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A cavitating aerofoil with a Prandtl-Batchelor eddy

Published online by Cambridge University Press:  04 July 2016

E. Zachariou
Affiliation:
Mathematical Institute Oxford
P. Wilmott
Affiliation:
Mathematical Institute Oxford
A. D. Fitt
Affiliation:
Faculty of Mathematical Studies University of Southampton

Abstract

A simple model is presented for an aerofoil with a recirculating Prandtl-Batchelor region behind a spoiler. Using thin aerofoil theory the model is posed as a pair of coupled nonlinear singular integrodifferential equations for the shape of the separating streamline and the distribution of vorticity along the aerofoil. These equations are solved numerically and results are presented. In particular, some conclusions are drawn regarding the lift on such aerofoils.

Type
Research Article
Copyright
Copyright © Royal Aeronautical Society 1994

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References

1. Batchelor, G.K. On steady laminar flow with closed streamlines at large Reynolds number, J Fluid Mech, 1956, 1, pp 177190 CrossRefGoogle Scholar
2. Childress, S. Solutions of Euler's equations containing finite eddies, Phys Fluids, 1966, 9, pp 860872 CrossRefGoogle Scholar
3. O'Malley, K., Fitt, A.D., Jones, T.V., Ockendon, J.R. and Wilmott, P. Models of high-Reynolds-number flow down a step, J Fluid Mech, 1991, 222, pp 139155.CrossRefGoogle Scholar
4. Woods, L.C. The Theory of Subsonic Plane Flow, Cambridge University Press, 1961.Google Scholar
5. Ockendon, H. and Tayler, A.B. Inviscid Fluid Flow, Springer-Verlag, 1983.CrossRefGoogle Scholar
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