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A theory for the core of a leading-edge vortex

Published online by Cambridge University Press:  28 March 2006

M. G. Hall
M. G. Hall
Affiliation:
Royal Aircraft Establishment, Farnborough, Hampshire
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Abstract

In the flow past a slender delta wing at incidence one can observe a roughly axially symmetric core of spiralling fluid, formed by the rolling-up of the shear layer that separates from a leading edge. The aim in this paper is to predict the flow field within this vortex core, given appropriate conditions at its outside edge.

The basic assumptions are (i) that the flow is continuous and rotational, and (ii) that viscous diffusion is confined to a relatively slender subcore. In addition it is assumed that the flow is axially symmetric and incompressible. Together, these admit outer and inner solutions for the core from the equations of motion. For the outer solution the subcore is ignored, and the flow is taken to be inviscid (but rotational) and conical. The resulting solution consists of simple expressions for the velocity components and pressure. For the inner solution, which applies to the diffusive subcore, the flow is taken to be laminar, and certain approximations are made, some based on the boundary conditions and some analogous to those of boundary-layer theory. The solution obtained in this case is a first approximation, and has been computed.

A sample calculation yields results which are in good qualitative and fair quantitative agreement with experimental measurements.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 11 , Issue 2 , September 1961 , pp. 209 - 228
Copyright
© 1961 Cambridge University Press

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References

Cox, A. P. 1959 Measurements of the velocity at the vortex centre on an A.R. 1 delta wing by means of smoke observations. Aero. Res. Coun., Lond., Rep. no. 21, 116.Google Scholar
Earnshaw, P. B. 1961 An experimental investigation of the structure of a leading edge vortex. Aero. Res. Coun., Lond., Rep. no. 22, 876.Google Scholar
Elle, B. J. 1958 An investigation at low speed of the flow near the apex of thin delta wings with sharp leading edges. Aero. Res. Coun., Lond., Rep. no. 19,780.Google Scholar
Hall, M. G. 1959 On the vortex associated with flow separation from a leading edge of a slender wing. Aero. Res. Coun., Lond., Rep. no. 21,117.Google Scholar
Hall, M. G. 1960 A theory for the core of a leading edge vortex. Aero. Res. Coun., Lond., Rep. no. 22,660.Google Scholar
Jeffreys, H. & Jeffreys, B. S. 1956 Methods of Mathematical Physics, 3rd ed. Cambridge University Press.
Jones, J. P. 1960 The breakdown of vortices in separated flow. University of Southampton, U.S.A.A. Report, no. 140.Google Scholar
Lambourne, N. C. & Bryer, D. W. 1959 Some measurements in the vortex flow generated by a sharp leading-edge having 65$ sweep. Aero. Res. Coun., Lond., Rep. no. 21,073, Curr. Pap. no. 477.Google Scholar
Mangler, K. W. & Smith, J. H. B. 1959 A theory of the flow past a slender delta wing with leading edge separation. Proc. Roy. Soc. A, 251, 200.Google Scholar
Newman, B. G. 1959 Flow in a viscous trailing vortex. Aero. Quart. 10, 149.Google Scholar
Peckham, D. H. 1958 Low speed wind tunnel tests on a series of uncambered slender pointed wings with sharp edges. Aero. Res. Coun., Lond., Rep. no. 20,727.Google Scholar
Rott, N. 1959 On the viscous core of a line vortex. II. Z. angew. Math. Phys. 10, 82.Google Scholar
Squire, H. B. 1960 Analysis of the ‘vortex breakdown’ phenomenon. Part 1. Imperial College Aero. Dep., Rep. no. 102.Google Scholar