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On moderate injection into a separated supersonic boundary layer, with reattachment

Published online by Cambridge University Press:  19 April 2006

C. Diver  and
K. Stewartson
C. Diver
Affiliation:
Department of Mathematics, University College London
K. Stewartson
Affiliation:
Department of Mathematics, University College London
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Abstract

We consider the problem of mass injection from a flat plate into uniform supersonic flow when the boundary layer is blown off at the leading edge to form a thin free shear layer separating the inviscid injectant layer from the external flow. The injection is moderate, i.e. of the same order of magnitude as the velocity of entrainment into the base of the shear layer. For simplicity, we consider similarity blowing, proportional to x*−½, where x* is measured along the plate from the leading edge. We find that the solution in the injectant region, based on initial conditions at the leading edge, is non-unique unless fixed by downstream conditions. When injection is cut off at a finite distance along the plate, this enables us to find a solution to the problem in which the shear layer eventually reattaches to the plate and for which the pressure and the height of the injectant layer are continuous at cut-off. The study provides a partial connexion between the earlier studies of weak blowing in which the boundary layer is not blown off and of strong blowing for which the boundary layer is blown off and the entrainment into the shear layer is negligible.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 88 , Issue 1 , 13 September 1978 , pp. 115 - 132
Copyright
© 1978 Cambridge University Press

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