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Energetics of oscillating lifting surfaces by the use of integral conservation laws

Published online by Cambridge University Press:  26 April 2006

Ali R. Ahmadi  and
Sheila E. Windnall
Ali R. Ahmadi
Affiliation:
California State Polytechnic University, Pomona, CA 91768, USA
Sheila E. Windnall
Affiliation:
Massachusetts Institute of Technology, Cambridge, MA 02139, USA
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Abstract

The energetics of oscillating lifting surfaces in two and three dimensions is calculated by the use of integral conservation laws in inviscid incompressible flow for general and harmonic transverse oscillations. Wing deformations are prescribed as a function of time and total thrust is calculated from the momentum theorem, and energy loss rate due to vortex shedding in the wake is calculated from the principle of conservation of mechanical energy. Total power required to maintain the oscillations and hydro-dynamic efficiency are also determined. In two dimensions, the results are obtained in closed form. In three dimensions, the distribution of vorticity on the lifting surface is also required as input to the calculations. Therefore, unsteady lifting-surface theory must be used as well. The analysis is applicable to oscillating lifting surfaces of arbitrary planform, aspect ratio and reduced frequency and does not require calculation of the leading-edge thrust.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 266 , 10 May 1994 , pp. 347 - 370
Copyright
© 1994 Cambridge University Press

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References

Abramowitz, M. & Stegun, I. A. (ed.) 1970 Handbook of Mathematical Functions. AMS 55, National Bureau of Standards.
Ahmadi, A. R. & Widnall, S. E. 1983 Energetics and optimum motion of oscillating lifting surfaces. AIAA Paper 83-1710.
Ashley, H. & Landahl, M. T. 1965 Aerodynamics of Wings and Bodies. Addison-Wesley.
Bisplinghoff, R. L., Ashley, H. & Halfman, R. L. 1955 Aeroelasticity. Addison-Wesley.
Carrier, G. F., Krook, M. & Pearson, C. E. 1966 Functions of a Complex Variable, Theory and Technique. McGraw-Hill.
Chopra, M. G. 1974 Hydrodynamics of lunate-tail swimming propulsion. J. Fluid Mech. 64, 375–391.Google Scholar
Chopra, M. G. 1976 Large amplitude lunate-tail theory of fish locomotion. J. Fluid Mech. 74, 161–182.Google Scholar
Chopra, M. G. & Kambe, T. 1977 Hydrodynamics of lunate-tail swimming propulsion. Part 2. J. Fluid Mech. 79, 49–69.Google Scholar
Dwight, H. B. 1961 Tables of Integrals and Other Mathematical Data. Macmillan.
Garrick, I. E. 1936 Propulsion of a flapping and oscillating airfoil. NACA Rep. 567.
von Kármán, T. & Burgers, J. M. 1935 General Aerodynamic Theory – Perfect Fluids, Division E, vol. 2, Aerodynamic Theory. (ed. W. F. Durand). Julius Springer.
Lan, C. E. 1979 The unsteady quasi-vortex-lattice method with applications to animal propulsion. J. Fluid Mech. 93, 747–765.Google Scholar
Lighthill, M. J. 1970 Aquatic animal propulsion of high hydrodynamic efficiency. J. Fluid Mech. 44, 265–301.Google Scholar
Mangler, K. W. 1951 Improper integrals in theoretical aerodynamics. ARC R & M 2424.
Reissner, E. 1947 Effect of finite span on the airload distributions for oscillating wings, I – Aerodynamic theory of oscillating wings of finite span. NACA TN 1194.
Schwarz, L. 1940 Berechnung der druckverteilung einer harmonisch sich verformenden tragfläche in ebener strömung. Luftfahrtforschung 17, Nr. 11 & 12.Google Scholar
Siekmann, J. 1962 Theoretical studies of sea animal locomotion, Part I. Ing. Archiv 31, 214–228.Google Scholar
Siekmann, J. 1963 Theoretical studies of sea animal locomotion, Part II. Ing. Archiv 32, 40–50.Google Scholar
Theodorsen, T. 1935 General theory of aerodynamic instability and the mechanism of flutter. NACA TR 496.
Van Dyke, M. D. 1956 Second-order subsonic airfoil theory including edge effects. NACA Rep. 1274.
Wu, T. Y. 1961 Swimming of a waving plate. J. Fluid Mech. 10, 321–344.Google Scholar
Wu, T. Y. 1971a Hydrodynamics of swimming propulsion. Part I. Swimming of a two-dimensional flexible plate at variable forward speed in an inviscid fluid. J. Fluid Mech. 46, 337–355.Google Scholar
Wu, T. Y. 1971b Hydrodynamics of swimming propulsion. Part I. Some optimum shape problems. J. Fluid Mech. 46, 521–544.Google Scholar