Hostname: page-component-cd9895bd7-hc48f Total loading time: 0 Render date: 2024-12-18T19:05:25.045Z Has data issue: false hasContentIssue false
  • English
  • Français

Lunate-tail swimming propulsion as a problem of curved lifting line in unsteady flow. Part 1. Asymptotic theory

Published online by Cambridge University Press:  20 April 2006

H. K. Cheng  and
Luis E. Murillo
H. K. Cheng
Affiliation:
Department of Aerospace Engineering, University of Southern California, Los Angeles
Luis E. Murillo
Affiliation:
Department of Aerospace Engineering, University of Southern California, Los Angeles Present address: Boeing Commercial Airplane Co., Seattle, Washington 98124.
Get access Rights & Permissions [Opens in a new window]

Abstract

The asymptotic theory of a high-aspect-ratio wing in an incompressible flow is generalized to an oscillating lifting surface with a curved centreline in the domain where the reduced frequency based on the half-span is of order unity. The formulation allows applications to lightly loaded models of lunate-tail swimming and ornithopter flight, provided that the heaving displacement does not far exceed the mean wing chord. The analysis include the quasi-steady limit, in which the crescent-moon wing problem considered earlier by Thurber (1965) is solved and several aerodynamic properties of swept wings are explained.

Among the important three-dimensional and unsteady effects are corrections for the centreline curvature and for the spanwise components of the locally shed vortices. Comparison of the lift distributions obtained for model lunate tails with data computed from the doublet-lattice method (Albano & Rodden 1969) lends support to the asymptotic theory.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 143 , June 1984 , pp. 327 - 350
Copyright
© 1984 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Ahmadi, A. R. 1980 Ph.D. dissertation, MIT.
Albano, E. & Rodden, W. P. 1969 AIAA J. 7, 279–285.
Ashley, H. & Landahl, M. 1965 Aerodynamics of Wings and Bodies. Addison-Wesley.
Ashley, H. & Rodden, W. P. 1972 Ann. Rev. Fluid Mech. 4, 431–472.
Batchelor, G. K. 1967 An Introduction to Fluid Dynamics, pp. 510, 523. Cambridge University Press.
Belotserkovskii, S. M. 1967 The Theory of Thin Wings in Subsonic Flow. Plenum.
Belotserkovskii, S. M. 1977 Ann. Rev. Fluid Mech. 9, 469–494.
Carter, G. S. 1940 A General Zoology of the Invertebrates, chap. 23. London.
Cheng, H. K. 1976 Univ. S. Calif., Dept Aerospace Engng Rep. USCAE 133.
Cheng, H. K. 1978a AIAA J. 16, 1211–1213.
Cheng, H. K. 1978b Univ. S. Calif., Dept Aerospace Engng Rep. USCAE 135.
Cheng, H. K. 1982a The transonic flow theories of high and low aspect ratio wings. In Physical and Numerical Aspects of Aerodynamic Flows (ed. T. Cebeci), Springer-Verlag.
Cheng, H. K. 1982b In Transonic, Shock and Multidimensional Flows (ed. R. E. Meyer), pp. 107–145. Academic.
Cheng, H. K. 1983 Transonic aerodynamics of forward swept wings analyzed as a lifting-line problem. In Proc. Intl Forward-Swept Wing Aircraft Conf. Bristol University, 24–26 March 1982.
Cheng, H. K., Chow, R. & Melnik, R. E. 1981 Z. angew. Math. Phys. 32, 481–496.
Cheng, H. K. & Meng, S. Y. 1979 AIAA J. 17, 121–124.
Cheng, H. K. & Meng, S. Y. 1980 J. Fluid Mech. 97, 531–556.
Cheng, H. K., Meng, S. Y., Chow, R. & Smith, R. 1981 AIAA J. 19, 961–968.
Cheng, H. K. & Murillo, L. E. 1982 Univ. S. Calif. Dept Aerospace Engng Rep. USCAE 139.
Chopra, M. E. 1974 In Swimming and Flying in Nature, vol. 2 (ed. T. Y. T. Wu et al.).
Chopra, M. G. 1976 J. Fluid Mech. 74, 161–181.
Chopra, M. G. & Kambe, T. 1977 J. Fluid Mech. 79, 49–69.
Cook, L. P. 1979 Q. Appl. Maths 32, 178–202.
Davis, D. E. 1963 Aero. Res. Counc. R & M 3409.
Dorodnitsyn, A. A. 1944 Prikl. Mat. Mech. 8, 33–64.
Gregory, W. K. 1936 Biol. Rev. 11, 310.
Hedman, S. G. 1965 Aero. Res. Inst. Sweden Rep. 105.
Holten, T. van 1976a J. Fluid Mech. 77, 561–599.
Holten, T. van 1976b Asymptotic theory of swept wings. Delft Univ. Dept. Aerospace Engng Rep.Google Scholar
James, E. C. 1975 J. Fluid Mech. 70, 735–771.
Jameson, A. & Caughey, D. A. 1977 New York Univ. ERDA Rep. C00-3077-140.
Jones, R. T. 1972 AIAA J. 10, 171–176.
Jones, R. T. 1980 Aero. J. R. Aero. Soc. July, 214–217.
Jones, R. T. & Cohen, D. 1957 Aerodynamics of wings at high speed. In Aerodynamic Components of Aircraft at High Speed (ed. A. F. Donovan & H. R. Lawrence), pp. 1–236. Princeton University Press.
Kármán, T. von & Burgers, J. M. 1934 General aerodynamic theory. In Aerodynamic Theory (ed. W. F. Durand), vol. 2, div. E.
Katz, J. & Weihs, D. 1978 J. Fluid Mech. 88, 485–487.
Kida, T. & Miyai, T. 1978 Z. angew. Math. Phys. 29, 519–607.
Kramer, M. O. 1960 J. Am. Soc. Nav. Engng 72, 25–34.
Lan, C. E. 1979 J. Fluid Mech. 93, 747–765.
Lighthill, M. J. 1960 J. Fluid Mech. 9, 305–317.
Lighthill, M. J. 1969 Ann. Rev. Fluid Mech. 1, 413–466.
Lighthill, M. J. 1970 J. Fluid Mech. 44, 265–301.
Lighthill, M. J. 1975 Mathematical Biofluiddynamics. SIAM.
Marshall, N. B. 1966 The Life of Fishes. The Universe Books.
Munk, M. M. 1922 NACA Rep. 142.
Murillo, L. E. 1979 Hydromechanical performance of lunate tails analyzed as a lifting-line problem in unsteady flow. Dissertation, University of Southern California.
Norman, J. R. & Fraser, F. C. 1937 Giant Fishes, Whales and Dolphines. Putnam.
Prandtl, L. 1918 Nachr. Ges. Wiss. Gött. Math.-Phys. Klass., 451–477.
Sears, W. R. 1938 In Proc. 5th Int. Congr. Appl. Mech. pp. 483–487.
Thurber, J. K. 1965 Commun. Pure Appl. Maths 18, 733–750.
Van Dyke, M. D. 1964a Perturbation Methods in Fluid Mechanics, p. 176. Academic. [See also annotated edition; Parabolic, 1975.]
Van Dyke, M. D. 1964b Q. Appl. Maths Mech. 28, 90–101.
Watkins, C. C., Runyan, H. L. & Cunningham, H. J. 1959 NASA TR R-48.
Weisshar, T. A. & Ashley, H. 1973 J. Aircraft. 10, 586–594.
Weissinger, J. 1947 NACA Tech. Memo. 1120. [Transl. FB 1553, Berlin—Adlershof 1942.]
Woodward, F. A. 1973 NASA CR 2228, parts I and II.
Wu, T. Y. T. 1971a J. Fluid Mech. 46, 337–355.
Wu, T. Y. T. 1971b J. Fluid Mech. 46, 521–544.
Wu, T. Y. T. 1971c J. Fluid Mech. 46, 545–568.