Analysis of the unstable Tollmien-Schlichting mode on bodies with a rounded leading edge using the parabolized stability equation

Turner, M.R. and Hammerton, P.W. (2009) Analysis of the unstable Tollmien-Schlichting mode on bodies with a rounded leading edge using the parabolized stability equation Journal of Fluid Mechanics, 623 . pp. 167-185. ISSN 1469-7645

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Abstract

The interaction between free-stream disturbances and the boundary layer on a body with a rounded leading edge is considered in this paper. A method which incorporates calculations using the parabolized stability equation (PSE) in the Orr-Sommerfeld region along with an upstream boundary condition derived from asymptotic theory in the vicinity of the leading edge, is generalised to bodies with an inviscid slip velocity which tends to a constant far downstream. We present results for the position of the lower branch neutral stability point and the magnitude of the unstable Tollmien-Schlichting (T-S) mode at this point for both a parabolic body and the Rankine body. For the Rankine body, which has an adverse pressure gradient along its surface far from the nose, we find a double maximum in the T-S wave amplitude for sufficiently large Reynolds numbers.

Item Type:Journal article
Additional Information:© The Author(s) and Cambridge University Press, 2009
Subjects:G000 Computing and Mathematical Sciences > G100 Mathematics
H000 Engineering
DOI (a stable link to the resource):10.1017/S0022112008005260
Faculties:Faculty of Science and Engineering > School of Computing, Engineering and Mathematics > Engineering and Product Design Research > Automotive Engineering
ID Code:6474
Deposited By:Dr Matthew Turner
Deposited On:26 Nov 2009
Last Modified:09 Oct 2013 09:25

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