Hostname: page-component-669899f699-cf6xr Total loading time: 0 Render date: 2025-05-04T19:33:22.064Z 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
Affiliation:
Department of Aerospace Engineering, University of Southern California, Los Angeles
Luis E. Murillo
Affiliation:
Department of Aerospace Engineering, University of Southern California, Los AngelesPresent address: Boeing Commercial Airplane Co., Seattle, Washington 98124.

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
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.)

Article purchase

Temporarily unavailable

References

Ahmadi,A. R.1980 Ph.D. dissertation,MIT.
Albano,E. &Rodden,W. P.1969AIAA J.7,279–285.
Ashley,H. &Landahl,M.1965Aerodynamics of Wings and Bodies.Addison-Wesley.
Ashley,H. &Rodden,W. P.1972Ann. Rev. Fluid Mech.4,431–472.
Batchelor,G. K.1967An Introduction to Fluid Dynamics,pp.510,523.Cambridge University Press.
Belotserkovskii,S. M.1967The Theory of Thin Wings in Subsonic Flow.Plenum.
Belotserkovskii,S. M.1977Ann. Rev. Fluid Mech.9,469–494.
Carter,G. S.1940A General Zoology of the Invertebrates, chap. 23.London.
Cheng,H. K.1976Univ. S. Calif., Dept Aerospace Engng Rep. USCAE 133.
Cheng,H. K.1978aAIAA J.16,1211–1213.
Cheng,H. K.1978bUniv. S. Calif., Dept Aerospace Engng Rep. USCAE 135.
Cheng,H. K.1982aThe transonic flow theories of high and low aspect ratio wings. InPhysical and Numerical Aspects of Aerodynamic Flows (ed.T.Cebeci),Springer-Verlag.
Cheng,H. K.1982b InTransonic, Shock and Multidimensional Flows (ed.R. E.Meyer),pp.107–145.Academic.
Cheng,H. K.1983Transonic aerodynamics of forward swept wings analyzed as a lifting-line problem. InProc. Intl Forward-Swept Wing Aircraft Conf. Bristol University,24–26March 1982.
Cheng,H. K.,Chow,R. &Melnik,R. E.1981Z. angew. Math. Phys.32,481–496.
Cheng,H. K. &Meng,S. Y.1979AIAA J.17,121–124.
Cheng,H. K. &Meng,S. Y.1980J. Fluid Mech.97,531–556.
Cheng,H. K.,Meng,S. Y.,Chow,R. &Smith,R.1981AIAA J.19,961–968.
Cheng,H. K. &Murillo,L. E.1982Univ. S. Calif. Dept Aerospace Engng Rep. USCAE 139.
Chopra,M. E.1974 InSwimming and Flying in Nature, vol. 2 (ed.T. Y. T.Wuet al.).
Chopra,M. G.1976J. Fluid Mech.74,161–181.
Chopra,M. G. &Kambe,T.1977J. Fluid Mech.79,49–69.
Cook,L. P.1979Q. Appl. Maths32,178–202.
Davis,D. E.1963Aero. Res. Counc. R & M 3409.
Dorodnitsyn,A. A.1944Prikl. Mat. Mech.8,33–64.
Gregory,W. K.1936Biol. Rev.11,310.
Hedman,S. G.1965Aero. Res. Inst. Sweden Rep. 105.
Holten,T. van1976aJ. Fluid Mech.77,561–599.
Holten,T. van1976bAsymptotic theory of swept wings.Delft Univ. Dept. Aerospace Engng Rep.Google Scholar
James,E. C.1975J. Fluid Mech.70,735–771.
Jameson,A. &Caughey,D. A.1977New York Univ. ERDA Rep. C00-3077-140.
Jones,R. T.1972AIAA J.10,171–176.
Jones,R. T.1980Aero. J. R. Aero. Soc. July,214–217.
Jones,R. T. &Cohen,D.1957Aerodynamics of wings at high speed. InAerodynamic 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.1934General aerodynamic theory. InAerodynamic Theory (ed.W. F.Durand), vol. 2, div. E.
Katz,J. &Weihs,D.1978J. Fluid Mech.88,485–487.
Kida,T. &Miyai,T.1978Z. angew. Math. Phys.29,519–607.
Kramer,M. O.1960J. Am. Soc. Nav. Engng72,25–34.
Lan,C. E.1979J. Fluid Mech.93,747–765.
Lighthill,M. J.1960J. Fluid Mech.9,305–317.
Lighthill,M. J.1969Ann. Rev. Fluid Mech.1,413–466.
Lighthill,M. J.1970J. Fluid Mech.44,265–301.
Lighthill,M. J.1975Mathematical Biofluiddynamics.SIAM.
Marshall,N. B.1966The Life of Fishes.The Universe Books.
Munk,M. M.1922NACA Rep. 142.
Murillo,L. E.1979Hydromechanical performance of lunate tails analyzed as a lifting-line problem in unsteady flow. Dissertation,University of Southern California.
Norman,J. R. &Fraser,F. C.1937Giant Fishes, Whales and Dolphines.Putnam.
Prandtl,L.1918Nachr. Ges. Wiss. Gött. Math.-Phys. Klass.,451–477.
Sears,W. R.1938 InProc. 5th Int. Congr. Appl. Mech.pp.483–487.
Thurber,J. K.1965Commun. Pure Appl. Maths18,733–750.
Van Dyke,M. D.1964aPerturbation Methods in Fluid Mechanics,p.176.Academic. [See also annotated edition; Parabolic, 1975.]
Van Dyke,M. D.1964bQ. Appl. Maths Mech.28,90–101.
Watkins,C. C.,Runyan,H. L. &Cunningham,H. J.1959NASA TR R-48.
Weisshar,T. A. &Ashley,H.1973J. Aircraft.10,586–594.
Weissinger,J.1947NACA Tech. Memo. 1120. [Transl. FB 1553, Berlin—Adlershof 1942.]
Woodward,F. A.1973NASA CR 2228, parts I and II.
Wu,T. Y. T.1971aJ. Fluid Mech.46,337–355.
Wu,T. Y. T.1971bJ. Fluid Mech.46,521–544.
Wu,T. Y. T.1971cJ. Fluid Mech.46,545–568.