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Some Remarks on the Behaviour of Surface Source Distributions near the Edge of a Body

Published online by Cambridge University Press:  07 June 2016

J W Craggs
Affiliation:
University of Southampton
K W Mangler
Affiliation:
Royal Aircraft Establishment, Farnborough
M Zamir
Affiliation:
University of Western Ontario
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Summary

When the incompressible potential flow past a three-dimensional body is represented by source distributions on the body surface, these source distributions have singularities near an edge or corner, for example á trailing edge of a wing or the (unfaired) intersection of a body and a wing. The nature of these singularities is discussed. When assuming slow variations of the geometry in the main flow direction we can consider a two-dimensional problem in the cross-flow plane. Here the tangential velocities and source distributions are proportional to certain powers of the distance from the corner. For example at a convex right-angled corner these powers are − ⅓ in the asymmetric case (the bisector is a potential line) and ⅓ in the symmetric case (the bisector is a streamline) for both sources and tangential velocities. At a concave right-angled corner the corresponding values for the source distributions are ⅓ (asymmetric case) and − ⅓ (symmetric case) whereas they are 1 and 3 respectively for the tangential velocities.

Type
Research Article
Copyright
Copyright © Royal Aeronautical Society. 1973

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References

1 Hess, J L Smith, A M O Calculation of potential now about arbitrary bodies. Progress in Aeronautical Sciences, Vol 8, Pergamon Press, 1967.Google Scholar
2 Lamb, H Hydrodynamics, (6th edition, 1932), p 60. Dover Publications, New York, 1945.Google Scholar