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Zbl 0589.76027
Ahmadi, Ali R.; Widnall, Sheila E.
Unsteady lifting-line theory as a singular-perturbation problem. (English)
[J] J. Fluid Mech. 153, 59-81 (1985). ISSN 0022-1120; ISSN 1469-7645/e

Summary: Unsteady lifting-line theory is developed for a wing of large aspect ratio oscillating at low frequency in inviscid incompressible flow. The wing is assumed to have a rigid chord but a flexible span. Use of the method of matched asymptotic expansions reduces the problem from a singular integral equation to quadrature. The pressure field and airloads, for a prescribed wing shape and motion, are obtained in closed form as expansions in inverse aspect ratio. A rigorous definition of unsteady induced downwash is also obtained. Numerical calculations are presented for an elliptic wing in pitch and heave; compared with numerical lifting-surface theory, computation time is reduced significantly. The present work also identifies and resolves errors in the unsteady lifting-line theory of {\it E. C. James} [ibid. 70, 753-771 (1975; Zbl 0363.76006)], and points out a limitation in that of {\it T. Van Holten} [e.g.: ibid. 77, 561-579 (1976; Zbl 0338.76009)].

MSC 2000:: *76B10 Free-streamline theory and appl.
76B25 Solitary waves, etc. (inviscid fluids)
76M99 Basic methods in fluid mechanics

Keywords: Unsteady lifting-line theory; wing of large aspect ratio oscillating at low frequency; matched asymptotic expansions; singular integral equation; airloads; unsteady induced downwash; elliptic wing in pitch and heave

Citations: Zbl 0363.76006; Zbl 0338.76009

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