Reynolds number effects on leading edge vortex development on a waving wing

The waving wing experiment is a fully three-dimensional simplification of the flapping wing motion observed in nature. The spanwise velocity gradient and wing starting and stopping acceleration that exist on an insect-like flapping wing are generated by rotational motion of a finite span wing. The flow development around a waving wing at Reynolds number between 10,000 and 60,000 has been studied using flow visualization and high-speed PIV to capture the unsteady velocity field. Lift and drag forces have been measured over a range of angles of attack, and the lift curve shape was similar in all cases. A transient high-lift peak approximately 1.5 times the quasi-steady value occurred in the first chord length of travel, caused by the formation of a strong attached leading edge vortex. This vortex appears to develop and shed more quickly at lower Reynolds numbers. The circulation of the leading edge vortex has been measured and agrees well with force data.     

The estimation of pressure on the surface of a flapping rigid plate by stereo PIV

The method to estimate the dynamic load of a flapping wing by the integration of pressure on the wing’s surface is discussed. The flapping wing was modeled as a plate flapping sinusoidally in hovering condition. The flow around the flapping plate was measured using stereo PIV on multiple measurement planes along the out-of-plane direction. The phase-averaged velocity field of each measurement plane was calculated so that three-dimensional analyses could be applied. The phase-averaged pressure field was obtained from the integration of the three-dimensional Poisson equation for pressure using the available information acquired from stereo PIV measurements. The pressure field is visualized on the measurement planes. In this study, the estimated load was the torque of the axis of rotation. This torque was compared with the result from strain gauge measurements. The torque estimation, although only on a partial surface of the plate, is within reasonable agreement with the measured torque. The integration of the Poisson equation based on stereo PIV measurements and estimations of the torque shows that an increase in the torque at the start of a flapping stroke is caused by the stagnation on the surface of the plate from the flow that is induced by the leading-edge vortices.     

Flow above the free end of a surface-mounted finite-height circular cylinder: A review

The wake of a surface-mounted finite-height circular cylinder and the associated vortex patterns are strongly dependent on the cylinder aspect ratio and the thickness of the boundary layer on the ground plane relative to the dimensions of the cylinder. Above a critical aspect ratio, the mean wake is characterized by streamwise tip vortex structures and Kármán vortex shedding from the sides of the cylinder. Below a critical aspect ratio, a unique mean wake structure is observed. Recent experimental studies in the literature that used phase-averaged techniques, as well as recent numerical simulations, have led to an improved physical understanding of the near-wake vortex flow patterns. However, the flow above the free end of the finite circular cylinder, and its relationship to the near wake, has not been systematically studied. The effects of aspect ratio and boundary layer thickness on the free-end flow field are also not completely understood, nor has the influence of Reynolds number on the free-end flow field been fully explored. Common features associated with the free end include separation from the leading edge, a mean recirculation zone containing a prominent cross-stream arch (or mushroom) vortex, and reattachment onto the free-surface. Other flow features that remain to be clarified include a separation bubble near the leading edge, one or two cross-stream vortices within this separation bubble, the origins of the streamwise tip or trailing vortices, and various critical points in the near-surface flow topology. This paper reviews the current understanding of the flow above the free end of a surface-mounted finite-height circular cylinder, with a focus on models of the flow field, surface oil flow visualization studies, pressure and heat flux distributions on the free-end surface, measurements of the local velocity field, and numerical simulations, found in the literature.     

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.     

Improving power-extraction efficiency of a flapping plate: From passive deformation to active control

A flapping plate flow energy harvester in a viscous uniform flow is simulated using a two-dimensional numerical approach. Our focus is to study the effects of flexibility and active control on the power-extraction capability of the flapping plate, and consequently to find a strategy to increase its power-extraction efficiency. Four typical cases with optimal kinematics predicted by previous studies are presented and discussed: a rigid plate, a flexible plate, a plate with a flexible leading segment and a rigid trailing segment, and a rigid plate with a simple active control on the leading segment. Our simulations show that with the kinematic parameters considered, the plate flexibility cannot significantly improve the power-extraction capability of the plate while the active control on the leading segment of the rigid plate increases the power coefficient by 11.3%. The analysis of flow fields shows that the changes in the power coefficient and drag force are related to the vortex structures and pressure distributions near the plate, as well as the projection area of the plate in the direction of the translational movement.     

Unsteady flow structure and vorticity convection over the airfoil oscillating at high reduced frequency

Unsteady vortex structures and vorticity convection over the airfoil (NACA 0012), oscillating in the uniform inflow, are studied by flow visualization and velocity measurements. The airfoil, pivoting at one-third of the chord, oscillates periodically near the static stalling angle of attack (AOA) at high reduced-frequency. The phase-triggering and modified phase-averaged techniques are employed to reconstruct the pseudo instantaneous velocity field over the airfoil. During the down stroke cycle, the leading-edge separation vortex is growing and the vortex near the trailing edge begins to shed into the wake. During the upstroke cycle, the leading-edge separation vortex is matured and moves downstream, and the counter clockwise vortex is forming near the trailing edge. Convection speeds and wavelength of the unsteady vortex structure over the airfoil equal to that of the counter clockwise vortex shed into the wake. This kind of vortex structure is termed as “synchronized shedding” type. The wavelength of unsteady vortex structure over the airfoil is significantly different from that at low reduced-frequency. Consistent convection speeds of the leading-edge separation vortex are acquired from the spatial-temporal variations of local circulation and local surface vorticity generation, and equals that predicted from flow visualization. Spatial-temporal variations of the local surface vorticity generation clearly reveal the formation and passage of the leading-edge separation vortex only in the region where the flow does not separate completely from the surface. Significant amounts of the surface vorticity are generated within the leading-edge region of the airfoil during the upstroke cycle. Only negligible amount of surface vorticity is produced within the region of complete flow separation. During the down stroke cycle, the surface vorticity generation is mild along the airfoil surface, except the leading-edge region where a small scale leading-edge separation vortex is forming and growing.     

Vortical structures on a flapping wing

A wing in the form of a rectangular flat plate is subjected to periodic flapping motion. Space–time imaging provides quantitative representations of the flow structure along the wing. Regions of spanwise flow exist along the wing surface; and depending on the location along the span, the flow is either toward or away from the tip of the wing. Onset and development of large-scale, streamwise-oriented vortical structures occur at locations inboard of the tip of the wing, and they can attain values of circulation of the order of one-half the circulation of the tip vortex. Time-shifted images indicate that these streamwise vortical structures persist over a major share of the wing chord. Space–time volume constructions define the form and duration of these structures, relative to the tip vortex.     

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

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

沟槽面湍流边界层结构实验研究

应用激光测速技术和氢气泡流动显示技术对沟槽面湍流边界层特性及近壁区拟序结构特征进行了精细的测量和观察。实验结果表明：与光滑面湍流边界层相比,沟槽面端流边界层的黏性底层厚度、过渡层厚度及流速分布对数公式中的积分常数C均有所增大,说明采用的沟槽面具有减阻特性。此外,无量纲低速带条间距明显减小,最多减小20%,说明无量钢低速带条平均间距的缩短与湍流减阻密切联系。     

Effects of free-stream turbulence on a transitional separated–reattached flow over a flat plate with a sharp leading edge

The transitional separated–reattached flow on a flat plate with a blunt leading edge under 2% free-stream turbulence (FST) is numerically simulated using the Large-eddy simulation (LES) approach. The Reynolds number based on the free-stream velocity and the plate thickness is 6500. A dynamic subgrid-scale model is employed and the LES results compare well with the available experimental data.It is well known that FST enhances shear-layer entrainment rates, reduces the mean reattachment distance, and causes early transition to turbulence leading to an early breakdown of the separated boundary layer. Many experimental studies have shown that different vortex shedding frequencies exist, specially the so called low-frequency flapping when there is a separation bubble but its mechanism is still not completely understood. The previous study by us without free-stream turbulence (NFST) did not show the existence of such a low-frequency flapping of the shear layer and it is not clear what the effects of FST will have on these shedding modes. Detailed analysis of the LES data has been presented in the present paper and the low-frequency flapping has not been detected in the current study.     

Experimental investigation of a flapping wing model

The main objective of this research study was to investigate the aerodynamic forces of an avian flapping wing model system. The model size and the flow conditions were chosen to approximate the flight of a goose. Direct force measurements, using a three-component balance, and PIV flow field measurements parallel and perpendicular to the oncoming flow, were performed in a wind tunnel at Reynolds numbers between 28,000 and 141,000 (3–15 m/s), throughout a range of reduced frequencies between 0.04 and 0.20. The appropriateness of quasi-steady assumptions used to compare 2D, time-averaged particle image velocimetry (PIV) measurements in the wake with direct force measurements was evaluated. The vertical force coefficient for flapping wings was typically significantly higher than the maximum coefficient of the fixed wing, implying the influence of unsteady effects, such as delayed stall, even at low reduced frequencies. This puts the validity of the quasi-steady assumption into question. The (local) change in circulation over the wing beat cycle and the circulation distribution along the wingspan were obtained from the measurements in the tip and transverse vortex planes. Flow separation could be observed in the distribution of the circulation, and while the circulation derived from the wake measurements failed to agree exactly with the absolute value of the circulation, the change in circulation over the wing beat cycle was in excellent agreement for low and moderate reduced frequencies. The comparison between the PIV measurements in the two perpendicular planes and the direct force balance measurements, show that within certain limitations the wake visualization is a powerful tool to gain insight into force generation and the flow behavior on flapping wings over the wing beat cycle.     

Using stereo multigrid DPIV (SMDPIV) measurements to investigate the vortical skeleton behind a finite-span flapping wing

The structure of the flow behind wings with finite span (3D) is significantly more complex than the flow behind infinite span (2D) wings. It has been shown that the presence of wingtip vortices behind finite span wings significantly modifies the geometry of the wake flow. It is felt that this modification alters the dynamics of interaction between leading and trailing edge vorticity in a manner that affects the ability of 2D flapping wings to produce thrust. A model of the mean flow skeleton has been proposed from qualitative flow visualization experiments. An unambiguous quantitative representation of the actual flow is required for comparison to the proposed model. To accomplish this the full 3D 3C velocity is required in the volume behind the 3D flapping wing. It is proposed to use stereoscopic multigrid digital particle image velocimetry (SMDPIV) measurements to investigate this unsteady oscillatory flow. This paper reports preliminary SMDPIV measurements along the plane of a symmetrical NACA-profile wing at a Strouhal number of 0.35. Phase averaged measurements are used to investigate the complex flow topology and the influence of the forcing flow on the evolution of the large scale structure of a jet-flow. This paper focuses on optimizing the SMDPIV experimental methodology applied to liquid flows. By refining the 2D 3C technique, the 3D topology of the flow can be investigated with a high degree of accuracy and repeatability. Preliminary results show that the flow is characterized by two pairs of coherent structures of positive and negative vorticity. The arrangement of these structures in the flow is controlled by the motion of the wing. Vorticity of opposite rotation is shed at the extreme heave and pitch positions of the aerofoil to set up a thrust indicative vortex street in support of the suggested topological model.     

Flow visualization and wall shear stress of a flapping model hummingbird wing

The unsteady low Reynolds number aerodynamics of flapping flight was investigated experimentally through flow visualization by suspended particle imagery and wall shear stress measurement from micro-array hot-film anemometry. In conjunction, a mechanism was developed to create a flapping motion with three degrees of freedom and adjustable flapping frequency. The flapping kinematics and wing shape were selected for dynamic similarity to a hummingbird during hovering flight. Flow visualization was used to validate the anemometry observations of leading edge vortex (LEV) characteristics and to investigate the necessity of spanwise flow in LEV stability. The shear sensors determined LEV characteristics throughout the translation section of the stroke period for various wing speeds. It was observed that a minimum frequency between 2 and 3.5 Hz is required for the formation and stabilization of a LEV. The vortex strength peaked around 30% of the flapping cycle (corresponding to just past the translation midpoint), which agrees with results from previous studies conducted by others. The shear sensors also indicated a mild growth in LEV size during translation sections of the wing’s motion. This growth magnitude was nearly constant through a range of operating frequencies.     

Measurement of tonal-noise characteristics and periodic flow structure around NACA0018 airfoil

The characteristics of tonal noise and the variations of flow structure around NACA0018 airfoil in a uniform flow are studied by means of simultaneous measurement of noise and velocity field by particle-image velocimetry to understand the generation mechanism of tonal noise. Measurements are made on the noise characteristics, the phase-averaged velocity field with respect to the noise signal, and the cross-correlation contour of velocity fluctuations and noise signal. These experimental results indicate that the tonal noise is generated from the periodic vortex structure on the pressure surface of the airfoil near the trailing edge of the airfoil. It is found that the vortex structure is highly correlated with the noise signal, which indicates the presence of noise-source distribution on the pressure surface. The vorticity distribution on the pressure surface breaks down near the trailing edge of the airfoil and forms a staggered vortex street in the wake of the airfoil.     

Investigation of flow mechanism of a robotic fish swimming by using flow visualization synchronized with hydrodynamic force measurement

When swimming in water by flapping its tail, a fish can overcome the drag from uniform flow and propel its body. The involved flow mechanism concerns 3-D and unsteady effects. This paper presents the investigation of the flow mechanism on the basis of a 3-D robotic fish model which has the typical geometry of body and tail with periodic flapping 2-freedom kinematical motion testing in the case of St = 0.78, Re = 6,600 and phase delay mode (φ = −75°), in which may have a greater or maximum propulsion (without consideration of the optimal efficiency). Using a special technique of dye visualization which can clearly show vortex sheet and vortices in detail and using the inner 3-component force balance and cable supporting system with the phase-lock technique, the 3-D flow structure visualized in the wake of fish and the hydrodynamic force measurement were synchronized and obtained. Under the mentioned flapping parameters, we found the key flow structure and its evolution, a pair of complex 3-D chain-shape vortex (S–H vortex-rings, S₁–H₁ and S₂–H₂, and their legs L₁ and L₂) flow structures, which attach the leading edge and the trailing edge, then shed, move downstream and outwards and distribute two anti-symmetric staggering arrays along with the wake of the fish model in different phase stages during the flapping period. It is different with in the case of St = 0.25–0.35. Its typical flow structure and evolution are described and the results prove that they are different from the viewpoints based on the investigation of 2-D cases. For precision of the dynamic force measurement, in this paper it was provided with the method and techniques by subtracting the inertial forces and the forces induced by buoyancy and gravity effect in water, etc. from original data measured. The evolution of the synchronized measuring forces directly matching with the flow structure was also described in this paper.     

Drag of a Plate Planing on the Shallow Water with Formation of Waves

The plane problem of the plate planing at a constant velocity on the surface of a heavy, ideal, incompressible, finite-depth fluid is considered. The approximate, depth-independent expression for the force acting on the plate is derived from the linear distribution of the fluid velocity along the plate and the height of the flow stagnation point, without regard for jet formation near the leading edge. In this approximate formulation the plate drag depends on its velocity and the trailing edge immersion and does not depend on the planing angle. Experiments and numerical calculations in the exact formulation are performed in the near-critical flow regimes. It is shown that the wave patterns in the experiments and numerical calculations coincide, the formula for the drag being in agreement with the numerical experiments. An approximate criterion of the formation of waves going away from the plate in the forward direction is proposed.     

Effect of multiple DBD plasma actuators on the tip leakage flow structure and loss of a turbine cascade

In this paper, the effects of multiple dielectric barrier discharge (DBD) plasma actuators on the leakage flow structures and loss conditions have been numerically studied in an axial turbine cascade. Kriging surrogate model is adopted to obtain the optimal cases. The physical mechanism of flow structures inside the gap that control leakage flow is presented, which is obtained by analyzing the flow topology, the evolution of the flow structures and its influence on the secondary velocity and loss conditions in the passage as well. The results show that the induced vortex caused by DBD actuators can change the leakage flow direction inside the tip gap and make the separation bubble break earlier, leading to a new type of the flow pattern. When the actuators are applied, the speed of leakage flow is significantly reduced and the angle between leakage flow and main flow has an obviously diminution, causing the reduction of mixing losses in the passage compared with the Baseline case. Furthermore, the comparison of secondary velocity shows that the tip leakage vortex (TLV) approaches the suction surface, resulting in reduced affected area and weakened loss strength. Plasma actuators can diminish the loss coefficient in both TLV and passage vortex near the casing (PVC) zones. The actuators arranged near the trailing edge mainly affect the strength of TLV, while the actuators in the leading edge area contribute to the loss reduction in the zone of PVC.     

Unsteady separated and reattaching turbulent flow over a two-dimensional square rib

The spatio-temporal characteristics of the separated and reattaching turbulent flow over a two-dimensional square rib were studied experimentally. Synchronized measurements of wall-pressure fluctuations and velocity fluctuations were made using a microphone array and a split-fiber film, respectively. Profiles of time-averaged streamwise velocity and wall-pressure fluctuations showed that the shear layer separated from the leading edge of the rib sweeps past the rib and directly reattaches on the bottom wall (x/H=9.75) downstream of the rib. A thin region of reverse flow was formed above the rib. The shedding large-scale vortical structures (fH/U₀=0.03) and the flapping separation bubble (fH/U₀=0.0075) could be discerned in the wall-pressure spectra. A multi-resolution analysis based on the maximum overlap discrete wavelet transform (MODWT) was performed to extract the intermittent events associated with the shedding large-scale vortical structures and the flapping separation bubble. The convective dynamics of the large-scale vortical structures were analyzed in terms of the autocorrelation of the continuous wavelet-transformed wall pressure, cross-correlation of the wall-pressure fluctuations, and the cross-correlation between the wall pressure at the time-averaged reattachment point and the streamwise velocity field. The convection speeds of the large-scale vortical structures before and after the reattachment point were U_c=0.35U₀ and 0.45U₀, respectively. The flapping motion of the separation bubble was analyzed in terms of the conditionally averaged reverse-flow intermittency near the wall region. The instantaneous reattachment point in response to the flapping motion was obtained; these findings established that the reattachment zone was a 1.2H-long region centered at x/H=9.75. The reverse-flow intermittency in one period of the flapping motion demonstrated that the thin reverse flow above the rib is influenced by the flapping motion of the separation bubble behind the rib.     

High-speed visualization and PIV measurements of cavitating flows around a semi-circular leading-edge flat plate and NACA0015 hydrofoil

Cavitating flows around a flat plate with semi-circular leading edge and a NACA0015 hydrofoil at attack angles ranging from 0° to 9° and with varying cavitation number are investigated using high-speed-imaging visualization (HIV) and particle-imaging velocimetry (PIV). Several known types of cavitation common to both foils, but also some different patterns, were observed. At small angles of incidence (less than 3°), cavitation on the plate begins in the form of a streak array (bubble-band) whereas on the hydrofoil as traveling bubbles. For the regimes with developed cavitation on the NACA0015 hydrofoil, the scattered and discontinuous bubble streaks branch and grow but subsequently merge into bubble clouds forming a remarkably regular lattice pattern. Once the incidence angle increased to 9°, the cavitation on the hydrofoil changed to a streaky pattern like that on the plate at small attack angles, whereas the regime on the plate showed no significant changes. The PIV method proved to be usable for measuring the instantaneous velocity also in the gas–vapor phase, albeit with reduced accuracy that was evaluated and accounted for on the basis of the effective (validation-surviving) number of imaging samples. The time-averaged velocity and turbulence moments show that the incipience of cavitation is governed by the development of the carrier-fluid flow around the foil leading edges, but the subsequent flow pattern depends strongly on the cavitation regime displaying markedly different distributions compared to the non-cavitating case. The main cavitation parameters: the maximum cavity length, the cloud cavity streamwise dimensions and the cloud shedding Strouhal number are analyzed and presented in function of the cavitation number and the attack angle in different scaling. The measurements confirm qualitatively the trends reported in the literature, but show also some quantitative differences, notably between the two foils considered.