Formation Of Leading-edge Vortex Research Articles

Enhancing Energy Harvesting Efficiency of Flapping Wings with Leading-Edge Magnus Effect Cylinder.

According to the Magnus principle, a rotating cylinder experiences a lateral force perpendicular to the incoming flow direction. This phenomenon can be harnessed to boost the lift of an airfoil by positioning a rotating cylinder at the leading edge. In this study, we simulate flapping-wing motion using the sliding mesh technique in a heaving coordinate system to investigate the energy harvesting capabilities of Magnus effect flapping wings (MEFWs) featuring a leading-edge rotating cylinder. Through analysis of the flow field vortex structure and pressure distribution, we explore how control parameters such as gap width, rotational speed ratio, and phase difference of the leading-edge rotating cylinder impact the energy harvesting characteristics of the flapping wing. The results demonstrate that MEFWs effectively mitigate the formation of leading-edge vortices during wing motion. Consequently, this enhances both lift generation and energy harvesting capability. MEFWs with smaller gap widths are less prone to induce the detachment of leading-edge vortices during motion, ensuring a higher peak lift force and an increase in the energy harvesting efficiency. Moreover, higher rotational speed ratios and phase differences, synchronized with wing motion, can prevent leading-edge vortex generation during wing motion. All three control parameters contribute to enhancing the energy harvesting capability of MEFWs within a certain range. At the examined Reynolds number, the optimal parameter values are determined to be a∗ = 0.0005, R = 3, and ϕ0 = 0°.

Tip effects on three-dimensional flow structures over low-aspect-ratio plates: mechanisms of spanwise fluid transport

Three-dimensional flows over low-aspect-ratio rectangular flat plates ( ${A{\kern-4pt}R} = 1.00$ – $1.50$ ) are investigated using tomographic and planar particle image velocimetry techniques. The chord-based Reynolds number is $5400$ , and the angle of attack is fixed at $6^\circ$ . This study reveals for the first time the interplay between spanwise fluid transport and downwash, both originating from the tip effects. Spanwise fluid transport promotes the formation and subsequent coherent development of leading-edge vortices, whereas downwash stabilizes the flow. Specifically, two mechanisms related to spanwise fluid transport are revealed. First, the spanwise fluid transport enhances the intensity of the reversed flow, promoting the shear layer roll-up and vortex shedding. Second, the near-wall spanwise flow interacts with the shed C-shape vortices, thereby strengthening the vortex heads. In particular, through these interactions, spanwise fluid transport can sustain the coherence of the C-shape vortices until the vortex heads split in a regular fashion. Consequently, the C-shape vortices are transformed into novel Þ-shape vortices for the plates of ${A{\kern-4pt}R} \leq 1.25$ , which supplements the previously discovered transformation from C-shape to M-shape vortices for larger ${A{\kern-4pt}R}$ plates. Downstream of this novel vortex-splitting transformation, two fundamental processes contribute to the formation of hairpin vortices. The above comprehensive understanding of complete vortex evolution routine provides valuable insights into the tip effects on the formation of three-dimensional flows over low- ${A{\kern-4pt}R}$ plates.

Hydrodynamic analysis of fin–fin interactions in two-manta-ray schooling in the vertical plane

This study investigates the interaction of a two-manta-ray school using computational fluid dynamics simulations. The baseline case consists of two in-phase undulating three-dimensional manta models arranged in a stacked configuration. Various vertical stacked and streamwise staggered configurations are studied by altering the locations of the top manta in the upstream and downstream directions. Additionally, phase differences between the two mantas are considered. Simulations are conducted using an in-house developed incompressible flow solver with an immersed boundary method. The results reveal that the follower will significantly benefit from the upstroke vortices (UVs) and downstroke vortices depending on its streamwise separation. We find that placing the top manta 0.5 body length (BL) downstream of the bottom manta optimizes its utilization of UVs from the bottom manta, facilitating the formation of leading-edge vortices (LEVs) on the top manta’s pectoral fins during the downstroke. This LEV strengthening mechanism, in turn, generates a forward suction force on the follower that results in a 72% higher cycle-averaged thrust than a solitary swimmer. This benefit harvested from UVs can be further improved by adjusting the phase of the top follower. By applying a phase difference of π/3 to the top manta, the follower not only benefits from the UVs of the bottom manta but also leverages the auxiliary vortices during the upstroke, leading to stronger tip vortices and a more pronounced forward suction force. The newfound interaction observed in schooling studies offers significant insights that can aid in the development of robot formations inspired by manta rays.

Leading-edge vortex and aerodynamic performance scaling in a simplified vertical-axis wind turbine

Numerical analysis is conducted to investigate the aerodynamic performance and characteristics of flow around a simplified vertical-axis wind turbine (VAWT) by varying the tip-speed ratio and number of blades. The tip-speed ratios considered are λ=RΩ/U0=0.8−2.4, and the numbers of blades are n=2−5 at the Reynolds number of Re=U0D/ν=80 000, where D(=2R) and Ω are the turbine diameter and rotation rate, respectively, U0 is the free-stream velocity, and ν is the kinematic viscosity. The primary flow feature observed around the VAWT is the formation and evolution of leading-edge vortices (LEVs) at lower tip-speed ratios of λ=0.8−1.2, which have a notable impact on the power coefficient in the upwind region. At high tip-speed ratios (λ>1.2), the LEV is not generated due to fast blade rotating speeds. Depending on the tip-speed ratio and solidity (σ=nc/πD, where c represents the blade chord length), these LEVs are generated at different azimuthal angles and exhibit varying strengths. A modified tip-speed ratio, λ′=λ/π(1−σ), proposed in the present study allows the flow structures with different λ's and n's to exhibit similarity when they are represented with λ′. Thus, the time-averaged power coefficient (i.e., aerodynamic performance; C¯PW) is a function of λ′ (rather than λ and n) in the range of σ=0.2−0.5 considered, and its maximum occurs at λ′=0.45−0.5 regardless of the number of blades, providing the optimal tip-speed ratio of λopt=γπ(1−σ), where γ=0.45−0.5. Finally, we show that C¯PW/(σλ3) is a function of λ′.

Dual-stage radial–tangential vortex tilting reverses radial vorticity and contributes to leading-edge vortex stability on revolving wings

The physics of leading-edge vortex (LEV) stability on flapping wings and autorotating seeds is still underexplored due to its complex dependency on Reynolds number ( $\textit {Re}$ ), aspect ratio (AR) and Rossby number (Ro). Our previous study observed an interesting dual-stage vortex tilting between radial and tangential components in a stable LEV. Here, the establishment of this novel mechanism, i.e. dual-stage radial–tangential vortex tilting (DS-VT $_{r-t}$ ), is investigated and explained in detail using numerical methods. The contributions of other tangential vorticity transport terms are also considered. It is shown that the stable LEV region coincides mostly with a constant ratio of tangential and radial vorticity components. The DS-VT $_{r-t}$ mechanism functions as a negative feedback loop for radial vorticity, thereby contributing to the LEV stability at $\textit {Re} > 500$ . Specifically, this mechanism involves a dual-stage vortex tilting starting from negative radial component to positive tangential component, and then back to positive radial component, thereby leading to a $180^{\circ }$ reversal of radial vorticity. The radial Coriolis acceleration can also assist the DS-VT $_{r-t}$ by enhancing the tangential vorticity component and the reduction of radial vorticity inside the LEV via the second stage of DS-VT $_{r-t}$ . The effects of $\textit {Re}$ , AR and Ro on the constant radial–tangential vorticity ratio and DS-VT $_{r-t}$ are then analysed. The coupled effects of AR and Ro are separated into rotational effects and those of tip and root vortices. Our results establish an evident relationship among the LEV stability, the constant radial–tangential vorticity ratio, and the DS-VT $_{r-t}$ , thereby deepening the understanding in the vorticity transport of LEV formation and stability.

Sound generation in the flapping wing flight of insects

Flapping wing flight has been topic of recent interest with respect to the maneuverability and agility of insects. Computational fluid dynamics methods have been used to investigate the aerodynamics though typically for incompressible flow. The underlying sound generation mechanism, though of fundamental biological and physical interest, have much less attention. Experimental acoustical and high speed video studies of the Coconut Rhinoceros Beetle (Oryctes rhinoceros) and the Oriental Flower Beetle (Protaetia orientalis) have motivated large scale simulations accounting for three dimension flow, compressibility, and fluid structure interactions. Computational fluid dynamics simulations were performed using the unsteady compressible flow solver (CAESIM, Adaptive Research, Inc.) using a high resolution (TVD) methodology. Models of the wing flapping motion were accomplished using mesh deformation techniques with the flapping following from rotation with prescribed bending and coupled rotation and translation from the wing’s hinge position. Fluid structure interactions with respect to the wing’s flexibility are investigated in terms of the wing bending and the leading edge vortex formation.

Identification of frequency modes and spectral content for noise suppression: Cavitation flow over 3-D hydrofoil with sinusoidal leading edge

The impetus of this study is to provide an in-depth insight into the unsteady hydrodynamic characteristics of the cavitating flow, effects of the wavy leading edge (WLE) on the noise suppression mechanism due to a cavity cloud formation, which contains condensation, detachment, collapse, spanwise flow, streamwise velocity fluctuation, and shedding phenomenon. NACA 634-021 hydrofoil was considered with WLE having a wavelength of 25% and an amplitude of 5% of the mean chord length and was compared to a straight-leading-edge (SLE) hydrofoil at cavitation numbers of [Formula: see text] and a chord-based Reynolds number of [Formula: see text]. Counter-rotation vortices were produced between the peaks of the WLE hydrofoil by destroying the horseshoe vortex and delaying the tail vortex, changing the frequency. Here, the hydrodynamic forces have also been discussed in addition to the noise. The results showed that the leading-edge vortex formation and flow separation dynamics fundamentally differed between the SLE and the WLE hydrofoil. The main difference between the WLE and SLE hydrofoil turbulent flow is the formation of counter-rotating streamwise vortices pairs. We solved the cavitating flow using the large eddy simulation (LES) approach, as well as the Kunz mass transfer model, which is performed under the framework of the OpenFOAM package.

The leading-edge vortex over a swift-like high-aspect-ratio wing with nonlinear swept-back geometry

The leading-edge vortex (LEV) is a common flow structure that forms over wings at high angles of attack. Over the years, LEVs were exploited for augmenting the lift of man-made slender delta wings aircraft. However, recent observations suggested that natural flyers with high-aspect-ratio (high-AR) wings, such as the common swift (Apus apus), can also generate LEVs while gliding. We hypothesize that the planform shape and nonlinear sweep (increasing towards the wingtip) enable the formation and control of such LEVs. In this paper, we investigate whether a stationary LEV can form over a nonlinear swept-back high-AR wing inspired by the swift’s wing shape and evaluate its characteristics and potential aerodynamic benefit. Particle image velocimetry (PIV) measurements were performed in a water flume on a high-AR swept-back wing inspired by the swift wing. Experiments were performed at four spanwise sections and a range of angles of attack for a chord-based Reynolds number of . Stationary LEV structures were identified across the wingspan by utilizing the proper orthogonal decomposition (POD) method for angles of attack of 5∘–15∘. The size and circulation of the stationary LEV were found to grow towards the wingtip in a nonlinear manner due to shear layer feeding and spanwise transport of mass and vorticity within the LEV, thus confirming that nonlinear high-AR swept-back wings can generate stationary LEVs. Our results suggest that the common swift can generate stationary LEVs over its swept-back wings to glide slower and at a higher rate of descent, with the LEVs potentially supporting up to 60% of its weight.

Effects of Geometry of Wings Submerged in Turbulent Bluff-Body Wake

The effects of the aspect ratio, the sweep angle, and the leading-edge geometry of wings placed in a turbulent wake were investigated in wind-tunnel experiments at a chord Reynolds number of . The poststall lift enhancement due to the leading-edge vortex formation was studied at optimal locations in the wake. The effects of the strength of the leading-edge vortices, the ratio of the spanwise length scale of the incident vortex to the wingspan, and the degree of two-dimensionality of the wake–wing interaction were studied. The competition between the effects of the spanwise length scale of the incident wake and the strength of the leading-edge vortices determined the optimal aspect ratio, which was found to be around four. Increasing the sweep angle decreased the mean lift due to the decreased two-dimensionality of the vortex formation. Airfoils with sharp leading edge produced the strongest leading-edge vortices but further away from the wing surface, resulting in lower maximum lift. Relative to the performance in the undisturbed freestream, the increases in the stall angle and maximum lift coefficient were not significantly affected by the leading-edge shape.

Experiments and numerical simulations on hovering three-dimensional flexible flapping wings

In this paper, the applicability and accuracy of high-fidelity experimental and numerical approaches in the analysis of three-dimensional flapping (revolving and pitching) wings operating under hovering flight conditions, i.e. where unsteady and three-dimensional rotational effects are strong, are assessed. Numerical simulations are then used to explore the role of mass and frequency ratios on aerodynamic performance, wing dynamics and flow physics. It is shown that time-averaged lift increases with frequency ratio, up to a certain limit that depends on mass ratio and beyond which upward wing bending and flexibility induced phase lag between revolving an pitching motions at stroke reversal become strong and contribute to phases of negative lift that counterbalances the initial lift increase. This wing dynamics, which is dominated by spanwise bending, also affects wing–wake interactions and, in turn, leading edge vortex formation.

Advances in aero-acoustics of flying beetles

An understanding of the acoustics of invasive species of beetles is needed for potential detection and tracking methods in agricultural monitoring. However, the underlying mechanisms of sound generation are not well understood, especially with respect to the higher harmonic sounds. The Coconut Rhinoceros Beetle (Oryctes rhinoceros) and the Oriental Flower Beetle (Protaetia orientalis) have been studied during tethered flight with synchronized microphone array measurements and high speed video (1000–10,000 fps). The larger Coconut Rhinoceros Beetles have fundamental ∼50 Hz with distinctive torsional wing rotation compared to Oriental Flower Beetle (∼100 Hz). Computational fluid dynamics simulations were performed using the unsteady compressible flow solver (CAESIM, Adaptive Research, Inc.) using a highresolution (TVD) methodology. Models of the wing flapping motion were accomplished using mesh deformation techniques with the flapping following from rotation with prescribed bending and coupled rotation and translation from the wing’s hinge position. Fluid structure interactions with respect to the wing’s flexibility are investigated in terms of the wing bending and the leading edge vortex formation.

NUMERICAL INVESTIGATION OF X-45A TYPE UNMANNED COMBAT AIR VEHICLE

In this paper, the low-speed aerodynamic performance of unmanned combat air vehicle (UCAV) X-45 delta wing was investigated by a numerical method using computational fluid dynamic approaches (CFD). The investigation was conducted with X-45 and the formation of leading-edge vortices (LEV) and vortex breakdown was studied by a varying angle of attack with the range of 5° to 30° at the Reynolds number of 10,000 using the SST turbulence model and are compared with experimental data to validate simulation accuracy of CFD. Stall conditions happened at around 30°, averaged vorticity layer demonstrates a prolonged form that goes along by narrow recirculation zones neighboring to the wing surface. Detail about flow field, including LEV formation, vortex breakdown, interaction, and nonlinear aerodynamic characteristics of X-45 was presented and discussed.

Interaction of quasi-two-dimensional vortical gusts with airfoils, unswept and swept wings

A nearly two-dimensional vortex of small core size has been produced by the transient plunging motion of an upstream airfoil and it interacted with the downstream wings. Depending on the offset distance of the vortex and wing angle of attack, the incident vortex filament deforms, diffuses, and loses coherence, while inducing leading-edge vortex formation and shedding from the wing. No significant spanwise flow develops in the incident vortices during the interaction. The interaction with the swept wing at each spanwise plane appears to be unaffected by the other spanwise planes. The counter-clockwise vortex induces a positive lift peak as it approaches the wing, which can be predicted by the potential flow assumption. The peak lift force is proportional to the circulation of the incident vortex and has its maximum near the zero-offset distance. The minimum lift coefficient is reached after the vortex has just passed and caused flow separation on the lower surface. The maximum lift coefficients for the finite unswept and swept wings can be estimated by making a correction for the aspect ratio and using the independence principle. The only exception is observed for the swept wing at a post-stall angle of attack for which the leading-edge vortex shedding becomes parallel to the leading-edge and increases the peak lift force.Graphical abstract

Leading edge vortex formation and wake trajectory: Synthesizing measurements, analysis, and machine learning

The strength and trajectory of a leading edge vortex (LEV) formed by a pitching-heaving hydrofoil (chord $c$) is studied. The LEV is identified using the $Q$-criterion method, which is calculated from the 2D velocity field obtained from PIV measurements. The relative angle of attack at mid-stroke, ${\alpha_{T/4}} $, proves to be an effective method of combining heave amplitude ($h_0/c$), pitch amplitude ($\theta_0$), and reduced frequency ($f^*$) into a single variable that predicts the maximum value of $Q$ over a wide range of operating conditions. Once the LEV separates from the foil, it travels downstream and rapidly weakens and diffuses. The downstream trajectory of the LEV has two characteristic shapes. At low values of ${\alpha_{T/4}}$, it travels straight downstream after separating from the foil, while at higher values of ${\alpha_{T/4}} $, an accompanying Trailing Edge Vortex (TEV) forms and the induced velocity generates a cross-stream component to the vortex trajectories. This behavior is accurately predicted using a potential flow model for the LEV and TEV. Supervised machine learning algorithms, namely Support Vector Regression and Gaussian Process Regression, are used to create regression models that predicts the vortex strength, shape and trajectory during growth and after separation. The regression model successfully captures the features of two vortex regimes observed at different values of ${\alpha_{T/4}} $. However, the predicted LEV trajectories are somewhat smoother than observed in the experiments. The strengths of the vortex is often under-predicted. Both of these shortcomings may be attributed to the relatively small size of the training data set.

The Drag of an Elliptical Airfoil at a Reynolds Number of 1000

There have been many studies on the mechanisms of unsteady aerodynamics, such as leading-edge vortex (LEV) formation, wing-wake interaction, and spanwise flow. Spanwise flow can only be observed on three-dimensional wing models; however other phenomena such as LEV and wing-wake interaction can be captured using two-dimensional airfoil models. This study focuses on two-dimensional elliptical airfoil because this profile can generate counter-rotating vortices used by insects to generate aerodynamic forces. This research aims to analyze the drag production of two-dimensional elliptical airfoils flapping with bumblebee-inspired kinematics in asymmetrical normal-hovering mode at a typical Reynolds number range of . It is found that drag is generated during the downstroke while thrust during the upstroke. It is also found that the creation and shedding of counter-rotating vortices are closely related to the generation of thrust. The results also indicate that asymmetrical strokes can be used in normal hovering to minimize drag or produce thrust.

Energy harvesting from the gust response of membrane wing using piezoelectrics

Micro-air vehicles face challenges in aerodynamic and endurance. This paper presents a novel gust response-based membrane wing energy harvester to solve these issues. An aero-electro-mechanical model based on CFD/CSD coupling method is established to investigate the dynamic response and the energy harvesting performance of this energy harvester under harmonic gust loads. The geometric nonlinearity of structure and aerodynamic nonlinearity are considered in this paper. The harmonic gust loads were obtained from a Navier–Stokes CFD solver based on unstructured meshes. The large deformation electro-mechanical finite element model was built based on the updated Lagrangian formulation and the principle of virtual work. The mean power density is defined to evaluate the energy harvesting performance. The effects of the external load resistance, the PVDF patch location, the gust amplitude and frequency, and Reynold number are studied, respectively. The results show that the optimal resistance of this energy harvester is 1.6kΩ, and the flexibility of the membrane wing improves the aerodynamic and energy harvesting performance greatly through increases the amplitude of odd super harmonics. The PVDF location has a relatively small impact on the energy harvesting performance except near end surfaces. The PVDF patch located at 0.1c–0.9c all can get better energy harvesting performance. When the equivalent angle of attack of gust amplitude exceeds 4 deg, the energy harvesting performance decreases slightly due to the formation and convection of leading-edge vortex. A sustained output power density of 5.31mW/cm3 is harvested at Re=25,000. The present work provides an effective theoretical basis for further studying energy harvesting of Micro air vehicles.

Effects of Reynolds number on leading-edge vortex formation dynamics and stability in revolving wings

The mechanisms of leading-edge vortex (LEV) formation and its stable attachment to revolving wings depend highly on Reynolds number ( $\textit {Re}$ ). In this study, using numerical methods, we examined the $\textit {Re}$ dependence of LEV formation dynamics and stability on revolving wings with $\textit {Re}$ ranging from 10 to 5000. Our results show that the duration of the LEV formation period and its steady-state intensity both reduce significantly as $\textit {Re}$ decreases from 1000 to 10. Moreover, the primary mechanisms contributing to LEV stability can vary at different $\textit {Re}$ levels. At $\textit {Re} <200$ , the LEV stability is mainly driven by viscous diffusion. At $200<\textit {Re} <1000$ , the LEV is maintained by two distinct vortex-tilting-based mechanisms, i.e. the planetary vorticity tilting and the radial–tangential vorticity balance. At $\textit {Re}>1000$ , the radial–tangential vorticity balance becomes the primary contributor to LEV stability, in addition to secondary contributions from tip-ward vorticity convection, vortex compression and planetary vorticity tilting. It is further shown that the regions of tip-ward vorticity convection and tip-ward pressure gradient almost overlap at high $\textit {Re}$ . In addition, the contribution of planetary vorticity tilting in LEV stability is $\textit {Re}$ -independent. This work provides novel insights into the various mechanisms, in particular those of vortex tilting, in driving the LEV formation and stability on low- $\textit {Re}$ revolving wings.

Vortex control strategy for unsteady aerodynamic optimization of a plunging airfoil at a low Reynolds number

This study has explored effective flow control strategies to improve unsteady aerodynamic performance of a plunging airfoil at a low Reynolds number of Re = 59 000 through controlling the leading-edge vortex (LEV) formation and development. The leading-edge blowing control is first utilized to directly strengthen the LEV by injecting momentum into the separated leading-edge shear layer. The influence of the momentum coefficient on the vortical evolution and aerodynamic forces is more significant than that of the exit width. As the momentum coefficient increases in a certain range, the LEV can be enhanced, thereby increasing the maximum unsteady lift. However, it is found that an accelerated detachment usually occurs with enhancement of the LEV as the secondary vortex is also promoted by blowing, leading to a reduced duration of high lift compared with the baseline case. In order to solve such a control problem of the LEV, the control strategy of the combined blowing and suction is further proposed, which could increase the LEV strength and concurrently delay the LEV detachment to some extent through inhibiting the growth of the secondary vortex. As a result, the unsteady aerodynamic performance of the plunging airfoil has been further improved with a significant increase in the maximum lift coefficient and a moderately prolonged duration of high lift.

Propulsive efficiency and efficacy of a pumping sail

This study presents a framework to analyze the propulsive performance of a sail under oscillatory pumping motion, which should be modified from the analysis framework for conventional flapping wings. A new set of metrics, including the propulsive efficiency ηs and efficacy ΔCx¯, which depend not only on the aerodynamic coefficient but also on kinematic conditions of the sailing vehicle, are proposed to characterize the propulsive performance of sail pumping. The necessity of the proposed metrics is illustrated by studying the propulsive performance of a two-dimensional airfoil under different heaving and kinematic conditions through computational fluid dynamic simulations. It was found that the sail pumping typically improves the propulsive performance by lift enhancement instead of drag reduction. Thus, the formation of leading-edge vortices may not be detrimental to the propulsive efficiency of a pumping sail, contrary to that for flapping wings. A propulsive efficiency greater than unity is achievable under certain sailing conditions because a sailing vehicle can extract energy from the wind.

Larger wavelengths suit hydrodynamics of carangiform swimmers

The wavelength of undulatory kinematics of fish is an important parameter to determine their hydrodynamic performance. This study focuses on numerical examination of this feature by reconstructing the real physiological model and kinematics of steadily swimmning Jack Fish. We perform three-dimensional numerical simulations for flows over these models composed of the trunk, and dorsal, anal, and caudal fins. Moreover, we prescribe the carangiform-like motion for its undulation for a range of wavelengths. Undulation with larger wavelengths improves the hydrodynamic performance of the carangiform swimmer in terms of better thrust production by the caudal fin, lower drag production on the trunk, and reduced power consumption by the trunk. This coincides with the formation of stronger posterior body vortices and leading-edge vortices with more circulation on the caudal fin. The real kinematics of Jack Fish surpasses the performance of those with prescribed motion owing to the flexibility of the caudal fin.