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This research work seeks to investigate the influence of spacing and heat transfer on the wake behavior of a triangular arrangement of spheres. Four experimental configurations have been investigated at three Reynolds numbers, Re1 = 350, Re2 = 700, and Re3 = 1050. Two isothermal cases were investigated with spacing between the spheres of zero and one sphere diameter, and two cases were investigated with an applied heat flux at the same spacing conditions. The time resolved particle image velocimetry results revealed various flow phenomena including flow separations, von Karman vortex shedding, and Kelvin–Helmholtz instabilities. The turbulent statistics reveal the effect of proximity and heat transfer on the time averaged values of the wake size, turbulent strengths, and Reynolds shear stress in the wake of each sphere, namely, the laminarization effects from the addition of heat and the suppression of the lead sphere wake from the proximity of the trailing spheres. These results are complemented by the application of proper orthogonal decomposition (POD) to the flow fields, which extracts the coherent structures from the flow. The modes that describe the coherent structures are extracted and described in detail, which provide further insight into effects of the experimental conditions on the temporal behavior of the flow. Many of the low order modes are found to be associated in pairs, corresponding to asymmetric structures or advection of a given structure downstream. The capability of POD to produce reduced order models of the flow is then utilized to facilitate vortex identification analysis. A turbulent kinetic energy based mode truncation criteria, which has been found to enhance vortex identification capability, is applied to select the POD modes and temporal coefficients to be used in the reduced order modeling. The reconstructed velocity fields are then analyzed with vortex identification algorithms to extract the vortex cores and boundaries. The combination of these approaches allows the study of the effect of proximity and heat transfer on the vortex characteristics, such as size, strength, and distribution.

The drag-thrust transition and wake structures of a pitching foil undergoing combinations of fast and slow pitching are systematically investigated. The foil locomotion having combinations of fast and slow pitching is made by setting a variable s defined as the fraction of the pitching time required on the upper side of the wake centerline. On the other hand, time 1-s is required for the foil to pitch on the lower side of the wake centerline. Compared to the symmetric pitching (s = 0.5) case, the time-mean thrust rapidly increases and the drag-thrust boundary advances with increasing |s − 0.5|. The Karman vortex street slants and produces thrust when |s − 0.5| is sufficiently large, which supersedes the previous thumb rule that only reverse Karman vortex street can produce thrust. The faster forward stroke determines the slant direction of the vortex street. The detailed wake structures produced by the pitching foil are discussed, showing how the combined pitching affects vortex dynamics, drag-thrust transition, slant direction, and wake jet. This work provides a physical basis for understanding the hydrodynamics of native swimmers which may be useful to design bio-inspired underwater robots.

The present study examines the energy efficiency of self-propelled hydrofoils for various modes and kinematics of swimming adopted by various body-caudal fin fish. In particular, this work considers the intermittent burst-and-coast (B&C) and continuous swimming modes, and examines the effect of the undulating and/or pitching swimming kinematics, adopted by the undulating body of anguilliform fish and pitching caudal fin of carangiform and thunniform fish. Notably, B&C swimming is adopted in nature mostly by the latter class but rarely by the former. This fact forms the basis of our study on the hydrodynamics and propulsion performance for both classes of fish-inspired swimming using a NACA0012 hydrofoil model. This analysis explores a large parameter space covering undulation wavelength, 0.8≤λ*

Alterations to the unsteady wake dynamics imposed by abrupt changes in the phase angle between two pitching side-by-side foils are computationally examined at the Reynolds number of 1000 and 4000 and Strouhal number of 0.25–0.5. Four hybrid modes are considered in this study inspired by the swimming habits of red nose tetra fish and burst-and-coast swimming phenomenon. At the higher Strouhal number of 0.50, abrupt changes in the phase angle result in the formation and growth of a secondary vortex street between the two primary streets, which enable and maintain a split-wake configuration. Furthermore, phase switching alters pressure levels on the top and bottom surfaces of both foils to similar levels, which attribute to lowering the side-force. The growth rate of the secondary vortex street remains consistent for all four hybrid modes. At lower Strouhal numbers ( 0.25–0.4), however, the abrupt change in the phase angle converts the wake to a single vortex street. Thus, this indicates that the wake reactions for such cases in synchronization substantially change at lower Strouhal number. Although a different behavior of total side force production is observed at a lower Reynolds number for Strouhal number of 0.50, the wake dynamics implies that phase alterations act as a similar flow control mechanism to stabilize the wake. Finally, it is identified that the suspension of oscillations significantly limits the implications of initiation of oscillations on wake dynamics and performance following abrupt changes in the phase angle.

This work examined the development of the large-scale vortex structures in the wake of two screen cylinders with porosities β = 48% and 61% in the intermediate region at a Reynolds number of 7000 using two X-type hot-wire probes. The screen cylinders were made of stainless steel screen meshes rolled into a cylindrical shape. The results were compared with those of a solid cylinder (β = 0%) under the same flow conditions. It was shown that the formation of the large-scale vortices in the screen cylinder wakes involves different mechanisms. For the screen cylinder with β = 48%, they were generated due to wake instability (Karman vortex), which closely resembled that of a solid cylinder. In contrast, for the screen cylinder with β = 61%, the vortices were formed owing to the shear-layer (Kelvin–Helmholtz) convective instability. These findings were justified by the streamwise evolution of the vortex shedding frequency, a stability analysis in the near wake using the mean streamwise velocity profiles, and the coherent and incoherent wake structures obtained by the phase-averaged analysis at different downstream locations.

Physically plausible fluid simulations play an important role in modern computer graphics and engineering. However, in order to achieve real-time performance, computational speed needs to be traded-off with physical accuracy. Surrogate fluid models based on neural networks (NN) have the potential to achieve both fast fluid simulations and high physical accuracy. However, these approaches rely on massive amounts of training data, require complex pipelines for training and inference, or do not generalize to new fluid domains. In this work, we present significant extensions to a recently proposed deep learning framework, which addresses the aforementioned challenges in two dimensions (2D). We go from 2D to three dimensions (3D) and propose an efficient architecture to cope with the high demands of 3D grids in terms of memory and computational complexity. Furthermore, we condition the neural fluid model on additional information about the fluid's viscosity and density, which allows for simulating laminar as well as turbulent flows based on the same surrogate model. Our method allows us to train fluid models without requiring fluid simulation data beforehand. Inference is fast and simple, as the fluid model directly maps a fluid state and boundary conditions at a moment t to a subsequent fluid state at t + dt. We obtain real-time fluid simulations on a 128 × 64 × 64 grid that include various fluid phenomena such as the Magnus effect or Karman vortex streets and generalize to domain geometries not considered during training. Our method indicates strong improvements in terms of accuracy, speed, and generalization capabilities over current 3D NN-based fluid models.

The reverse vortex street differs from the ordinary Karman vortex street in the direction of the rotation of the vortices. Such a street is formed behind the oscillating airfoils in the flow. It is of interest in connection with studies of the aerodynamics of flapping wings. It is known that the vortex wake behind a symmetric airfoil performing symmetric oscillations in a certain range of parameters becomes asymmetric, which leads to the appearance of a nonzero average lift. Reasons of the symmetry violation are associated with the instability of the reverse vortex street, but the mechanism of this instability is currently not well understood. In this work, the analysis of the stability of the reverse vortex street is carried out on the basis of the theory developed by Karman for infinite rows of point vortices. In contrast to the Karman model, in this work, semi-infinite rows with periodically arising new vortices at their ends are considered. This is the first time this model has been used. It is shown that the periodic appearance of new vortices radically affects the characteristics of the street stability. It is found that the violation of the symmetry of the reverse vortex street is associated with its instability to bending perturbations, while the ordinary Karman vortex street behind the body is unstable to varicose perturbations. Regions of instability are determined.

In the proximity of stagnation points, flow instabilities tend to arise at relatively low Reynolds numbers (Re). These instabilities often manifest as vortices that can evolve time-periodic patterns as Re is increased. These types of flows are well studied in cases for which the stagnation point is fixed on an obstacle and the resulting vortices are in the spanwise direction (e.g., the von Karman vortex street). However, they are less understood in intersecting flows, where the stagnation point is not wall-attached and the resulting vortices are stretched by the flow in the streamwise direction. In this study, quantitative flow velocimetry measurements and three-dimensional numerical simulations are used to characterize two types of steady vortical flow fields in rectangular, intersecting microfluidic geometries with different aspect ratios, α, of the intersecting channels. We show that by changing α, it is possible to precisely tune the features of the steady-state vortical flow field, including the number of vortices, their relative rotation direction, nearby circulation areas, and even vortex core structure. The unique steady-state features determine the onset parameters, dynamics, and frequency of time-periodic fluctuations that develop at higher Re. Our results can be directly applied for enhancing the control over the vortical motion of transported fluids in inertial microfluidics and lab-on-a-chip devices. Additionally, these findings contribute to the fundamental knowledge on vortical motion with the potential to improve the control over vortex-induced vibrations on obstacles in both terrestrial and marine environments.

The effect of stochastic inflow fluctuations on the jet-switching characteristics of a harmonically plunging elliptic foil at a low Reynolds number regime has been analyzed in the present study. The inflow fluctuations are generated by simulating an Ornstein–Uhlenbeck process—a stationary Gauss–Markov process—with a chosen correlation function. In the absence of fluctuations, quasi-periodic movement of the wake vortices plays a key role in bringing out jet-switching at κh ≥ 1.5. However, fluctuating inflow alters the organized arrangement of the vortex street even at a lower κh (κh = 1.0), giving way to an advanced jet-switching onset. More frequent switching with a larger deflection angle is also observed at κh = 1.5 as compared to the no fluctuation case. Effects of inflow timescales on the deflection angle and switching frequency of the wake are investigated by varying the input correlation-lengths. The underlying flow physics are investigated through a qualitative study of the near-field interactions as well as various quantitative measures derived from the unsteady flow-field.

Imperfectly round bridge stay cable cross section is speculated to be a key factor for wind-induced large-amplitude cable vibrations observed on site. A delayed detached eddy simulation implemented in Open source Field Operation and Manipulation is used to investigate the flow structure around and in the near-wake of an imperfectly round circular cylinder and the corresponding aerodynamic forces at a Reynolds number of 104 and an attack angle of 0° or 45°. With the increase in roundness imperfection, both monotonic and non-monotonic changes of the mean surface pressure and the wake velocity are found when the cylinder is normal to the flow. At an attack angle of 45° and when the roundness ratio is e/D = 4%, it is found that the geometric imperfection in the cross-sectional shape of the cylinder allows it to the retention of more axial flow in the proximity of the cylinder leeward surface due to a shorter recirculation length. The vortex formed by the intensified axial flow would interact with the conventional von Karman vortex formation at a frequency a few times lower than that of the latter and lead to intermittently amplified transverse lift. This reveals that imperfect roundness in the cross section of a circular cylinder could be an excitation source of low frequency vibration. Thus, it provides evidence that this kind of geometric imperfection, which commonly exists in real stay cables, could contribute to the mechanisms that trigger large-amplitude or even divergent cable motion, such as dry inclined cable galloping on site.

Turbulent wake behind five wall-mounted rectangular prisms is measured by time-resolved particle-image velocimetry with an aim to generalize the effects of prism geometry (in terms of aspect ratio, AR, and side ratio, SR) on the wake characteristics. For the time-averaged wake, the arch-type topology is well supported. With AR increasing from 1 to 4 for the square prisms, a transition process between the “dipole” and “quadrupole” wake patterns is observed. On the other hand, an increase in SR does not seem to greatly influence the mean wake structure behind rectangular prisms unless reattachment occurs on the side walls. The turbulent wake velocity fields are analyzed with a proper orthogonal decomposition method, considering the intrinsic symmetries of vortex shedding activities. In the extraction of dominant low-order flow structures, the low-frequency shift mode and periodic vortex shedding mode pair are always captured as the most important turbulent kinetic energy contributors but with significant nonlinear cross-superposition. A low-pass Gaussian filter is then introduced to achieve separation between these two types of coherent structures via new spatial modes, which maintain the same mode shape patterns. The size of the shift mode vortex is found closely related to the time-averaged wake structure, while the pattern of the Karman vortex shedding mode pair seems completely independent. The two separated pure modes develop continuously and compete with each other along the model height. The present study appears to be the first one to investigate the effects of prism geometry on large-scale coherent wake motions from this perspective.Turbulent wake behind five wall-mounted rectangular prisms is measured by time-resolved particle-image velocimetry with an aim to generalize the effects of prism geometry (in terms of aspect ratio, AR, and side ratio, SR) on the wake characteristics. For the time-averaged wake, the arch-type topology is well supported. With AR increasing from 1 to 4 for the square prisms, a transition process between the “dipole” and “quadrupole” wake patterns is observed. On the other hand, an increase in SR does not seem to greatly influence the mean wake structure behind rectangular prisms unless reattachment occurs on the side walls. The turbulent wake velocity fields are analyzed with a proper orthogonal decomposition method, considering the intrinsic symmetries of vortex shedding activities. In the extraction of dominant low-order flow structures, the low-frequency shift mode and periodic vortex shedding mode pair are always captured as the most important turbulent kinetic energy contributors but with significant no...

We present a two-dimensional numerical study for uniform flow past a streamwise oscillating square cylinder at a Reynolds number of 200. To overcome the limitations with an oscillating inlet flow as used in earlier studies, a dynamic meshing feature is used to oscillate the cylinder. A parametric study is carried out by varying amplitude and frequency of cylinder oscillation. Two symmetric modes, named here as S-II-I and S-IV-D, have been found. In S-II-I mode, a pair of vortices are shed symmetrically on each side of the cylinder in one cycle (S-II mode), and in S-IV-D mode, two pairs of vortices of opposite sense are shed on each side of the cylinder. A vortex flapping mode has also been obtained for low to moderate amplitude and frequency ratios. A new mode of vortex shedding termed the “vortex dipole” mode is found and involves the alternate arrangement of vortex pairs unlike the zigzag arrangement of single vortices in a Karman vortex street. As in most nonlinear oscillators, vortex shedding becomes chaotic when forced sufficiently strongly and is usually associated with nonlinear interactions between competing frequencies. Many modes observed in the current study become chaotic when the peak cylinder velocity becomes comparable with the inlet velocity. The 0-1 test for chaos is applied to the time series of lift coefficient to show that the signals are truly chaotic. We also observe chaos due to mode competition when shedding transitions from an antisymmetric to symmetric modes.

Destruction events of momentum transfer as represented by the Reynolds (shear) stress via the pressure–rate-of-strain interaction in a plane jet are investigated using direct numerical simulation data. To obtain three-dimensional pictures of the turbulent structures, pseudo-three-dimensional data are constructed on the basis of Taylor’s frozen hypothesis from time series of the relevant quantities. The coherent motion in the plane jet is extracted by means of conditional sampling analogous to variable-interval time averaging. We obtain a large-scale coherent structure consisting of horseshoelike vortices and a Karman-vortex-like very large spanwise vortex street. Furthermore, we find that the active Reynolds stress destruction is localized around the large-scale coherent vortex structure. However, the coherent structure itself does not contribute to the Reynolds stress destruction, but the remaining incoherent motions do. For the significant pressure–rate-of-strain events in the incoherent motion, we display invariant maps of the velocity gradient tensor and the principal axes of strain to facilitate a discussion of the consistency of the numerical results with an illustration by Hinze [Turbulence, 2nd ed. (McGraw-Hill, 1975), pp. 325–328] and with our own experimental results [Takahashi et al., “Experimental investigation on destruction of Reynolds stress in a plane jet,” Exp. Fluids 60, 46 (2019)]. Consequently, the present results suggest that the illustration of the Reynolds stress destruction by Hinze is not completely applicable to a plane jet.

Flow around an inclined circular cylinder at yaw angles of α = 0°, 30°, 45°, and 60° has been numerically studied using the delayed detached eddy simulation at a Reynolds number of 1.4 × 104. Periodic boundary conditions are utilized to minimize the end effect. The focus is to explore the effect of yaw angle on the flow structure and the spatial distribution of the cross-flow forces. For the normal flow case, the modulation of the span-wise averaged lift force coefficient is found to be related to the unstable shear layer. For the inclined cases, contours of the sectional lift force coefficient show that the local vortex shedding staggers in time along the axial span at the early stage of the simulation, when the flow approaches the cylinder. After the flow reaches the quasi-periodic state, the axial difference disappears for α > 45° but not for α = 30°. In particular, the axial difference of the sectional lift force coefficient results in a near-zero value of the span-wise averaged lift force coefficient. The transition from a two-dimensional flow to a three-dimensional one is not captured in the current simulation. However, wake visualization indicates a mitigation of von Karman vortex shedding when the yaw angle is greater than 30°. Although the Strouhal number is well predicted by the Independence Principle (IP), other flow properties are less agreeable with the prediction by IP.

The flow and heat transfer topology of an isothermal cylinder (diameter D) in the wake of another smaller (diameter d) cylinder is numerically investigated for a spacing ratio of L/d = 5.5 and at a Reynolds number of 200. The governing Navier-Stokes and energy equations are solved using the finite volume method. The focus is given on how the size of the upstream cylinder influences the flow and heat transfer topology around the downstream cylinder when the diameter ratio d/D is varied from 0.15 to 1.0. The upstream-cylinder shear layers for d/D < 0.3 reattach on the downstream cylinder and shed vortices behind it. They for 0.3 ≤ d/D ≤ 1.0, on the other hand, shed vortices in the gap, and the wake of the downstream cylinder features a primary vortex street followed by a secondary vortex street. The primary street evolves into the secondary street through merging and isolated-shedding processes. The arrival of a gap vortex on the front surface of the downstream cylinder generates an impulse that has the greatest impact on the heat transfer. The surface-averaged heat transfer enhances when d/D is decreased from 1.0 to 0.4, and it declines for a further decrease in d/D. The enhancement in heat transfer is ascribed to an increased shear layer velocity, reduced wake-recirculation size, and enhanced recirculation strength. A novel tertiary frequency in heat transfer fluctuation is identified. The correlation between the flow and heat transfer fluctuation at the tertiary frequency is explicatively done through first Fourier transform and wavelet analysis.

The present study is concerned with the numerical simulation of the pressure-driven flow around a confined cylinder subjected to a DC electric field. The flow situation differs from the conventional von Karman vortex street flow in terms of confinement. Additionally, the DC electric field induces a very small but finite electrokinetic velocity at the cylinder surface in contrast to the no-slip velocity in the conventional case. Various numerical simulations are performed in the Laminar Vortex Shedding Regime to investigate the influence of the confinement and the direction and strength of the electric field. For flows without electrokinetic manipulation, the blockage ratio shifts the critical Reynolds number to higher values. Likewise, the dimensionless shedding frequency (Strouhal number) at a given Reynolds number increases with increasing blockage ratio. For flows with electrokinetic manipulation, the time that is required to obtain a steady Laminar Vortex Shedding Regime is reduced compared to the corresponding pure pressure-driven flow. Steady electrokinetic manipulation does not influence the dimensionless shedding frequency. The reduction of the transient is related to differences in the flow topologies around the cylinder. The electrokinetic velocity breaks the axial flow symmetry of the Laminar Steady Regime and therefore accelerates the onset of the Laminar Vortex Shedding Regime.The present study is concerned with the numerical simulation of the pressure-driven flow around a confined cylinder subjected to a DC electric field. The flow situation differs from the conventional von Karman vortex street flow in terms of confinement. Additionally, the DC electric field induces a very small but finite electrokinetic velocity at the cylinder surface in contrast to the no-slip velocity in the conventional case. Various numerical simulations are performed in the Laminar Vortex Shedding Regime to investigate the influence of the confinement and the direction and strength of the electric field. For flows without electrokinetic manipulation, the blockage ratio shifts the critical Reynolds number to higher values. Likewise, the dimensionless shedding frequency (Strouhal number) at a given Reynolds number increases with increasing blockage ratio. For flows with electrokinetic manipulation, the time that is required to obtain a steady Laminar Vortex Shedding Regime is reduced compared to the cor...

A generic kinematic model is presented for a unified hydrodynamics study covering the various types of motion found in real as well as hypothetical fish-like undulation. Undulating motion is presented here as a generic motion, considering chordwise forced flexibility-modelled by wavelength of undulation lambda*-of a rigid NACA0012 hydrofoil in a free-stream flow. Using a level-set immersed boundary method-based in-house code, a non-dimensional study is presented for variouswavelengths, lambda* (0.8-8.0), and frequency of undulation, St (0.2-0.7), at a constant maximum amplitude of undulation of 0.1 and Reynolds number of 5000. A unified cause-and-effect-based analysis is presented with the help of flow patterns and propulsive performance parameters. Pressure contour demonstrates how the travelling wave distributes momentum in the streamwise direction and reduces the lateral force coefficient. Vorticity contours elucidate the mechanism of formation of reverse von Karman an vortex street and the secondary vortices. A correlation is proposed for thrust coefficient as a function of lambda* and St. Good qualitative agreement is observed between the simulated results at smaller lambda*-based undulating and larger lambda*-based pitching foil and the published results for the anguilliform and thunniform fishes, respectively. The agreement with the real fishes is presented for the relative magnitude of thrust coefficient, propulsive efficiency, dynamic stabilization, and signal of the prey fish for the predator fish. Similar to propulsive performance of real fishes, larger (smaller) flexibility based undulation (pitching) results in larger propulsive efficiency (thrust generation)-which can be used for the design of fish-like biomimetic propulsion system. Published by AIP Publishing.

The influence of an inverted flag’s length-to-channel-width ratio (C* = L/W) on its oscillating behavior in a channel flow and the resultant vortex dynamics and heat transfer are determined experimentally. Three systems with C* values of 0.125, 0.250, and 0.375 were chosen for comparison. The interaction of highly unsteady flow with the inverted flag is measured with time-resolved particle image velocimetry. Variations in the underlying flow physics are discussed in terms of the statistical flow quantities, flag displacement, phase-averaged flow field, and vortex dynamics. The results show that the increase in C* shifts the occurrence of the flapping regime at high dimensionless bending stiffness. With the flag in the flapping region, three distinct vortex dynamics—the von Karman vortex street, the G mode, and the singular mode—are identified at C* values of 0.375, 0.250, and 0.125, respectively. Finally, the heat transfer enhancement from the self-oscillating inverted flag is measured to serve as complem...

Different schemes were experimentally investigated of the closed-loop control of vortex shedding from a spring-supported square cylinder in cross flow. The control action was implemented through the perturbation of one cylinder surface, which was generated by three piezoelectric ceramic actuators, embedded underneath the surface and controlled by a proportional-integral-derivative controller. Three control schemes were investigated using different feedback signals, including the turbulent flow signal measured by a hot wire, flow-induced structural oscillation signal obtained by a laser vibrometer, and a combination of both signals. An investigation was conducted at the resonance condition, when the vortex-shedding frequency coincided with the natural frequency of the fluid-structure system. The flow and structural vibration were measured using particle image velocimetry, laser-induced fluorescence flow visualization, a laser Doppler anemometer, and a laser vibrometer. It was observed that the control scheme based on the feedback of both flow and structural oscillation led to the almost complete destruction of the Karman vortex street and a reduction in the structural vibration, vortex shedding strength, and drag coefficient by 82%, 65%, and 35%, respectively, outperforming by far an open-loop control as well as the other two closed-loop schemes.

We show how the location of Lagrangian coherent structures, such as unstable manifolds of Lagrangian separation points, can be controlled via feedback control in two-dimensional shear flows. Such control can be used, for instance, to guide fuel transport into designated regions of the flame in a combustor. Motivated by this example, we consider an unsteady vortex model for flow past a bluff body, and create unstable manifolds in this model at prescribed locations by applying control along the boundary. We find that oscillating the newly created unstable manifolds in 1:1 resonance with the von Karman vortex shedding frequency enhances mixing in the wake significantly.

The wake structure of two side-by-side cylinders was experimentally investigated using the laser-induced fluorescence flow visualization, particle image velocimetry and hot-wire techniques. The investigation was focused on the asymmetrical flow regime, i.e., T/d=1.2–1.6, where T is the center-to-center cylinder spacing and d is the cylinder diameter. Experiments were conducted in both the water tunnel and the wind tunnel at a Reynolds number (Re) range of 150–14 300. It has been found that, as Re increases, the flow structure behind the cylinders may change from one single vortex street to two streets with one narrow and one wide for the same T/d. The one-street flow structure is dominated by one frequency f0*=f0d/U∞≈0.09, where f0 is the dominant frequency and U∞ is the free-stream velocity. On the other hand, two frequencies, f0*≈0.3 and 0.09, characterized the two-street flow structure. These are associated with the narrow and wide street, respectively. It is further observed that the critical Re, at w...

To examine in detail the behavior of a new vortex shedding mode found in a previous investigation [Phys. Fluids 14, 3160 (2002)], a two-dimensional numerical study on the laminar incompressible flow past a rotating circular cylinder in the Reynolds number range 60⩽Re⩽200 and at rotational rates 0⩽α⩽6 was carried out. The results obtained clearly confirm the existence of the second shedding mode for the entire Reynolds number range investigated. A complete bifurcation diagram α(Re) was compiled defining both kind of shedding modes. The unsteady periodic flow in the second mode is characterized by a frequency much lower than that known for classical von Karman vortex shedding of the first mode. The corresponding Strouhal number shows a strong dependence on the rotational velocity of the cylinder, while only a weak dependence is observed for the Reynolds number. Furthermore, the amplitudes of the fluctuating lift and drag coefficients are much larger than those characterizing classical vortex shedding behind...

The aim of this paper is to present the results of experiments conducted in a stratified fluid with a momentum source modeled by a moving jet in the asymptotic case when the size of the source is negligibly small but the resulting force (momentum flux), which acts on the fluid, remains finite. In this case the forcing may be considered as a “point” force moving in the fluid and the problem has no obvious characteristic length scale, compared to the case of a bluff body. The latter, towed horizontally in the stratified fluid, frequently leaves behind a highly organized vortex street, the characteristics of which strongly depend on the body diameter. It is shown that a similar type of the vortex streets may be generated by a “point” momentum source and conditions when this occurs are found. Experimental data on the characteristics of the vortex streets are presented and compared with the towed body case.

The propulsive performance of two flapping foils with the tandem configuration has been analysed. The trajectories of the foils are prescribed with typical propulsive motions. The hind foil performs oscillatory motion in the wake of the fore foil. The local flow around the hind foil and the effective attack angle have been changed by the vortex street. The velocity potential theory and the boundary element method are introduced to study the interactions of the vortices and the foils. The propulsive performance of the tandem flapping foils is affected significantly when various longitudinal distances and phase differences are adopted. The typical vortex interaction modes are investigated in terms of global phase shift. The thrust coefficient and the propulsive efficiency of tandem NACA0012 foils at typical global phases are analysed. The optimal global phase shifts for the highest thrust and highest efficiency have been found.

It is well known that the occurrence of vortex-induced vibration (VIV) at a subcritical Reynolds number, which is lower than 47, is induced by fluid-structure interaction. However, for the free flow, this phenomenon disappears at a Reynolds number about 20. The current study provides an explanation to the disappearance of the VIV by capturing the evolution of the purely fluid modes at Reynolds numbers between 12 and 55. To ensure accurate mode extraction, the dynamic mode decomposition technique is utilized. Results show that the stable von Karman vortex shedding mode exists in a subcritical flow regime but becomes less distinct as the Reynolds number decreases. When the Reynolds number is lower than 18, this mode nearly vanishes, characterizing the lower boundary of fluid-structure instability.

A two-dimensional computational hydrodynamic model is developed to investigate the propulsive performance of a flapping foil system in viscous incompressible flows, which consists of two anti-phase flapping foils in side-by-side arrangement. In the simulations, the gap between the two foils is varied from 1.0 to 4.0 times of the diameter of the semi-circular leading edge; the amplitude-based Strouhal number is changed from 0.06 to 0.55. The simulations therefore cover the flow regimes from negligible to strong interference in the wake flow. The generations of drag and thrust are investigated as well. The numerical results reveal that the counter-phase flapping motion significantly changes the hydrodynamic force generation and associated propulsive wake. Furthermore, the wake interference becomes important for the case with a smaller foil-foil gap and induces the inverted Benard von Karman vortex streets. The results show that the hydrodynamic performance of two anti-phase flapping foils can be significantly different from an isolated pitching foil. Findings of this study are expected to provide new insight for developing hydrodynamic propulsive systems by improving the performance based on the foil-foil interaction.

Wake of two side-by-side square cylinders was investigated through direct numerical simulation at low Reynolds numbers (16-200). The gap between the two cylinders varied from 0 to 10D, where D is the dimension of the square cylinder (edge length). 9 different wake patterns and their dependency on both the Reynolds number and gap spacing were identified and analysed. A system classification map, demarcated by the Reynolds number and gap ratio g* (g/D, where g is the gap spacing between 2 cylinders), was derived for these 9 wake modes. Steady-state wake (mode I) was observed when the Reynolds number is lower than the critical Reynolds number, which depends on g*. For the gap ratio less than 0.7, only single vortex street was observed. The single vortex street wake can be either symmetric and periodic (mode II), or asymmetric and periodic (mode III), or irregular (mode IV). In this gap ratio range (less than 0.7), shedding frequency decreases with the gap ratio due to the damping role of the gap flow. For the gap ratio larger than 0.7, two vortex streets were also observed. For the gap ratio larger than 1, only two vortex streets were observed. Vortex shedding can be either synchronized and in-phase (mode V), synchronized and anti-phase (mode VI), in-phase dominated with low frequency modulation (mode VII), anti-phase dominated with low frequency modulation (mode VIII), asymmetric synchronized anti-phase (mode IX), or irregular (mode IV). For the gap ratio larger than 4, only synchronized anti-phase mode was observed under the conditions of this study. In the two vortex streets regime, shedding frequency is higher than that of a single cylinder, due to a stronger gap flow than that in the freestream side. The impact of gap ratio and Reynolds number on the drag and lift forces was also studied. Published by AIP Publishing.

A Karman vortex street is created in a flowing soap film by a rod penetrating the film. The velocity field generated by this rod is modified by the addition of the polymer polyethylene oxide having a molecular weight of 5×106 and a concentration of 30 wppm. The rms velocity fluctuations behind the rod are strongly suppressed by the polymer additive and the power spectrum of the velocity fluctuations is modified as well. The experiments show that the polymer additive decreases the rate at which energy is injected into the flow. The measurements further indicate that the polymer introduces an elongational viscosity term into the Navier–Stokes equation.

It is well known that at early stages an impulsively started flow past a circular cylinder consists of twin vortices which are images of one another by reflection through the mid-plane. While the twin vortices are stable for Reynolds numbers below the critical Reynolds number value (Rec≃48), they become unstable above the critical Reynolds number. At Re>Rec, the flow keeps its symmetric recirculating bubble structure for a short time, undergoes a symmetry-breaking instability, and develops into a Karman vortex street. Foppl’s vortex model is studied here as a low-dimensional model for the symmetric bubble. The stability analysis of a fixed bubble in the model shows that there are two asymmetric eigenmodes, a stable mode and an unstable one. In this paper, we show by two-dimensional direct numerical simulations (DNS) of the impulsively started flow past a circular cylinder how the instability properties of the model qualitatively mimic those of the real flow.

A pattern‐recognition analysis of the near region of a plane turbulent wake generated by a high solidity mesh strip reveals a markedly regular vortex street. In fact, the ratio of the ‘‘coherent’’ to ‘‘incoherent’’ (or ‘‘random’’) fluctuations is significantly larger than for many other plane turbulent wakes of similar Reynolds number. Since these incoherent fluctuations are so weak, the vortex street persists. This is in contrast to what is observed to happen in many other wakes, where secondary vortices, which are associated with the incoherent fluctuations, act to deform the main vortices of the vortex street into horseshoe‐like vortices very early in the development. Here, the secondary structures must be too weak in the near region to influence the vortex street to any significant effect.

This experimental study is devoted to visualisation and ultrasonic velocity measurement of the wakes formed behind a row of parallel cylinders placed side by side, perpendicular to an incoming flow at low Reynolds numbers. When the distance separating the cylinders is small compared to their diameter, two instability mechanisms, associated with different patterns and dynamics compete. A first spatial symmetry breaking appears when the stationary wakes behind each cylinder are deviated towards one side or the other and form large clusters containing from two to sometimes more than ten wakes. These clusters are separated by intense recirculating zones. When the Reynolds number is increased, the wakes belonging to the widest clusters experience a secondary temporal oscillatory bifurcation. Classical Benard‐Von Karman vortex streets are thus shed in phase by these cylinders (acoustic mode), by contrast with the wakes outside these cells which stay stationary. Finally, the flow around far apart cylinders is al...

A horizontal cylinder intersecting a free surface is subjected to controlled vertical perturbations, and the consequent vortex formation is characterized by high‐image‐density particle image velocimetry, which leads to instantaneous patterns of velocity, vorticity, and streamlines. For the limiting case of the stationary cylinder, the near wake does not exhibit rapid formation of organized vortical structures in a manner similar to Karman vortices. Application of perturbations, however, generates phase‐locked vortex formation over a wide range of excitation frequencies, even at relatively low amplitudes, indicating that the near wake in presence of a free surface is convectively, rather than absolutely, unstable. At a sufficiently high value of excitation frequency, the formation of the initial vortex undergoes an abrupt change in timing, which is analogous to that occurring for Karman vortex formation from a completely submerged cylinder. All of these features of the near wake are interpreted in terms of foci, saddle points, and reattachment points of the streamwise topology.

The temporal evolution of Karman vortex shedding patterns in the wake of a cylinder placed at right angles to a uniform flow is studied for Reynolds numbers (based on cylinder diameter) between 80 and 140. Focusing on the dynamics of the vortex shedding phase in the wake planview (the plane spanned by the free‐stream direction and the cylinder axis) we study experimentally and model the response of shedding patterns to time‐dependent boundary conditions imposed at the cylinder ends. By appropriate impulsive changes of end conditions, spanwise wave number ‘‘shocks’’ can be produced that travel along the cylinder span. These shock experiments, together with data from steady oblique shedding patterns, are used to determine the parameters for the spanwise Ginzburg–Landau model, which has already been used successfully to describe many of the phenomena observed in cylinder wakes. We then demonstrate experimentally that, in analogy to gasdynamics, it is also possible to produce ‘‘expansion waves’’ of the spanwise wave number, which are well described by the Ginzburg–Landau model without further adjustment of its parameters.

The full and partial ground effects on the lift generation of a flapping airfoil in normal hovering mode are investigated numerically using the discrete vortex method in two dimensions. To achieve full ground effect, the airfoil of chord c is made to hover above the center of a finite-sized platform of length 10c. We have observed the force-enhancement, force-reduction, and force-recovery regimes at low, medium, and high ground clearances in line with the existing literature. This paper puts special focus on partial ground effect when the airfoil is hovering near the edge of the platform. Lift-modifying mechanisms not previously observed under full ground effect have been discovered. When stroke reversal occurs near the edge of the platform, a relatively stationary strong vortex may form above the platform edge. This strong vortex can either increase or decrease the instantaneous lift force on the airfoil depending on the position of the airfoil relative to the platform edge. Also, the platform edge may lead to the formation of an additional vortex pair which increases the instantaneous lift force as the airfoil sweeps past the edge under suitable conditions. Lastly, the platform edge can lead to the formation of a reverse von Karman vortex street that extends well below the stroke plane under suitable geometric arrangements.

A new family of bifurcations is detected in a cylinder wake. The simulations reveal the presence of physically significant spanwise wavy flow undulation in the near-wake of a square cylinder which plays an important role in the modal transition. The alternate process of vortex shedding initiates a systematic cross-stream momentum transfer that activates self-sustained spanwise oscillation of the physical wake, leading to the growth of sequence of Hopf bifurcations along the topological cores of von Karman vortices. The study exhibits how exactly such self-excited spanwise oscillatory fluctuations of pressure, velocity, and KE keep growing along a vortex-core for increased Re and distinctly influence the growth of “Mode A” and “Mode B” instability. It reports existence of two distinct stages of wake undulation over 125 ≤ Re ≤ 240. While the weakly subcritical spanwise-periodic oscillations of pressure, velocity, vorticity, and associated uniform and wider length-scale bifurcations along the von Karman vortex corelines dominate during “Mode A” instability, the transition to the “Mode B” is prompted following faster and random eruption (and swapping) of significantly smaller but variable length-scaled bifurcations and accompanied low frequency non-uniform fluctuation of flow variables. Such unstable flow perturbations and resulting bifurcations along the von Karman vortex cores apparently influence generation of longitudinal vortical ribs (Mode A and Mode B) in the wake. The appearance of a slow varying secondary frequency at the bifurcation points seemed crucial for initiating the spanwise flow irregularity and transition to “Mode B.”

The von Karman vortex street behind a circular cylinder in a laminar homogeneous jet core is experimentally investigated. The Strouhal–Reynolds number relationships are measured for various shear‐layer thicknesses and aspect ratios. The experimental Strouhal number values are found to collapse with the discrete vortex shedding modes, which were observed for boundary‐layer end conditions. The results indicate that the shedding modes are independent from the end conditions, but are an intrinsic feature of the shedding process of an infinitely long cylinder. The experimentally assumed shedding mode, however, is strongly dependent of the geometric parameters, like the shear‐layer thickness and the aspect ratio. The observed tendencies can be made physically plausible.

The formation of organized structures resulting from the evolution of two parallel opposite vortex sheets in a two‐dimensional perfect fluid is studied, employing an equilibrium statistical theory. The system is confined in a channel in which periodic solutions of the statistical equilibrium equations are considered. It is found that the statistical equilibrium state of maximum entropy is a staggered arrangement of alternating vortex patches—the turbulent counterpart to the von‐Karman vortex street. However, these vortices spread over the whole width of the channel and the pattern with the maximum allowed wavelength is always preferred: the confinement by the boundary conditions is essential. The theoretical predictions are supported by direct numerical simulations of the two‐dimensional Navier–Stokes equation at high Reynolds number.

A computational study of the feedback control of von Karman vortex shedding behind a circular cylinder at low Reynolds numbers is reported. The two‐dimensional Navier–Stokes equations with feedback are solved numerically. The control actuators are a pair of blowing/suction slots located at ±110° from the leading stagnation point. A single feedback sensor is used and the actuators are 180° out of phase with each other. Complete suppression of vortex shedding is achieved for the simulation at Reynolds number Re=60. The suppression window in the feedback sensor location xs is narrow. With the feedback sensor location fixed at the optimum location, vortex shedding becomes suppressed with increasing feedback gain α. However, further increase of the feedback gain destabilizes the flow again. At Reynolds number Re=80, and above, the feedback control stabilizes the primary vortex shedding mode, but a secondary mode which may be lower or higher in frequency than the primary depending upon the phase of the feedback...

This paper presents a numerical study of vortex-induced vibration of four rigidly connected and four separately mounted circular cylinders in an inline square configuration at a Reynolds number of 150, a low mass ratio of 2.5, and a range of spacing ratio L from 1.5 to 4, where the spacing ratio is defined as the centre-to-centre distance of two adjacent cylinders normalized by the cylinder diameter. For the rigidly connected cylinder array, the maximum and minimum response amplitudes occur at L = 1.5 and L = 2.0, respectively, for the range of spacing ratio covered in this study and the maximum response amplitude at L = 1.5 is accompanied by a wide lock-in range. The large response amplitude at a small spacing ratio L = 1.5 is because the cylinder array responds to the flow as a single cylinder with an overall size that is much larger than the diameter of the single cylinder while the small response amplitude observed at L = 2.0 is attributed to the strong interaction of the vortices through the gap between the top and bottom rows of the cylinder and also in the wake of the cylinder array. For spacing ratio L ≥ 2.5, the lock-in regime of four rigidly connected cylinders is similar to that of a single cylinder and the response amplitudes in the lock-in regime are slightly higher than that of a single cylinder. The energy transfer analysis between fluid flow and individual cylinders in the array shows that the hydrodynamic forces on individual cylinders either excite or damp the vibration, depending on the reduced velocity. An interesting flow feature observed at L = 2, 2.5, and 3 is the biased vortex street in the wake of four rigidly connected cylinders. The biased vortex street leads to a shift of the mean position of the cylinder array with the largest mean position shift being observed at L = 3. Four response modes are identified for four separately mounted cylinders. These are the in-phase mode, the anti-phase mode, the correlated out-of-phase mode, and the uncorrelated mode. It is found that the response mode chosen by the cylinders is dependent not only on the spacing ratio but also on the initial condition of the flow. The response amplitude under the in-phase mode is generally higher than that under the anti-phase mode at identical spacing ratios. This is attributed to the interaction of vortices in the wake of the cylinders.

The supercritical instability leading to the Benard-von Karman vortex street in a cylinder wake is a well known example of supercritical Hopf bifurcation: the steady solution becomes linearly unstable and saturates into a periodic limit cycle. Nonetheless, a simplified physical formulation accurately predicting the transition dynamics of the saturation process is lacking. Building upon our previous work, we present here a simple self-consistent model that provides a clear description of the saturation mechanism in a quasi-steady manner by means of coupling the instantaneous mean flow with its most unstable eigenmode and its instantaneous amplitude through the Reynolds stress. The system is coupled for different oscillation amplitudes, providing an instantaneous mean flow as function of an equivalent time. A transient physical picture is described, wherein a harmonic perturbation grows and changes in amplitude, frequency, and structure due to the modification of the mean flow by the Reynolds stress forcing, saturating when the flow is marginally stable. Comparisons with direct numerical simulations show an accurate prediction of the instantaneous amplitude, frequency, and growth rate, as well as the saturated mean flow, the oscillation amplitude, frequency, and the resulting mean Reynolds stresses. (C) 2015 AIP Publishing LLC.

We develop a model to numerically study the dynamics of vortex streets in channel flows. Previous work has studied the vortex wakes of specific vortex generators. Here, we study a wide range of vortex wakes including regular and reverse von Karman streets with various strengths, geometries, and Reynolds numbers (Re) by applying a smoothed von Karman street as an inflow condition. We find that the spatial structure of the inflow vortex street is maintained for the reverse von Karman street and altered for the regular street. For regular streets, we identify a transition to asymmetric dynamics which happens when Re increases, or vortices are stronger, or vortex streets are compressed horizontally or extended vertically. We also determine the effects of these parameters on vortex street inversion.

A vortex decay model for predicting spatial evolution of peak vorticity in a wake behind a cylinder is presented. For wake vortices in the stable region behind the formation region, results have shown that the presented model has a good capability of predicting spatial evolution of peak vorticity within an advecting vortex across 0.1 ≤ β ≤ 0.4, 500 ≤ H ≤ 5000, and 1500 ≤ ReL ≤ 8250. The model is also generalized to predict the decay behaviour of wake vortices in a class of quasi-two-dimensional magnetohydrodynamic duct flows. Comparison with published data demonstrates remarkable consistency.

Combination modes appear in the spectrum of the surface pressure signals when a circular cylinder is forced to oscillate at a frequency different from the von Karman vortex shedding frequency. The spatial symmetry of the sum and difference modes depends on the direction of cylinder oscillation, and is predictable with a simple set of symmetry relations. As a result of the symmetry relations, cross-flow oscillations of the cylinder aimed at enhancing fluctuating lift also channel energy into the fluctuating drag component through the combination modes.

A low‐dimensional Galerkin method, initiated by Noack and Eckelmann [Physica D 56, 151 (1992)], for the prediction of the flow field around a stationary two‐dimensional circular cylinder in a uniform stream at low Reynolds number is generalized to the case of a rotating and translating cylinder. The Hopf bifurcation describing the transition from steady to time‐periodic solution is investigated. A curve indicating the transitional boundary is given in the two‐dimensional parameter plane of Reynolds number Re and rotating parameter α. Our results show that rotation may delay the onset of vortex street and decrease the vortex‐shedding frequency.

In this Letter, we demonstrate the coexistence of two distinct systems of streamwise vortices in a bluff body wake. It appears that there exist conditions to amplify streamwise vorticity in bluff body wakes, by vortex stretching, in both the separating shear layers from the sides of the body and also in the vortex street wake. The length scale governing the streamwise vortices in the shear layer has a 1/√Re dependence, whereas the scale of such structures in the wake is independent of Reynolds number, Re (over a large range of Re). The proposition that there should exist two distinct, and possibly disparate, spanwise length scales in the cylinder wake is well supported by compiled measurements, particularly those of Williams and co‐workers (Mansy et al. [J. Fluid Mech. 270, 277 (1994)]), as well as those from Chyu and Rockwell (submitted to J. Fluid Mech.).