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UNIVERSITY OF BUCHAREST
FACULTY OF PHYSICS Guest
2024-11-23 18:15 |
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Conference: Bucharest University Faculty of Physics 2023 Meeting
Section: Theoretical Physics and Applied Mathematics
Title:
On a generalized Prandtl type equation for curved and swept wing
Authors:
Adrian STOICA
Affiliation:
Faculty of Physics, University of Bucharest, 405 Atomistilor, POB MG-11, RO-077125 Bucharest-Magurele, Roumania
E-mail
adrian.stoica@unibuc.ro
Keywords:
Lifting Line Theory, Swept Wing, Prandtl's Singular Integral Equation
Abstract:
The classical Prandtl's lifting line theory for straight wings of high aspect ratio was extended in [1] to curved and swept wings. In the present paper the lifting line is placed such that in any cross-section, the moment about a point located on the lifting line is zero. For a wing of constant angle of attack, the lifting line is placed at the quarter-chord point, i.e. where it is also placed by Weissinger [4]. Unlike Weissinger's equation, the singular integral equation obtained by us captures both the curvature and the swept of the wing. It is proposed a numerical scheme of solving, based on the approximation of the spanwise circulation distribution with the Lagrange interpolation of the Chebyshev nodes of the second kind. The numerical method was applied for the oblique wing, V-shape wing and for the parabolic wing. In the case of the oblique wing, the numerical results show a good agreement with Guermond's asymptotic solution.
References:
[1] J.L.Guermond, Generalized lifting-line theory for curved and swept wings, Journal of Fluid Mechanics, 211, 497-513 (1990)
[2] Ph.Devinant, T.Gallois, Swept and curved wings: a numerical approach based on generalized lifting-line theory, Computational Mechanics, 29(4), 322-331 (2002)
[3] S.Prossdorf, B.Silbermann, Numerical analysis for integral and related operator equations, Akademie Verlag 1990
[4] J.Weissinger, The lift distribution of swept-back wings, ARC R&M, No1120 (1947)
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