Vortex dynamics of a sphere wake in proximity to a wall

Toward getting the vortex dynamics characteristics and wake structure of a sphere in proximity to a wall, the effect of a proximal flat plate on the wake of a stationary sphere is investigated via direct numerical simulation. The vortex shedding process and the significant variation of the wake structure are described in detail. The drag coefficient reduces and the wake structure of the sphere becomes complex due to the combined effect of the wake flow and the wall. A jet flow forms between the sphere and the flat plate, which suppresses the vortex separation on the bottom of the sphere. The asymmetric distributions of the coherent structures and the recirculation region behind the sphere are discussed. Besides vortex shedding patterns, the time-averaged velocity distribution, vortex dynamics, distribution regularities of turbulent kinetic energy and enstrophy are investigated.     

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.

     

Vortex dynamics in the wake of a mechanical fish

A novel Stereo PIV technique, with improvements over other techniques, is presented. The key feature of the new technique is the direct measurement of calibration data at each point in space on the measurement grid, so that no interpolation is necessary. This is achieved through the use of a contiguous target which can be analysed using standard PIV processing software. The technique results in three-dimensional measurements of high accuracy with a significantly simpler calibration phase. This has the benefit of improving ease of use and reducing the time taken to obtain data. Thorough error analysis shows that while previously-described error trends are correct, additional facets of the technique can be optimised to allow highly accurate results. The new technique is rigorously validated here using pure translation and rotation test cases. Finally, the technique is used to measure a complex swirling flow within a cylindrical vessel.     

Influence of wall proximity on characteristics of wake behind a square cylinder: PIV measurements and POD analysis

Influence of wall proximity on characteristics of the wake behind a two-dimensional square cylinder was experimentally studied in the present work. A low-speed recirculation water channel was established for the experiment; the Reynolds number based on the free-stream velocity and cylinder width (D) was kept at Re_D = 2250. Four cases with different gap width, e.g., G/D = 0.1, 0.2, 0.4 and 0.8, were chosen for comparison. Two experimental techniques, e.g., the standard PIV with high image-density CCD camera and TR-PIV with a high-speed camera were employed in measuring the wake field, enabling a comprehensive view of the time-averaged wake pattern at high spatial resolution and the instantaneous flow field at high temporal resolution, respectively. For the four cases, the difference in spatial characteristics of the wake in the vicinity of the plane wall was analyzed in terms of the time-averaged quantities measured by the standard PIV, e.g., the streamline pattern, the vector field, the streamwise velocity fluctuation intensity and the reverse-flow intermittency. The proper orthogonal decomposition (POD) method was extensively used to decompose the TR-PIV measurements, giving a close-up view of the energetic POD modes buried in the wake. The low-order flow model of the wake at G/D = 0.8 and 0.4 was constructed by using the linear combination of the first two POD modes and the time-mean flow field, which reflected well the vortex shedding process in the sense of the phase-dependent patterns. The intermittent appearance of the weakly separated region near the wall was found at G/D = 0.4. On going from G/D = 0.8 to 0.4, the remarkable variation of the instantaneous wake in the longitudinal direction confirmed that the wall constraint stretches the vortices in the plane of the wall and transfers the energy to the longitudinal component at the expense of the lateral one.     

Control of three-dimensional phase dynamics in a cylinder wake

Recently there has been a surge of new interest in three-dimensional wake patterns. In the present work, we have devised a method to control the spanwise end conditions and wake patterns using “end suction”, which is both continuously-variable and admits transient control. Classical steady-state patterns, such as parallel or oblique shedding or the “chevron” patterns are simply induced. The wake, at a given Reynolds number, is receptive to a continuous range of oblique shedding angles (θ), rather than to discrete angles, and there is excellent agreement with the “cos θ” formula for oblique-shedding frequencies. We show that the laminar shedding regime exists up to Reynolds numbers (Re) of 205, and that the immense disparity among reported critical Re for wake transition (Re = 140–190) can be explained in terms of spanwise end contamination. Our transient experiments have resulted in the discovery of new phenomena such as “phase shocks” and “phase expansions”, which can be explained in terms of a simple model assuming constant normal wavelength of the wake pattern. Peter Monkewitz (Lausanne) also predicts such transient phenomena from a Guinzburg-Landau model for the wake.     

Vortex shedding from a circular cylinder near a moving wall

Flow over a circular cylinder near a moving plane wall is simulated numerically. The influence of the moving wall on the vortex shedding from the cylinder is demonstrated and the corresponding mechanism is illustrated using instability theory. A critical gap ratio between the circular cylinder and the moving wall is defined, and a precise method for determining the critical gap ratio is proposed. The drag and lift forces and the pressure coefficient are presented as a function of the gap ratio. The scaling of the Strouhal number is discussed.     

Vortex shedding from a square cylinder in presence of a moving wall

A numerical study on the flow past a square cylinder placed parallel to a wall, which is moving at the speed of the far field has been made. Flow has been investigated in the laminar Reynolds number (based on the cylinder length) range. We have studied the flow field for different values of the cylinder to wall separation length. The governing unsteady Navier–Stokes equations are discretized through the finite volume method on a staggered grid system. A SIMPLE type of algorithm has been used to compute the discretized equations iteratively. A shear layer of negative vortex generates along the surface of the wall, which influences the vortex shedding behind the cylinder. The flow‐field is distinct from the flow in presence of a stationary wall. An alternate vortex shedding occurs for all values of gap height in the unsteady regime of the flow. The strong positive vortex pushes the negative vortex upwards in the wake. The gap flow in the undersurface of the cylinder is strong and the velocity profile overshoots. The cylinder experiences a downward force for certain values of the Reynolds number and gap height. The drag and lift are higher at lower values of the Reynolds number. Copyright © 2005 John Wiley & Sons, Ltd.     

Influence of wall proximity on vortex shedding from a square cylinder

Mean and fluctuating surface pressure data are presented for a square cylinder of side length D placed near a solid wall at Re _D=18,900. One oncoming boundary layer thickness, d=0.5 D was used. Measurements were made for cylinder to wall gap heights, S, from S/ D=0.07 to 1.6. Four gap-dependent flow regimes were found. For S/ D>0.9, the flow and the vortex shedding strength are similar to the no-wall case. Below the critical gap height of 0.3 D, periodic activity is fully suppressed in the near wake region. In between, for 0.3< S/ D<0.9, the wall exerts a greater influence on the flow. For 0.6< S/ D<0.9, the mean drag and the strength of the shed vortices decrease as the gap is reduced, while the mean lift towards the wall increases. Evidence is presented that for S/ D>0.6 the influence of the viscous wall flow in the gap is not dominant and that, consequently, inviscid flow theory can describe changes in the mean lift as S/ D decreases. For 0.3< S/ D<0.6, the flow reattaches intermittently on the bottom face of the cylinder and viscous effects become important. Below the gap height of 0.4 D, periodic activity cannot be observed on the cylinder.     

Effect of cylinder proximity to the wall on channel flow heat transfer enhancement

Heat-transfer enhancement in a uniformly heated slot mini-channel due to vortices shed from an adiabatic circular cylinder is numerically investigated. The effects of gap spacing between the cylinder and bottom wall on wall heat transfer and pressure drop are systemically studied. Numerical simulations are performed at Re=100$\mathit{Re}=100$, 0.1?Pr?10$0.1?\mathrm{Pr}?10$ and a blockage ratio of D/H=1/3$D/H=1/3$. Results within the thermally developing flow region show heat transfer augmentation compared to the plane channel. It was found that when the obstacle is placed in the middle of the duct, maximum heat transfer enhancement from channel walls is achieved. Displacement of circular cylinder towards the bottom wall leads to the suppression of the vortex shedding, the establishment of a steady flow and a reduction of both wall heat transfer and pressure drop. Performance analysis indicates that the proposed heat transfer enhancement mechanism is beneficial for low-Prandtl-number fluids.     

On the vortex dynamics in the wake of a finite surface-mounted square cylinder

The shedding process in the near wake of a surface-mounted, square cross-section cylinder of height-to-width aspect ratio 4 at a Reynolds number of 12,000 based on free-stream velocity and the obstacle width was investigated. The boundary layer thickness was 0.18 obstacle heights based on 99% free-stream velocity. The study is performed using planar high frame-rate particle image velocimetry synchronized with pressure measurements and hot-wire anemometry. Spatial cross-correlation, instantaneous phase relationships, and phase-averaged velocity data are reported. Two dominant vortex-shedding regimes are observed. During intervals of high-amplitude pressure fluctuations on the obstacle side faces, alternate formation and shedding of vortices is observed (regime A) similar to the von Kármán process. Regime B is characterized by two co-existing vortices in the obstacle lee throughout the shedding cycle and is observed within low-amplitude pressure fluctuation intervals. Despite the coexisting vortices in the base region, opposite sign vorticity is still shed out-of-phase downstream of this vortex pair giving rise to a staggered arrangement of counter-rotating vortices downstream. While the probability of occurrence of Regime B increases toward the free end, the amplitude modulation remains coherent along the obstacle height. Conditionally phase-averaged reconstructions of the flow field are consistent with the spatial distribution of the phase relationships and their probability density function. Earlier observations are reconciled showing that the symmetric shedding of vortices is a rare occurrence.     

Approach to local axisymmetry in a turbulent cylinder wake

The objective of this experimental study is to characterise the small-scale turbulence in the intermediate wake of a circular cylinder using measured mean-squared velocity gradients. Seven of the twelve terms which feature in ε, the mean dissipation rate of the turbulent kinetic energy, were measured throughout the intermediate wake at a Reynolds number of Re _d  ≈ 3000 based on the cylinder diameter (d). Earlier measurements of the nine major terms of ε by Browne et al. (J Fluid Mech 179: 307–326 1987) at a downstream distance (x) of x = 420d and Re _d  ≈ 1170 are also used. Whilst departures from local isotropy are significant at all locations in the wake, local axisymmetry of the small-scale turbulence with respect to the mean flow direction is first satisfied approximately at x = 40d. The approach towards local axisymmetry is discussed in some detail in the context of the relative values of the mean-squared velocity gradients. The data also indicate that axisymmetry is approximately satisfied by the large scales at x/d ≥ 40, suggesting that the characteristics of the small scales reflect to a major extent those of the large scales. Nevertheless, the far-wake data of Browne et al. (1987) show a discernible departure from axisymmetry for both small and large scales.     

Fluid-dynamic forces and wake frequencies on a tilted rectangular cylinder near a solid wall

We investigate the impact of different boundary conditions on the flow field developing around a tilted rectangular cylinder with two different values of the aspect ratio (l/s=3 and 4). We are mainly interested in analyzing the changes in force coefficients and in the vortex shedding Strouhal number when the cylinder is placed at various distances from a bottom wall and different values of attack angle. The angle of attack ranges between −30° and +30° and the cylinder elevation above the bottom wall is varied between almost zero and 5 times the thickness of the cylinder. A large body of experimental results is related to the small elevation conditions at different attack angles, where the presence of the wall has a non-negligible effect on the behavior of the force coefficients and Strouhal number of the vortex shedding.     

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     

Vortex dynamics and scalar transport in the wake of a flat-plate controlled by a vibrating trailing-edge flap

We investigate the onset and development of vortical flow disturbances introduced into the wake of a horizontally fixed flat-plate by means of the controlled motion of a trailing edge flap. The vibrating mechanics of the flap allows for the introduction of both impulsive and harmonic weak amplitude velocity disturbances which are propagated downstream into the wake flow of the flat-plate. Quantitative experimental and numerical predictions of both steady and unsteady wake flow velocity resulting from different flapping frequencies are made at low Reynolds numbers (Re < 10⁴). Frequency response tests of the wake confirmed the existence of two dominant frequencies where the wake flow organises with a particular arrangement of downstream moving vortex structures. Numerical predictions of steady (unforced) and forced wake velocity profiles and kinetic energy profiles are in good agreement with the experimental results. In order to understand practical implications of the dominant vortex structures in scalar transport, we have extended the numerical part of the study solving for the concentration equation of a passive scalar being injected in particular regions of the physical domain. A spatial correlation between the trajectory of vortex structures and the scalar concentration downstream the wake is observed. Moreover, the onset of tip vortex structures produced during the forcing cycle seems to be responsible of a local increase of scalar concentration near the span wise flap ends.     

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.     

Vortex systems in the stratified wake of a sphere

The fine structure of the flow and the characteristics of the principal types of vortex structures in the wake of a sphere moving uniformly and horizontally in an exponentially stratified fluid have been experimentally investigated.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 82–90, July–August, 1991.The authors are grateful to G. Yu. Stepanov for his careful analysis of the first version of this article and his valuable comments.