Effect of Leading-Edge Separation on the Lift of a Delta Wing

Brown, Clinton E.; Michael, W. H.

doi:10.2514/8.3180

Cited by 179 publications

(63 citation statements)

References 3 publications

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“…Detailed analysis of the three-dimensional wake is beyond the scope of this paper. Note that the original model developed by Brown & Michael (1954) also applied the two-dimensional approximation to solve a three-dimensional problem, which was the LEV of a delta wing in that case.…”

Section: Discussionmentioning

confidence: 99%

Closed-form solution for the edge vortex of a revolving plate

Chen

Kolomenskiy

2017

J. Fluid Mech.

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Flapping and revolving wings can produce attached leading edge vortices (LEVs) when the angle of attack is large. In this work, a low order model is proposed for the edge vortices that develop on a revolving plate at 90 degrees angle of attack, which is the simplest limiting case, yet showing remarkable similarity with the generally known LEVs. The problem is solved analytically, providing short closed-form expressions for the circulation and the position of the vortex. A good agreement with the numerical solution of the Navier-Stokes equations suggests that, for the conditions examined, the vorticity production at the sharp edge and its subsequent three-dimensional transport are the main effects that shape the edge vortex.

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Section: Discussionmentioning

confidence: 99%

Closed-form solution for the edge vortex of a revolving plate

Chen

Kolomenskiy

2017

J. Fluid Mech.

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“…49,50 Equations (6) and (7) are further solved by a similarity method, 51 obtaining the following relations:…”

Section: A Discrete Vortex Model Of the Vorticity Motion At The Openingmentioning

confidence: 99%

Flow-excited acoustic resonance of a Helmholtz resonator: Discrete vortex model compared to experiments

Dai

Sun

2015

Physics of Fluids

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The acoustic resonance in a Helmholtz resonator excited by a low Mach number grazing flow is studied theoretically. The nonlinear numerical model is established by coupling the vortical motion at the cavity opening with the cavity acoustic mode through an explicit force balancing relation between the two sides of the opening. The vortical motion is modeled in the potential flow framework, in which the oscillating motion of the thin shear layer is described by an array of convected point vortices, and the unsteady vortex shedding is determined by the Kutta condition. The cavity acoustic mode is obtained from the one-dimensional acoustic propagation model, the time-domain equivalent of which is given by means of a broadband time-domain impedance model. The acoustic resistances due to radiation and viscous loss at the opening are also taken into account. The physical processes of the self-excited oscillations, at both resonance and off-resonance states, are simulated directly in the time domain. Results show that the shear layer exhibits a weak flapping motion at the off-resonance state, whereas it rolls up into large-scale vortex cores when resonances occur. Single and dual-vortex patterns are observed corresponding to the first and second hydrodynamic modes. The simulation also reveals different trajectories of the two vortices across the opening when the first and second hydrodynamic modes co-exist. The strong modulation of the shed vorticity by the acoustic feedback at the resonance state is demonstrated. The model overestimates the pressure pulsation amplitude by a factor 2, which is expected to be due to the turbulence of the flow which is not taken into account. The model neglects vortex shedding at the downstream and side edges of the cavity. This will also result in an overestimation of the pulsation amplitude.

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“…where z n and Γ n respectively refer to the position and intensity of the point vortex.w n is the desingularized complex velocity at the vortex position and the overbar denotes a complex conjugate. Equation (12) is known as the Brown-Michael equation [32], and enforces the conservation of fluid momentum around the vortex and associated branch cut in an integral sense [27]. The omission of the corrective term on the left-hand-side would lead to an unphysical unbalanced force on the branch cut linking the vortex to its generating corner ζ e [33].…”

Section: A Solid Modelmentioning

confidence: 99%

“…In particular, the motion (other than the main translation) [36,40] is also plotted for comparison (solid line). TS was computed from (32) using the values of the vortex street intensity, width and induced velocity obtained with our model. and deformation of the body are irrelevant in Von Kármán's derivation.…”

Section: Classical and Reversed Von Kármán Streets And Thrust/drag Prmentioning

confidence: 99%

Resonance and propulsion performance of a heaving flexible wing

2009

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The influence of the bending rigidity of a flexible heaving wing on its propulsive performance in a two-dimensional imposed parallel flow is investigated in the inviscid limit. Potential flow theory is used to describe the flow over the flapping wing. The vortical wake of the wing is accounted for by the shedding of point vortices with unsteady intensity from the wing's trailing edge. The trailing-edge flapping amplitude is shown to be maximal for a discrete set of values of the rigidity, at which a resonance occurs between the forcing frequency and a natural frequency of the system. A quantitative comparison of the position of these resonances with linear stability analysis results is presented. Such resonances induce maximum values of the mean developed thrust and power input. The flapping efficiency is also shown to be greatly enhanced by flexibility.Comment: 21 pages, 13 figures, to appear in Physics of Fluid

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Effect of Leading-Edge Separation on the Lift of a Delta Wing

Cited by 179 publications

References 3 publications

Closed-form solution for the edge vortex of a revolving plate

Closed-form solution for the edge vortex of a revolving plate

Flow-excited acoustic resonance of a Helmholtz resonator: Discrete vortex model compared to experiments

Resonance and propulsion performance of a heaving flexible wing

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