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A resolution of the blow-off singularity for similarity flow on a flat plate

Published online by Cambridge University Press:  29 March 2006

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

A study is made of uniform flow past a semi-infinite flat plate with a similarity injection distribution of boundary-layer magnitude. Attention is focused on a solution at exactly the critical injection rate for which classical boundary-layer theory predicts the blow-off singularity. Following a description of the more recent interaction analyses which also fail at the critical rate, a new theory is developed which leads to physically meaningful results. In particular, it is shown that the non-monotonic variation in wall shear with increasing injection rate near the critical value, noted by Klemp & Acrivos (1972), is real. A delicate interplay of weak pressure interactions and viscous effects is shown to be responsible for this surprising phenomenon.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 62 , Issue 1 , 8 January 1974 , pp. 145 - 161
Copyright
© 1974 Cambridge University Press

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References

Catherall, D., Stewartson, K. & Williams, P. G. 1965 Viscous flow past a flat plate with uniform injection. Proc. Roy. Soc. A284, 370.Google Scholar
Chang, I.-D. 1961 Navier–Stokes solutions at large distances from a finite body J. Math. Mech. 10, 811.Google Scholar
Cole, J. D. 1968 Perturbation Methods in Applied Mathematics, p. 158. Blaisdell.
Emmons, H. & Leigh, D. C. 1954 Tabulation of the Blasius function with blowing and suction. Aero. Res. Counc. Current Paper, no. 157.Google Scholar
Kassoy, D. R. 1970 On laminar boundary-layer blow-off SIAM Appl. Math. 17, 24.Google Scholar
Kassoy, D. R. 1971 On laminar boundary-layer blow-off. Part 2 J. Fluid Mech. 48, 209.Google Scholar
Kassoy, D. R. 1973 The singularity at boundary-layer separation due to mass injection SIAM Appl. Math. 25, 105.Google Scholar
Klemp, J. & Acrivos, A. 1972 High Reynolds number flow past a flat plate with strong blowing J. Fluid Mech. 51, 337.Google Scholar
Lagerstrom, P. A. & Cole, J. D. 1955 Examples illustrating expansion procedures for the Navier–Stokes equations J. Rat. Mech. Anal. 4, 817.Google Scholar
Lock, R. C. 1951 The velocity distribution in the laminar boundary layer between parallel streams Quart. J. Mech. Appl. Math. 4, 42.Google Scholar
Van Dyke, M. 1964 Perturbation Methods in Fluid Mechanics, p. 131. Academic.