Transition phenomena in the wake of an inclined square cylinder

The division of flow regimes in a square cylinder wake at various angles of attack (α) is studied. This study provides evidence of the existence of modes A and B instabilities in the wake of an inclined square cylinder. The critical Reynolds numbers for the inception of these instability modes were identified through the determination of discontinuities in the Strouhal number versus Reynolds number curves. The spectra and time traces of wake streamwise velocity were observed to display three distinct patterns in different flow regimes. Streamwise vortices with different wavelengths at various Reynolds numbers were visualized. A PIV technique was employed to quantitatively measure the parameters of wake vortices. The wavelengths of the streamwise vortices in the modes A and B regimes were measured by using the auto-correlation method. From the present investigation, the square cylinder wake at various angles of attack undergoes a similar transition path to that of a circular cylinder, although various quantitative parameters measured which include the critical Reynolds numbers, spanwise wavelength of secondary vortices, and the circulation and vorticity of wake vortices all show an α dependence.     

Streamwise evolution of a high-Schmidt-number passive scalar in a turbulent plane wake

The concentration fluctuation c of diluted fluorescein dye, a high-Schmidt-number passive scalar (Sc=ν/D ≈ 2000, ν and D are the fluid momentum and dye diffusivities, respectively), is measured in the wake of a circular cylinder using a single-point laser-induced fluorescence (SPLIF) technique. The streamwise decay rate of the mean and rms values of c is slow in comparison to that of θ, the temperature fluctuation for which the molecular Prandtl number Pr=ν/κ is about 0.7 (κ is the thermal diffusivity). The comparison between mean and rms distributions of c and θ highlights the combined role the Reynolds and Schmidt numbers play in terms of dispersing the scalar. The streamwise evolution of the probability density functions (pdfs) of c and θ suggest that while p(θ) is approximately Gaussian in the intermediate wake (x/d ≈ 80), p(c) is strongly non-Gaussian, and depends on both x/d and Re. The skewness of c is larger than that of θ along the wake centreline. Arguably, the asymmetry of p(c) reflects the relatively strong organisation of the large-scale motion in the far-wake. Received: 27 July 2000/Accepted: 22 December 2000     

Flow regimes and frequency selection of a cylinder oscillating in an upstream cylinder wake

This paper describes flow around a pair of cylinders in tandem arrangement with a downstream cylinder being fixed or forced to oscillate transversely. A sinusoidal parietal velocity is applied to simulate cylinder oscillation. Time-dependent Navier-Stokes equations are solved using finite element method. It is shown that there exist two distinct flow regimes: ‘vortex suppression regime’ and ‘vortex formation regime’. Averaged vortex lengths between the two cylinders, pressure variations at back and front stagnant points as well as circumferential pressure profiles of the downstream cylinder are found completely different in the two regimes and, thus, can be used to identify the flow regimes. It is shown that frequency selection in the wake of the oscillating cylinder is a result of non-linear interaction among vortex wakes upstream and downstream of the second cylinder and its forced oscillation. Increasing cylinder spacing results in a stronger oscillatory incident flow upstream of the second cylinder and, thus, a smaller synchronization zone.     

Numerical simulation of force and wake mode of an oscillating cylinder

The turbulent flow behind a circular cylinder subjected to forced oscillation is numerically studied at a Reynolds number of 5500 by using three-dimensional Large Eddy Simulations (3-D LES) technique with the Smagorinsky model. The filtered equations are discretised using the finite volume method with an O-type structured grid and a second-order accurate method in both time and space. Firstly, the main wake parameters of a stationary cylinder are examined and compared in the different grid resolutions. Secondly, a transversely oscillating cylinder with a constant amplitude in a uniform flow is investigated. The cylinder oscillation frequency ranges between 0.75 and 0.95 of the natural Kármán frequency, and the excitation amplitude is moderate, 50% of the cylinder diameter. The flow characteristics of an oscillating cylinder are numerically examined and the corresponding wake modes are captured firstly in 3-D LES at Re=5500. A transition between different wake modes is firstly investigated in a set of numerical simulations.     

Evolution of three-dimensional cavitation following water entry of an inclined cylinder

The water entry of an inclined cylinder is firstly studied experimentally for low Froude number. The cylinder is 50 mm in diameter and 200 mm in length, with a moderate length to diameter ratio. As it is submerged below the water surface, the cavity is fully three-dimensional. Due to the rotation of the cylinder caused by the initial inclined impact, the cavity evolution is quite complicated and a new phenomenon is revealed. The cylinder moves along a curved trajectory in water, which greatly affects the evolution of the cavities. The cavity breaks up into two sub-cavities, and finally collapses because of hydrostatic pressure.     

System identification of the kinematics of an oscillating cylinder using wake velocities

A classical problem in vortex-induced vibration is to know the flow field past an oscillating cylinder. In this paper we use system theory to identify the oscillatory behaviour of a circular cylinder from flow variables in the wake. We use numerical simulations (CFD) of the flow past a cylinder oscillating in the cross-flow direction at different oscillation frequencies and amplitudes to construct a transfer function that relates the displacement of the cylinder and the resulting flow field. This transfer function can then be inverted to ‘predict’ the displacement of the cylinder given the flow field (as determined by simulations or measurements). We investigate this technique in the so-called lock-in region, where the vortex shedding frequency is synchronised with the oscillation frequency of the cylinder.     

Closed-loop-manipulated wake of a stationary square cylinder

Vortex shedding from a fixed rigid square cylinder in a cross flow was manipulated by perturbing the cylinder surface using piezo-ceramic actuators, which were activated by a feedback hot-wire signal via a proportional–integral–derivative (PID) controller. The manipulated flow was measured at a Reynolds number (Re) of 7,400 using particle image velocimetry (PIV), laser-induced fluorescence (LIF) flow visualisation, two-component laser Doppler anemometry (LDA), hot wires and load cells. It is observed that the vortex circulation, fluctuating streamwise velocity, lift and drag coefficients and mean drag coefficient may decrease by 71%, 40%, 51%, 42% and 20%, respectively, compared with the unperturbed flow, if the perturbation velocity of the cylinder surface is anti-phased with the flow lateral velocity associated with vortex shedding. On the other hand, these quantities may increase by 152%, 90%, 60%, 67% and 37%, respectively, given in-phased cylinder surface perturbation and vortex shedding. Similar effects are obtained at Re=3,200 and 9,500, respectively. The relationship between the perturbation and flow modification is examined, which provides insight into the physics behind the observation.     

A review of rotating cylinder wake transitions

Recent work on the flow past a rotating cylinder is reviewed and further investigated at low Reynolds numbers. The various two- and three-dimensional transitions that occur as the rotation rate is increased are detailed. Two steady states, steady state I and steady state II, are identified based on the physical characteristics of the wake and the drag force on the body. Steady state I occurs at lower rotation rates, while state steady state II occurs at higher rotation rates. Linear stability analysis shows that two three-dimensional modes become unstable on steady state I and steady state II. Floquet stability analysis of the unsteady base flows that occur at very low rotation rates shows the presence of five three-dimensional modes. The curves of marginal stability are presented, followed by a comparison of numerical simulations to their experimentally obtained counterparts. Furthermore, the spatio-temporal characteristics of each mode and the likely underlying physical mechanisms are briefly discussed.     

Aerodynamic characteristics of an inclined and yawed circular cylinder with artificial rivulet

Stay cables of cable-stayed bridges often experience vibrations with large amplitudes induced by wind or jointly by both wind and rain. To understand the aerodynamic characteristics of the stay cables and excitation mechanics of rain–wind-induced vibration (RWIV), an inclined and yawed circular cylinder with and without an artificial upper rivulet is studied through a series of wind tunnel tests. The impacts of upper rivulet and axial flow on the aerodynamics of the cylinder are investigated. It is found that for an inclined and yawed cylinder without rivulet there exists a non-zero lift force at large wind angle. Furthermore, the wind pressures and aerodynamic forces acting on both the cylinder and the upper rivulet are obtained, which can be used to develop more rational theoretical models for RWIV of stay cables. Results show that the upper rivulet can both enhance and depress Karman vortex shedding depending on the position of the rivulet. As a result, dramatic variations of the aerodynamic forces acting on the cylinder and the rivulet will occur, which may eventually result in RWIV. Also axial flow may have a noticeable influence on the aerodynamic characteristics of the inclined and yawed cylinder. And the presence of the rivulet can enhance such influence from the axial flow.     

Two-dimensionality of a cantilevered-cylinder wake in the presence of an oscillating upstream cylinder

The effect of a longitudinally oscillating cylinder on the two-dimensionality of flow around a downstream cylinder is studied based on a two-point correlation measured using two hot-wires. The oscillation amplitude is A/d=0.472 and the oscillation frequency f_e/f_s=0.0372 and 0.186, where d is the cylinder diameter and f_s the frequency of natural vortex shedding from an isolated stationary cylinder. Three centre-to-centre spacing (L) ratios of the two cylinders were examined, i.e., L/d=1.8, 2.5 and 4.8, representing three typical flow regimes. The experiment was conducted at a Reynolds number (Re) of 5920, based on d and the free-stream velocity. It is found that the spanwise correlation of the flow depends on not only the oscillation but also the flow regimes. At L/d=1.8, the correlation is strongest among the three regimes, but worst in the co-shedding regime (L/d=4.8). The upstream cylinder oscillation improves the spanwise correlation of the flow in the gap of the cylinders, irrespective of regimes, especially for L/d=1.8 and 2.5, but impairs that behind the cylinders for L/d=1.8 and 2.5 due to a change in the flow regime. A theoretical analysis based on the boundary vorticity theory indicates that the oscillation increases the vorticity flux, in particular, in the spanwise direction between the cylinders, resulting in a significantly improved spanwise correlation, though this increase is negligibly small behind the downstream cylinder.     

Three-dimensional phase dynamics in a cylinder wake

Recently there has been a new surge of interest in three-dimensional wake patterns, from both an experimental and analytical standpoint. One of the central discoveries is that the patterns of vortex shedding are dependent on the specific end conditions of a long cylinder span. However, a number of outstanding questions have remained unanswered, in part because techniques had not existed to control such patterns in a continuous fashion and from outside a test facility. In the present work, we have devised a method to control the end conditions of a cylinder span by non-mechanical and continuously-variable means, namely by the use of end suction. The technique allows a continuous variation of end conditions and admits transient or impulsive control. With the method, the classical steady-state patterns, such as parallel or oblique shedding or the chevron patterns are simply induced. These experiments demonstrate that the wake, at a given Reynolds number, is receptive to a continuous (but limited) range of oblique shedding angles (), rather than to discrete angles. There is excellent agreement in these results with the cos formula for collapsing oblique-shedding frequencies onto a single universal frequency curve. The use of suction has avoided the grossly unsteady motions at the ends of the cylinder span brought about by the wakes of mechanical end manipulators, and we show that the laminar shedding regime exists up to Reynolds numbers (Re) of 205. The surprisingly large disparity among reported measurements of criticalRe for wake transition (Re=140–200), over the last forty years, can now be explained in terms of spanwise end contamination.The control technique has also allowed experiments to be performed, which have resulted in the discovery of new phenomena such as phase shocks and phase expansions. A major difference between these phenomena is that phase shocks (involving regions of straight vortices) translate spanwise at constant speed, crossing the complete span in a finite time, whereas a phase expansion (involving curved vortices) requires an infinite time to complete its development across the span. These transient wake patterns are well illustrated using a simple model, based on experimental measurements, that thenormal wavelength for oblique or parallel vortices remains constant. However, a detailed and close comparison between our experimental results and those results from analytical modelling of the wake using Ginzburg-Landau modelling (in collaboration with Peter Monkewitz at Lausanne) is presently underway. These equations yield a Burger's equation for the spanwise wavenumber (or phase gradient), from which both (phase) shocks and expansions are well-known solutions.

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Sommario Recentemente è rinato l'interesse per i modelli tridimensionali di scie, sia da un punto di vista sperimentale che da uno analitico. Una delle scoperte centrali è che le modalità di produzione dei vortici sono dipendenti dalle condizioni agli estremi di un lungo cilindro. Nel presente lavoro, è stato formulato un metodo per controllare le condizioni finali agli estremi di un cilindro per mezzo di variabili continue di significato non-meccanico, cioè per mezzo dell'aspirazione agli estremi. La tecnica permette una variazione continua delle condizioni agli estremi ed ammette controllo transitorio od impulsivo. Con questo metodo sono semplicemente indotti i classici modelli a stato fissato, come anche quelli che prevedono produzioni di vortici parallele od oblique o quellichevron. Questi esperimenti dimostrano che la scia, ad un dato numero di Reynolds, ammette una distribuzione continua (ma limitata) di angoli per distribuzioni oblique, piuttosto che una discreta. In questi risultati c'è un eccellente accordo con la formula del coseno per frequenze di produzioni oblique e collassanti su di una curva di frequenzauniversale. L'uso dell'aspirazione ha evitato i moti largamente instabili alle estremità del cilindro, provocati dalle scie delle parti terminali dei manipolatori, e si osserva che il regime laminare diffondente esiste oltre un numero di Reynolds pari a 205. La sorprendentemente larga disparità tra le misure di numeri di Reynolds critici, riportati per transizioni di scia (Re=140÷200) durante gli ultimi quattro anni, può essere ora spiegata in termini di contaminazione della estensione della lunghezza del cilindro.

     

Three-dimensional vorticity in a turbulent cylinder wake

The three components of the vorticity vector in the intermediate region of a turbulent cylinder wake were measured simultaneously using a multi-hot-wire probe. This probe has an improved spatial resolution compared with those reported in the literature. The behavior of the instantaneous velocity and vorticity signals is examined. Both coherent and incoherent vorticity fields are investigated using a phase-averaged technique. The iso-contours of the phase-averaged longitudinal and lateral vorticity variances, and , wrap around the spanwise structures of opposite sign and run through the saddle point along the diverging separatrix. The observation conforms to the previous reports of the occurrence of the longitudinal structures based on flow visualizations and numerical simulations. The magnitude of these contours is about the same as that of the maximum coherent spanwise vorticity at the vortex center, indicating that the strength of the longitudinal structures is comparable to that of the spanwise vortices. Furthermore, and exhibit maximum concentration away from the vortex center, probably because of a combined effect of the large-scale spanwise vortices and the intermediate-scale longitudinal structures. Coherent structures contribute about 36% to the spanwise vorticity variance at x/d=10. The contribution decreases rapidly to about 5% at x/d=40. The present results suggest that vorticity largely reside in relatively small-scale structures.     

Convection velocity measurements in a cylinder wake

The convection velocity of vortices in the wake of a circular cylinder has been obtained by two different approaches. The first, implemented in a wind tunnel using an array of X-wires, consists in determining the velocity at the location of maximum spanwise vorticity. Four variants of the second method, which estimates the transit time of vortices tagged by heat or dye, were used in wind and water tunnels over a relatively large Reynolds number range. Results from the two methods are in good agreement with each other. Along the most probable vortex trajectory, there is only a small streamwise increase in the convection velocity for laminar conditions and a more substantial variation when the wake is turbulent. The convection velocity is generally greater than the local mean velocity and does not depend significantly on the Reynolds number.Nomenclature d diameter of circular cylinder - f frequency in spectrum analysis - f _v average vortex frequency - r _v vortex radius - Re Reynolds number U _o d/v - t time - Th , Th , Th _r thresholds for _zp, , and r _v respectively - U _o free stream velocity - U ₁ maximum value of (U _o – U) - U _c convection velocity of the vortex, as obtained either by Eq. (1) or Eq. (2) - U _co convection velocity used in Eq. (3) U _cd, U _cu average convection velocities of downstream and up-stream regions respectively of the vortex - U _cv the value of U _c at y = 0.5 - u, v the velocity fluctuations in x and y directions respectively - U, V mean velocity components in x and y directions respectively - U,V U = U + u, V = V + v - x, y, z co-ordinate axes, defined in Fig. 1 Greek Symbols circulation - mean velocity half-width - x spacing between two cold wires or grid spacing - ₁, ₂ temperature signals from upstream and downstream cold wires respectively - v kinematic viscosity - _c transit time for a vortex to travel a distance x - phase in the cross-spectrum of ₁ and ₂ - _z instantaneous spanwise vorticity - _zc cut-off vorticity used in determining the vortex size - _zp peak value of _z - a denotes conditional average, defined in Eq. (12) - a prime denoting rms value     

POD analysis of a finite-length cylinder near wake

The near wake of a wall-mounted finite-length square cylinder with an aspect ratio of 7 is investigated based on the proper orthogonal decomposition (POD) of the PIV data measured in three spanwise planes, i.e., z/d = 6, 3.5 and 1.0, near the cylinder free end, mid-span and fixed end (wall), respectively. The Reynolds number based on free-stream velocity (U _∞) and cylinder width (d) is 9,300. A two-dimensional (2D) square cylinder wake is also measured and analyzed at the same Reynolds number for the purpose of comparison. The structures of various POD modes show marked differences between the two flows. While the coefficients, a ₁ and a ₂, of the POD modes 1 and 2 occur within an annular area centered at a ₁ = a ₂ = 0 in the 2D wake, their counterparts are scattered all over the entire circular plane at z/d = 1.0 and 3.5 of the finite-length cylinder wake. Flow at z/d = 6 is dominated by POD mode 1, which corresponds to symmetrical vortex shedding and accounts for 54.0 % of the total turbulent kinetic energy (TKE). On the other hand, the POD modes 1 and 2, corresponding to anti-symmetrical vortex shedding, are predominant, accounting for about 45.0 % of the total TKE, at z/d = 3.5 and 1. It has been found that the flow structure may be qualitatively and quantitatively characterized by the POD coefficients. For example, at z/d = 6, a larger a ₁ corresponds to a smaller length of flow reversal zone and a stronger downwash flow. At z/d = 3.5 and 1, two typical flow modes can be identified from a ₁ and a ₂. While large a ₁ and/or a ₂ correspond to anti-symmetrical vortex shedding, as in a 2D cylinder wake, small a ₁ and a ₂ lead to symmetrical vortex shedding. Any values between the large and small a ₁ and/or a ₂ correspond to the flow structure between these two typical flow modes. As such, the probability of occurrence of a flow structure may be determined from the distribution of the POD coefficients.     

Instability of cylinder wake under open-loop active control

Instability of a wake controlled by a streamwise Lorentz force is investigated through a Floquet stability analysis. The streamwise Lorentz force, which is a two-dimensional control input created by an electromagnetic actuator located on the cylinder surface,adjusts the base flow to affect the three-dimensional wake instability and achieve wake stabilization and transition delay. The instability mode at a Reynolds number Re = 300 can be transformed from B to A with N = 1.0, where N is an interaction number representing the strength of the Lorentz force relative to the inertial force in the fluid. The wake flow is Floquet stable when N increases to 1.3. The spanwise perturbation wavelengths are 3.926 D and 0.822 D in the modes A and B, respectively, where D is the cylinder diameter. In addition, the oscillating amplitudes of drag and lift are reduced with the increase in the interaction number. Particle tracing is used to explore the essential physical mechanism for mode transformation. The path lines show that suppression of flow separation hinders the fluid deformation and rotation, leading to the decrease in elliptic and hyperbolic instability regions, which is the material cause of mode transformation.All of the results indicate that wake stabilization and transition delay can be achieved under open-loop active control via the streamwise Lorentz force.     

The near wake structure of a square cylinder

The near wake structure of a square cross section cylinder in flow perpendicular to its length was investigated experimentally over a Reynolds number (based on cylinder width) range of 6700–43,000. The wake structure and the characteristics of the instability wave, scaling on θ at separation, were strongly dependent on the incidence angle () of the freestream velocity. The nondimensional frequency (St_θ) of the instability wave varied within the range predicted for laminar instability frequencies for flat plate wakes, jets and shear layers. For = 22.5°, the freestream velocity was accelerated over the side walls and the deflection of the streamlines (from both sides of the cylinder) towards the center line was higher compared to the streamlines for = 0°. This caused the vortices from both sides of the cylinder to merge by x/d 2, giving the mean velocity distribution typical of a wake profile. For = 0°, the vortices shed from both sides of the cylinder did not merge until x/d 4.5. The separation boundary layer for all cases was either transitional or turbulent, yet the results showed good qualitative, and for some cases even quantitative, agreement with linearized stability results for small amplitude disturbances waves in laminar separation layers.     

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.