Vortex Shedding Cycle Research Articles

On the prediction of the turbulent flow behind cylinder arrays via echo state networks

This study aims at the prediction of the turbulent flow behind cylinder arrays by the application of Echo State Networks (ESN). Three different arrangements of arrays of seven cylinders are chosen for the current study. These represent different flow regimes: single bluff body flow, transient flow, and co-shedding flow. This allows the investigation of turbulent flows that fundamentally originate from wake flows yet exhibit highly diverse dynamics. The data is reduced by Proper Orthogonal Decomposition (POD) which is optimal in terms of kinetic energy. The Time Coefficients of the POD Modes (TCPM) are predicted by the ESN. The network architecture is optimized with respect to its three main hyperparameters, Input Scaling (INS), Spectral Radius (SR), and Leaking Rate (LR), in order to produce the best predictions in terms of Weighted Prediction Score (WPS), a metric leveling statistic and deterministic prediction. In general, the ESN is capable of imitating the complex dynamics of turbulent flows even for longer periods of several vortex shedding cycles. Furthermore, the mutual interdependencies of the TCPM are well preserved. However, optimal hyperparameters depend strongly on the flow characteristics. Generally, as flow dynamics become faster and more intermittent, larger LR and INS values result in better predictions, whereas less clear trends for SR are observable.

Flow past two diamond-section cylinders in tandem arrangement at a low Reynolds number

The unsteady flow surrounding two fixed diamond cylinders is analyzed at Reynolds number 100 over normalized center-to-center spacing ratios 2−15. By analyzing the contours of instantaneous vorticity, variations of recirculation length, surface pressure, and fluid forcing of cylinders, the value of normalized critical spacing is found to be 3.4. In the reattachment zone below critical spacing, vortex-shedding from the upstream (UC) and downstream (DC) cylinders is anti-phase. At the critical spacing, regular vortex-shedding commences also from the UC, and vortex-shedding from the cylinders becomes phase synchronized for the first time. The analysis of a vortex-shedding cycle at the critical spacing reveals that the cylinders shed vortices at the same frequency, but with a time delay. Impingement of vortices shed from the UC on the DC strengthens vorticity around the DC and shifts the instantaneous position of its forward stagnation point from the leading edge. The understanding that locations of stagnation points govern the direction and magnitude of lift force comes from the analysis of flow at the critical gap. When the surface bounded by stagnation points is occupied mostly with negative vorticity, the instantaneous lift is negative and vice versa. At critical spacing, mean streamlines show the emergence of an anti-wake at forward stagnation point of the DC for the first time. Over the entire range of cylinder separation, nine distinct patterns of separation topologies are identified. Below critical spacing, both pressure and viscous drag components, and hence, total drag of the DC are negative or upstream-acting.

Drag reduction in a spanwise-infinite boat-tailed body through multiple transverse grooves

Appropriately-designed spanwise-extruded small grooves, oriented transverse to the freestream flow, may delay flow separation in adverse pressure gradients by generating local and stable recirculation zones. In this study, we explore the potential of multiple grooves to reduce the drag on a boat-tailed bluff body characterized by vortex shedding. Numerical simulations reveal that the presence of two consecutive transverse grooves results in a maximum boat-tail drag reduction of 23.2%, further decreasing the drag by 15% when compared to the performance of the same boat-tailed bluff body with a single groove. This flow-control mechanism proves effective when the flow reattachment takes place downstream of both grooves throughout the entire vortex-shedding cycle, leading to the formation of two distinct local recirculation zones within the grooves. Lower frictional losses are observed along the streamline bounding the recirculation within the grooves as compared to the friction losses caused by the no-slip boundary conditions along the lateral walls of a plain boat tail (i.e., without grooves). Consequently, the boundary layer exhibits higher momentum downstream of the grooves, resulting in a delayed flow separation and an improved reduction in body drag for the boat tail.

Optimal waveform for fast synchronization of airfoil wakes

We obtain an optimal actuation waveform for fast synchronization of periodic airfoil wakes through the phase reduction approach. Using the phase reduction approach for periodic wake flows, the spatial sensitivity fields with respect to the phase of the vortex shedding are obtained. The phase sensitivity fields can uncover the synchronization properties in the presence of periodic actuation. This study seeks a periodic actuation waveform using phase-based analysis to minimize the time for synchronization to modify the wake shedding frequency of NACA0012 airfoil wakes. This fast synchronization waveform is obtained theoretically from the phase sensitivity function by casting an optimization problem. The obtained optimal actuation waveform becomes increasingly non-sinusoidal for higher angles of attack. Actuation based on the obtained waveform achieves rapid synchronization within as low as two vortex shedding cycles irrespective of the forcing frequency, whereas traditional sinusoidal actuation requires ${O}(10)$ shedding cycles. Further, we analyse the influence of actuation frequency on the vortex shedding and the aerodynamic coefficients using force-element analysis. The present analysis provides an efficient way to modify the vortex lock-on properties in a transient manner with applications to fluid–structure interactions and unsteady flow control.

The use of GANs and transfer learning in model-order reduction of turbulent wake of an isolated high-rise building

The high cost of computational fluid dynamics (CFD) simulations has limited their use for real-time and long-term simulations. To address this limitation, reduced-order modeling has been developed, and recent advancements in artificial intelligence (AI) algorithms have led to the creation of non-intrusive reduced-order models (NIROMs). The present study proposes a framework for using various AI techniques to develop NIROMs for the turbulent wake of an isolated high-rise building. The framework is demonstrated using datasets from two different flow conditions, isothermal and unstable thermal stratification. A residual adversarial autoencoder (AAE) network with convolutional layers and Wasserstein generative adversarial network (WGAN) is first used to reduce the dimensionality of the unstable dataset. Afterward, a parallel bidirectional long short-term memory (BiLSTM) network computes its evolution through time. The proposed framework provides commendable predictions of the airflow field. The weights of the trained model are utilized to create a NIROM based on transfer learning (TL) for a smaller dataset that represents the isothermal condition. The results showed that when the training dataset is limited and the model cannot be trained on sufficient vortex shedding cycles, the proper use of TL can lead to better outcomes compared to the traditional training method (i.e., training from scratch).

Particle dispersion over side-by-side square cylinders: Proximity interference effects

This paper investigates the dispersion of tiny inertial particles in the two-dimensional laminar wake from a pair of square cylinders placed side-by-side to each other. The flow Reynolds number (defined based on the cylinder size h and uniform inflow velocity Uc) in our study is fixed at 75. The wake pattern resulting from the interaction between vortices shed from individual cylinders depends on the cross-stream spacing between the cylinders, i.e. spacing ratio s/h. We examine the effect of varying the cross-stream spacing between the cylinders on the body impaction and dispersion of particles in the wake flow over a range of their responses. Three different spacing ratios, s/h = 0.3, 2, and 4 are considered. We find that the impaction efficiency of Stokes number St = 0.1 particles is not sensitive to the spacing ratio. However, the impaction efficiency of St = 1 and 10 particles is dependent on the spacing ratio and increases with the latter. We illustrate how the distribution and clustering of representative inertial particles (i.e., with Stokes number unity) evolve over a vortex shedding cycle uniquely due to the wake flow in each spacing ratio configuration and explain the physical mechanism of particle clustering using backward tracking. The non-uniform clustering of particles with different responses to the wake flow in each spacing ratio configuration is analyzed using the Voronoï diagrams. The spacing ratio effects on the dispersion of particles are quantified in terms of mean statistical quantities such as mean local concentration, clustering intensity, and velocity statistics. The local concentration of St = 1 and 10 particles at streamwise positions away from cylinders is significantly influenced by the wake flow behavior governed by the choice of the spacing ratio. Further, the combined effect of gravity and hydrodynamic drag forces on the impaction and clustering behavior of particles is reported, where the Froude number Fr=0.32. In all the cases, particles exhibit ballistic behavior, showing a significantly reduced tendency to form clusters and a drastic increase in the impaction efficiency.

Vortex evolution near the Coanda surface of a circulation control airfoil with pulsed actuation

A special vortex evolution process was found near the Coanda surface for circulation control airfoil with pulsed actuation. For the jet-on process, two successive shedding vortices from the lower lip edge and the separation vortex on the Coanda surface collide and interact with each other, and periodic vortex shedding forms after several vortex shedding and collision cycles. For the jet-off process, the periodic shedding vortices were replaced by a row of vortices with reverse rotation direction from the upper lip edge, and then reverse vortices broke into small-scale vortices.

Experimental study of coherent wall-pressure fluctuations associated with the turbulent near wake of a cylinder

The objective of this work is to present a coherent detection method to determine relationships between pressure fluctuations and wake velocity in the case of the flow past a cylinder in a turbulent regime. We report experimental results and pressure–velocity statistics measured simultaneously on the surface boundary layer and the near wake in the range of Reynolds numbers (2×103<Re<3.5×104). The novelty of the analysis lies in the application of a coherent mean method to determine conditioned wall pressure statistics to velocity events observed in the turbulent cylinder wake. The method allows one to associate wake turbulent events with a corresponding wall-pressure signal profile on the cylinder surface performing discrete angular measurements with a minimum number of pressure sensors. Simultaneous measurements of both time series of wake velocity and wall pressure allow us to characterize the mutual influence of hydrodynamic perturbations from the boundary layer surface pressure with the near wake velocity fluctuations. Large scale turbulent vortex shedding is well correlated with surface pressure fluctuations as expected in the low frequency range. Near wake velocity signals were used as timing signals to determine the coherent influence of a representative velocity pattern on the statistical properties of wall pressure fluctuations. The dynamics of low-frequency large-scale structures is consistent with the presence of counter-rotating vortices and is well correlated with a great part of the pressure fluctuations of the boundary layer. Conditional statistics using the velocity pattern obtained from the coherent averaging method provided the instantaneous pressure fluctuating profile associated with the large-scale vortex shedding cycle, thus, enabling a coherent estimation of the fluctuating lift and drag forces. Conditional statistics on wake velocity are well influenced by the phase of the vortex life-cycle.

Real-time estimation and prediction of unsteady flows using reduced-order models coupled with few measurements

The estimation and prediction of unsteady flows in real time offers significant advantages for the monitoring and active control of complex hydrodynamic and aerodynamic systems, such as wind turbine blades, hydrofoils and aircraft wings. A new data assimilation algorithm is proposed for the estimation and prediction of unsteady flows, coupling in real time onboard measurements and fluid dynamics simulations at minimal computational expense. The procedure combines a Proper Orthogonal Decomposition Galerkin method, a model under location uncertainty stochastic closure, and a particle filtering scheme. The algorithm is validated using case studies of two- and three-dimensional wake flows at low and moderate Reynolds numbers respectively. Following an initial learning window to train the algorithm, and using only a single measurement point, our method is shown to perform well against conventional reduced data assimilation algorithms for up to 14 vortex shedding cycles.

Wake Vortices and Dissipation in a Tidally Modulated Flow Past a Three‐Dimensional Topography

AbstractLarge eddy simulations are employed to investigate the role of tidal modulation strength on wake vortices and dissipation in flow past three‐dimensional topography, specifically a conical abyssal hill. The barotropic current is of the form Uc + Ut sin(Ωtt), where Uc and Ut are the mean and oscillatory components, respectively, and Ωt is the tidal frequency. A regime with strong stratification and weak rotation is considered. The velocity ratio R = Ut/Uc is varied from 0 to 1. Simulation results show that the frequency of wake vortices reduces gradually with increasing R from its natural shedding frequency at R = 0 to Ωt/2 when R ≥ 0.2. The ratio of R and the excursion number, denoted as , controls the shift in the vortex frequency. When , vortices are trapped in the wake during tidal deceleration, extending the vortex shedding cycle to two tidal cycles. Elevated dissipation rates in the obstacle lee are observed in the lateral shear layer, hydraulic jet, and the near wake. The regions of strong dissipation are spatially intermittent, with values exceeding during the maximum‐velocity phase, where D is the base diameter of the hill. The maximum dissipation rate during the tidal cycle increases monotonically with R in the downstream wake. Additionally, the normalized area‐integrated dissipation rate in the hydraulic response region scales with R as (1 + R)4. Results show that the wake dissipation energetically dominates the internal wave flux in this class of low‐Froude number geophysical flows.

Unsteady aerodynamics of a plunging airfoil in transient motion

The peak loads experienced by aircraft of all scales will typically be during gusts, turbulence or extreme manoeuvres. Understanding the aerodynamic response to these transient disturbances is therefore crucial, particularly when Leading-Edge Vortices (LEVs) occur. This fundamental study investigates the aerodynamic response to a wide range of transient plunging motions. The peak loads exhibited a strong dependence to motion amplitude yet remained relatively insensitive to motion duration. Within the parameter range tested (motion duration of T ¡ 20τ, or equivalent reduced frequency k ¡ 1, and plunge amplitude of αpl,peak≤ 30°), the peak lift did not exceed that of the quasi-static thin airfoil theory prediction, permitting its use as a safe limit for structural design. The normalized peak lift change displayed weak collapse with the timescale of the motion and instead showed better correlation with the non-dimensional plunge rate. The peak pitching moment scales well with plunge rate according to the theoretical prediction due to the added-mass component for plunge-up motions, but quickly diverges for plunge-down motions. At post-stall angles of attack, large-scale vortex shedding was observed and caused decaying oscillations in the loads long after the transient motion ends. For both a NACA 0012 and flat plate airfoil, the first vortex shedding cycle after the transient motion occurs around the subharmonic of the static shedding frequency. Subsequent shedding cycles then increase in frequency and asymptotically approach the static shedding frequency in around 15 to 20 convective times. This is the first study to experimentally quantify this behavior and is an aspect currently missing in existing reduced-order models, which could be significant for the prediction of successive transient disturbances. Finally, Reynolds number insensitivity was demonstrated for transient disturbances between 20,000 and 150,000, even for post-stall angles of attack where large-scale vortex shedding can occur.

Modeling the Flow State Sensitivity of Actuation Response on a Stalled Airfoil

In this work, we perform direct numerical simulations of leading-edge momentum injection of a NACA0009 airfoil at poststall angles of attack. It is found that the lift response is highly dependent upon the instantaneous state of the wake at the time of actuation, which is characterized by the phase of the vortex-shedding limit cycle present in the unactuated system. In particular, we find that actuating at a phase of the limit cycle corresponding to the maximum lift gives the largest maximum in transient lift response, whereas actuating near the lift minimum gives a smaller initial transient lift enhancement and can lead to a significant reduction in the amplitude of the limit cycle. As well as characterizing this phase dependency, we develop a reduced-order model that can capture this behavior. This is achieved by applying dynamic mode decomposition with control to a concatenation of velocity and lift measurements from several training datasets. The resulting models can accurately capture the dynamics of the training datasets as well as for phases not included in the training data. We show that for this method of actuation, multiple control objectives with the same actuator can be achieved.

Acoustic wave propagation and its application to fluid structure interaction using the Cumulant Lattice Boltzmann Method

Splitter plates attached to a cylinder looking like hair (SPCH) is one of the self-adaptive devices used to control actual flow conditions, which in turn interact with Aeolian tones constituting a typical case of study in engineering industries. The direct numerical simulation of the sound waves stimulated by such devices is a complicated task due to the small levels of sound pressure and the time-consuming existing solvers. However, the Cumulant Lattice Boltzmann Method (LBM) provides stability and robustness at high Reynolds numbers and carries out these simulations satisfactorily. First, the fundamental acoustical properties of the Cumulant LBM are studied in this paper. Propagation of point and planar acoustic waves is considered including the temporal decay of a standing plane wave, the spatial decay of a planar acoustic pulse, and the propagation of spherical waves. Then, the Cumulant LBM as a fluid flow solver is coupled with a Finite Element structural mechanics solver to predict the effects of SPCH on the noise generated by cylinders at high Reynolds numbers as a practical fluid structure interaction (FSI) application. The spectral modification and possible acoustic damping impact of such flaps, plus the sound propagation from one and two circular cylinders are studied. A comparison of the theoretical and numerical results shows a reasonable capability of the Cumulant LBM to predict acoustical events with small errors in dissipation and dispersion. Furthermore, the results show that SPCH alter the phase of the vortex shedding cycle and decrease the transversal distance from the center line of the shed vortices. Flaps, thus, control the wake generated past a cylinder and have an effective impact on decreasing sound generation.

Low-frequency unsteadiness in the flow around a square cylinder with critical angle of [formula omitted] at the Reynolds number of [formula omitted

Numerical simulations with high grid resolutions are conducted to investigate the flow past a square cylinder at the Reynolds number of 2.2×104 and the critical angle of attack of 14°. The focus is on the unsteadiness with a much lower frequency than that of von Karman vortex shedding. This study confirms the existence of low-frequency unsteadiness even for the square cylinder. The qualitative and quantitative features of low-frequency unsteadiness are systematically analyzed in terms of forces, vortex shedding and separation bubble. The low frequency with the outstanding peak is much lower than the frequency of von Karman vortex shedding; specifically, it is about 0.14fvK, where fvK is the vortex-shedding frequency. The low-frequency unsteadiness can be “felt” in the time series of forces and in the dynamics of vortex shedding and separation bubble. For both drag and lift, the unsteadiness is manifested by the low-frequency modulation of force amplitude and by the low-frequency periodic variation between the high and low values of the mean drag and lift over a vortex shedding cycle. The smaller force amplitude is accompanied simultaneously by the vortex shedding with longer formation length and weaker spanwise correlation, together with longer separation bubble on the flow-reattachment side of the cylinder.

Nonlinear Characteristics of a Rectangular Cavity in Supersonic Flow

Time-resolved schlieren images and unsteady pressure measurements were employed to understand the flowfield characteristics of a rectangular cavity at Mach number 1.8 with a unit Reynolds number of . It was illustrated that the vortex dynamics in the cavity shear layer were found to be nonlinear, where the vortex speed was observed to be varied from to with an average value of . Unsteady pressure measurements inside the cavity revealed six tones, among which the third tone was dominant. The uniqueness of the flow features both outside as well as inside the cavity was studied for one vortex shedding cycle. Analyses using different techniques divulged that the occurrence of the first and second tones was due to wave propagation and vortex shedding, respectively. On the other hand, frequency that corresponds to one time period was correlated to the third tone. Further investigations unveiled that the entrainment of freestream between shear-layer vortices generated type 5 acoustic waves, which were responsible for the production of other cavity tones. The wavelet analyses indicated that the frequencies were amplitude modulated in time, and the wavelet spectra of the second and third tones contain high-energy events along with sporadic distribution of low-energy events without mode switching phenomenon.

Wake structures and vortex-induced forces of a controlled in-line vibrating circular cylinder

A two-dimensional numerical study was performed to investigate wake structures and fluid forces on a circular cylinder with prescribed vibrations in the in-line direction. Reynolds number was fixed at 500, and the SST k-w model was used to simulate turbulence in the flow. A wake map for in-line vibrations, which includes six wake patterns named AS, SS, S(AS), S(2Po), S(P + S) and S(2P), is drawn in the plane of non-dimensional frequency from 0.2 to 0.9 and an amplitude ratio from 0.01 to 0.275. The S(2Po) mode is a newly discovered wake pattern that consists of two pairs of symmetric vortex shedding per cycle. The S(P + S) mode and S(2P) mode follow similar wake patterns as the P + S mode and the 2P mode for cross flow vibrations, and it takes two in-line cycles to complete one S(P + S) or S(2P) vortex shedding cycle. Extensive numerical investigations show that similar wake structures can be produced if the maximum and minimum values of relative velocity between the flow and the vibrating cylinder are kept the same, regardless of the motion directions. One positive excitation coefficient region is observed for the non-dimensional frequency ranging from 0.38 to 0.43, and the peak amplitude ratio of the zero contour line for the excitation coefficient reaches 0.056. The changing sign of energy transfer between flow and structure is not necessarily caused by the change of wake modes, but it results from the changing time of vortex shedding. Typical 'figure eight' profiles are captured for simultaneous values of lift and drag forces within the positive excitation region.

Modulation of sound waves for flow past a rotary oscillating cylinder in a non-synchronous region

Modulation of sound waves for the laminar flow past a rotary oscillating circular cylinder has been studied for a free-stream Reynolds number Re = 150 and Mach number M = 0.2. Modulation of sound waves has been observed if the combination of applied rotary oscillation frequency and amplitude belongs to the nonsynchronous region where the hydrodynamic and acoustic quantities vary with the vortex shedding frequency as well as the applied forcing frequency. Two-dimensional direct numerical simulations (DNS) are carried out on a highly refined grid using high resolution physical dispersion relation preserving schemes for a nondimensional forcing frequency-ratio range 0.1 ≤ fr ≤ 2.0 at a nondimensional surface speed A1 = 0.1. Both the synchronous and the nonsynchronous zones are identified based on the time-varying fluctuations in the lift and the drag coefficients. In the nonsynchronous zone, modulation phenomena of the lift and the drag coefficients are explained by plotting the stream-function contours over multiple vortex shedding cycles. The modulation periods associated with the fluctuating lift and the drag coefficients are different for some cases. This particular observation is in contrast with the observation expressed in the previous studies investigating similar problems. Disturbance pressure fields obtained from the present DNS data are used to analyze the characteristics of radiated sound fields, especially in the nonsynchronous zone. Information related to aerodynamic sound sources has been obtained using approximated Lighthill’s stress tensor, and it is shown that the aerodynamic sound sources also display the modulation phenomenon similar to that observed in the vortex shedding process. Sound fields related to the nonsynchronous zone also exhibit the modulation phenomenon and are governed by the shedding frequency, the forcing frequency, and their linear combinations. Radiated sound field characteristics are further related to the time-varying fluctuations of the lift and the drag coefficients using Curle’s acoustic analogy. Modulated sound waves observed along the upstream and the transverse directions have similar time variation as that of the drag and the lift coefficients, respectively. The phenomenon of beat formation has been observed for the ranges 0.9 ≤ fr ≤ 0.99 and 1.2 ≤ fr ≤ 1.4. Although the observed modulation of sound waves varies significantly with the forcing frequency-ratio, the net radiated sound power has almost remained constant in the nonbeating, nonsynchronous zone. Furthermore, it is confirmed that the dominant sound modes obtained during the proper orthogonal decomposition of disturbance pressure fields in the nonsynchronous zone are related to the shedding frequency-ratio, the forcing frequency-ratio, and their linear combinations.

Aerodynamic characteristics of rectangular cylinders in steady and accelerating wind flow

Aerodynamic actions on three two-dimensional rectangular cylinders were studied in steady and accelerating wind tunnel experiments. The aim of these experiments was to determine how body aerodynamics is modified during flow acceleration. The acceleration rate studied roughly scales to that experienced during a strong thunderstorm downburst. As such, conclusions are drawn about wind loading during these events. Cylinders with side ratios of B/D = 1/3, 1 and 3 were tested. Results show that when accelerating flow from initially quiescent conditions, the onset of wake instability is delayed to higher Reynolds numbers than expected in steady flow. Following this, 5 or 6 vortex shedding cycles are required for most aerodynamic characteristics to collapse onto expected steady flow values. During this period, drag and lift force coefficients are generally less than in steady flow conditions. Cases that accelerated flow from an initial Reynolds number of 9,300 also led to modified aerodynamic loads, but no such modification occurred when initial Reynolds numbers were larger. This suggests that initial flow conditions, as well as body side ratio, play an important role in defining how flow acceleration modifies aerodynamic loads. Despite the existence of aerodynamic modifications throughout these experiments, pressures or forces greater than experienced during steady flow conditions at the target velocity (as observed by others in impulsively started flow tests) were not observed. As such, when considering the practical application of this work, for the body configurations tested, the level of flow acceleration experienced during strong thunderstorm downbursts are not expected to lead to larger wind loads than in steady flow conditions.

Numerical simulation of flow with large eddy simulation at Re = 3900

PurposeOver the past few decades, the flow around circular cylinders has been one of the highly researched topics in the field of offshore engineering and fluid-structure interaction (FSI). In the current study, numerical simulations for flow around a fixed circular cylinder are performed at Reynolds number (Re) = 3900 with the LES method using the ICEM-CFD and ANSYS Fluent tool for meshing and analysis, respectively. Previously, similar studies have been conducted at the same Reynolds number, but there have been discrepancies in the results, particularly in calculating the recirculation length and angle of separation. In addition, the purpose of this study is to address the impact of time interval averaging to obtain the fully converged solution.Design/methodology/approachThis study presents the LES method, using the ICEM-CFD and ANSYS fluent tool for meshing and analysis.FindingsIn the current study, turbulence statistics are sampled for 25, 50, 75 and 100 vortex-shedding cycles with the CFL value O (1). The recirculation length, angle of separation, hydrodynamic coefficients and the wake behind the cylinder are investigated up to ten diameters. The drag coefficient and Strouhal number are observed to be less sensitive, whereas the recirculation length appeared to be highly dependent on the average time statistics and the non-dimensional time step. Similarly, the mean streamwise and cross-flow velocity are observed to be sensitive to the average time statistics and non-dimensional time step in the wake region near the cylinder.Originality/valueIn the current investigation, turbulence statistics are sampled for 25, 50, 75 and 100 vortex-shedding cycles with the CFL value O (1), using large eddy simulation method at Re = 3900 around a circular cylinder. The impact of time interval averaging to obtain the fully converged mean flow field is addressed. No such consideration is yet published in the literature.

Measurement of vortex shedding in the wake of a sphere at

Flow in the wake of a sphere has been studied for at least the last hundred years. The three-dimensional (3-D) flow structure has been observed many times using dye visualization and prior to the direct numerical simulations by Johnson & Patel (J. Fluid Mech., vol. 378, 1999, pp. 19–70), its structure at a Reynolds number of approximately 300, was believed to consist of a one-sided chain of hairpin-like vortices. However, the numerical simulations by Johnson & Patel (J. Fluid Mech., vol. 378, 1999, pp. 19–70) also showed that so-called ‘induced’ vortices were generated. The present results are the first spatially resolved measurements that elucidate the 3-D vortex shedding cycle in the wake of a sphere at a Reynolds number of 465. Tomographic particle image velocimetry (tomo-PIV) enabled snapshots of the vortical structure and by combining these results with temporally resolved planar PIV, the ensemble averaged shedding cycle in the wake of the sphere was reconstructed. The present results clearly indicate that besides the ‘primary’ vortex chain shed from the sphere, secondary (‘induced’) vortices are generated by transforming transverse vorticity into streamwise vorticity as a result of the interaction between the sphere’s separating shear layer and the counter-rotating longitudinal vortices extending downstream from the sphere.