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Development of a laminar boundary layer under conditions of continuous incipient separation*

Published online by Cambridge University Press:  14 February 2012

N. Curle
N. Curle
Affiliation:
Department of Applied Mathematics, University of St Andrews
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Synopsis

This paper, extending the work of Stratford [6] considers a boundary layer with uniform pressure when x < x0, and with the pressure in x > x0 so chosen that the layer is just on the point of separation for all x >x0. The required pressure distribution is shown to be

The displacement and momentum thicknesses are also derived as series in powers of ξ (and log ξ), and the shape parameter H then obtained as a similar series. The continuous change in H from the Blasius value (when ξ = 0) towards the Falkner-Skan [3] separation value is convincingly demonstrated, with the aid of the leading terms of an asymptomatic expansion for large ξ.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 76 , Issue 1 , 1976 , pp. 55 - 66
Copyright
Copyright © Royal Society of Edinburgh 1976

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References

1Chen, K. K. and Libby, P. A.. Boundary layers with small departures from the Falkner-Skan profile. J. Fluid Mech. 33 (1968), 273.CrossRefGoogle Scholar
2Curle, N.. Development and separation of a laminar boundary layer, under the action of a very sharp constant adverse pressure gradient. Proc. Roy. Soc. Edinburgh Sect. A. 74 (1976), 119.CrossRefGoogle Scholar
3Falkner, V. M. and Skan, S. W.. Some approximate solutions of the boundary layer equations. Rep. Memo. Aeronaut. Res. Council 1314 (1930).Google Scholar
4Goldstein, S.. Concerning some solutions of the boundary layer equations in hydrodynamics. Proc. Cambridge Philos. Soc. 26 (1930), 1.CrossRefGoogle Scholar
5Libby, P. A. and Fox, H.. Some perturbation solutions in laminar boundary-layer theory. Part 1. The momentum equation. J. Fluid Mech. 17 (1963), 433.CrossRefGoogle Scholar
6Stratford, B. S.. Flow in the laminary boundary layer near separation. Rep. Memo. Aeronaut. Res. Council 3002 (1954).Google Scholar