Time-resolved wake structure and kinematics of bat flight

We present synchronized time-resolved measurements of the wing kinematics and wake velocities for a medium sized bat, Cynopterus brachyotis, flying at low-medium speed in a closed-return wind tunnel. Measurements of the motion of the body and wing joints, as well as the resultant wake velocities in the Trefftz plane are recorded at 200 Hz (approximately 28–31 measurements per wing beat). Circulation profiles are found to be quite repeatable although variations in the flight profile are visible in the wake vortex structures. The circulation has almost constant strength over the middle half of the wing beat (defined according the vertical motion of the wrist, beginning with the downstroke). A strong streamwise vortex is observed to be shed from the wingtip, growing in strength during the downstroke, and persisting during much of the upstroke. At relatively low flight speeds (4.3 m/s), a closed vortex structure behind the bat is postulated.     

An experimental study of the unsteady vortex structures in the wake of a root-fixed flapping wing

An experimental study was conducted to characterize the evolution of the unsteady vortex structures in the wake of a root-fixed flapping wing with the wing size, stroke amplitude, and flapping frequency within the range of insect characteristics for the development of novel insect-sized nano-air-vehicles (NAVs). The experiments were conducted in a low-speed wing tunnel with a miniaturized piezoelectric wing (i.e., chord length, C = 12.7 mm) flapping at a frequency of 60 Hz (i.e., f = 60 Hz). The non-dimensional parameters of the flapping wing are chord Reynolds number of Re = 1,200, reduced frequency of k = 3.5, and non-dimensional flapping amplitude at wingtip h = A/C = 1.35. The corresponding Strouhal number (Str) is 0.33, which is well within the optimal range of 0.2 < Str < 0.4 used by flying insects and birds and swimming fishes for locomotion. A digital particle image velocimetry (PIV) system was used to achieve phased-locked and time-averaged flow field measurements to quantify the transient behavior of the wake vortices in relation to the positions of the flapping wing during the upstroke and down stroke flapping cycles. The characteristics of the wake vortex structures in the chordwise cross planes at different wingspan locations were compared quantitatively to elucidate underlying physics for a better understanding of the unsteady aerodynamics of flapping flight and to explore/optimize design paradigms for the development of novel insect-sized, flapping-wing-based NAVs.     

Application of digital particle image velocimetry to insect aerodynamics: measurement of the leading-edge vortex and near wake of a Hawkmoth

Some insects use leading-edge vortices to generate high lift forces, as has been inferred from qualitative smoke visualisations of the flow around their wings. Here we present the first Digital Particle Image Velocimetry (DPIV) data and quantitative analysis of an insect’s leading-edge vortex and near wake at two flight speeds. This allows us to describe objectively 2D slices through the flow field of a tethered Tobacco Hawkmoth (Manduca sexta). The near-field vortex wake appears to braodly resemble elliptical vortex loops. The presence of a leading-edge vortex towards the end of the downstroke is found to coincide with peak upward force production measured by a six-component force–moment balance. The topology of Manduca’s leading-edge vortex differs from that previously described because late in the downstroke, the structure extends continuously from wingtip across the thorax to the other wingtip.     

The influence of the wake of a flapping wing on the production of aerodynamic forces

The effect of the wake of previous strokes on the aerodynamic forces of a flapping model insect wing is studied using the method of computational fluid dynamics. The wake effect is isolated by comparing the forces and flows of the starting stroke (when the wake has not developed) with those of a later stroke (when the wake has developed). The following has been shown. (1) The wake effect may increase or decrease the lift and drag at the beginning of a half-stroke (downstroke or upstroke), depending on the wing kinematics at stroke reversal. The reason for this is that at the beginning of the half-stroke, the wing ``impinges' on the spanwise vorticity generated by the wing during stroke reversal and the distribution of the vorticity is sensitive to the wing kinematics at stroke reversal. (2) The wake effect decreases the lift and increases the drag in the rest part of the half-stroke. This is because the wing moves in a downwash field induced by previous half-stroke's starting vortex, tip vortices and attached leading edge vortex (these vortices form a downwash producing vortex ring). (3) The wake effect decreases the mean lift by 6%–18% (depending on wing kinematics at stroke reversal) and slightly increases the mean drag. Therefore, it is detrimental to the aerodynamic performance of the flapping wing. The project supported by the National Natural Science Foundation of China (10232010) and the National Aeronautic Science Fund of China(03A51049) The English text was polished by Xing Zhang     

PIV study of near-field tip vortex behind perforated Gurney flaps

The impact of Gurney flaps, of different heights and perforations, on the growth and development of a tip vortex, both along the tip and in the near field of a finite NACA 0012 wing, at Re = 1.05 × 10⁵ was investigated by using particle image velocimetry (PIV). Wind-tunnel force balance measurements were also made to supplement the PIV results. This study is a continuation of the work of Lee and Ko (Exp Fluids 46(6):1005–1019, 2009) on the near-wake measurements behind perforated Gurney flaps. The present results show that along the tip, the overall behavior of the secondary vortices and their interaction with the primary, or tip, vortex remained basically unchanged, regardless of flap height and perforation. The peak vorticity of the tip vortex, however, increased with flap height and always exhibited a local maximum at x/c = 0.8 (from the leading edge). In the near field, the strength and structure of the near-field tip vortex were found to vary greatly with the flap height and perforation. The small flaps produced a more concentrated tip vortex with an increased circulation, while the large Gurney flaps caused a disruption of the tip vortex. The disrupted vortex can, however, be re-established by the addition of flap perforation. The larger the flap perforation the more organized the tip vortex. The Gurney flaps have the potential to serve as an alternative off-design wake vortex control device.     

An experimental investigation of flow past a dual step cylinder

Flow development in the wake of a dual step cylinder has been investigated experimentally using Laser Doppler Velocimetry and flow visualization. The dual step cylinder model is comprised of a large diameter cylinder (D) mounted at the mid-span of a small diameter cylinder (d). The experiments have been performed for a Reynolds number (Re _D ) of 1,050, a diameter ratio (D/d) of 2, and a range of large cylinder aspect ratios (L/D). The results show that the flow development is highly dependent on L/D. The following four distinct flow regimes can be identified based on vortex dynamics in the wake of the large cylinder: (1) for L/D ≥ 15, three vortex shedding cells form in the wake of the large cylinder, one central cell bounded by two cells of lower frequency, (2) for 8 < L/D ≤ 14, a single vortex shedding cell forms in the wake of the large cylinder, (3) for 2 < L/D ≤ 6, vortex shedding from the large cylinder is highly three-dimensional. When spanwise vortices are shed, they deform substantially and attain a hairpin shape in the near wake, (4) for 0.2 ≤ L/D ≤ 1, the large cylinder induces vortex dislocations between small cylinder vortices. The results show that for Regimes I to III, on the average, the frequency of vortex shedding in the large cylinder wake decreases with L/D, which is accompanied by a decrease in coherence of the shed vortices. In Regime IV, small cylinder vortices connect across the large cylinder wake, but these connections are interrupted by vortex dislocations. With decreasing L/D, the frequency of dislocations decreases and the dominant frequency in the large cylinder wake increases toward the small cylinder shedding frequency.     

Two- and three-dimensional numerical simulations of the clap–fling–sweep of hovering insects

The importance of three-dimensional effects for flapping wings is addressed by means of numerical simulation. In particular, the clap–fling–sweep mechanism is examined. The flow at the beginning of the downstroke is shown to be in reasonable agreement with the two-dimensional approximation. After the wings move farther than one chord length apart, three-dimensional effects become essential. Two values of the Reynolds number are considered. At Re=128, the spanwise flow from the wing roots to the wing tips is driven by the centrifugal forces acting on the mass of the fluid trapped in the recirculation bubble behind the wings. It removes the excess of vorticity and delays the periodic vortex shedding. At Re=1400, vortex breakdown occurs past the outer portion of the wings, and multiple vortex filaments are shed into the wake.     

Aerodynamic forces and flow fields of a two-dimensional hovering wing

This paper reports the results of an experimental investigation on a two-dimensional (2-D) wing undergoing symmetric simple harmonic flapping motion. The purpose of this investigation is to study how flapping frequency (or Reynolds number) and angular amplitude affect aerodynamic force generation and the associated flow field during flapping for Reynolds number (Re) ranging from 663 to 2652, and angular amplitudes (α _A) of 30°, 45° and 60°. Our results support the findings of earlier studies that fluid inertia and leading edge vortices play dominant roles in the generation of aerodynamic forces. More importantly, time-resolved force coefficients during flapping are found to be more sensitive to changes in α _A than in Re. In fact, a subtle change in α _A may lead to considerable changes in the lift and drag coefficients, and there appears to be an optimal mean lift coefficient around α _A = 45°, at least for the range of flow parameters considered here. This optimal condition coincides with the development a reverse Karman Vortex street in the wake, which has a higher jet stream than a vortex dipole at α _A = 30° and a neutral wake structure at α _A = 60°. Although Re has less effect on temporal force coefficients and the associated wake structures, increasing Re tends to equalize mean lift coefficients (and also mean drag coefficients) during downstroke and upstroke, thus suggesting an increasing symmetry in the mean force generation between these strokes. Although the current study deals with a 2-D hovering motion only, the unique force characteristics observed here, particularly their strong dependence on α _A, may also occur in a three-dimensional hovering motion, and flying insects may well have taken advantage of these characteristics to help them to stay aloft and maneuver. An erratum to this article can be found at     

Identification of vortex pairs in aircraft wakes from sectional velocity data

The dynamics of multiple-vortex wake systems behind aircraft endangering air traffic can be assessed also from physical modelling. Large-scale laboratory investigations of multiple-vortex systems have been performed in a free-flight laboratory and in a water towing tank. Specialized PIV measurements provide time-resolved flow velocity fields normal to the wake axis. The applicability of various ∇u-based vortex identification schemes to planar velocity data is addressed and demonstrated for unequal-strength co- and counter-rotating vortex pairs. Large vortices shed off the wing tips and flaps are identified employing a ∇u-based criterion. Their cooperative mechanisms of generation and decay are evidenced from iso-surfaces of squared swirling strength and from further characteristic vortex parameters.

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Unsteady aerodynamic forces and power requirements of a bumblebee in forward flight

Aerodynamic forces and power requirements in forward flight in a bumblebee (Bombus terrestris) were studied using the method of computational fluid dynamics. Actual wing kinematic data of free flight were used in the study (the speed ranges from 0 m/s to 4.5 m/s; advance ratio ranges from 0–0.66). The bumblebee employs the delayed stall mechanism and the fast pitching-up rotation mechanism to produce vertical force and thrust. The leading-edge vortex does not shed in the translatory phase of the half-strokes and is much more concentrated than that of the fruit fly in a previous study. At hovering and low-speed flight, the vertical force is produced by both the half-strokes and is contributed by wing lift; at medium and high speeds, the vertical force is mainly produced during the downstroke and is contributed by both wing lift and wing drag. At all speeds the thrust is mainly produced in the upstroke and is contributed by wing drag. The power requirement at low to medium speeds is not very different from that of hovering and is relatively large at the highest speed (advance ratio 0.66), i.e. the power curve is J-shaped. Except at the highest flight speed, storing energy elastically can save power up to 20%–30%. At the highest speed, because of the large increase of aerodynamic torque and the slight decrease of inertial torque (due to the smaller stroke amplitude and stroke frequency used), the power requirement is dominated by aerodynamic power and the effect of elastic storage of energy on power requirement is limited.The project supported by the National Natural Science Foundation of China (10232010) and the National Aeronautic Science fund of China (03A51049)The English text was polished by Xing Zhang.     

Spatial perturbation of a wing-tip vortex using pulsed span-wise jets

The separation distance required between transport aircraft to avoid wake vortices remains a limiting factor on airport capacity. The dissipation of the wake can be accelerated by perturbing co-operative instabilities between multiple pairs of vortices. This paper presents the results of a preliminary experimental investigation into the use of pulsed span-wise air jets in the wing tip to perturb a single tip vortex in the very near field. Velocity measurements were made using PIV and hot-wire anemometry. The results demonstrate that the vortex position can be modulated at frequencies up to 50 Hz and, as such, the method shows promise for forcing instability in multiple vortex wakes.     

Near-field tip vortex behind a swept wing model

The near-field flow structure of a tip vortex behind a sweptback and tapered NACA 0015 wing was investigated and compared with a rectangular wing at the same lift force and Re=1.81×10⁵. The tangential velocity decreased with the downstream distance while increased with the airfoil incidence. The core radius was about 3% of the root chord c _r, regardless of the downstream distance and α for α<8°. The core axial velocity was always wake-like. The core Γ_c and total Γ_o circulation of the tip vortex remained nearly constant up to x/c _r=3.5 and had a Γ_c/Γ_o ratio of 0.63. The total circulation of the tip vortex accounted for only about 40% of the bound root circulation Γ_b. For a rectangular wing, the axial flow exhibited islands of wake- and jet-like velocity distributions with Γ_c/Γ_o=0.75 and Γ_o/Γ_b=0.70. For the sweptback and tapered wing tested, the inner region of the tip vortex flow exhibited a self-similar behavior for x/c _r≥1.0. The lift force computed from the spanwise circulation distributions agreed well with the force-balance data. A large difference in the lift-induced drag was, however, observed between the wake integral method and the inviscid lifting-line theory.     

Wake patterns of the wings and tail of hovering hummingbirds

The flow fields of slowly flying bats and faster-flying birds differ in that bats produce two vortex loops during each stroke, one per wing, and birds produce a single vortex loop per stroke. In addition, the circulation at stroke transition approaches zero in bats but remains strong in birds. It is unknown if these difference derive from fundamental differences in wing morphology or are a consequence of flight speed. Here, we present an analysis of the horizontal flow field underneath hovering Anna’s hummingbirds (Calypte anna) to describe the wake of a bird flying at zero forward velocity. We also consider how the hummingbird tail interacts with the wake generated by the wings. High-speed image recording and analysis from three orthogonal perspectives revealed that the wing tips reach peak velocities in the middle of each stroke and approach zero velocity at stroke transition. Hummingbirds use complex tail kinematic patterns ranging from in phase to antiphase cycling with respect to the wings, covering several phase shifted patterns. We employed particle image velocimetry to attain detailed horizontal flow measurements at three levels with respect to the tail: in the tail, at the tail tip, and just below the tail. The velocity patterns underneath the wings indicate that flow oscillates along the ventral–dorsal axis in response to the down- and up-strokes and that the sideways flows with respect to the bird are consistently from the lateral to medial. The region around the tail is dominated by axial flows in dorsal to ventral direction. We propose that these flows are generated by interaction between the wakes of the two wings at the end of the upstroke, and that the tail actively defects flows to generate moments that contribute to pitch stability. The flow fields images also revealed distinct vortex loops underneath each wing, which were generated during each stroke. From these data, we propose a model for the primary flow structures of hummingbirds that more strongly resembles the bat model. Thus, pairs of unconnected vortex loops may be shared features of different animals during hovering and slow forward flight.     

Near wake vortex dynamics of a hovering hawkmoth

Numerical investigation of vortex dynamics in near wake of a hovering hawkmoth and hovering aerodynamics is conducted to support the development of a biology-inspired dynamic flight simulator for flapping wingbased micro air vehicles. Realistic wing-body morphologies and kinematics are adopted in the numerical simulations. The computed results show 3D mechanisms of vortical flow structures in hawkmoth-like hovering. A horseshoe-shaped primary vortex is observed to wrap around each wing during the early down- and upstroke; the horseshoe-shaped vortex subsequently grows into a doughnut-shaped vortex ring with an intense jet-flow present in its core, forming a downwash. The doughnut-shaped vortex rings of the wing pair eventu- ally break up into two circular vortex rings as they propagate downstream in the wake. The aerodynamic yawing and rolling torques are canceled out due to the symmetric wing kinematics even though the aerodynamic pitching torque shows significant variation with time. On the other hand, the time- varying the aerodynamics pitching torque could make the body a longitudinal oscillation over one flapping cycle.     

Large aerodynamic forces on a sweeping wing at low Reynolds number

The aerodynamic forces and flow structure of a model insect wing is studied by solving the Navier-Stokes equations numerically. After an initial start from rest, the wing is made to execute an azimuthal rotation (sweeping) at a large angle of attack and constant angular velocity. The Reynolds number (Re) considered in the present note is 480 (Re is based on the mean chord length of the wing and the speed at 60% wing length from the wing root). During the constant-speed sweeping motion, the stall is absent and large and approximately constant lift and drag coefficients can be maintained. The mechanism for the absence of the stall or the maintenance of large aerodynamic force coefficients is as follows. Soon after the initial start, a vortex ring, which consists of the leading-edge vortex (LEV), the starting vortex, and the two wing-tip vortices, is formed in the wake of the wing. During the subsequent motion of the wing, a base-to-tip spanwise flow converts the vorticity in the LEV to the wing tip and the LEV keeps an approximately constant strength. This prevents the LEV from shedding. As a result, the size of the vortex ring increases approximately linearly with time, resulting in an approximately constant time rate of the first moment of vorticity, or approximately constant lift and drag coefficients. The variation of the relative velocity along the wing span causes a pressure gradient along the wingspan. The base-to-tip spanwise flow is mainly maintained by the pressure-gradient force. The project supported by the National Natural Science Foundation of China (10232010)     

Wingtip vortex control via the use of a reverse half-delta wing

The effect of a 65° sweep reverse half-delta wing (RHDW), mounted at the squared tip of a rectangular NACA 0012 wing, on the tip vortex was investigated experimentally at Re?=?2.45?×?10⁵. The RHDW was found to produce a weaker tip vortex with a lower vorticity level and, more importantly, a reduced lift-induced drag compared to the baseline wing. In addition to the lift increment, the RHDW also produced a large separated wake flow and subsequently an increased profile drag. The reduction in lift-induced drag, however, outperformed the increase in profile drag and resulted in a virtually unchanged total drag in comparison with the baseline wing. Physical mechanisms responsible for the RHDW-induced appealing aerodynamics and vortex flow modifications were discussed.     

Coherent vortical and straining structures in the finite wall-mounted square cylinder wake

Topological aspects of the turbulent wake of a finite, surface-mounted, square-cross-section cylinder of h/d = 4 are addressed by decomposing the velocity field into a quasi-periodic coherent part and the unresolved incoherent fluctuations. The three-dimensional large scale structure is educed through a reconstruction of planar phase-averaged PIV measurements using the simultaneously sampled surface pressure difference on opposing sides of the obstacle as a phase reference. A topological model for the vortex structure is educed and mean streamwise wake vorticity is explained in terms of the connections between initially vertical structures shed alternately from either side of the obstacle, rather than previously proposed ‘tip’ vortex structures generated at the obstacle free-end. The coherent structure educed accounts for a significant portion of the fluctuating energy in the wake. The turbulent field is further analyzed by finding Lagrangian straining structures that form by induction of the coherent vorticity field, and these structures are related to the energy transfer from the base phase-averaged flow since they act to stretch incoherent vorticity fluctuations in their neighbourhood.     

Structural Analysis of a Dragonfly Wing

Dragonfly wings are highly corrugated, which increases the stiffness and strength of the wing significantly, and results in a lightweight structure with good aerodynamic performance. How insect wings carry aerodynamic and inertial loads, and how the resonant frequency of the flapping wings is tuned for carrying these loads, is however not fully understood. To study this we made a three-dimensional scan of a dragonfly (Sympetrum vulgatum) fore- and hindwing with a micro-CT scanner. The scans contain the complete venation pattern including thickness variations throughout both wings. We subsequently approximated the forewing architecture with an efficient three-dimensional beam and shell model. We then determined the wing’s natural vibration modes and the wing deformation resulting from analytical estimates of 8 load cases containing aerodynamic and inertial loads (using the finite element solver Abaqus). Based on our computations we find that the inertial loads are 1.5 to 3 times higher than aerodynamic pressure loads. We further find that wing deformation is smaller during the downstroke than during the upstroke, due to structural asymmetry. The natural vibration mode analysis revealed that the structural natural frequency of a dragonfly wing in vacuum is 154 Hz, which is approximately 4.8 times higher than the natural flapping frequency of dragonflies in hovering flight (32.3 Hz). This insight in the structural properties of dragonfly wings could inspire the design of more effective wings for insect-sized flapping micro air vehicles: The passive shape of aeroelastically tailored wings inspired by dragonflies can in principle be designed more precisely compared to sail like wings —which can make the dragonfly-like wings more aerodynamically effective.     

Wake structures and vortex-induced vibrations of a long flexible cylinder—Part 2: Drag coefficients and vortex modes

Drag coefficients and vortex structures in the wake of a vertical long flexible cylinder vibrating at low mode numbers are presented in this paper. A model with an external diameter of 16 mm and a total length of 1.5 m giving an aspect ratio of about 94 was used to perform more than 100 runs in which Reynolds numbers ranged between 1200 and 12 000. Only the lower 40% of its length was exposed to the water current in the flume and applied top tensions varied from 15 to 110 N giving fundamental natural frequencies in the range from 3 to 7.1 Hz. Reduced velocities based on the fundamental natural frequency up to 16 were reached. The mass ratio was 1.8 and the combined mass-damping parameter about 0.05. The largest drag coefficients were found related to the largest x–y synchronised motions. Digital particle image velocimetry was used to investigate the vortex structures in the wake of the cylinder model. Two modes of vortex shedding were observed, depending on the response branch and the position along the length of the model at which the interrogations were performed.