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Plate-injection into a separated supersonic boundary layer

Published online by Cambridge University Press:  29 March 2006

F. T. Smith  and
K. Stewartson
F. T. Smith
Affiliation:
Department of Mathematics, University College London Present address: Department of Mathematics, University of Southampton.
K. Stewartson
Affiliation:
Department of Mathematics, University College London
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Abstract

The structure of a supersonic laminar boundary layer near a flat plate is examined when fluid is injected into it with velocity of O(ε3U*∞) over a distance of O(L). Here U*∞ is the undisturbed fluid velocity, L the length of the plate and ε−8 is a representative Reynolds number. An essential requirement of the theory is that separation must have occurred upstream of the blow through a free interaction. It is assumed that between separation and the blow the reversed flow region has a wedge-like shape, of semi-angle in which O(ε2), the fluid velocity has decayed to insignificant values at points just upstream of the blowing region. The blown fluid fills this wedge and the favourable pressure gradient necessary to drive this fluid downstream causes the boundary of the wedge to curve until at the end of the blow it is parallel to the plate. Explicit expressions for the pressure variation and boundary-layer thickness are worked out using a (crucially) modified form of the Cole-Aroesty theory. The relation. between the strong injection studied here and massive injection, when the blowing velocity is of O(U*∞), is also discussed.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 58 , Issue 1 , 20 March 1973 , pp. 143 - 159
Copyright
© 1973 Cambridge University Press

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