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On the stability of attachment-line boundary layers. Part 2. The effect of leading-edge curvature

Published online by Cambridge University Press:  25 February 1997

RAY-SING LIN  and
MUJEEB R. MALIK
RAY-SING LIN
Affiliation:
High Technology Corporation, PO Box 7262, Hampton VA 23666, USA
MUJEEB R. MALIK
Affiliation:
High Technology Corporation, PO Box 7262, Hampton VA 23666, USA
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Abstract

The stability of the incompressible attachment-line boundary layer has been studied by Hall, Malik & Poll (1984) and more recently by Lin & Malik (1996). These studies, however, ignored the effect of leading-edge curvature. In this paper, we investigate this effect. The second-order boundary-layer theory is used to account for the curvature effects on the mean flow and then a two-dimensional eigenvalue approach is applied to solve the linear stability equations which fully account for the effects of non-parallelism and leading-edge curvature. The results show that the leading-edge curvature has a stabilizing influence on the attachment-line boundary layer and that the inclusion of curvature in both the mean-flow and stability equations contributes to this stabilizing effect. The effect of curvature can be characterized by the Reynolds number Ra (based on the leading-edge radius). For Ra = 104, the critical Reynolds number R (based on the attachment-line boundary-layer length scale, see §2.2) for the onset of instability is about 637; however, when Ra increases to about 106 the critical Reynolds number approaches the value obtained earlier without curvature effect.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 333 , 25 February 1997 , pp. 125 - 137
Copyright
© 1997 Cambridge University Press

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