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 in the Orr–Sommerfeld region, along with an upstream boundary condition derived from asymptotic theory in the vicinity of the leading edge, is generalized 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:	Article
Faculty \ School:	Faculty of Science > School of Mathematics (former - to 2024)
UEA Research Groups:	Faculty of Science > Research Groups > Fluid and Solid Mechanics (former - to 2024) Faculty of Science > Research Groups > Fluids & Structures
Depositing User:	Paul Hammerton
Date Deposited:	06 Mar 2012 10:01
Last Modified:	07 Nov 2024 12:33
URI:	https://ueaeprints.uea.ac.uk/id/eprint/37419
DOI:	10.1017/S0022112008005260

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