Vortex Formation Mode Research Articles

Flow-induced vibration of a flexible splitter-plate in the wake of a stationary cylinder

The present work is on free-stream flow across a circular cylinder, with a detached flexible-plate. Using a levelset function-based immersed interface method, the effect of Reynolds number Re(75−150), non-dimensional gap G*(0.5−3.5) between the two structures and non-dimensional length L*(0.5−3) of the plate—with constant structural properties and thickness—is numerically studied. The effect of these parameters on the vibration characteristics of the plate along with the accompanying flow structures and engineering parameters are presented. The study demonstrates a correlation between the plate dynamics and the two flow-phenomenon: vortex-formation mode and vortex-interaction mode. Vortex-formation relates to the position of the leading and the trailing edge of the plate relative to the recirculation region behind the cylinder and is classified into three-regimes: pre-vortex formation regime-a, pre-vortex formation regime-b, and post-vortex formation regime, corresponding to smaller, intermediate, and larger plate-amplitudes, respectively. The vortex-interaction mode refers to the nature of interaction between the cylinder and the plate vortices and is classified into two-modes: constructive and destructive interactions, corresponding to larger and smaller amplitudes, respectively. The study shows that the plate oscillates with very large amplitude at larger Re, intermediate G*, and with plate length equal to the cylinder diameter. The flexible plate leads to a large suppression in the hydrodynamic forces and the vortex shedding frequency of the cylinder in the pre-vortex formation regime, with complete suppression in the vortex-shedding for larger plate-length L* at intermediate gap G*. Thus, the present system can be utilized as a plate-based energy harvesting device as well as a vortex-shedding control device.

Wind energy, a new direction of the Balabekov School on the Karman vortex street

The article presents the main directions, achievements of the academic school of academician O.S. Balabekov. The application of the main developments in renewable energy sources, that is, using the kinetic energy of the wind in the generation of electricity, increasing efficiency due to the simultaneous vortex formation mode. To do this, a laboratory unit with a regular structure of the transducers was designed. Describes in detail the process of simultaneous vortex formation to improve performance, with the same structural and operational parameters of the installation. The optimal location parameters of the vibrating elements in the working area of the installation are determined. The vibration frequency and vibration amplitude of the plates are determined.

Two-stage growth mode for lift-off mechanism in oblique shock-wave/jet interaction

The lift-off flow of the supersonic streamwise vortex in oblique shock-wave/jet interaction (OS/JI), extracted from a wall-mounted ramp injector in the scramjet, is studied through the large-eddy simulation method. The shocked helium jet deforms into a pair of the streamwise vortex with a co-rotating companion vortex. The trajectory of the streamwise vortex center is lifted by the shock interaction. Based on the objective coordinate system in the frame of oblique shock, it is found that the nature of the three-dimensional lift-off structure of the OS/JI is inherently and precisely controlled by the structure kinetics of a corresponding shock bubble interaction (SBI). The striking similarities of both qualitative and quantitative results between the OS/JI and the SBI support the proposition that the lift-off of the streamwise vortex is the result of an underlying two-dimensional vortical motion. By combining the first-stage linear growth mode of Richtmyer–Meshkov instability with the second-stage vortex formation mode, a two-stage vortex propagation model suitable for the SBI is proposed and validated. The lift-off growth of a shocked jet in the OS/JI concerned and in the wall-mounted ramp injector cases from the literature is well explained under the two-stage vortex propagation model of SBI. This model further predicts that increasing ramp compression shows little effect on elevating the streamwise vortex for higher free-stream Mach numbers (Ma > 5). In comparison, evident lift-off may occur for lower Mach numbers (Ma < 3.5), which offers the new way for the preliminary design of a streamwise vortex-based ramp injector in the scramjet.

Formation of Vortex Flows in Liquid Crystal Phases Encapsulated in Microliter Volumes under the Action of Focused Laser Radiation

A theoretical description of the process of formation of vortex flows v(t, r) and the evolution of the director field $$\hat n$$ in microliter liquid crystal (LC) volumes with a free surface under the influence of a temperature gradient ∇T(t, r), which is initiated by focused laser radiation, has been proposed. Thermomechanical contributions to both the stress tensor and viscous moment which are acting per unit volume of the LC phase were taken into account in the framework of the nonlinear generalization of the classical Ericksen−Leslie theory, which allowed describing the origin and formation of vortex flows in nematics formed by 4-n-pentyl- 4'-cyanobiphenyl molecules. Various hydrodynamic modes of vortex formation in microsized LC volumes under the action of focused laser radiation have been investigated by numerical methods.

Large-eddy simulations of the vortex-induced vibration of a low mass ratio two-degree-of-freedom circular cylinder at subcritical Reynolds numbers

The vortex induced vibration phenomenon of a low mass ratio (m*=2.6) two-degree-of-freedom circular cylinder at subcritical Reynolds numbers (Re=3900, 5300, 11,000) has been investigated by means of large-eddy simulations. A low-dissipative spatial and time discretisation finite element schemes have been implemented and combined with the Wall-Adapting Local-Eddy viscosity (WALE) subgrid-scale model to solve the filtered incompressible flow equations. Several values of the reduced velocity in the range 3 ⩽ U* ⩽ 12 have been considered. The numerical results are extensively compared with available experimental and numerical data. Particular interest has been placed in the region of maximum cross-flow amplitudes, the super-upper branch, where previous high-fidelity numerical simulations have underestimated the peak amplitudes compared with experimental results. The transition between the super-upper and lower branches is also shown and described. The numerical simulations successfully reproduce the three-branch response maximum oscillation amplitudes and associated vortex formation modes. The 2T vortex formation mode, i.e. two triplets of vortices per oscillation period, has been observed to occur in the super-upper branch, for the three different values of the Reynolds number investigated. These results contradict the claim made in previous works [27] that the vortex formation mode in the super-upper branch is Reynolds number dependent. Beats are observed to appear prior the transition from the super-upper to the lower branch. It is argued that they may be related with the coherence and strength of the third vortex shed at the shoulder of the cylinder each half-cycle, which is finally suppressed in the transition to the lower branch.

Формирование вихревых течений в жидкокристаллических фазах инкапсулированных в микролитровые объемы под действием сфокусированного лазерного излучения

AbstractA theoretical description of the process of formation of vortex flows v ( t , r ) and the evolution of the director field $$\hat n$$ n ^ in microliter liquid crystal (LC) volumes with a free surface under the influence of a temperature gradient ∇ T ( t , r ), which is initiated by focused laser radiation, has been proposed. Thermomechanical contributions to both the stress tensor and viscous moment which are acting per unit volume of the LC phase were taken into account in the framework of the nonlinear generalization of the classical Ericksen−Leslie theory, which allowed describing the origin and formation of vortex flows in nematics formed by 4-n-pentyl- 4'-cyanobiphenyl molecules. Various hydrodynamic modes of vortex formation in microsized LC volumes under the action of focused laser radiation have been investigated by numerical methods.

Locked-on vortex shedding modes from a rotationally oscillating circular cylinder

Numerical simulations of unsteady two-dimensional flow around a rotationally oscillating circular cylinder, placed in a uniform cross flow of a constant property Newtonian fluid, are performed at a fixed Reynolds number of 200. The investigation is based on the solutions of stream function-vorticity formulation of Navier-Stokes equations on non-uniform polar grids using a higher order compact (HOC) formulation. The flow field is mainly influenced by Reynolds number, Re, maximum angular velocity of the cylinder, αm, and the frequency ratio, f/f0, which represents the ratio between the frequency of oscillation, f, and the natural vortex shedding frequency, f0. The ranges considered for these parameters are 0.5⩽αm⩽6.0 and 0.5⩽f/f0⩽3.0. The resulting vortex formation modes and lock-on phenomena behind the cylinder as well as the fluid forces acting on the cylinder are analyzed. Occurrence of new multiple lock-on regions is demonstrated in detail by the variation of f and αm. The instances of high drag reduction at high values of αm are confirmed. Comparisons with previous numerical and experimental results verify the accuracy and validity of the present study.

Flow patterns of a low mass-damping cylinder undergoing vortex-induced vibration: Transition from initial branch and upper branch

This paper presents an experimental study of the structural dynamics and the wake vortex modes of a lightly damped, elastically mounted cylinder undergoing vortex-induced vibration (VIV) in the transverse direction. The cylinder is neutrally buoyant with the mass ratio m*=1.0, and has a low damping coefficient ζ=0.0173. The influence of variation in the free-stream velocity (corresponding to the reduced velocity range 1.53≤U*≤6.62, or the Reynolds number range 3000≤Re≤13,000) on the structural dynamics of the cylinder is examined, in conjunction with detailed flow measurements around the cylinder using digital Particle Image Velocimetry (PIV). The cylinder is stationary at U*≤2.55, and begins to vibrate at U*≥3.05 (or in synchronization regime). The vibrating cylinder exhibits the so-called “soft” synchronization phenomenon that the vortex shedding frequency is synchronous with the structural vibration frequency (or response frequency) of the cylinder, rather than with the natural frequency of the system. The measured data for the cylinder undergoing VIV fall within the initial branch and the upper branches, and agree well with published data on free vibrating cylinders at similar low mass and damping. The transition from initial- to upper-branch is characterized by a switch of vortex formation mode from the classical 2S mode to the newly-discovered 2PO mode by Morse and Williamson (2009, Journal of Fluid Mechanics, Vol. 634, pp. 5–39) based on a forced vibrating cylinder. The distinction between the 2S and 2PO modes is vivid in terms of length- and velocity-scales of the shed vortices, and is also reflected by quantitative characterization of near-wake flow statistics, including the mean and turbulence properties.

Numerical study on instabilities behind a circular disk in a uniform flow

Instabilities behind a circular disk, which is normal to a uniform free-stream with aspect ratio of χ=5, are numerically studied in the range of Re from 115 to 1000. The onsets of three characteristic instabilities including natural vortex shedding, shear-layer instability and a very low frequency instability, which are associated with the Reynolds number, are reported. When Re<152, the wake stays steady and no vortex shedding occurs. A regular bifurcation leading to two-thread wake is observed for Re from 120 to 152. When Re increases to 152, the hairpin vortices begin to be periodically shed in a regular pattern. A reflectional-symmetry-breaking (RSB) mode is observed for Re from 152 to 155, a standing-wave (SW) mode is captured for Re from 156 to 247, and an unsteady state with planar symmetry and non-zero mean lift is captured for Re from 248 to 264. It is found that the hairpin vortices are always shedding in a fixed orientation for RSB mode, while shedding from diametrically opposite orientations at SW mode and the unsteady state with planar symmetry and non-zero mean lift. When Re increases to 265, a low frequency instability attributed to the irregular rotation of vortex shedding location is observed. The hairpin vortices are periodically shed in an irregular pattern and a new ‘4L’ vortex formation mode is identified. When Re increases to 650, the shear-layer instability starts to be detected in the shear layer. The critical Reynolds number is firstly identified in the range of 601–650. The cylindrical shear layer surrounding the vortex formation zone rolls up to form oblate ring vortices. The hairpin vortices break into pieces and small-scale vortices associated with the shear-layer instability are observed.

Modes of vortex formation and transition to three-dimensionality in the wake of a freely vibrating cylinder

The present work is aimed to give some insight into the relation between vortex shedding modes and transition to three-dimensionality in the wake of a freely vibrating cylinder by establishing a numerical model and analyzing the relevant results of two- and three-dimensional simulations. The compressible flow past an elastically-mounted cylinder is solved by using the immersed boundary method (IB method). The cylinder is free to vibrate in the transverse direction with zero structure damping. The response of displacement amplitude is studied with the variation of reduced velocity. Whether P+S mode exists in three-dimensional flow and the occurrence of 2P mode is caused by flow transition from two-dimensional to three-dimensional are problems of concern. Both 2P and P+S wake modes are observed in two- and three-dimensional simulations. The numerical results indicate that the flow transition from two-dimensional to three-dimensional is coupled with the cylinder vibration in the synchronization/lock-in regime. The wake formation given by three-dimensional simulations suggests that the P+S mode might exist in reality when the flow is reverted to two-dimensional by vortex induced vibration (VIV) at Re=300–350. When Reynolds number increases to 425, the wake formation undergoes transition to three-dimensionality and 2P mode is observed. The effect of mass ratio on the flow transition to three-dimensionality is studied. The relationship between wake modes and aerodynamic forces is discussed.

Thermal relaxation and critical instability of near-critical fluid microchannel flow

We present two-dimensional numerical investigations of the temperature and velocity evolution of a pure near-critical fluid confined in microchannels. The fluid is subjected to two sides heating after it reached isothermal steady state. We focus on the abnormal behaviors of the near-critical fluid in response to the sudden imposed heat flux. New thermal-mechanical effects dominated by fluid instability originating from the boundary and local equilibrium process are reported. Near the microchannel boundaries, the instability grows very quickly and an unexpected vortex formation mode is identified when near-critical thermal-mechanical effect is interacting with the microchannel shear flow. The mechanism of the new kind of Kelvin-Helmholtz instability induced by boundary expansion and density stratification processes is also discussed in detail. This mechanism may bring about innovations in the field of microengineering.

Streamwise oscillations of a cylinder beneath a free surface: Free surface effects on vortex formation modes

A computational study of a viscous incompressible two-fluid model with an oscillating cylinder is investigated at a Reynolds number of 200 and at a dimensionless displacement amplitude of A=0.13 and for the dimensionless forcing cylinder oscillation frequency-to-natural vortex shedding frequency ratios, f/f0=1.5,2.5,3.5. Specifically, two-dimensional flow past a circular cylinder subject to forced in-line oscillations beneath a free surface is considered. The method is based on a finite volume discretization of the two-dimensional continuity and unsteady Navier–Stokes equations (when a solid body is present) on a fixed Cartesian grid. Two-fluid model based on improved volume-of-fluid method is used to discretize the free surface interface. The study focuses on the laminar asymmetric flow structure in the near wake region and lock-on phenomena at a Froude number of 0.2 and for the dimensionless cylinder submergence depths, h=0.25, 0.5 and 0.75. The equivorticity patterns and pressure distribution contours are used for the numerical flow visualization. The code validations in special cases show good comparisons with previous numerical results.

Vortex-induced vibration of a rising and falling cylinder

In this study, we investigate the dynamics of a freely rising and falling cylinder. This is, in essence, a vortex-induced vibration (VIV) system comprising both transverse (Y) and streamwise (X) degrees-of-freedom (d.o.f.), but with zero spring stiffness and zero damping. This problem represents a limiting case among studies in VIV, and is an extension of recent research of elastically mounted bodies having very low spring stiffness, as well as bodies with very low mass and damping. We find that if the mass ratio (where m* = cylinder mass/displaced fluid mass) is greater than a critical value, m*crit = 0.545, the body falls or rises with a rectilinear trajectory. As the mass ratio is reduced below m*crit = 0.545, the cylinder suddenly begins to vibrate vigorously and periodically, with a 2P mode of vortex formation, as reported in the preliminary study of Horowitz &amp; Williamson (J. Fluids Struct. vol. 22, 2006, pp. 837–843). The similarity in critical mass between freely rising and elastically mounted bodies is unexpected, as it is known that the addition of streamwise vibration can markedly affect the response and vortex formation in elastically mounted systems, which would be expected to modify the critical mass. However, we show in this paper that the similarity in vortex formation mode (2P) between the freely rising body and the elastically mounted counterpart is consistent with a comparable phase of vortex dynamics, strength of vortices, amplitudes and frequencies of motion and effective added mass (CEA). All of these similarities result in comparable values of critical mass. The principal fact that the 2P mode is observed for the freely rising body is an interesting and consistent result; based on the previous VIV measurements, this is the only mode out of the known set {2S, 2P, 2T} to yield negative effective added mass (CEA &lt; 0), which is a condition for vibration of a freely rising body. In this paper, we deduce that there exists only one possible two degree-of-freedom elastically mounted cylinder system, which can be used to predict the dynamics of freely rising bodies. Because of the symmetry of the vortex wake, this system is one for which the natural frequencies are fNX = 2fNY. Although this seems clear in retrospect, previous attempts to predict critical mass did not take this into account. Implementing such an elastic system, we are able to predict vibration amplitudes and critical mass (m*crit = 0.57) for a freely rising cylinder in reasonable agreement with direct measurements for such a rising body, and even to predict the Lissajous figures representing the streamwise–transverse vibrations for a rising body with very small mass ratios (down to m* = 0.06), unobtainable from our direct measurements.

The effect of Reynolds number on the dynamics and wakes of freely rising and falling spheres

In this paper, we study the effect of the Reynolds number (Re) on the dynamics and vortex formation modes of spheres rising or falling freely through a fluid (whereRe= 100–15000). Since the oscillation of freely falling spheres was first reported by Newton (University of California Press, 3rd edn, 1726, translated in 1999), the fundamental question of whether a sphere will vibrate, as it rises or falls, has been the subject of a number of investigations, and it is clear that the mass ratiom* (defined as the relative density of the sphere compared to the fluid) is an important parameter to define when vibration occurs. Although all rising spheres (m* &lt; 1) were previously found to oscillate, either chaotically or in a periodic zigzag motion or even to follow helical trajectories, there is no consensus regarding precise values of the mass ratio (m*crit) separating vibrating and rectilinear regimes. There is also a large scatter in measurements of sphere drag in both the vibrating and rectilinear regimes.In our experiments, we employ spheres with 133 combinations ofm* andRe, to provide a comprehensive study of the sphere dynamics and vortex wakes occurring over a wide range of Reynolds numbers. We find that falling spheres (m* &gt; 1) always move without vibration. However, in contrast with previous studies, we discover that a whole regime of buoyant spheres rise through a fluid without vibration. It is only when one passes below a critical value of the mass ratio, that the sphere suddenly begins to vibrate periodically and vigorously in a zigzag trajectory within a vertical plane. The critical mass is nearly constant over two ranges of Reynolds number (m*crit≈ 0.4 forRe= 260–1550 andm*crit≈ 0.6 forRe&gt; 1550). We do not observe helical or spiral trajectories, or indeed chaotic types of trajectory, unless the experiments are conducted in disturbed background fluid. The wakes for spheres moving rectilinearly are comparable with wakes of non-vibrating spheres. We find that these wakes comprise single-sided and double-sided periodic sequences of vortex rings, which we define as the ‘R’ and ‘2R’ modes. However, in the zigzag regime, we discover a new ‘4R’ mode, in which four vortex rings are created per cycle of oscillation. We find a number of changes to occur at a Reynolds number of 1550, and we suggest the possibility of a resonance between the shear layer instability and the vortex shedding (loop) instability. From this study, ensuring minimal background disturbances, we have been able to present a new regime map of dynamics and vortex wake modes as a function of the mass ratio and Reynolds number {m*,Re}, as well as a reasonable collapse of the drag measurements, as a function ofRe, onto principally two curves, one for the vibrating regime and one for the rectilinear trajectories.

Prediction of vortex-induced vibration response by employing controlled motion

In order to predict response and wake modes for elastically mounted circular cylinders in a fluid flow, we employ controlled-vibration experiments, comprised of prescribed transverse vibration of a cylinder in the flow, over a wide regime of amplitude and frequency. A key to this study is the compilation of high-resolution contour plots of fluid force, in the plane of normalized amplitude and wavelength. With such resolution, we are able to discover discontinuities in the force and phase contours, which enable us to clearly identify boundaries separating different fluid-forcing regimes. These appear remarkably similar to boundaries separating different vortex-formation modes in the map of regimes by Williamson &amp; Roshko (J. Fluids Struct., vol. 2, 1988, pp. 355–381). Vorticity measurements exhibit the 2S, 2P and P + S vortex modes, as well as a regime in which the vortex formation is not synchronized with the body vibration. By employing such fine-resolution data, we discover a high-amplitude regime in which two vortex-formation modes overlap. Associated with this overlap regime, we identify a new distinct mode of vortex formation comprised of two pairs of vortices formed per cycle, where the secondary vortex in each pair is much weaker than the primary vortex. This vortex mode, which we define as the 2POVERLAP mode (2PO), is significant because it is responsible for generating the peak resonant response of the body. We find that the wake can switch intermittently between the 2P and 2PO modes, even as the cylinder is vibrating with constant amplitude and frequency. By examining the energy transfer from fluid to body motion, we predict a free-vibration response which agrees closely with measurements for an elastically mounted cylinder. In this work, we introduce the concept of an ‘energy portrait’, which is a plot of the energy transfer into the body motion and the energy dissipated by damping, as a function of normalized amplitude. Such a plot allows us to identify stable and unstable amplitude-response solutions, dependent on the rate of change of net energy transfer with amplitude (the sign of dE*/dA*). Our energy portraits show how the vibration system may exhibit a hysteretic mode transition or intermittent mode switching, both of which correspond with such phenomena measured from free vibration. Finally, we define the complete regime in the amplitude–wavelength plane in which free vibration may exist, which requires not only a periodic component of positive excitation but also stability of the equilibrium solutions.

Fluid forcing, wake modes, and transitions for a cylinder undergoing controlled oscillations

Abstract In this study, we make extensive measurements of the fluid forces on a cylinder that is controlled to oscillate transverse to a free stream at Re = 4000 . These measurements are used to create very high resolution contour plots (considerably higher than in any previous study) of the magnitude of fluid forcing, and its phase relative to the cylinder motion (as well as other fluid forcing quantities) in the plane of normalized amplitude and wavelength. Previous contours of force have been assumed to be continuous in the amplitude–wavelength plane, despite the fact that jumps in the fluid forcing and vortex formation modes were known to occur in other studies, including free vibration. In this investigation, we find clear discontinuities in the force contours, and we are thus able to identify boundaries separating different fluid forcing regimes. These appear remarkably similar to boundaries separating different vortex shedding modes in the regime map of Williamson and Roshko [1988. Vortex formation in the wake of an oscillating cylinder. Journal of Fluids and Structures 2, 355–381]. Measurements of vorticity fields confirm the modes of vortex formation in each regime; we find the 2S, 2P, and P + S modes, as well as a regime where the vortex formation is not synchronized with the cylinder oscillation. A new characteristic, which is only observable with very high-resolution data, is the existence of a region where two vortex formation regimes overlap. In the overlap region, we identify a distinct mode of vortex formation where two pairs of vortices are shed per cycle of oscillation (similar to the 2P mode) but the secondary vortex is much weaker, which we have termed ‘ 2 P OVERLAP ’, or simply the ‘ 2 P O ’ mode. The wake can switch intermittently between the 2P and 2 P O modes, even as the cylinder is oscillating with constant amplitude and frequency. The highest amplitude yielding positive fluid excitation lies inside the overlap region, therefore a study of the vortex dynamics in this region is essential to understanding the behavior of a free vibration system at peak amplitude response.

The effect of Reynolds number on the critical mass phenomenon in vortex-induced vibration

In this study, we investigate the critical mass phenomenon in vortex-induced vibration over a wide range of Reynolds numbers (Re=4000–30 000). We consider an elastically mounted cylinder that is able to vibrate transverse to a fluid flow. If we remove the restoring spring (k=0), then above a certain critical mass ratio (m∗ is oscillating body mass/displaced fluid mass), the cylinder will experience almost no motion, despite its unrestrained freedom to move transverse to the flow. However, when the mass ratio is decreased below a special critical value, without altering anything else in the system, we see a catastrophic increase in amplitude, and the body settles into a large amplitude periodic vibration. This corresponds to a change from a desynchronized wake to a 2P mode of vortex formation, where two pairs of vortices are formed per cycle of motion. Since a system with no restoring force represents a case of infinite normalized velocity (U∗→∞), the observation of high amplitude motion indicates that the regime of U∗ giving resonant vibration extends to infinity, for sufficiently small mass ratio. In this work, we measure the critical mass directly from experiments with no spring stiffness, and we show also how the critical mass may be accurately predicted from force measurements from controlled vibration experiments, or from free vibration measurements of elastically mounted cylinders. Critical mass gradually increases with Reynolds number from a value of 0.36 to 0.54, over the regime Re=4000–30 000. The fact that the critical mass is a function of Reynolds numbers should be expected because it depends on the vortex-induced forces, which are influenced by gradual changes in vortex formation as Re increases. The evaluation of critical mass in this configuration, and indeed in other diverse vortex-induced vibration (VIV) systems, is important because it can predict the regime of normalized velocities that will yield large amplitude vibration, and which one may wish to avoid in practice. The fact that critical mass, at moderate Reynolds numbers, in several diverse VIV systems, including cylinders in one or two degrees of freedom, pivoted bodies, cantilevers, and tethered spheres, are all within a small range 0.36–0.6, remains an interesting question.

Feedback control of a circular cylinder wake with rotational oscillation

A new feedback control algorithm for controlling vortex shedding from a circular cylinder in a uniform flow is proposed and tested. The lift coefficient (CL) is employed as a feedback signal and the control forcing is given by a rotational oscillation of the cylinder. A fractional form of the transfer function for the controller is designed, into which the interaction of the phase and magnitude of the controller is fully incorporated. In the proposed feedback control algorithm, the main emphasis is placed on controlling the phase of the feedback signal. When the feedback control forcing is imposed ‘out of phase’ with the response (i.e. outside the range of lock-on), the response is significantly reduced. In contrast, the response is increased when the feedback forcing is imposed in an ‘in phase’ manner. The effect of the feedback signal phase is ascertained by calculations using the Van der Pol oscillator, and the feedback control process is analyzed in terms of energy transfer between an actuator and an oscillator. Based on the analysis, the proposed feedback control method is applied to the wake behind a circular cylinder. The mechanism by which CL is reduced is delineated by examining the vortex formation modes as a function of the forcing phase.

Critical mass and a new periodic four-ring vortex wake mode for freely rising and falling spheres

In this letter, we study the dynamics and vortex wakes of spheres rising or falling freely through a fluid. Since this problem was first considered by Newton in 1726, the conditions under which a sphere will vibrate are still not understood clearly. In our experiments, all falling spheres (where the relative density, m∗&amp;gt;1) descend rectilinearly. Although previous studies conclude that all rising spheres (m∗&amp;lt;1) vibrate, we find instead that there exists a critical value of the relative density (for example, mcrit∗=0.36, for Reynolds numbers 400–500) above which there is a significant regime where rising spheres do not vibrate. Lighter spheres undergo large-amplitude periodic oscillations, confined to a single vertical plane. We discover a new mode of vortex formation comprising four vortex rings formed in each cycle, distinct from previous vortex modes for fixed and tethered bodies.

Two-degree-of-freedom vortex-induced vibrations of a spring-mounted rigid cylinder with low mass ratio

Abstract This work studies the vortex-induced vibrations of an elastically mounted rigid cylinder able to move in-line and transverse to the flow, with equal mass ratio and natural frequencies in both directions. A compact and simple set-up using torsion springs was designed for this purpose. Although the mass ratio is close to 1, the mass-damping parameter α is high enough so that the system exhibits a two-branch type response. Consequently, the ‘super-upper’ branch is not observed, and the peak transverse response is unaffected compared to transverse-only oscillations. We also note that measurement points associated with a ‘2S’ mode of vortex formation are found in the ‘2P’ area of the map of vortex regimes. This discrepancy is discussed in light of the influence of streamwise motion on the critical curve separating the ‘2S’ and ‘2P’ regimes.