Viscous modes within the compressible boundary-layer flow due to a broad rotating cone

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.

Publication DOI: https://doi.org/10.1093/imamat/hxw041
Divisions: College of Engineering & Physical Sciences
Additional Information: © The author 2016. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved. This is a pre-copyedited, author-produced version of an article accepted for publication in IMA Journal of Applied Mathematics following peer review. The version of record is available online at: https://doi.org/10.1093/imamat/hxw041 Funding Information: Engineering and Physical Sciences Research Council (grant EP/G061637/1 to S.J.G. and P.D.T.); Royal Academy of Engineering and the Leverhulme Trust (LSRF1415/11/29 to S.J.G and P.T.G.).
Uncontrolled Keywords: Rotating cone,Type II,Compressible boundary-layer flow
Publication ISSN: 1464-3634
Last Modified: 18 Jun 2024 07:41
Date Deposited: 28 Sep 2022 14:07
Full Text Link:
Related URLs: https://academi ... 1/5/940/2198354 (Publisher URL)
PURE Output Type: Article
Published Date: 2016-10-01
Published Online Date: 2016-08-29
Accepted Date: 2016-08-09
Authors: Towers, P. D.
Hussain, Z.
Griffiths, Paul (ORCID Profile 0000-0002-2078-0118)
Garrett, Stephen (ORCID Profile 0000-0002-0671-160X)

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