Vortex Street Pattern Research Articles

An unsteady RANS simulation of the performance of an oscillating hydrofoil at a high Reynolds number

The oscillating hydrofoil has been widely used in ocean engineering applications such as ships, underwater vehicles and ocean energy devices. However, Reynolds number of existing research are lower than real ocean applications.This study reports our recent numerical effort in studying a sinusoidally oscillating hydrofoil under unsteady conditions by solving the Reynolds-averaged Navier–Stokes equations. By using experimental test data, the numerical method is well validated. Three wake patterns are identified to fundamentally affect the propulsive performance of the oscillating hydrofoil. Only the wake in the reverse von Kármán vortex street pattern is found to generate thrust for purely oscillating motion. The leading-edge vortex is demonstrated todirectly influence the pressure distribution over the foil’s surface but not the thrust.Furthermore, impact of 3D effect on vortex shedding on the hydrodynamic performance of the hydrofoil is presented. This study is expected to provide guidance on both academics and industries in relevant fields.

Underwater oscillation performance and 3D vortex distribution generated by miniature caudal fin-like propulsion with macro fiber composite actuation

Underwater biomimetic propulsion systems that mimic the BCF (Body and/or Caudal Fin) fishes have attracted considerable attention. A miniature caudal fin-like propulsion device, whose design is based on the morphology and kinematics of the koi fish, is proposed in this paper. The propulsion is actuated by flexible fiber-based piezoelectric actuators, Macro Fiber Composite (MFC). A vacuum fabrication procedure is employed to bond the components of the proposed device. The underwater oscillation performances of the proposed propulsion at different steady-state sinusoidal excitations are experimentally investigated. Computational fluid dynamic (CFD) analysis is conducted to investigate the three-dimensional flow generated by the oscillation propulsion system. A simplified model, where the internal bending moment provided by the MFC actuators is replaced by a shear force, is created based on the obtained experimental data. The CFD simulations demonstrate that the maximum instantaneous and mean thrusts generated by the propulsion system during the stable period are 21.5 and 9.5 mN, respectively. These are consistent with the Lighthill’s elongated-body theory. Then, the uneven spatial distributions of the instantaneous vorticity around the propulsion are visualized, using seven two-dimensional planes intersecting at various locations. The CFD results suggest that the vorticity distributions around the trailing and leading edges of the caudal fin considerably differ because of the fin’s unique shape. A reverse Karman vortex street pattern is observed behind the trailing edge of the caudal fin. This indicates a thrust-producing pattern. On the other hand, a Karman vortex street pattern is distinctly observed before the leading edge. This indicates a drag-producing pattern. The geometry and shape effects of the caudal fin-like propulsion device are identified consequently. Those obtain results may be beneficial for the design of underwater vehicles with oscillation fin-like propulsion system.

Vortex-induced vibrations of a neutrally buoyant circular cylinder near a plane wall

This paper presents an experimental study of the motions, drag force and vortex shedding patterns of an elastically mounted circular cylinder, which is held at various heights above a plane wall and is subject to vortex-induced vibration (VIV) in the transverse direction. The cylinder is neutrally buoyant with a mass ratio m⁎=1.0 and has a low damping ratio ζ=0.0173. Effects of the gap ratio (S/D) ranged from 0.05 to 2.5 and the free-stream velocity (U) ranged from 0.15 to 0.65m/s (corresponding to 3000≤Re≤13 000, and 1.53≤U⁎≤6.62) are examined. The flow around the cylinder has been measured using particle image velocimetry (PIV), in conjunction with direct measurements of the dynamic drag force on the cylinder using a piezoelectric load cell. Results of the vibrating cylinder under unbounded (or free-standing) condition, as well as those of a near-wall stationary cylinder at the same gap ratios, are also provided. For the free-standing cylinder, the transition from the initial branch to the upper branch is characterized by a switch of vortex pattern from the classical 2S mode to the newly-discovered 2PO mode by Morse and Williamson (2009). The nearby wall not only affects the amplitude and frequency of vibration, but also leads to non-linearities in the cylinder response as evidenced by the presence of super-harmonics in the drag force spectrum. In contrast to the case of a stationary cylinder that vortex shedding is suppressed below a critical gap ratio (S/D≈0.3), the elastically mounted cylinder always vibrates even at the smallest gap ratio S/D=0.05. Due to the proximity of the plane wall, the vortices shed from the vibrating cylinder that would otherwise be in a double-sided vortex street pattern (either 2S or 2PO mode) under free-standing condition are arranged into a single-sided pattern.

Shallow-flow visualization analysis by proper orthogonal decomposition

The identification of the spatial characteristics and the shedding frequencies of coherent structures in shallow flows usually involves the use of sophisticated equipment for velocity measurements such as laser Doppler anemometry or particle image velocimetry. In this work, a simple and low-cost alternative for the quantitative characterization of quasi two-dimensional shallow coherent structures is presented. The technique is based on the image pre-processing of flow visualizations and post-processing by means of the proper orthogonal decomposition. As an illustration of the method, the analysis of a shallow flow in the wake of a cylinder with a vortex-street pattern is presented. The method is able to discriminate concentration patches attached to the vortices and their advection, providing frequencies in excellent agreement with a previous study.

The unsteady three-dimensional wake produced by a trapezoidal pitching panel

AbstractParticle image velocimetry (PIV) is used to investigate the three-dimensional wakes of rigid pitching panels with a trapezoidal geometry, chosen to model idealized fish caudal fins. Experiments are performed for Strouhal numbers from 0.17 to 0.56 for two different trailing edge pitching amplitudes. A Lagrangian coherent structure (LCS) analysis is employed to investigate the formation and evolution of the panel wake. A classic reverse von Kármán vortex street pattern is observed along the mid-span of the near wake, but the vortices realign and exhibit strong interactions near the spanwise edges of the wake. At higher Strouhal numbers, the complexity of the wake increases downstream of the trailing edge as the spanwise vortices spread transversely and lose coherence as the wake splits. This wake transition is shown to correspond to a qualitative change in the LCS pattern surrounding each vortex core, and can be identified as a quantitative event that is not dependent on arbitrary threshold levels. The location of this transition is observed to depend on both the pitching amplitude and free stream velocity, but is not constant for a fixed Strouhal number. On the panel surface, the trapezoidal planform geometry is observed to create additional vortices along the swept edges that retain coherence for low Strouhal numbers or high sweep angles. These additional swept-edge structures are conjectured to add to the complex three-dimensional flow near the tips of the panel.

Combined action of transverse oscillations and uniform cross-flow on vortex formation and pattern of a circular cylinder

This paper attempts to study the roles of lateral cylinder oscillations and a uniform cross-flow in the vortex formation and wake modes of an oscillating circular cylinder. A circular cylinder is given lateral oscillations of varying amplitudes (between 0.28 and 1.42 cylinder-diameters) in a slow uniform flow stream (Reynolds number=284) to produce the 2S, 2P and P+S wake modes. Detailed flow information is obtained with time-resolved particle-image velocimetry and the phase-locked averaging techniques. In the 2S and 2P mode, the flow speeds relative to the cylinder movement are less than the uniform flow velocity and it is found that initial formation of a vortex is caused by shear-layer separation of the uniform flow on the cylinder. Subsequent development of the shear-layer vortices is affected by the lateral cylinder movement. At small cylinder oscillation amplitudes, vortices are shed in synchronization with the cylinder movement, resulting in the 2S mode. The 2P mode occurs at larger cylinder oscillation amplitudes at which each shear-layer vortex is found to undergo intense stretching and eventual bifurcation into two separate vortices. The P+S mode occurs when the cylinder moving speeds are, for most of the time, higher than the speed of the uniform flow. These situations are found at fast and large-amplitude cylinder oscillations in which the flow relative to the cylinder movement takes over the uniform flow in governing the initial vortex formation. The formation stages of vortices from the cylinder are found to bear close resemblance to those of a vortex street pattern of a cylinder oscillating in an otherwise quiescent fluid at Keulegan–Carpenter numbers around 16. Vortices in the inclined vortex street pattern so formed are then convected downstream by the uniform flow as the vortex pairs in the 2P mode.

Using hyperbolic Lagrangian coherent structures to investigate vortices in bioinspired fluid flows

We use direct Lyapunov exponents to identify Lagrangian coherent structures (LCSs) in a bioinspired fluid flow: the wakes of rigid pitching panels with a trapezoidal planform geometry chosen to model idealized fish caudal fins. When compared with commonly used Eulerian criteria, the Lagrangian method has previously exhibited the ability to define structure boundaries without relying on a preselected threshold. In addition, qualitative changes in the LCS have previously been shown to correspond to physical changes in the vortex structure. For this paper, digital particle image velocimetry experiments were performed to obtain the time-resolved velocity fields for Strouhal numbers of 0.17 and 0.27. A classic reverse von Karman vortex street pattern was observed along the midspan of the near wake at low Strouhal number, but at higher Strouhal number the complexity of the wake increased downstream of the trailing edge. The spanwise vortices spread transversely across the wake and lose coherence, and this event was shown to correspond to a qualitative change in the LCS at the same time and location.

1902 回転円柱まわりの流れ場に関する研究 : 回転振動時の渦列パターン(OS19-1 超音波を利用した流動場の計測,オーガナイズドセッション)

1902 回転円柱まわりの流れ場に関する研究 : 回転振動時の渦列パターン(OS19-1 超音波を利用した流動場の計測,オーガナイズドセッション)

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.

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.

The vortex shedding of a streamwise-oscillating sphere translating through a linearly stratified fluid

The flow past a horizontally translating, streamwise oscillating sphere through a linearly stratified fluid is investigated in a series of laboratory experiments. The pertinent governing parameters are shown to be the internal Froude number Fi, the Reynolds number Re, the Keulegan–Carpenter number KC, and the normalized forcing frequency Sf. A KC against Sf regime diagram for flows at Fi=0.07 and Re=190 is developed; for these parameters the flow is approximately two dimensional in the horizontal zone, −1/2≲z/D≲1/2, where z is the vertical coordinate and D is the sphere diameter. Numerous flow regimes are delineated, and it is shown that the regime boundaries approximate the lines of constant u1/u0=2π(KC)(Sf), where u1 is the amplitude of the sphere oscillation and u0 is the magnitude of the mean background flow. Vortex shedding occurs for the entire range of experiments at these Fi, Re values. Lock-on of the shedding frequency to the sphere oscillation frequency occurs for u1/u0≳0.1. Flows at large Fi are shown to exhibit three-dimensional motions in the near wake, and, owing to stratification, exhibit vertical collapse at a certain distance downstream. The far wake develops into a horizontal vortex street pattern for all flows when stratification is present. At large Fi, Re combinations, turbulent patches are found in the wake. The inverse normalized streamwise distance between shed vortices (an effective Strouhal number) is shown to scale as Sf, independent of KC. Measurements of the horizontal separation angles and times for the collapse of the vertical structure are also presented.

A study of the structure of a plane stationary computer-simulated free-shear turbulence

Computer experiments are carried out on a two-dimensional, time-stationary, turbulent free shear flow. The aim is to visualize in a motion picture the time history of the entire field of all variables that are deemed interesting: velocity, pressure, vorticity, dissipation, etc..., and to observe the connection between these deterministic motions and the corresponding space-time statistics drawn once the ergodicity is admitted. The simple flow behind a truncated base and confined by frictionless sidewalls is considered. The two-dimensional unsteady Navier–Stokes equations in the stream function form are replaced by their finite difference counterpart, using a centered difference scheme in both the space and time derivative and some artifices to secure numerical stability. Realizations are computed at a nominal Reynolds number referred to the base height of Re=300, 3000, and 300 000, for a duration of about T≃800 in reduced time. The one-point one-signal statistics, including probability density, time-correlation, power spectral density, are drawn from these realizations. The Re=300 case exhibits a von Karman vortex street pattern and its statistics are in perfect accordance with a periodic flow. At the two higher Reynolds numbers, the primary vortices break into secondary and higher order vortices. The probability density becomes more and more Gaussian, and, in the power spectrum, more and more energy is transferred from the Strouhal ray and its harmonics to other frequencies. The one-point two-signal statistics are also examined. In particular, the contribution of the successive moving vortices or eddies to the joint probability density of the velocity components u and v shows the way the Reynolds shear stress is generated. Other statistics will also be discussed. Despite the notorious inability of a discretized calculation to resolve the ever smaller scale motions at high Reynolds numbers, it is suggested that numerical simulation can cast light on turbulent processes, especially on those that make use of not readily measured variables. This work was supported by contract DRME 75/354.

The Effect of Base Bleed on the Flow behind a Two-Dimensional Model with a Blunt Trailing Edge

SummaryThe effects of base bleed on the flow about a two-dimensional model with a blunt trailing edge were examined at Reynolds numbers, based on model base height, between 1·3×104 and 4·1×104. The ratio of boundary layer thickness at the trailing edge to half the model base height was approximately 0·4. Measurements were made of base pressure, vortex shedding frequency and the distance to vortex formation. With a sufficiently large bleed quantity the regular vortex street pattern disappeared and the base drag of the section was reduced to about a third of its value without bleed. The base pressure was found to vary linearly with the inverse of the vortex formation distance. Results of a previous splitter plate investigation were found to agree closely with those of the present experiments.

Mesoscale Eddies in Wake of Islands

The properties of mesoscale eddies in the wake of islands are investigated in the light of their apparent resemblance to the Kármán vortex-street pattern. By use of the theoretical results from drag theory and the observed quantities such as cross-stream diameter of the obstacle, wind speed and the dimensions of the pattern, estimates are made for the rate of shedding of eddy pairs, the lateral and longitudinal spacing between the vortices, and the life-time of the eddies and drag of the island. These estimates for the various characteristic parameters of the eddy pattern are in good agreement with their corresponding values in the laboratory experiments where stable vortex streets become discernible. Effects of the tip, ground, and neighboring obstacles are neglected and the problem is treated essentially as two-dimensional flow. Use of this theory makes possible a computation of the lateral coefficient of eddy viscosity. The results provide support for the usual assumption made in meteorological studies that viscosity which is used in the equations of motion and which enters into various dimensionless parameters such as Reynolds number, is the eddy viscosity rather than the kinematic viscosity used in hydrodynamic theory. General meteorological considerations applied to these results indicate that the vertical flux of momentum must be included to account for the lifetime of the eddies.

Karman vortex streets in wakes of islands.

W satellites equipped with narrow-angle cameras have revealed the existence of mesoscale eddies, which are on a scale too small to be delineated by the standard weather observation network and are too large to be seen by an observer on the ground or even pictured from a high-flying aircraft. Hubert and Krueger have described the characteristic properties of mesoscale eddies formed in the wakes of islands that are steep-sided and extend far above the lowlying inversion. These eddies are made visible by patterns in stratocumulus clouds lying beneath a strong inversion about 0.5 to 2.0 km above the ocean surface and have been observed to persist several hundred kilometers downstream. The bandwidth of the eddies is of the order of the cross-stream diameter of the island. Under favorable conditions, the pattern of the eddies bears a strong resemblance to the classical Karman vortex street pattern observed in laboratory studies of wakes behind obstacles. Figure 1 is a typical example of these eddies in the vicinity of the Madeira Islands. Recently, Chopra and Hubert examined the properties of the eddies downstream of the Tenerife and the Gran Canaria Islands in the light of this apparent resemblance between the meteorological mesoscale eddies and the classical vortex street pattern of Fig. 2. This analogy is analyzed further in this note. Viscosity plays two roles in the flow pattern of a Karman vortex street. First, it leads to the formation of the boundary layer in which vorticity is generated and the vortex pairs are formed, the vortices being shed alternately near each edge of the obstacle. Second, the strength of the eddies is dissipated by the mechanism of diffusion; the size of an eddy increases, and its strength decreases as it propagates downstream, until its region of influence overlaps that of a neighboring eddy of opposite circulation. In all of the other respects, the fluid may be regarded as perfect (inviscid). The rate N of shedding of the eddy pair is given by .V ue/a = (l/a)foo (k/2a) taDh(irh/a)] (1) where ue is the speed of propagation downstream of the eddies in a coordinate system fixed to the obstacle, UQ is the speed of the undisturbed flow, a is the longitudinal spacing (pitch) between two eddies of similar circulation of strength k, and h is the lateral spacing (bandwidth) between the two vortex rows. Drag and Spacing Ratio

Hot-wire investigation of the wake behind cylinders at low Reynolds numbers

The hot-wire technique has been used to measure the regular vortex street pattern behind a cylinder at low Reynolds number. Measurements of mean velocity distribution were made both below and above the critical Reynolds number at which the periodic motion appears. Amplitude and phase measurements gave sufficient information for computation of the instantaneous flow pattern of the vortex system. The important points resulting from the investigation are that (i) the critical Reynolds number at which vortices are shed is 40, (ii) in the range of Reynolds numbers investigated the vortices are not shed directly from the cylinder but appear some distance downstream as an instability of the laminar wake.