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.     

Pressure/velocity coupling induced by a near wall wake

A combined wall pressure/velocity analysis of the wake of a disk located in the vicinity of a flat wall is presented in this paper. One gap ratio only is selected. In this situation, the footprint of the flow unsteadiness on the magnitude of the wall fluctuating pressure is significant while the natural vortex shedding properties of the wake are only slightly altered. Spatio-temporal velocity and pressure/velocity correlations are analyzed. They carry the signature of the large-scale coherence and periodicity associated with vortex shedding and exhibit characteristic phase relations. Advanced statistical analysis techniques are adapted and developed. A conditional phase averaging of the pressure and velocity fields is obtained. The proper orthogonal decomposition of a spatio-temporal pressure data set on the axis of the near wake is shown to be efficient (1) to determine the phase of the spatio-temporal pressure field projected on the two first modes and (2) to distinguish between quiescent random signatures and more energetic phases. Conditional statistics show very clearly that the large-scale structures interact with the flat wall. Finally, a linear stochastic estimation (LSE) of the velocity field is computed from the fluctuating pressure data. We show the superiority of the spatio-temporal LSE over the spatial LSE in predicting the kinetic energy and the coherent spectral properties of the fluctuating velocity field. Moreover, the linear stochastic estimation is very good in predicting the phase-averaged conditional velocity field.     

Symmetric vortex shedding in the near wake of a circular cylinder due to streamwise perturbations

Symmetric perturbations imposed on cylinder wakes may result in a modification of the vortex shedding mode from its natural antisymmetric, or alternating, to a symmetric one where twin vortices are simultaneously shed from both sides of the cylinder. In this paper, the symmetric mode in the wake of a circular cylinder is induced by periodic perturbations imposed on the in-flow velocity. The wake field is examined by PIV and LDV for Reynolds numbers about 1200 and for a range of perturbation frequencies between three and four times the natural shedding frequency of the unperturbed wake. In this range, a strong competition between symmetric and antisymmetric vortex shedding occurs for the perturbation amplitudes employed. The results show that symmetric formation of twin vortices occurs close to the cylinder synchronized with the oscillatory component of the flow. The symmetric mode rapidly breaks down and gives rise to an antisymmetric arrangement of vortex structures further downstream. The downstream wake may or may not be phase-locked to the imposed oscillation. The number of cycles for which the symmetric vortices persist in the near wake is a probabilistic function of the perturbation frequency and amplitude. Finally, it is shown that symmetric shedding is associated with positive energy transfer from the fluid to the cylinder due to the fluctuating drag.     

Dynamics of interaction modes in excited annular jets

Evolution of coherent structures and their interaction dynamics are educed in the near field of an acoustically excited basic annular jet using conditional sampling technique based on a multiple triggering criterion to detect the two dominating modes of structure pattern. Acoustic excitation is applied with an aim to better organize the phase alignment of initial rolling and pairing process in the outer shear layer. Negligible modification of the time-averaged flow field results from the excitation. The educed coherent vorticities show that the two modes of evolution are due to the corresponding two modes of shedding pattern of the wake structures from the centerbody, namely the mode one wake and the mode zero wake. In both modes, the shear-layer mode jet vortex rings in the outer layer are perturbed by the shedding of wake structures in the inner region and interaction involving primary merging of three successive jet vortex rings or their partial circumferential sections is found. This results in the formation of wake-induced structures of the corresponding mode pattern, which possesses concentration of coherent vorticity and fluid circulation over a large spatial extent at 1 < x/D < 2. Secondary interactions, such as vortex tearing, are also observed.     

Conditional averaging of PIV plane wake data using a cross-correlation approach

A new approach is investigated for conditional averaging of a series of random snapshots of periodic velocity fields obtained from PIV measurements. This approach departs from conventional conditional averaging approaches that require a reference signal for extracting phase information and uses the cross-correlation between the velocity fields as a phase identifier. The methodology is applied on the natural and forced turbulent wake of a circular cylinder, the latter serving also as a validation/verification case. The results show that the vortex formation and shedding processes in the wake are drastically affected by inflow oscillations and reveal the underlying vortex dynamics. Additionally, detailed velocity measurements are reported for the two cases investigated.     

Phase-resolved characterization of vortex shedding in the near wake of a square-section cylinder at incidence

The vortex formation and shedding process in the near wake region of a 2D square-section cylinder at incidence has been investigated by means of particle image velocimetry (PIV). Proper orthogonal decomposition (POD) is used to characterize the coherent large-scale flow unsteadiness that is associated with the wake vortex shedding process. A particular application of the POD analysis is to extract the vortex-shedding phase of individual velocity fields, which were acquired at asynchronous low rate with respect to the vortex shedding cycle. The phase of an individual flow field is determined from its projection on the first pair of POD modes, allowing phase averaging of the measurement data to be performed. In addition, a low-order representation of the flow, constructed from the mean and the first pair of POD modes, is found to be practically equivalent to the phase-averaged results. It is shown that this low-order representation corresponds to the basic Fourier component of the flow field ensemble with respect to the reconstructed phase. The phase-averaged flow representations reveal the dominant flow features of the vortex-shedding process and the effect of the angle of incidence upon it.     

Effect of buoyancy on the wakes of circular and square cylinders: a schlieren-interferometric study

Wakes behind heated cylinders, circular, and square have been experimentally investigated at low-Reynolds numbers. The electrically heated cylinder is mounted in a vertical airflow facility such that buoyancy aids the inertia of main flow. The operating parameters, i.e., Reynolds number and Richardson number are varied to examine flow behavior over a range of experimental conditions from forced to mixed convection regime. Laser schlieren-interferometry has been used for visualization and analysis of flow structures. Complete vortex shedding sequence has been recorded using a high-speed camera. The results on detailed dynamical characteristics of vortical structures, i.e., their size, shape and phase, Strouhal number, power spectra, convection velocity, phase shift, vortex inception length, and fluctuations are reported. On heating, alteration of organized (coherent) structures with respect to shape, size and their movement is readily perceived from instantaneous Schlieren images before they reduce to a steady plume. For both cylinders, Strouhal number shows a slow increase with an increase in Richardson number. At a critical value, there is complete disappearance of vortex shedding and a drop in Strouhal number to zero. The corresponding spectra evolve from being highly peaked at the vortex shedding frequency to a broadband appearance when vortex shedding is suppressed. The geometry of vortex structures transforms to a slender shape before shedding is suppressed. At this heating level, absence of multiple peaks in power spectra at cylinder centerline indicates absence of interaction between opposite shear layers. The convection velocity of vortices increases in stream wise direction to an asymptotic value and its variation is a function of Richardson number. The convection speed abruptly falls to zero at critical Richardson number. The phase difference of shed vortices between upstream and downstream location increases with an increase in Richardson number. Velocity profiles show an increase in fluid speed and beyond the critical point, buoyancy forces add enough momentum to cancel momentum deficit due to the cylinder. Overall, the combined effect of temperature gradient on the separating shear layer velocity profile in near field and vortical structures interaction in far field influences wake instability of a heated cylinder. Electronic supplementary material The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Observations of large-scale structures in wakes behind axisymmetric bodies

Wakes behind disk-shaped axisymmetric bodies of varying solidity are studied using flow visualization and two-dimensional Fourier decomposition of velocity measurements. Evidence of a reverse flow region behind some of the bodies is observed to coincide with the presence of large-scale structures in the near and far wake. Fourier analysis shows that these large-scale structures are predominately helical (m= ±1) and occur at a characteristic frequency which corresponds to their wavelength as observed from flow visualization. Our measured value for this characteristic frequency agrees with vortex shedding frequencies observed for these types of wakes.     

Mechanical forcing of the wake of a flat plate

We report experimental results of the forced wake of a thin symmetric flat plate, placed parallel to an uniform air stream, in the range of thickness-based Reynolds number 50< Re _e <200. External wake forcing was introduced by small harmonic oscillations of a moving flap, placed at the trailing-edge of the flat plate. When the flap remains in a fixed horizontal position, the mean velocity profiles obtained by hot wire measurements, for different Reynolds numbers, are self similar. In the presence of harmonic forcing, within a certain range of the forcing frequency, the mean velocity profiles change and coherent structures are formed in the wake. Two independent flow-type resonances were observed: (i) when the inverse of the forcing frequency matches the flight time of the fluid particles along the flap. (ii) when the forcing frequency of the flap equals one half of the vortex shedding frequency of the flat plate and flap system. Implications of the two observed resonances on the wake structure are important. The first resonance (i) is associated to a wide but less intense (energy fluctuations) wake flow and the second resonance (ii) generates a thin but intense resultant wake flow.     

VORTEX SHEDDING RESONANCE FROM A ROTATIONALLY OSCILLATING CYLINDER

Vortex shedding resonance of a circular cylinder wake to a forced rotational oscillation has been investigated experimentally by measuring the velocity fluctuations in the wake, pressure distributions over the cylinder surface, and visualizing the flow field with respect to cylinder oscillations. The vortex shedding resonance occurs near the natural shedding frequency at small amplitude of cylinder oscillations, while the peak resonance frequency shifts to a lower value with an increase in oscillation amplitude. The drag and lift forces acting on the cylinder at fixed forcing Strouhal number indicate that the phase lag of fluid forces to the cylinder oscillations increases with an increase in oscillation amplitude, supporting the variation of resonance frequency with oscillation amplitude. The comparative study of the measured pressure distributions and the simultaneous flow visualizations with respect to cylinder rotation shows the mechanisms of phase lag, which is due to the strengthened vortex formation and the modification of the surface pressure distributions.     

Buoyancy-Driven Coherent Structures in Free Round Flame

Complex interactions between fluid dynamics and combustion processes areamong the topics most often undertaken in recent years. The free roundflames dominated by large-scale vortex structures seem to be a veryinteresting type of flow as indicated by the many experimental resultsavailable in literature. The so-called outer coherent structures whichare believed to be generated as a result of buoyancy-driven instabilitywere experimentally investigated by means of laser Doppler anemometry.The results of spectral analysis of fluctuating velocity componentsrevealed the regular oscillations of the flow field with well-defineddiscrete frequencies depending upon the mixture composition. Theexternal excitation of coherent structures at a frequency matching theirnatural shedding frequency allowed the construction of velocity vectormaps of organised vorticity. From the results obtained one may statethat the coherent vortices are located in the outer part of flame withthe trajectory of their centres moving far from the flame front. Theirlocation and very large sizes (comparable with the flow width) suggesttheir important role in mixing and, especially, in the entrainmentprocesses which are the essential in combustion systems.The dimensionalanalysis taking into account the characteristic parameters of vorticesand thermal structure of the flame suggests that buoyancy forces havesignificant impact on organised vorticity and can be considered asresponsible for its origin.     

Asymmetric vortex shedding flow past an inclined flat plate at high incidence

This paper reports an experimental investigation of the vortex shedding wake behind a long flat plate inclined at a small angle of attack to a main flow stream. Detailed velocity fields are obtained with particle-image velocimetry (PIV) at successive phases in a vortex shedding cycle at three angles of attack, α=20°, 25° and 30°, at a Reynolds number Re≈5,300. Coherent patterns and dynamics of the vortices in the wake are revealed by the phase-averaged PIV vectors and derived turbulent properties. A vortex street pattern comprising a train of leading edge vortices alternating with a train of trailing edge vortices is found in the wake. The trailing edge vortex is shed directly from the sharp trailing edge while there are evidences that the formation and shedding of the leading edge vortex involve a more complicated mechanism. The leading edge vortex seems to be shed into the wake from an axial location near the trailing edge. After shedding, the vortices are convected downstream in the wake with a convection speed roughly equal to 0.8 the free-stream velocity. On reaching the same axial location, the trailing edge vortex, as compared to the leading edge vortex, is found to possess a higher peak vorticity level at its centre and induce more intense fluid circulation and Reynolds stresses production around it. It is found that the results at the three angles of attack can be collapsed into similar trends by using the projected plate width as the characteristic length of the flow.     

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.     

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.     

Direct numerical simulation of turbulent wake behind a surface-mounted square cylinder

In this research, direct numerical simulation has been performed to study the turbulent wake behind a wall-mounted square cylinder with aspect ratio 4 and Reynolds number 12 000 (based on the free-stream velocity and obstacle side length) in a developing boundary layer. Owing to the relatively high Reynolds number and high aspect ratio of the cylinder tested, the wake is wide spread behind the cylinder and exhibits complex and energetic vortex motions. The lateral and tip vortex shedding patterns at different frequencies, coherent structures downstream of the obstacle, the production rate and distribution of turbulent kinetic energy, and the instantaneous pressure distribution in the wake region have been thoroughly investigated. In order to validate the numerical results, the first- and second-order flow statistics obtained from the simulations have been carefully compared against available wind-tunnel measurement data.     

OBLIQUE VORTEX SHEDDING BEHIND TAPERED CYLINDERS

The vortex shedding in the wake behind linearly tapered circular cylinders has been considered for the two taper ratios 75:1 and 100:1. The Reynolds number based on the velocity of the incoming flow and the largest diameter was in the range from 130 to 180. The low Reynolds number assured that laminar flow prevailed in the entire flow field. The full unsteady three-dimensional Navier–Stokes equations were solved numerically with the view of exploring the rather complex vortex shedding phenomena caused by the variation of the natural shedding frequency along the span of the cylinder. The accurate computer simulations showed that this variation gave rise to discrete shedding cells, each with its own characteristic frequency and inclined with respect to the axis of the cylinder. Flow visualizations revealed that vortex dislocation and splitting took place in the numerically simulated flow fields. The computer simulations compared surprisingly well with the extensive laboratory experiments reported by Piccirillo & Van Atta in 1993 for a range of comparable conditions; this has enabled detailed analyses of other flow variables (notably pressure and vorticity) than those readily accessible in a physical experiment. However, distinct differences in the vortex dynamics are observed in some of the cases.     

Accurate model reduction of transient and forced wakes

Some applications of a precise method to model the transient dynamics of large scale structures in the laminar flow past a bluff body are presented. The flow is described using empirical eigenfunctions obtained by “proper orthogonal decomposition” and the models are constructed projecting the Navier–Stokes equations onto such eigenfunctions. The linear terms in the expansion coefficients as well as in the control inputs are adjusted to exactly mimic some reference solutions. Applications shown are relative to the development of flow instabilities leading to vortex shedding and the dynamics of the vortex wake under external actuation.     

Active vortex-induced vibration control of a circular cylinder at low Reynolds numbers using an adaptive fuzzy sliding mode controller

An adaptive fuzzy sliding mode control (AFSMC) scheme is applied to actively suppress the two-dimensional vortex-induced vibrations (VIV) of an elastically mounted circular cylinder, free to move in in-line and cross-flow directions. Laminar flow regime at Re=90, low non-dimensional mass with equal natural frequencies in both directions, and zero structural damping coefficients, are considered. The natural oscillator frequency is matched with the vortex shedding frequency of a stationary cylinder at Re=100. The strongly coupled unsteady fluid/cylinder interactions are captured by implementing the moving mesh technology through integration of an in-house developed User Define Function (UDF) into the main code of the commercial CFD solver Fluent. The AFSMC approach comprises of a fuzzy system designed to mimic an ideal sliding-mode controller, and a robust controller intended to compensate for the difference between the fuzzy controller and the ideal one. The fuzzy system parameters as well as the uncertainty bound of the robust controller are adaptively tuned online. A collaborative simulation scheme is realized by coupling the control model implemented in Matlab/Simulink to the plant model constructed in Fluent, aiming at determination of the transverse control force required for complete suppression of the cylinder streamwise and cross-flow oscillations. The simulation results demonstrate the high performance and effectiveness of the adopted control algorithm in attenuating the 2D-VIV of the elastic cylinder over a certain flow velocity range. Also, the enhanced transient performance of the AFSM control strategy in comparison with a conventional PID control law is demonstrated. Furthermore, the effect of control action on the time evolution of vortex shedding from the cylinder is discussed. In particular, it is observed that the coalesced vortices in the far wake region of the uncontrolled cylinder, featuring the C(2S)-type vortex shedding characteristic mode, are ultimately forced to switch to the classical von Kármán vortex street of 2S-type mode, displaying wake vortices of moderately weaker strengths very similar to those of the stationary cylinder. Lastly, robustness of AFSMC is verified against relatively large structural uncertainties as well as with respect to a moderate deviation in the uniform inlet flow velocity.     

Response of the Sphere Wake to Freestream Fluctuations

Direct numerical simulations have been used to investigate the response of the wake of a sphere to freestream fluctuations. This study has been motivated by the need to understand particle-induced turbulence enhancement in particulate flows. A sequence of simulations of flow past a sphere have been carried out where the frequency and amplitude of the freestream fluctuations and the flow Reynolds number has been varied systematically. It has been suggested that turbulence enhancement is primarily caused by vortex shedding from particles (Gore and Crowe, 1989; Hetsroni, 1989). Our simulations of the forced wake indicate that turbulence enhancement may be attributed to natural vortex shedding only when the freestream fluctuation level is low and the Reynolds number is greater than about 300. In addition to natural vortex shedding, the current simulations also suggest another mechanism for turbulence enhancement. It is found that in the presence of freestream fluctuations, the wake behaves like an oscillator and returns large amounts of kinetic energy to the surrounding fluid at resonance. This mechanism is not associated with natural vortex shedding and is therefore capable of enhancing freestream turbulence even at Reynolds numbers less than 300. Simulations also indicate that when the turbulence intensity of the carrier fluid is high, this resonance mechanism might be solely responsible for turbulence enhancement. Finally, our simulations also suggest a possible explanation for the correlation between turbulence enhancement and the ratio of the particle size to the size of energy containing eddies of turbulence found by Gore and Crowe (1989). Received 5 October 1999 and accepted 14 October 1999