Circulation Redistribution in Leading-Edge Vortices with Spanwise Flow

Wong, Jaime G.; Gillespie, Graeme; Rival, David E.

doi:10.2514/1.j057030

Cited by 8 publications

(9 citation statements)

References 24 publications

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“…where u is the shear-layer velocity. A numerically identical result can be obtained for an LEV formed on a wing through a distinct derivation, in which mass enters and feeds the leading edge vortex through the shear layer at the wing's leading edge, and likewise for the circulation generated in a boundary layer [6][7][8].…”

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confidence: 70%

“…For instance, many previous modelling efforts have required knowledge of the vorticity field to determine spanwise flow [4]. One possible simplification is to model circulation transport as species transport, neglecting the complex vortex tilting behaviour, when the case permits [5,6]. In this paradigm, the circulation transport is characterized by two terms: the circulation feeding rate (∂Ŵ/∂t) in and its spanwise transport via spanwise flow (∂Ŵ/∂t) out .…”

mentioning

confidence: 99%

“…For a stable LEV in steady state, such as that found on rotating wings, this balance must be zero. This simplication has been previously validated for a translating delta-wing, where spanwise flow is relatively constant [6].…”

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confidence: 99%

“…Since the circulation flux through the leading-edge shear layer depends strongly on the shear-layer velocity, the distribution of shear-layer velocity along the span must be determined. The shear-layer velocity profile has been investigated in many studies, as its evaluation is tied to the understanding of the vortex growth [6,9,10]. However, most of the available models or relationships to define the shear-layer velocity profile are confronted with unknown parameter limitations, such that their insights are difficult to adapt into a completely predictive tool.…”

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confidence: 99%

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A species-transport model for circulation in a leading-edge vortex

Giner-Morency

Wong

2022

Adv. Aerodyn.

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In this study, we propose a model to predict circulation growth along the span of a rotating wing, in which circulation transport is represented as species transport. Fluid particles entering the vortex shear layer at the leading edge are initialized as vorticity-containing mass and are advected by the flow along the span. A circulation budget is presented, consisting of a generation and transport term, the latter derived from the vorticity transport equation, which leaves only two unknowns for the modeller to determine: the shear-layer thickness and the spanwise flow distribution. We find that the model is insensitive to the value chosen for the shear-layer thickness, as varying the thickness by an order of magnitude only changes the output by a few percent. Meanwhile, we use Bernoulli equation in a rotating coordinates system as a basic model for spanwise flow. To verify the accuracy of the model, the predicted circulation values are compared against experimental circulation values and show good agreement to measurements close to the axis of rotation, which corresponds to the spanwise locations at which the spanwise flow model best matches experimental data. It is suggested, therefore, that this model produces accurate results subject to an appropriate spanwise flow model.

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confidence: 70%

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confidence: 99%

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confidence: 99%

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confidence: 99%

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A species-transport model for circulation in a leading-edge vortex

Giner-Morency

Wong

2022

Adv. Aerodyn.

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“…For 3-D flows, Wong, Gillespie & Rival (2018) proposed a shear-layer feeding model for the LEV circulation and its spanwise advection using vorticity-containing mass. The circulation feeding-rate error is 10 % when compared with delta-wing experiments.…”

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confidence: 99%

A simple vortex-loop-based model for unsteady rotating wings

Chowdhury

Ringuette

2019

J. Fluid Mech.

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An analytical model is developed for the lift force produced by unsteady rotating wings; this configuration is a simple representation of a flapping wing. Modelling this is important for the aerodynamic and control-system design for bio-inspired drones. Such efforts have often been limited to being two-dimensional, semi-empirical, sometimes computationally expensive, or quasi-steady. The current model is unsteady and three-dimensional, yet simple to implement, requiring knowledge of only the wing kinematics and geometry. Rotating wings produce a vortex loop consisting of the root vortex, leading-edge vortex, tip vortex and trailing-edge vortex, which grows with time. This is modelled as a tilted planar loop, geometrically specified by the wing size, orientation and motion. By equating the angular impulse of the vortex loop to that of the fluid volume driven by the wing, the circulatory lift force is derived. Potential flow theory gives the fluid-inertial lift. Adding these two contributions yields the total lift formula. The model shows good agreement with a range of experimental and computational cases. Also, a steady-state lift model is developed that compares well with previous work for various angles of attack.

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Vorticity dynamics and stability of the leading-edge vortex on revolving wings

Chen,

Cheng,

2023

Physics of Fluids

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The leading-edge vortex (LEV) is well known for its contribution to the high-lift generation in a wide variety of biological organisms, such as flying insects, auto-rotating samaras, and gliding snakes. Based on revolving wings, the temporal–spatial evolution of the LEV, including the fundamental vorticity dynamics and stabilizing mechanisms, is reviewed here, considering the effects of Reynolds number (Re), Rossby number (Ro), and aspect ratio (AR). The literature agrees that the saturation of LEV intensity at the steady state can be predicted by the chord length of travel at the radius of gyration, which falls between 2 and 4 within a large variety of wing geometries and kinematics. In contrast, the lift almost arrives at a constant value by the end of acceleration. These findings indicate distinct mechanisms for the steady-state LEV vorticity and constant lift. For the stabilizing mechanisms of LEV, four existing hypotheses are reviewed, followed by the introduction of a novel vorticity transport-based perspective. Two vortex-tilting-based mechanisms, named planetary vorticity tilting and dual-stage radial-tangential vortex tilting, were recently proposed to expand our understanding of LEV stability. It is concluded that the vorticity transport inside the LEV is strongly correlated with the local Ro as well as Re and AR. This review presents a comprehensive summary of existing work on LEV dynamics, stabilizing mechanisms, and high-lift generation.

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Circulation Redistribution in Leading-Edge Vortices with Spanwise Flow

Cited by 8 publications

References 24 publications

A species-transport model for circulation in a leading-edge vortex

A species-transport model for circulation in a leading-edge vortex

A simple vortex-loop-based model for unsteady rotating wings

Vorticity dynamics and stability of the leading-edge vortex on revolving wings

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