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Title: Viscous modes within the compressible boundary-layer flow due to a broad rotating cone
Authors: Towers, P. D.
Hussain, Z.
Griffiths, P. T.
Garrett, S. J.
First Published: 29-Aug-2016
Publisher: Oxford University Press (OUP) for Institute of Mathematics and its Applications
Citation: IMA Journal of Applied Mathematics (Institute of Mathematics and Its Applications), 2016, 81 (5), pp. 940-960
Abstract: We investigate the effects of compressibility and wall cooling on the stationary, viscous (Type II) instability mode within the 3D boundary layer over rotating cones with half-angle greater than 40°. The stationary mode is characterised by zero shear stress at the wall and a triple-deck solution is presented in the isothermal case. Asymptotic solutions are obtained which describe the structure of the wavenumber and the orientation of this mode as a function of local Mach number. It is found that a stationary mode is possible only over a finite range of local Mach number. Our conclusions are entirely consistent with the results of Seddougui 1990, A nonlinear investigation of the stability models of instability of the trhee-dimensional Compresible boundary layer due to a rotating disc Q. J. Mech. Appl. Math., 43, pt. 4. It is suggested that wall cooling has a significant stabilising effect, while reducing the half-angle is marginally destabilising. Solutions are presented for air.
DOI Link: 10.1093/imamat/hxw041
ISSN: 0272-4960
eISSN: 1464-3634
Version: Post-print
Status: Peer-reviewed
Type: Journal Article
Rights: Creative Commons “Attribution Non-Commercial No Derivatives” licence CC BY-NC-ND, further details of which can be found via the following link: Archived with reference to SHERPA/RoMEO and publisher website.
Description: Author confirmed manuscript is post-print.
Appears in Collections:Published Articles, Dept. of Mathematics

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