Growth Of Leading-edge Vortex Research Articles

Vorticity dynamics of fully developed leading-edge vortices on revolving wings undergoing pitch-up maneuvers

In nature, birds and insects usually execute pitch-up maneuvers, which is either an active perching or a passive response against gusts. During such maneuvers, their wings flap with a concomitant nose-up rotation around an axis, and thus, both vortex structures and aerodynamic forces of the wings are influenced. This research focuses on the impact of pitch-up maneuvers on the evolution and underlying vorticity dynamics of a fully developed leading-edge vortex (LEV), which has received limited interest in previous research. Based on data obtained from numerical simulations, an analysis of vortex dynamics and vorticity transport is conducted at different pitch rates and pitch axis locations. Our findings show that an increase in pitch rate and a shift of pitch axis toward the trailing edge can both terminate the growth of LEV and then initiate its movement toward the trailing edge via strong downward convection. However, the contributions of spanwise convection and vortex stretching (or compression) are distinct in these two scenarios, leading to different lift generations. Other vortex-tilting-based mechanisms, e.g., the planetary vorticity tilting and the dual-stage radial-tangential vortex tilting, are reduced during pitch-up maneuvers. Moreover, a rapid pitch-up around the leading edge is encouraged to maximize the lift during the maneuver, although this should be accompanied by constraints in flight height and kinetic energy when being applied to guide the perching of bio-inspired flapping wing micro air vehicles.

The effect of dynamic twisting on the flow field and the unsteady forces of a heaving flat plate

Many marine animals can dynamically twist their pectoral fins while swimming. The effects of such dynamic twisting on the unsteady forces on the fin and its surrounding flow field are yet to be understood in detail. In this paper, a flat plate executing a heaving maneuver is subjected to a similar dynamic twisting. In particular, the effects of the direction of twist, non-dimensional heaving amplitude, and reduced frequency are studied using a force sensor and particle image velocimetry (PIV) measurements. Two reduced frequencies, , and , and two twisting modes are investigated. In the first twisting mode, the plate is twisted in the direction of the heave (forward-twist), and in the second mode, the plate is twisted opposite to the direction of the heave (backward-twist). Force sensor measurements show that the forward-twist recovers some of the lift that is usually lost during the upstroke of flapping locomotion. Additionally, the forward-twist maintains a near-constant lift coefficient during the transition between downstroke and upstroke, suggesting a more stable form of locomotion. PIV results show that forward-twist limits circulation and leading-edge vortex growth during the downstroke, keeping at the cost of the reduced lift. By contrast, backward-twist increases the circulation during the downstroke, resulting in large increases in both lift and drag coefficients. Force sensor data also showed that this effect on the lift is reversed during the upstroke, where the backward-twist causes a negative lift. The effects of each twisting mode are mainly caused by the changes in the shear layer velocity that occur as a result of twisting about the spanwise axis along the mid-chord. The twisting performed by forward-twist reduces the effective angle of attack through the upstroke and downstroke, resulting in a reduced shear layer velocity and lower circulation. The twisting performed by backward-twist does the exact opposite, increasing the effective angle of attack through the upstroke and downstroke and consequently increasing the shear layer velocity and circulation.

Comparison of Edge Vortices from Normal and Elliptic Flapping Flat Plates

Computational analysis of elliptic and normal flat plate geometries, sized to wings of small fliers and in a two-dimensional plunging–pitching–flapping motion resulting in hover, is conducted to investigate circulation growth at the leading-edge vortex (LEV) and trailing-edge vortex (TEV). The models are sized to the same aspect ratio, and a Reynolds number of 225 is chosen as it is similar to that observed in small fliers in hover. Results show similar LEV growth and lift production trends for both cases but with differing energy flux mechanisms. A vorticity transport analysis is done to quantify these energy fluxes. The LEV growth and shearing is closely related to the TEV growth and shearing, and the plunging–pitching profile, while the geometry plays a role in the magnitude of vortex creation and intensity of spanwise fluxes only.

Investigating sweep effects on the stability of leading-edge vortices over finite-aspect ratio pitch-up wings

The flow field around a finite-span flat wing in pitch motion is modeled by means of large-eddy simulation. The effect of moderate sweep angles on the stability of the leading-edge vortex (LEV) is investigated. The relative stability of LEVs on flapping profiles can be improved by moderating LEV growth through spanwise vorticity convection and vortex stretching. The LEV growth over an unswept wing and two sweep angles, namely, Λ=15°; 30°, is studied by investigating the spanwise flow. The calculated results are in good agreement with experimental data, establishing confidence in the approach. Results show that sweeping the wing profile increases not only the scale of the secondary vortices but also expedites the initiation of the vortices at lower angles of attack. For the sweep angle of Λ=30°, increasing the angle of attack is associated with annihilation of vorticity and thereby limits the vortex growth as a necessary condition for LEV stability. Analysis shows that increasing the sweep angle results in a higher circulation intensity, especially in the inner region of the wing, and significant spanwise flow is observed through the vortex core. The pattern of vorticity remains stable and attached to the surface as the angle of attack continues to grow for the swept wing, while the patterns of vorticity depart the wing surface for the unswept wing. It is suspected that sweeping the wing can control the scale of the vortex by introducing a substantial vortex stretching.

Insights into leading edge vortex formation and detachment on a pitching and plunging flat plate

The present study is a prelude to applying different flow control devices on pitching and plunging airfoils with the intention of controlling the growth of the leading edge vortex (LEV); hence, the lift under unsteady stall conditions. As a pre-requisite the parameters influencing the development of the LEV topology must be fully understood and this constitutes the main motivation of the present experimental investigation. The aims of this study are twofold. First, an approach is introduced to validate the comparability between flow fields and LEV characteristics of two different facilities using water and air as working media by making use of a common baseline case. The motivation behind this comparison is that with two facilities the overall parameter range can be significantly expanded. This comparison includes an overview of the respective parameter ranges, control of the airfoil kinematics and careful scrutiny of how post-processing procedures of velocity data from time-resolved particle image velocimetry (PIV) influence the integral properties and topological features used to characterise the LEV development. Second, and based on results coming from both facilities, the appearance of secondary structures and their effect on LEV detachment over an extended parameter range is studied. A Lagrangian flow field analysis based on finite-time Lyapunov Exponent (FTLE) ridges allows precise identification of secondary structures and reveals that their emergence is closely correlated to a vortex Reynolds number threshold computed from the LEV circulation. This threshold is used to model the temporal onset of secondary structures. Further analysis indicates that the emergence of secondary structures causes the LEV to stop accumulating circulation if the shear layer angle at the leading edge of the flat plate has ceased to increase. This information is of particular importance for advanced flow control applications, since efforts to strengthen and/or prolong LEV growth rely on precise knowledge about where and when to apply flow control measures.Graphical abstract

Experimental investigation on the leading-edge vortex formation and detachment mechanism of a pitching and plunging plate

Abstract

Energy harvesting of an oscillating foil at low reduced frequencies with rigid and passively deforming leading edge

The aerodynamic performance of an oscillating heaving and pitching foil operating in the energy harvesting mode was experimentally investigated at reduced frequencies (k=fc∕U∞) of 0.04 to 0.08, corresponding to Reynolds numbers (Re=U∞c∕ν) of 24,000 to 48,000. The goal is to better understand the operational conditions that lead to improved power output when operating at off-peak efficiency conditions, in particular, those corresponding to high approach velocities for a given oscillation frequency. The operational parameters include a range of pitching amplitudes of θ0=45∘ to 75∘, a phase shift between sinusoidal pitching and heaving motions of Φ=30∘ to 120∘ and a heaving amplitude of 0.3c. Aerodynamic force measurements are used to determine the energy extraction performance and flow field measurements using phase-locked particle image velocimetry are used to identify flow features that contribute to energy extraction. In addition, inertia-induced chord-wise deformation at the leading edge (LE) of the foil is investigated to assess its feasibility to enhance power output. Results indicate that for the range of k values studied the optimal efficiency occurs near θ0=45∘ and Φ=90∘, whereas the optimal power extraction occurs near θ0=60∘ and Φ=60∘, both for k = 0.08. As k is decreased (through increased freestream velocity) to 0.04, overall performance becomes relatively insensitive to θ0 and Φ. This is supported by the PIV measurements, which show at lower k a premature leading edge vortex (LEV) formation and detachment from the foil surface. Efficiency and power coefficient results are shown versus the feathering parameter, χ, indicating a rapid decline in performance as χ increases due to increasing pitching amplitude or with decreasing k. The relative strength of the LEV is found to increase with decreasing k, however the timing of the LEV formation and detachment is such that there is reduced power production. Study of the inertia-induced leading edge deformation shows that only during a small portion of the cycle is the lift force enhanced. This is a consequence of the inertial response of the leading edge and an enhancement of the LEV growth rate. These results indicate that use of a deforming surface to improve overall performance requires proper tuning relative to the heaving motion.

Effect of butterfly-scale-inspired surface patterning on the leading edge vortex growth

The effects of longitudinal square grooves on the growth of the leading edge vortex (LEV) produced by an impulsively-started flat plate are investigated experimentally. The Reynolds numbers are 1416, 2833 and 5667, and the maximum vortex formation time is 2.8. The square grooves are inspired by the surface patterning (scales) on butterfly wings. It is hypothesized that the grooves play a role in the LEV formation and development by creating a stronger secondary vortex near the LE that impedes the growth of the LEV. To evaluate this hypothesis, circulation curves of the total positive vorticity field and LEV of a smooth plate and grooved plate are compared. Also, the secondary vorticity generated by the LEV interaction with the patterned surface is studied, as well as the subsequent effect on the LEV’s growth rate and peak circulation. The vortex development process varies for each Reynolds number. At the lowest number, the effects of the grooves are minimal; however, they are most significant at the highest Reynolds number where the unsteady interactions between the secondary vortex and the leading edge shear layer become stronger for the grooved plate causing an earlier separation of the LEV. Therefore, contrary to the hypothesis, the data shows that stronger secondary vortex causes a stronger LEV with an earlier separation. The stronger secondary vortex interacts more rigorously with the LE shear layer causing the latter to feed more concentrated vorticity to the LEV.

Vortex formation and shedding from a cyber-physical pitching plate

We report on the dynamics of the formation and growth of the leading-edge vortex and the corresponding unsteady aerodynamic torque induced by large-scale flow-induced oscillations of an elastically mounted flat plate. All experiments are performed using a high-bandwidth cyber-physical system, which enables the user to access a wide range of structural dynamics using a feedback control system. A series of two-dimensional particle image velocimetry measurements are carried out to characterize the behaviour of the separated flow structures and its relation to the plate kinematics and unsteady aerodynamic torque generation. By modulating the structural properties of the cyber-physical system, we systematically analyse the formation, strength and separation of the leading-edge vortex, and the dependence on kinematic parameters. We demonstrate that the leading-edge vortex growth and strength scale with the characteristic feeding shear-layer velocity and that a potential flow model using the measured vortex circulation and position can, when coupled with the steady moment of the flat plate, accurately predict the net aerodynamic torque on the plate. Connections to previous results on optimal vortex formation time are also discussed.

The leading-edge vortex and quasisteady vortex shedding on an accelerating plate

A computational inquiry focuses on leading-edge vortex (LEV) growth and shedding during acceleration of a two-dimensional flat plate at a fixed 10°–60° angle of attack and low Reynolds number. The plate accelerates from rest with a velocity given by a power of time ranging from 0 to 5. During the initial LEV growth, subtraction of the added mass lift from the computed lift reveals an LEV-induced lift augmentation evident across all powers and angles of attack. For the range of Reynolds numbers considered, a universal time scale exists for the peak when α≥30°, with augmentation lasting about four to five chord lengths of translation. This time scale matches well with the half-stroke of a flying insect. An oscillating pattern of leading- and trailing-edge vortex shedding follows the shedding of the initial LEV. The nondimensional frequency of shedding and lift coefficient minima and maxima closely match their values in the absence of acceleration. These observations support a quasisteady theory of vortex shedding, where dynamics are determined primarily by velocity and not acceleration. Finally, the nondimensional vortex formation time is found to be a function of the Reynolds number, but only weakly when the Reynolds number is high.