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Unsteady lifting-line theory as a singular-perturbation problem. (English) Zbl 0589.76027
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 E. C. James [ibid. 70, 753-771 (1975; Zbl 0363.76006)], and points out a limitation in that of T. Van Holten [e.g.: ibid. 77, 561-579 (1976; Zbl 0338.76009)].

76B10 Jets and cavities, cavitation, free-streamline theory, water-entry problems, airfoil and hydrofoil theory, sloshing
76B25 Solitary waves for incompressible inviscid fluids
76M99 Basic methods in fluid mechanics
Full Text: DOI
[1] DOI: 10.1017/S0022112071000570 · Zbl 0242.76009 · doi:10.1017/S0022112071000570
[2] DOI: 10.1017/S0022112071000685 · doi:10.1017/S0022112071000685
[3] Van Holten, Vertica 1 pp 239– (1977)
[4] DOI: 10.1017/S0022112076002255 · Zbl 0338.76009 · doi:10.1017/S0022112076002255
[5] Van Holten, Delft Univ. Tech., Dept Aerosp. Engng Rep. 8 pp 104– (1975)
[6] Sears, J. Aero. Sci. 8 pp 104– (1941) · doi:10.2514/8.10655
[7] Landahl, AIAA J. 6 pp 345– (1968)
[8] DOI: 10.1007/BF02086522 · JFM 63.0774.04 · doi:10.1007/BF02086522
[9] Guiraud, Rech. Aerospat 1 pp 327– (1981)
[10] DOI: 10.1017/S0022112075002339 · Zbl 0363.76006 · doi:10.1017/S0022112075002339
[11] Cheng, J. Fluid Mech. 143 pp 327– (1984)
[12] DOI: 10.1017/S0022112080002686 · Zbl 0444.76042 · doi:10.1017/S0022112080002686
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