particle Image Velocimetry (TRPIV) of 1 kHz and 8 kHz. The bi-stable flow regimes including a flow pattern I with a strong vortex shedding past the upstream and the downstream cylinder, as well as a flow pattern II corresponding to a weak alternating vortex shedding with reattachment past the upstream cylinder are investigated. The structure of this “reattachment regime” has been analyzed in association with the vortex dynamics past the downstream cylinder, by means of POD and phase-average decomposition. These elements allowed interconnection among all the measured PIV planes and hence analysis of the reattachment structure and the flow dynamics past both cylinders. The results highlight fundamental differences of the flow structure and dynamics around each cylinder and provide the ‘gap’ flow nature between the cylinders. Thanks to a high-speed camera of 8 kHz, the shear-layer vortices tracking has been possible downstream of the separation point and the quantification of their shedding frequency at the present high Reynolds number range has been achieved. This issue is important regarding fluid instabilities involved in the fluid–structure interaction of cylinder arrays in nuclear reactor systems, as well as acoustic noise generated from the tandem cylinders of a landing gear in aeronautics.     

Vortex shedding and acoustic resonance of single and tandem finned cylinders

The effect of fins on vortex shedding and acoustic resonance is investigated for isolated and two tandem cylinders exposed to cross-flow in a rectangular duct. Three spacing ratios between the tandem cylinders (S/D_e=1.5, 2 and 3) are tested for a Reynolds number range from 1.6×10⁴ to 1.1×10⁵. Measurements of sound pressure as well as mean and fluctuating velocities are performed for bare and finned cylinders with three different fin densities. The effect of fins on the sound pressure generated before the onset of acoustic resonance as well as during the pre-coincidence and coincidence resonance is found to be rather complex and depends on the spacing ratio between cylinders, the fin density and the nature of the flow-sound interaction mechanism.For isolated cylinders, the fins reduce the strength of vortex shedding only slightly, but strongly attenuate the radiated sound before and during the occurrence of acoustic resonance. This suggests that the influence of the fins on correlation length is stronger than on velocity fluctuations. In contrast to isolated cylinders, the fins in the tandem cylinder case enhance the vortex shedding process at off-resonant conditions, except for the large spacing case which exhibits a reversed effect at high Reynolds numbers. Regarding the acoustic resonance of the tandem cylinders, the fins promote the onset of the coincidence resonance, but increasing the fin density drastically weakens the intensity of this resonance. The fins are also found to suppress the pre-coincidence resonance for the tandem cylinders with small spacing ratios (S/D_e=1.5, 2 and 2), but for the largest spacing case (S/D_e=3), they are found to have minor effects on the sound pressure and the lock-in range of the pre-coincidence resonance.     

Identification of flow regimes around two staggered square cylinders by a numerical study

The flow over two square cylinders in staggered arrangement is simulated numerically at a fixed Reynolds number (\(Re =150\)) for different gap spacing between cylinders from 0.1 to 6 times a cylinder side to understand the flow structures. The non-inclined square cylinders are located on a line with a staggered angle of \(45^{\circ }\) to the oncoming velocity vector. All numerical simulations are carried out with a finite-volume code based on a collocated grid arrangement. The effects of vortex shedding on the various features of the flow field are numerically visualized using different flow contours such as \(\lambda _{2}\) criterion, vorticity, pressure and magnitudes of velocity to distinguish the distinctive flow patterns. By changing the gap spacing between cylinders, five different flow regimes are identified and classified as single body, periodic gap flow, aperiodic, modulated periodic and synchronized vortex shedding regimes. This study revealed that the observed multiple frequencies in global forces of the downstream cylinder in the modulated periodic regime are more properly associated with differences in vortex shedding frequencies of individual cylinders than individual shear layers reported in some previous works; particularly, both shear layers from the downstream cylinder often shed vortices at the same multiple frequencies. The maximum Strouhal number for the upstream cylinder is also identified at \({G}^{*}=1\) for aperiodic flow pattern. Furthermore, for most cases studied, the downstream cylinder experiences larger drag force than the upstream cylinder.     

Passive control of wake flow by two small control cylinders at Reynolds number 80

Passive control of the wake behind a circular cylinder in uniform flow is studied by numerical simulation at Re_D=80. Two small control cylinders are placed symmetrically along the separating shear layers at various stream locations. In the present study, the detailed flow mechanisms that lead to a significant reduction in the fluctuating lift but maintain the shedding vortex street are clearly revealed. When the stream locations lie within 0.8≤X_C/D≤3.0, the alternate shedding vortex street remains behind the control cylinders. In this case, the symmetric standing eddies immediately behind the main cylinder and the downstream delay of the shedding vortex street are the two primary mechanisms that lead to a 70–80% reduction of the fluctuating lift on the main cylinder. Furthermore, the total drag of all the cylinders still has a maximum 5% reduction. This benefit is primarily attributed to the significant reduction of the pressure drag on the main cylinder. Within X_C/D>3.0, the symmetry of the standing eddy breaks down and the staggered vortex street is similar to that behind a single cylinder at the same Reynolds number. In the latter case, the mean pressure drag and the fluctuating lift coefficients on the main cylinder will recover to the values of a single cylinder.     

侧柱与串列双柱绕流之间的干扰

本文给出了关于串列双柱与创柱间流动干扰的实验研究结果。当三个圆柱排成等边三角形并靠得很近时，由于三圆柱间强烈的缝隙流动，大大地改变了绕流其中的串列双圆柱的流态。特别，当三圆柱中心距等于二倍圆柱直径时，在串列双柱的前、后柱之间形成了强烈的偏斜的缝隙流，出现了独特的压力分布以及要比单柱高出三倍以上的旋涡脱落频率。     

串列双圆柱绕流问题的数值模拟

本文运用有限体积方法,对绕串列放置的双圆柱的二维不可压缩流动进行了数值计算。为研究两圆柱不同间距对圆柱相互作用和尾流特征的影响,选取间距比Ｌ／Ｄ（Ｌ为两圆柱中心间的距离,Ｄ为圆柱直径）在１．５～５．０之间每隔０．５共八个有代表性的间距进行了计算模拟。计算均在Ｒｅ＝２００条件下进行。计算结果表明：对该绕流问题,流动特征在很大程度上取决于间距的大小。且间距存在一临界值,间距比从小于临界值变化到大于临界     

Effect of acoustic resonance on the dynamic lift forces acting on two tandem cylinders in cross-flow

Direct measurements of the dynamic lift force acting on two tandem cylinders in cross-flow are performed in the presence and absence of acoustic resonance. The dynamic lift force is measured because it represents the integrated effect of the unsteady wake and therefore it is directly related to the dipole sound source generated by vortex shedding from the cylinder. Three spacing ratios inside the proximity interference region, L/D=1.75, 2.5 and 3 are considered. During the tests, the first transverse acoustic mode of the duct housing the cylinders is self-excited. In the absence of acoustic resonance, the measured dynamic lift coefficients agree with those reported in the literature. When the acoustic resonance is initiated, a drastic increase in the dynamic lift coefficient is observed, especially for the downstream cylinder. This can be associated with abrupt changes in the phase between the lift forces and the acoustic pressure. The dynamic lift forces on both cylinders are also decomposed into in-phase and out-of-phase components, with respect to the resonant sound pressure. The lift force components for the downstream cylinder are found to be dominant. Moreover, the out-of-phase component of the lift force on the downstream cylinder is found to become negative over two different ranges of flow velocity and to virtually vanish between these two ranges. Acoustic resonance of the first mode is therefore excited over two ranges of flow velocity separated by a non-resonant range near the velocity of frequency coincidence. It is therefore concluded that the occurrence of acoustic resonance is controlled by the out-of-phase lift component of the downstream cylinder, whereas the effect of the in-phase lift component is confined to causing small changes in the acoustic resonance frequency.     

NUMERICAL INVESTIGATION ON FLOW-INDUCED VIBRATION OF TWO CYLINDERS IN TANDEM ARRANGEMENTS AND ITS COUPLING MECHANISMS

对雷诺数Re= 100 条件下串列双圆柱的流致振动进行了数值模拟. 圆柱的质量比m^*均为2.0,间距比L/D 为2.0 5.0. 考虑两种工况:(a) 上游圆柱固定,下游圆柱可沿横流向自由振动;(b) 上、下游圆柱均可沿横流向自由振动. 结果表明:无论上游圆柱静止或者振动,下游圆柱横向振幅明显大于单圆柱的. 工况(b) 的下游圆柱最大振幅要大于工况(a) 的,这是由于两圆柱均振动时,两圆柱之间耦合作用增强,上游圆柱的尾流和下游圆柱的振动之间“相互调节” 作用显著. 对工况(b) 的下游圆柱振动和间隙流之间的作用机制进行了详细的研究,发现当上游圆柱脱落的自由剪切层重新附着于下游圆柱上并且完全从间隙之间通过时,下游圆柱的振幅最大.     

串列双圆柱流致振动的数值模拟及其耦合机制

对雷诺数Re= 100 条件下串列双圆柱的流致振动进行了数值模拟. 圆柱的质量比m*均为2.0,间距比L/D 为2.0 5.0. 考虑两种工况:(a) 上游圆柱固定,下游圆柱可沿横流向自由振动;(b) 上、下游圆柱均可沿横流向自由振动. 结果表明:无论上游圆柱静止或者振动,下游圆柱横向振幅明显大于单圆柱的. 工况(b) 的下游圆柱最大振幅要大于工况(a) 的,这是由于两圆柱均振动时,两圆柱之间耦合作用增强,上游圆柱的尾流和下游圆柱的振动之间“相互调节” 作用显著. 对工况(b) 的下游圆柱振动和间隙流之间的作用机制进行了详细的研究,发现当上游圆柱脱落的自由剪切层重新附着于下游圆柱上并且完全从间隙之间通过时,下游圆柱的振幅最大.      

A numerical investigation of the flow over a pair of identical square cylinders in a tandem arrangement

This paper describes a numerical study of the two‐dimensional and three‐dimensional unsteady flow over two square cylinders arranged in an in‐line configuration for Reynolds numbers from 40 to 1000 and a gap spacing of 4D, where D is the cross‐sectional dimension of the cylinders. The effect of the cylinder spacing, in the range G = 0.3D to 12D, was also studied for selected Reynolds numbers, that is, Re = 130, 150 and 500. An incompressible finite volume code with a collocated grid arrangement was employed to carry out the flow simulations. Instantaneous and time‐averaged and spanwise‐averaged vorticity, pressure, and streamlines are computed and compared for different Reynolds numbers and gap spacings. The time averaged global quantities such as the Strouhal number, the mean and the RMS values of the drag force, the base suction pressure, the lift force and the pressure coefficient are also calculated and compared with the results of a single cylinder. Three major regimes are distinguished according to the normalized gap spacing between cylinders, that is, the single slender‐body regime (G < 0.5), the reattach regime (G < 4) and co‐shedding or binary vortex regime (G ≥4). Hysteresis with different vortex patterns is observed in a certain range of the gap spacings and also for the onset of the vortex shedding. Copyright © 2011 John Wiley & Sons, Ltd.     

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.     

Characteristics and suppression of flow-induced vibrations of two side-by-side circular cylinders

A free-vibration experiment was conducted to examine flow-induced vibration (FIV) characteristics of two identical circular cylinders in side-by-side arrangements at spacing ratio T^⁎ (=T/D)=0.1–3.2, covering all possible flow regimes, where T is the gap spacing between the cylinders and D is the cylinder diameter. Each of the cylinders was two-dimensional, spring mounted, and allowed to vibrate independently in the cross-flow direction. Furthermore, an attempt to suppress flow-induced vibrations was undertaken by attaching flexible sheets at the rear stagnation lines of the cylinders. Based on the vibration responses of the two cylinders, four vibration patterns I, II, III and IV are identified at 0.1≤T^⁎<0.2, 0.2≤T^⁎≤0.9, 0.9<T^⁎<2.1 and 2.1≤T^⁎≤3.2, respectively. Pattern I is characterized by the two cylinders vibrating inphase^, with the maximum amplitudes occurring at the same reduced velocity Ur=10.47 almost two times that (Ur=5.25) for an isolated cylinder. Pattern II features no vibration generated for either cylinder. Pattern III exemplifies the occurrence of the maximum vibration amplitude of a cylinder at a smaller Ur and that of the other cylinder at a higher Ur compared to its counterpart in an isolated cylinder. Pattern IV represents each cylinder response resembling an isolated cylinder response; the vibrations of the two cylinders are, however, coupled inphase or antiphase. Linking maximum vibration amplitudes to fluctuating lift forces acting on fixed cylinders reveals that fluid–structure interactions between two fixed cylinders and between two elastic cylinders are not the same, even though vibration is not significant. As such, while two fixed cylinders generate narrow and wide wakes at 0.2≤T^⁎<1.7, two elastic cylinders do the same for a longer range of T^⁎ (0.2≤T^⁎<2.1). The flexible sheets effectively suppress FIV of the two cylinders in patterns III and IV, and reduce the vibration amplitude in pattern I. For the effectively controlled cases (patterns III and IV), the flexible sheet of each cylinder folds into a semicircle at the base, forming two free edges.