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Airfoils moving in air close to a dynamic water surface

Published online by Cambridge University Press:  17 February 2009

I. H. Grundy
I. H. Grundy
Affiliation:
Department of Applied Mathematics, The University of Adelaide, Adelaide, South Australia, 5000.
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Abstract

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Steady potential flow about a thin wing, flying in air above a dynamic water surface, is analysed in the asymptotic limit as the clearance-to-length ratio tends to zero. This leads to a non-linear integral equation for the one-dimensional pressure distribution beneath the wing, which is solved numerically. Results are compared with established “rigid-ground” and “hydrostatic” theories. Short waves lead to complications, including non-uniqueness, in some parameter ranges.

Type
Research Article
Information
The ANZIAM Journal , Volume 27 , Issue 3 , January 1986 , pp. 327 - 345
Copyright
Copyright © Australian Mathematical Society 1986

References

[1]Abramowitz, M. and Stegun, I. A. (eds.), Handbook of mathematical functions (Dover, New York, 1964).Google Scholar
[2]Lamb, H., Hydrodynamics (Cambridge University Press, 1932).Google Scholar
[3]Strand, T., Royce, W. W. and Fujita, T., “Cruise performance of channel-flow ground-effect machines”, J. Aero. Sci. 29 (1962), 702–711.Google Scholar
[4]Tuck, E. O., “On air flow over free surfaces of stationary water”, J. Austral. Math. Soc. Ser. B 19 (1975), 66–80.Google Scholar
[5]Tuck, E. O., “A nonlinear unsteady one-dimensional theory for wings in extreme ground effect”, J. Fluid. Mech. 98 (1980), 33–47.CrossRefGoogle Scholar
[6]Tuck, E. O., “Steady flow and Static stability of airfoils in extreme ground effect”, J. Eng. Math. 15 (1981), 89–102.CrossRefGoogle Scholar
[7]Tuck, E. O., “Linearized planing-surface theory with surface tension. Part I: Smooth detachment”, J. Austral. Math. Soc. Ser. B 23 (1982), 241–258.CrossRefGoogle Scholar
[8]Tuck, E. O., “A simple one-dimensional theory for air-supported vehicles over water”, J. Ship. Re. 28 (1984), 290–292.CrossRefGoogle Scholar
[9]Tuck, E. O. and Bentwich, M., “Sliding sheets: Lubrication with comparable viscous and inertia forces”, J. Fluid. Mech. 135 (1983), 51–69.CrossRefGoogle Scholar
[10]Wehausen, J. V. and Laitone, E. V., “Surface waves”, in Handhuch der Physik, Vol. 9, (ed. Flugge, S.), (Springer-Verlag, Berlin, 1960).Google Scholar
[11]Widnall, S. E. and Barrows, T. M., “An analytic solution for two- and three-dimensional wings in ground effect”, J. Fluid. Mech. 41 (1970), 769–792.CrossRefGoogle Scholar