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On laminar boundary-layer blow-off. Part 2

Published online by Cambridge University Press:  29 March 2006

D. R. Kassoy
D. R. Kassoy
Affiliation:
Mechanical Engineering Department, University of Colorado
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Abstract

Several examples of incipient blow-off phenomena described by the compressible similar laminar boundary-layer equations are considered. An asymptotic technique based on the limit of small wall shear, and the use of a novel form of Prandtl's transposition theorem, leads to a complete analytical description of the blow-off behaviour. Of particular interest are the results for overall boundarylayer thickness, which imply that, for a given large Reynolds number, classical theory fails for a sufficiently small wall shear. A derivation of a new distinguished limit of the Navier–Stokes equations, the use of which will lead to uniformly valid solutions to blow-off type problems for Re → ∞, is included. A solution for uniform flow past a flat plate with classical similarity type injection, based on the new limit, is presented. It is shown that interaction of the injectant layers and the external flow results in a favourable pressure gradient, which precludes the classical blow-off catastrophy.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 48 , Issue 2 , 28 July 1971 , pp. 209 - 228
Copyright
© 1971 Cambridge University Press

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