Motion of a cylinder adjacent to a free-surface: flow patterns and loading

The flow structure and loading due to combined translatory and sinusoidal motion of a cylinder adjacent to a free-surface are characterized using a cinema technique of high-image-density particle image velocimetry and simultaneous force measurements. The instantaneous patterns of vorticity and streamline topology are interpreted as a function of degree of submergence beneath the free-surface. The relative magnitudes of the peak vorticity and the circulation of vortices formed from the upper and lower surfaces of the cylinder, as well as vortex formation from the free-surface, are remarkably affected by the nominal submergence. The corresponding streamline topology, interpreted in terms of foci, saddle points, and multiple separation and reattachment points also exhibit substantial changes with submergence. All of these features affect the instantaneous loading of the cylinder. Calculation of instantaneous moments of vorticity and the incremental changes in these moments during the cylinder motion allow identification of those vortices that contribute most substantially to the instantaneous lift and drag. Furthermore, the calculated moments are in general accord with the time integrals of the measured lift and drag acting on the cylinder for sufficiently large submergence. Received: 18 May 1998/Accepted: 18 August 1999     

Topology of vortex creation in the cylinder wake

We analyze the topology of the two-dimensional flow around a circular cylinder at moderate Reynolds numbers in the regime where the vortex wake is created. A normal form for the stream function close to the cylinder is presented and used to predict the streamline pattern both in the steady and the periodic regime, where two different vortex shedding scenarios are identified. The theoretical predictions are verified numerically. For the vorticity, a very different topology occurs with infinite nested sequences of iso-curves moving downstream. General equations of motion for critical points are derived.     

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.     

Flow structure on a rotating plate

The flow structure on a rotating plate of low aspect ratio is characterized well after the onset of motion, such that transient effects are not significant, and only centripetal and Coriolis accelerations are present. Patterns of vorticity, velocity contours, and streamline topology are determined via quantitative imaging, in order to characterize the leading-edge vortex in relation to the overall flow structure. A stable leading-edge vortex is maintained over effective angles of attack from 30° to 75°, and at each angle of attack, its sectional structure at midspan is relatively insensitive to Reynolds number over the range from 3,600 to 14,500. The streamline topology, vorticity distribution, and circulation of the leading-edge vortex are determined as a function of angle of attack, and related to the velocity field oriented toward, and extending along, the leeward surface of the plate. The structure of the leading-edge vortex is classified into basic regimes along the span of the plate. Images of these regimes are complemented by patterns on crossflow planes, which indicate the influence of root and tip swirl, and spanwise flow along the leeward surface of the plate. Comparison with the equivalent of the purely translating plate, which does not induce the foregoing flow structure, further clarifies the effects of rotation.     

Vortex shedding flow behind a slowly rotating circular cylinder

This paper investigates flow past a rotating circular cylinder at 3600?Re?5000 and α?2.5. The flow parameter α is the circumferential speed at the cylinder surface normalized by the free-stream velocity of the uniform cross-flow. With particle image velocimetry (PIV), vortex shedding from the cylinder is clearly observed at α<1.9. The vortex pattern is very similar to the vortex street behind a stationary circular cylinder; but with increasing cylinder rotation speed, the wake is observed to become increasing narrower and deflected sideways. Properties of large-scale vortices developed from the shear layers and shed into the wake are investigated with the vorticity field derived from the PIV data. The vortex formation length is found to decrease with increasing α. This leads to a slow increase in vortex shedding frequency with α. At α=0.65, vortex shedding is found to synchronize with cylinder rotation, with one vortex being shed every rotation cycle of the cylinder. Vortex dynamics are studied at this value of α with the phase-locked eduction technique. It is found that although the shear layers at two different sides of the cylinder possess unequal vorticity levels, alternating vortices subsequently shed from the cylinder to join the two trains of vortices in the vortex street pattern exhibit very little difference in vortex strength.     

Quantitative interpretation of vortices from a cylinder oscillating in quiescent fluid

 The instantaneous, quantitative patterns of vortices arising from sinusoidal oscillation of a cylinder in quiescent fluid are experimentally characterized for the first time using high-image-density particle image velocimetry. The near-wake does not indicate a separated layer of distributed vorticity leading to a single, large-scale vortex. Rather, for sufficiently high Reynolds number, a sequence of small-scale vorticity concentrations is formed. Agglomeration of only a fraction of the adjacent concentrations forms a larger-scale vortex. Simultaneously, vorticity concentrations of opposite sense are formed along the base (rear) of the cylinder. Streamline patterns typically indicate, however, only the larger-scale vortex; it has a circulation smaller than the total circulation of all vorticity concentrations that are not revealed by the streamlines. These observations are interpreted in the context of the effective resolution of the flow images. Received: 27 October 1995 / Accepted: 27 August 1996     

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.     

Application of local grid refinement to vortex motion due to a solitary wave passing over a submerged body

A numerical method based on the streamfunction–vorticity formulation is applied to simulate the two‐dimensional, transient, viscous flow with a free surface. This method successfully uses the locally refined grid in an inviscid–viscous model to explore the processes of vortex formation due to a solitary wave passing over a submerged bluff body. The two particular bodies considered here are a blunt rectangular block and a semicircular cylinder. Flow visualization to track dyelines is carried out in the laboratory in order to confirm the validity of the numerical results. Numerical results examined by different grid configurations ensure the locally refined grid to be useful in practical application. Flow phenomena, including the vortex motion and wave patterns during non‐linear wave–structure interaction, are also discussed. Copyright © 2002 John Wiley & Sons, Ltd.     

Unsteady flow around impacting bluff bodies

The flow resulting from the collision without rebound of generic bluff bodies with a wall in a still viscous fluid is investigated both computationally and experimentally. Emphasis is on the case of a circular cylinder impact (two-dimensional geometry), but comparisons with the flow generated by the impact of a sphere (axisymmetric geometry) are included. For normal cylinder impacts, the two counter-rotating vortices forming behind the body during its motion continue their trajectory towards the wall after the collision, leading to the generation of opposite-signed secondary vorticity at the cylinder and wall surfaces. Secondary vortices forming from this vorticity at higher Reynolds numbers exhibit a short-wavelength three-dimensional instability. Comparison with the sphere impact reveals significant differences in the scales of the vortices after the collision, due to the additional vortex stretching acting in the axisymmetric geometry. This leads to a delay in the onset of three-dimensionality and to a different instability mechanism. Oblique cylinder impacts are also considered. For increasing impact angles, the wall effect is gradually reduced on one side of the cylinder, which favours the roll-up of the secondary vorticity and increases the rebound height of the vortex system.     

Vortex shedding around a near-wall circular cylinder induced by a solitary wave

This study developed a two-dimensional generalized vortex method to analyze the shedding of vortices and the hydrodynamic forces resulting from a solitary wave passing over a submerged circular cylinder placed near a flat seabed. Numerical results for validation are compared with other numerical and experimental results, and satisfactory agreement is found. A series of simulations were performed to study the effects of gap-to-diameter ratio and incident wave height on vorticity pattern as well as the forces exerted on the cylinder. The range of the heights of incident waves is from 0.3h to 0.7h, where h is the still water depth. The range of the gap-to-diameter ratios is from 0.1 to 0.8. The results indicate that the flow pattern and the pressure distribution change significantly because of the close proximity of the seabed where the vorticity flux on the seabed-side surface of the cylinder is suppressed. Placing the cylinder nearer the seabed increases the drag and the positive lift on the cylinder. When the gap-to-diameter ratio increases, the pattern of vortices changes because of the interaction between the main recirculation zone and the shear layers separated from the gap. The maxima of drag, lift and total force increase linearly with the height of the incident wave.     

FLOW PAST TWO CYLINDERS IN TANDEM: INSTANTANEOUS AND AVERAGED FLOW STRUCTURE

A technique of high-image-density particle image velocimetry is employed to characterize the instantaneous and averaged patterns of velocity, vorticity and Reynolds stress due to flow past two cylinders in tandem. These features of the flow patterns are characterized in the gap region as a function of the distance between the cylinders. In turn, they are related to the patterns in the near-wake of the two-cylinder system. Along the gap between the cylinders, small-scale concentrations of vorticity are formed in the separated shear layers. These concentrations buffet the surface boundary layer on the downstream cylinder, and thereby influence the eventual shedding of large-scale vortices. Within the gap, the instantaneous structure of the recirculation zones can exhibit both symmetrical and asymmetrical patterns. In the near-wake of the downstream cylinder, the form of the vortex shedding, as well as the averaged patterns of the flow structure, are substantially altered, relative to the case of a single cylinder. The width of the near-wake, as represented by averaged patterns of vorticity, is substantially narrower and the magnitudes of the peak Reynolds stress are significantly attenuated. On the other hand, if the gap region is sufficiently large such that Kármán-like vortices form between the cylinders, the near-wake of the downstream cylinder shows distinctive patterns, and both the wake width and the magnitude of the Reynolds stresses become larger, relative to those at smaller gap width.     

横向振荡圆柱绕流的格子Boltzmann方法模拟

基于格子Boltzmann方法(LBM)对不可压横向振荡圆柱绕流问题进行了数值研究. 与传统的求解宏观的N-S方程的数值方法不同, LBM求解此类问题不需要采用动网格, 而且不需要对网格进行特殊处理, 从而节约了计算成本. 结果显示, 当振荡频率增加到相应的静止圆柱绕流的自然涡脱落频率附近时, 圆柱后最新形成的集中涡距离柱体越来越近, 直到达到一个极限位置. 随后, 集中涡突然转向圆柱体另一侧脱落. 当振荡频率接近于静止圆柱的自然涡脱落频率时, 发生频率同步的现象. 随着振荡频率远离自然涡脱落频率, 同步现象消失. 在几种次谐振荡和超谐振荡下, 尾流区的涡脱落频率仍为相应的静止圆柱绕流的自然涡脱落频率.      

Flow pattern transition in liquid-liquid flows with a transverse cylinder

The effect of a cylindrical bluff body on the interface characteristics of stratified two-phase, oil-water, pipe flows is experimentally investigated with high speed Particle Image Velocimetry (PIV). The motivation was to study the feasibility of flow pattern map actuation by using a transverse cylinder immersed in water in the stratified pattern, and particularly the transition from separated to dispersed flows. The cylinder has a diameter of 5 mm and is located at 6.75 mm from the bottom of the pipe in a 37 mm ID acrylic test section. Velocity profiles were obtained in the middle plane of the pipe. For reference, single phase flows were also investigated for Reynolds numbers from 1550 to 3488. It was found that the flow behind the cylinder was similar to the two dimensional cases, while the presence of the lower pipe wall diverted the vorticity layers towards the top. In two-phase flows, the Froude number (from 1.4 to 1.8) and the depth of the cylinder submergence below the interface affected the generation of waves. For high Froude numbers and low depths of submergence the counter rotating von Karman vortices generated by the cylinder interacted with the interface. In this case, the vorticity clusters from the top of the cylinder were seen to attach at the wave crests. At high depths of submergence, a jet like flow appeared between the top of the cylinder and the interface. High speed imaging revealed that the presence of the cylinder reduced to lower mixture velocities the transition from separated to dual continuous flows where drops of one phase appear into the other.     

Unsteady flow structure and vorticity convection over the airfoil oscillating at high reduced frequency

Unsteady vortex structures and vorticity convection over the airfoil (NACA 0012), oscillating in the uniform inflow, are studied by flow visualization and velocity measurements. The airfoil, pivoting at one-third of the chord, oscillates periodically near the static stalling angle of attack (AOA) at high reduced-frequency. The phase-triggering and modified phase-averaged techniques are employed to reconstruct the pseudo instantaneous velocity field over the airfoil. During the down stroke cycle, the leading-edge separation vortex is growing and the vortex near the trailing edge begins to shed into the wake. During the upstroke cycle, the leading-edge separation vortex is matured and moves downstream, and the counter clockwise vortex is forming near the trailing edge. Convection speeds and wavelength of the unsteady vortex structure over the airfoil equal to that of the counter clockwise vortex shed into the wake. This kind of vortex structure is termed as “synchronized shedding” type. The wavelength of unsteady vortex structure over the airfoil is significantly different from that at low reduced-frequency. Consistent convection speeds of the leading-edge separation vortex are acquired from the spatial-temporal variations of local circulation and local surface vorticity generation, and equals that predicted from flow visualization. Spatial-temporal variations of the local surface vorticity generation clearly reveal the formation and passage of the leading-edge separation vortex only in the region where the flow does not separate completely from the surface. Significant amounts of the surface vorticity are generated within the leading-edge region of the airfoil during the upstroke cycle. Only negligible amount of surface vorticity is produced within the region of complete flow separation. During the down stroke cycle, the surface vorticity generation is mild along the airfoil surface, except the leading-edge region where a small scale leading-edge separation vortex is forming and growing.     

Orbital flow past a cylinder: A numerical approach

Orbital flow past a cylinder is relevant to offshore structures. The numerical scheme presented here is based on a finite-difference solution of the Navier–Stokes equations. Alternating-directional-implicit (ADI) and successive-over-relaxation (SOR) techniques are used to solve the vorticity-transport and stream-function equations. Theoretical simulations to low Reynolds number flows (up to 1000) are discussed for cases involving uniform flow past stationary and rotating cylinders and orbital flow past a cylinder. The separation points for cylinders that are rotating or immersed in an orbital flow are deduced from velocity profiles through the boundary layer using a hybrid mesh scheme. During the initial development of orbital flow surface vorticity on the impulsively started cylinder dominates the flow. A vortex then detaches from behind the cylinder and establishes the flow pattern of the orbit. After some time a collection of vortices circles the orbit and distorts its shape a great deal. These vortices gradually spiral outward as others detach from the cylinder and join the orbital path.     

Control of vortex formation from a vertical cylinder in shallow water: Effect of localized roughness elements

Vortex formation from a vertical cylinder in shallow water is controlled by placement of a narrow transverse strip of roughness elements on the bed (bottom surface). A technique of high-image-density particle image velocimetry is employed to obtain global, instantaneous representations of the flow patterns, which lead to phase- and time-averaged patterns of streamline topology and Reynolds stress on planes at and above the bed. Near the bed, the overall form of the streamline topology is maintained, even at larger heights of the roughness elements. With increasing height of the elements, the downstream saddle point is further displaced in the streamwise direction. Correspondingly, the streamwise extent of the negative pocket of the streamwise velocity component, i.e., the region of reverse flow along the bed surface, increases substantially in the streamwise direction. The Reynolds stress in the very near-wake, at locations upstream of the roughness elements, is significantly attenuated, even for small height of roughness. This attenuation occurs not only near the bed surface, but also at the midplane of the shallow water wake, and thereby indicates that the consequence of localized roughness is to exert a global influence. In fact, corresponding patterns of instantaneous velocity and vorticity indicate that consistent formation of large-scale vortices in the very near-wake region is attenuated with relatively small surface roughness on the bed. Downstream of the roughness elements, the patterns of Reynolds stress near the bed surface, as well as at the midplane of the water layer, are significantly altered relative to the case of no roughness. Near the bed, highly concentrated patterns of positive and negative Reynolds stress in the absence of roughness give way to lower-level regions of Reynolds stress in the form of alternating concentrations; the particular pattern depends on the height of the roughness elements. At the midplane of the water layer, the Reynolds stress patterns maintain their same overall form, but the extrema of the Reynolds stress concentrations are attenuated in magnitude and are shifted in the downstream direction, with increasing height of the roughness elements. These observations are complemented by patterns of instantaneous velocity and vorticity.     

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.     

Formation of vortex street and vortex pair from a circular cylinder oscillating in water

The flow around a circular cylinder undergoing sinusoidal oscillating movement in still water is investigated by phase-locked PIV measurements. The pattern and development of large-scale vortex structures in the flow are studied from the velocity vectors and vorticity contours obtained at eight successive phases of an oscillating cycle. Experiments are performed at three Keulegan–Carpenter numbers; KC=12, 6.28 and 4.25. Results at KC=12 reveal the mechanism of vortex formation and the development of the shed vortices into a vortex street at a lateral direction to the line of cylinder movement. The role of a biased flow stream and the length of the cylinder stroke in the formation of the vortex street are discussed. At the lower KC numbers, a symmetric pair of vortices is found attached to the leeward face of the cylinder. The vortex pair exhibits an increasing degree of asymmetry when KC increases from 4.25 to 6.28. An explanation in terms of the length of the cylinder strokes and the degree of flow asymmetry is offered for the transition of flow regimes from a vortex pair to a vortex street. The present results are compared with the observations made in previous experimental and numerical studies in the literature.     

Nonlinear interaction of a vortex pair with clean and surfactant-covered free surfaces

Two-dimensional unsteady viscous-flow problem associated with the normal incidence of a counter-rotating vortex pair on a free surface is analyzed. Effects of surface tension and insoluble surfactants on the generation of free-surface vorticity and surface waves are investigated. A recently developed finite-difference method based on boundary-fitted coordinates is used to solve the fully-nonlinear problem. Results show that in the absence of surfactants and at low Froude number (based on circulation strength and initial separation distance of the vortex pair), waves of short lengths are generated. However, secondary vorticity generated in this case is not strong enough to affect the outward translation of the primary vortices. At intermediate Froude number, a transient wave developing outboard of the primary vortex becomes steep, and eventually breaks because of local instability. Consequently, free-surface vorticity inhibits the outward translation of the primary vortices. Surface tension in a clean free surface dampens the steep short waves, hence also the generation of free-surface vorticity. However, variation in surface tension induced by surfactants intensifies the generation of surface vorticity, thereby causing the primary vortices to rebound. The increase in the rotational part of wave motion results in the dampening of overall free-surface deformations. However, it is found that the shear stress associated with a large gradient of surfactant concentration could cause local steepening of the short wave generated outboard of the primary vortex.